0 Dual-beam oscilloscope Goals of the work • Learn basic operation principles of a dual-beam oscilloscope • Learn how to use a dual-beam oscilloscope • Learn to measure periodic signals • Learn the meaning of a probe and to use it • Learn how to make a document of the measurements For what purposes an oscilloscope is used? The oscilloscope is very commonly utilized measuring device. By utilizing oscilloscope, very high-speed periodic phenomena can be observed in an illustrative way. In addition to the voltage, the oscilloscope can be utilized to measure other electrical and non-electrical quantities. It is utilized in the maintenance and the testing of the electrical equipment as well in the research, the educational purposes etc.

0.1 Operational principle of the analog oscilloscope For historical reasons the operational principle of the oscilloscope is approached through an analog oscilloscope. The screen is in significant role in analog oscilloscopes since it affects outstandingly to the performance of the oscilloscope. Whereas in digital oscilloscopes the conversion of the continuos signal to the discrete samples is matter that is in focus. Analog oscilloscopes can’t offer as varied characteristics as the digital oscilloscopes. The introduction of the analog oscilloscope however brings out the basic characteristics of the oscilloscope. The measured periodic voltage-signal is seen on the screen. The graph on the oscilloscopes screen represents the voltage (vertical direction, y) as a fuction of the time (horizontal direction, x). The signal is amplified in the vertical deflection block to the deflection voltage to the cathode ray tube, CRT (fig. 6) The trigger block defines the moment when the vertical deflection block starts up the vertical deflection voltage. Understanding these basic block is important since the adjusters are groupped into the blocks on the front-panel of the device. In the following, these blocks and all adjusters and connectors are considered in details. It is not a description of any particular device, only a description of the basic functions. In the simpliest devices all these functions doesn’t even exist, and in the advanced devices there are much more functions and adjusters that are described below.

0.1.1 Screen In a cathode-ray tube a deflection voltage controlled electron beam is bombarding a phosphorized screen. As a consequence a visible point is composed on the screen. While the electron beam is moving, the afterglow duration of the phosphorized surface make it easier to see the beam. The screen is divided with vertical and horizontal lines into square shaped parts. Adjusters required for the beam control Intensity The intensity of the beam has to be adjustable, since illumination circumstances varies in different places. If the phenomena is very fast and its frequency is very low, the beam travels throgh the screen only a fractional part of the total time. In that case the intensity of the beam needs to be increased. Obs. Do not ”light” the laboratory by an oscilloscope. Too intense beam wears down the phosphorized surface of the screen.

Vertical deflection

Trigger source

Coupling HF-reject

x-amplifier

y-amplifier

Beam intensity amplifier

Comp- arator Level Slope Mode Holdoff

Ch. 1 Ch. 2

Alt Chop Add

Ch. 1 Ch. 2

Ext.

Line

Volts/div Cal.

XY

Time/div ramp gen.

Returning beam cutoff

CRT

Ch. 1 input

Ch. 2 input

preamplifier

Z-input

mains frequnecy

Ext. trigger input

AC

DC

Coupling

AC

DC

level control

GND

Electronic switch / summing

Invert

Channel 2 invert

Intensity

Focus Beam finder

Triggering

Horizontal deflection

Figure 6. Block diagram of an oscilloscope . Texts in oscilloscope front panel are italicized.

Beam finder If the beam is missing, the beam finder –button helps you to do the correct adjustments. The beam finder adjuster pass the intensity control and decrease horizontal and vertical deflection voltages so that the beam certainly come into

view. The point in the screen shows in what direction it has to be adjusted to make it normally appear on the screen. Focus, astigmatism These adjusters have affect on the shape of the point. In general, the point or the line is adjusted to be as sharp as possible.

0.1.2 Vertical deflection block The measured signal is amplified and the vertical deflection voltage is formed from it. This voltage moves the beam in vertical direction (y-axis). The amplification can be controlled and therefore signals of very different size can be measured with the device. In dual-beam oscilloscopes there are two y-channels. Behind the pre-amplifiers there are a fast switch. With this switch the y-channels are chosen by turns to control the deflection voltage and thus it seems that there are beams for both y-channels on the screen. Normally these channels are called Ch1 and Ch2 (or Y1 and Y2) Upper frequency limit and sensitivity Upper frequency limit is typically called the bandwidth of the oscilloscope, the lower frequency limit is normally DC-voltage. The characteristics of the vertical deflection bolck define two charcteristics of the oscilloscope: the upper frequency limit and the sensitivity. The sensitivity of the vertical deflection defines the maximum amplification per spacing (volts/div). Usual maximum sensitivity per spacing is 1 mV.

x

y

Figure 7. Graticule of the oscilloscope

The bandwidth of the amplifier specifies the upper frequency limit. The frequency with which the amplification is decreased 3 dB from the normal is generally determined as the upper frequency limit. (the power of the constant resistance is

decreased ½, and the voltage has decreased 1 2 0 708= , of the initial value). The upper frequency limit is not any absolute limit to the oscilloscope functioning. Frequencies above the upper frequency limit seems to be more damped. While measuring the digital signals, it has to be taken into account that for example the rectangular wave of 10 MHz might include frequency components as high as 100 MHz and even over. Thus, the real shape of this kind of rcctangular wave can’t be seen with an oscilloscope of 30 MHz. The usual frequency limit of an oscilloscope is 10…100 MHz. Adjusters of the vertical deflection block Amlification (volts/div) Vertical deflection sensitivity is chosen separately for channel 1 and channel 2. Sensitivity is expressed per spacing and it varies between few millvolts to several volts. Sensitivity can also be adjusted continuous (variable-adjustment), if there is need to fit the signal to some certain spacing to enable the studying the signal shape. In many oscilloscopes there are an ’uncal’-light, which is switched on while using the variable-control, to indicate that the sensitivity chosen by volts/div –adjuster is not true. Vertical position Beams from both cannels can be moved independently in vertical direction. Input coupling The measured signal is coupled straight to the vertical deflection amplifier in DC-position. Although it is called DC-position, it can be used as well to measure AC-voltages. In AC-position the DC-component is filtered off with a high-pass-filter. The limiting frequency is usually 1-3 Hz. With frequencies under 10 Hz the oscilloscope is damping the signal considerably in AC-position. AC-position is used when there is a need to distinguish a small AC-component from the DC-voltage. In GND-position the voltage of 0 V is feeded to the input of the amplifier instead of the measured signal, thus the zero level of the signal can be adjusted with the vertical position control to the desired level. If the sensitivity (volts/div) is changed, the zero level needs to be recontrolled. Mode In dual-beam oscilloscopes the proper function mode needs to be chosen. In ALT-mode the beams from y-channels are swept by turns over the screen. With high sweeping velocities the rotation can’t be seen, but with low velocities the rotation is disturbing and the ALT-mode is not useful. Another alternative is the rotation of the beams in fast tempo determined by the internal chopper of the oscilloscope. With

low sweeping velocities it seems like the both beams are travelling on the screen at the same time, but with high velocities the rotation is visible and disturbs the measurement.Some oscilloscopes are choosing the mode automatically on grounds of the sweeping velocity adjustment. In addition, the beams from both channels can be switched on or off (Ch1 on/off, Ch2 on/off) and the sum signal can be formed. Usually at least one of the two channels can be inverted, thus it is pobbible to obtain the difference signal. Connectors of the vertical block Input Both channels (Ch1 and Ch2) have their own connectors to couple the measured voltage. The connector is usually so called BNC-connector. The signal has to be connected to the oscilloscopewith as short protected cable as possible to prevent the coupling of the mains-borne disturbance and the rf interference. If high frequrncies are measured and the impedance of the measured object is not low, it is very useful to utilize probes. Even while measuring the low frequencu phenomena, the rf interferences interfere with the measurement, if the protection is not well done.

Horizontal deflection voltage

time

ramp Return ramp Suspension periodTrigger

holdoff Triggering moment Triggering moment

Figure 8. Waveform of the horizontal deflection voltage

0.1.3 Horizontal deflection block Also the deflection voltage in horizontal direction (x-axis) is neededto draw the beam. A ramp generator is forming the horizontaldeflection voltage which is formed of a ramp, a retrace, a holdoff and a wait condition (fig. 8). The beam is drawed during the increasing ramp, but it is switced of during the retrace, holdoff and wait condition. The lenght of the holdoff is normally the same than the lenght of the retrace but the user can lenghten it by controlling the holdoff-adjuster. During the wait condition the ramp generator is ready to start from the triggering of the ramp. The increasing time of the ramp is adjustable in very large scale and thus the

oscilloscope can be utilized to observe very slow and very fast phenomena (from microseconds to few seconds). Adjusters of the horizontal deflection block Sweep speed (sec/div) With this adjuster the travelling speed of the beam in horizontal direction (x-axis) is chosen. The time scale is quantified per division and it is usually scaled 3 steps/decade. For example 1 ms, 2 ms, 5 ms, 10 ms…/scaling. The sweep speed can also be adjusted variable, if there is need to fit the signal to some certain spacing to enable the studying the signal shape. In this case the ‘uncal’-light may switch on for that the variable-control is not forgotten on. In contact with the sweep speed adjuster there are usually also the xy-position. If using this xy-position one of the inputs (Ch1) is coupled to the horizontal deflection amplifier instead of the sweep generator. x-position The beam can be moved in x-direction and e.g. the start point of a period can be shifted to start at a division line. Magnification, ×5, ×10 The image can be amplified in horizontal direction by a constant (for example 5 or 10), so that only a part of the normal sweeping scale is on the screen. The beam can be moved in x-direction.

0.1.4 Trigger block Triggering moment defines when the oscilloscope begins to draw the beam (fig. 8). It is important that the signal drawing begins every time at the same phase of the period. Triggering moment is controlled indirectly with the gate trigger voltage. A multi-functional trigger block enables studying a variety of different signals. Most of the problems in utilizing the oscilloscope deals with the selecting of the trigger level and the trigger mode/source. Adjusters of the trigger block Trigger source In dual-beam oscillators there are several alternatives for the triggering source: signal from either Ch 1 or Ch 2, external triggering or triggering from the line. Trigger level and trigger slope

The trigger level control by hand is important to achieve clear graph on the screen. If the waveshape is complicated, the graph on the screen needs to be adjusted with the trigger level control to achieve a stabile and unambiguous graph. The trigger slope defines if the triggering is done from increasing or decreasing edge of the signal. Trigger mode In normal mode the triggerin takes place, if the triggerin signal cuts the trigger level in chosen direction in wait condition (fig. 8). If the trigger condition is not realized, the wait condition continues, which usually is the reason why there is anything visible on the screen. In auto-trigger mode the oscilloscope is ready to trigger in wait condition for a moment, but if the condition is not realized, it triggers automatically even if the condition is not fullfilled. The auto-trigger mode is oblicatory for example to make the DC-signal visible on the screen. For signals that are repeated in low frequency the auto-trigger occurs too early, and the normal mode is needed. Usually it is also possible to utilize the single sweep, in which case the oscilloscope stays in the holdoff condition after single sweep and continues to the wait condition when the single sweep is chosen again. Trigger coupling The input of the trigger circuit might be coupled straight (DC) or through a high-pass filter (AC), in which case it is easier to synchronize to a small ripple voltage. Trigger holdoff The holdoff condition can be made longer with the holdoff-button. It might be useful if for example the measured signal fulfills the trigger condition several times during a period. The triggering has to occur at the same phase of the period than during previous period. Whit holdoff-control some phases that fulfill the trigger condition can be bypassed. Connectors of the trigger block Ext trigger Triggering is done in time with an external signal coupled to this connector, if the trigger source –adjuster is in ext-position.

0.1.5 Calibration signal In the oscilloscope there is a calibration signal output. The calibration signal is typically 1 kHz rectangular wave with amplitude of 1 V.

0.2 Oscilloscope with a delayed time axis

0.2.1 Delayed sweep In the oscilloscopes which are equipped with a delayed sweep there are two separate horizontal deflection ramp generators (fig. 9 and 10). The B-deflection is like the A-deflection and it is used a kind of auxiliary time-axis in sweep delay. The B-deflection differs however from the A in the way that there is a delay circuit in the B-ramp generator. The trigger produced by the studied phenomenon release the A-ramp, which after reaching some certain voltage release the B-ramp with a particuliar calibration circuit. The reference level and thus delay time can be controlled by a potentiometer. The beginning of the B-horizontal deflection ramp can be delayed about 0,1…10 s depending on the oscilloscope.

A-pyyhkäisynliipaisutaso

B-pyyhkäisynliipaisutasoA-pyyhkäisyn

B-pyyhkäisyn

B-pyyhkäisyn pituinen kirkastuspulssiA-säteeseen

mitattavasignaali

ramppi

ramppi

t

Figure 9. Scheme for generating a delayed sweep. A-sweep beam is brightened for the time period of B-sweep in order to see what part of the A-beam the B-sweep is displaying.

kirkastettuosuus

A-pyyhkäisyn säde

B-pyyhkäisyn säde

Figure 10. Measured signal of figure 9 on the oscilloscope screen when A and B beams are chosen to be displayed at the same time.

0.3 Digital oscilloscope Compared to the analog oscilloscopes, digital oscilloscopes have many useful properties and in consequence the digital oscilloscopes have captured the market from the analog oscilloscopes. Such properties are for example possibility to save measured waveform, print the results with a printer connected to the oscilloscope, automatic measurements, ability to utilize cursors and controlling the oscilloscope with a PC in order to automatize measurement and processing of data.

0.3.1 Operational principle of the digital oscilloscope Measured signal is sampled and converted to digital form with a fast AD-converter1, typically with 8-bit resolution. These bytes are saved at sampling frequency to memory, from which the data is collected for microprocessor system. Fast single phenomena or very slowly varying signals can be easily detected. A typical oscilloscope display provides a VGA-resolution. Because the signal is stored in the microprocessor system many different kind of signal processing and signal analyzing activitiess can be carried out to support the measurement. In addition, printing the results with an ordinary printer and transferring data to computer for the further processing is possible.

channel 1

channel 2

externaltriggering

vertical deflection amplifier

vertical deflection amplifier

AD-converter

AD-converter

AD-memory

triggercomparator

microprocessorsystem TV-screen

AD-memory

crystal oscillatordelay counterrecordingstop

Figure 11. Block diagram of the digital oscilloscope

0.3.2 Peculiarities of the sampling Some issues concernig the sampling that highlight the specialities of the digital system: 1 Voltage is transferred to numerical values

Progressive scanning The bandwidth of the vertical deflection amplifier of the oscillator used in this work is 100 MHz. Shannon sampling theorem says that there must be at least two samples per period in order to be able to perfectly construct a sinusoidal signal (samplig must happen at least at Nyquist frequency). In practice the oscilloscope needs more samples per period. 400 million samples per second would be enough in order to get enough samples from a signal the bandwidth of which reaches up to 100 MHz. However, the oscilloscope digidizing speed is only 20 million samples per second (20 MS/s) for one channe and 10 MS/s for two channels. The price of the oscilloscope can be much lower if the sampling frequency is kept slow if compared to an oscilloscope that has a sampling frequency of 400 Ms/s. With a progressive scanning a bandwidth of 100 MHz can be reached. A repeated signal at 100 MHz can be detected by utilizing the progressive scanning. The functioning of an oscilloscope is based on an occasional repeated sampling. Repeated sampling means that samples are taken from the signal during several scannings. Sampling moment relative to the signal phase alters and finally a signal can be constructed, figure 12.

1

3 4

5 6

7

8

910

11 12

2liipaisutaso

Figure 12. Digidizing of the signal during several scanning (liipaisutaso=triggering level).

Asynchronous means that signal is continuously digidized with the phase of the oscilloscope own clock regardless of the triggering moment. When signal cuts the triggering level in chosen direction, the oscilloscope puts the stored points as well as those points coming after triggering to the places where they belong. Because the measured signal frequency and sampling frequency are not syncronized, the sampling moment relative to the triggering moment is varying from one scanning to other and, finally, there exists measured points dense enough to construct the whole signal. There are two benefits in the asynchronous system. First, signal can be displayed already before the triggering moment, which would be very difficult to carry out with analog oscilloscopes. Second, asynchronous system makes the aliasing2 in 2When oscilloscope is used at slow scanning speed, the sampling frequency is typically decreased due to the limited memory capacity. Because the preamplifier passes frequencies up to over

which the aliased signal is stable on the screen very unlikely. Sometimes there is a fast rolling aliased signal on the screen and there is a possibility to have a wrong idea about the signal frequency. When the triggering is functioning so that there is no rolling on the screen, the real signal should be displayed. One disadvantage of digital oscilloscopes is the bottleneck due to the microprocessor system. The rate at which the microprocessor system can update the screen is typically very slow compared to the sampling frequency. The screen can be updated few tens of times per second although the scanning speed requires screen updating 20 000 times per second. E.g. if there is an occasionally 50 times per minute existing noise peak that occurs only every 20000th scan in the measurement signal, it may take one hour to get the noise peak visible on the screen. Analog oscilloscope updates the screen with every sweep and thus there are realistic possibilities to find out the noise peak. Single scan Single scan is one of the most significant advantage in the digital oscilloscopes in comparison with the analog oscilloscopes. (Even if before the digital oscilloscopes there were analog oscilloscopes which were capable to the single scan.) Many phenomena are non-recurring or so slow, that they can’t be observed with an oscilloscope without data storage. Remember that there might exist aliasing while utilizing single scan. Due to the low sampling frequency of the used oscilloscope, the manufacturer has reported that in the single scan mode the oscilloscope is capable to work only under frequencies of 2 MHz while utilizing one channel and under 1 MHz while utilizing two channels. The oscilloscope does however not filter out higher frequencies, thus there exist aliasing with frequencies which are over half of the sampling frequency. While utilizing the single scan even the asynchronous sampling can not save the situation if the signal frequency is near to the sampling frequency or its multiple. For example sinusoidal wave of 20,05 MHz appears in the screen like sinusoidal wave of 50 kHz.

0.4 Probe There exist a variety of probes for different purposes; to convert non-electrical and electrical quantities to the voltage which can be measured with the oscilloscope (current probe, pressure converter etc.) The probe can be either active or passive.

100 MHz to the AD-converter, there may exist aliasing at the frequencies that exceed half of the sampling frequency. E.g. if the signal frequency is exactly the same as sampling frequency, the sample will be taken always in the same phase of the signal and there is a DC-signal displayed on the screen. If the signal frequency is 1 Hz over or below the sampling frequency, there will be a 1 Hz signal on the screen, the amplitude of which is the same as the original signal. So, a high frequency signal is aliased to low frequency.

0.4.1 High-impedance probe If an oscilloscope is coupled to the measured circuit without the probe, the oscilloscope become a part of the circuit, which interfere with the original functioning of the circuit. The finite input impedance of the oscilloscope is loading the circuit. Oscilloscope input impedance is a transversal resistance, typically 1 MΩ, and there is a capacitor of 20 pF parallel to it. At low frequencies the impedance is normally high enough, but at high frequencies the capacitance lowers the impedance which may dramatically alter the functioning of the circuit. The may also exist bit errors in the fast digital circuits due to the reflections in the signal cable. E.g. a signal entering a 1,5 m long signal cable reflects from the oscilloscope and return back to the circuit after ca. 10 ns. So, there exist additional pulses in the circuit. Most common probe type is a passive high-impedance probe and input impedance can be increased at the cost of sensitivity. Figure 0 shows the connection of a probe to the oscilloscope input. The resistance of the probe is close to probe tip in order to let the reflection due to the probe to return back as fast as in ca. 100 ps and even a fast circuit can not interpret the reflection as a new pulse. Basically, a probe is a volt divider, although a resistance is not enough but also a compensating capacitance is needed parallel to the resistance in order to guarantee a constant attenuation ratio at a vast frequency range. Capacitor value depends on the voltage division ratio and input capacitances of measurement cable and oscilloscope. Thus the probe capacitance must be adjustable. Sometimes the capacitance value is fixed and an additional capacitance is placed in a connector that connects the probe to the oscilloscope. This capacitance is electrically parallel to the oscilloscope input. Resistive voltage division ratio of the probe is

11

:mR

R Ri

i

=+

, (0.1)

where the resistances are as in the fig. 8. The attenuation of the probe is m-fold. In order to keep the voltage division ratio of the probe constant regardless of the frequency, the capacitive voltage division must be the same.

1

1

1 12

2 1

1

1 2

:m C C

C C C

CC C C

i

i

i

= +

++

=+ +

(0.2)

Connection to earth

Probe Cable

Oscilloscope

Metal shielding

Earth conductor works as shielding

Metal shielding

C i

C 1 C 2

R 1 R i

Mains earth

head

Figure 13. Probe, cable and amplifier input. Oscilloscope amplifier input sees a voltage that is generated over Ri , Ci and cable capacitance C2 (ca. 80 pF/m). Note that oscilloscope earth and thus also the earth connection of the probe are connected to mains earth through the mains cable of the oscilloscope.

It follows that:

C R C C Ri i1 1 2= +( ) . (0.3)

0.4.2 Calibrating the probe The probe can be calibrated with a rectangular wave. The rectangular wave is commonly taken from the calibration output of the oscilloscope and it is coupled to the input through the probe. When the sweep time and the other controls have been adjusted so that the rectangular wave is clearly visible in the screen, the rectangular wave is adjusted as right-angled as possible with the capacitor of the probe. There might be a switch on the probe, which affect to the damping properties. In 1× position the damping resistance and capacitance are passed (normally by a small resistance), in 10× position the damping is on and in ref –position the switch short circuits the central cable to earth and position of neutral (zero) level can be checked on the oscilloscope screen.

is too largeis too small right value C 1 C 1 Figure 14. Calibrating the probe with an adjustable capacitor.

0.5 The usual measurement with the oscilloscope In most cases it is enough to see the waveshape on the screen and it is not necessary to specify numerical values.

0.5.1 Measuring the amplitude, the frequency and the period lenght When reading signal values from the screen, the scale adjusters must be put on cal-position (volts/div and sec/div).

0.5.2 Measuring the rise time and the pulse width An ideal step-function response is composed of unlimited amount of frequency components. Due to the limited frequency band the step-function response has always a finite rise time. Because in practise the step-function response can be very complicated, it has been agreed that the rise time is between 10 % and 90 % of the initial and the final level of the step. A continuos adjuster of the vertical deflection facilitates the reading of the rise time. The length of the positive pulse is defined from the midpoint of the increasing edge to the midpoint of the decreasing edge.

0.5.3 Measuring the phase difference The phase between two equifrequent sinusoidal signal can be measured as follows. Adjust the amplitude of the both signal to be equal. Read the time difference from the screen. The relation between the time difference and the period length multiplied by 360° is the phase difference.

10%

50%

90% droop

Pulse width

Rise time

crossing

Setting time

50%

Underswing before rising edge

Figure 15. Definitions of pulse characteristics

0.6 Measurement Equipment

• Dual-beam oscilloscope • Probe • Signal generator • RC-circuit and rectifier circuit

The experimental work in the laboratory is not only filling the answering forms. Making clear notes about the used equipment, the measuring system and the measurement results is as important as the data itself.

0.6.1 Becoming acquainted with the oscilloscope What are the type identification markings, the input resistance and the input capacitance, the most sensitive voltage range and the shortest sweep time of the used oscilloscope? What kind of functional blocks there are in the oscilloscope? Label them and list adjusters and connections related to each block. Is there some adjuster or connection that is not mentioned in the summary above? Mention as well if in your opinion some fundamental adjuster or connection is missing.

0.6.2 Adjusters of the display and the calibration Switch on the oscilloscope and wait a while till the CRT warms up. Adjust the beam intensity and sharpen the line or the point. If you can’t find the signal, ask for help for the assistant. Couple probes to the oscilloscope and calibrate them. What is the attenuation ratio and the magnitude of the damping resistance of the used probe? Find out the frequency and the amplitude of the internal calibration signal.

0.6.3 Measurement of amplitude, phase and period Couple sinusoidal signal to the input of the RC –low-pass filter. Connect probes from the oscilloscope to the input an output of the RC-circuit. Measure the complex transfer function U UOut In (amplitude/phase) with the frequencies given in the answering form. Measure the period length with the oscilloscope and calculate the frequency of the signal.

R

CUin Uout

Figure 16. RC -low-pass filter

Compare measured transfer function values with those calculated in the pre-laboratory exercises and explain what might be the reason for the differences between these two values. With what frequency the signal level has decreased 3 dB? What is the phase difference with this frequency?

0.6.4 Rectifier circuit Couple 50 Hz sinusoidal signal ( 8 V peak-to-peak ) from the signal generator to the input of the rectifier circuit. Measure the magnitude of the rectified output voltage and the ripple (AC-component). Measure the ripple as well with the frequency of 1 kHz.

0.6.5 Measurement of pulse, rise time Couple 10 kHz rectangular wave (amplitude 5 V) from the signal generator to the other input of the oscilloscope. Measure the rise time and the pulse width, in other words the time that the signal is over 50 % of its maximum value (fig. 15). Measure as well the rise time of the decreasing part of the signal (from decreasing edge) and the pulse width (time that the signal is under 50 % of its maximum value). Compare these results.

1 Multimeter measurements Goal of the laboratory work • To learn the basics of the structure of the multimeters • To learn the capability of the studied multimeters • To learn the restrictions of the studied multimeters • To learn to effectively use the usual multimeters.

1.1 Operation principles of a digital multimeter Multimeters can usually be utilized to measure voltage, current and resistance. Voltage and current measurements can be carried out with AC- or DC-signals. In addition to these basic properties it can be possible to measure a lot of other measurands such as capacitance, frequency or transistor current amplification. The digital multimeters studied in this work are Fluke 8050 and Metex M-4650.

1.1.1 Block diagram of a multimeter Figure 17 illustrates a block diagram of a typical multimeter. There is a attenuator in the front part of the multimeter so that desired voltage, current or resistance range can be selected. When resistances are measured the altering of the range adjusts the current value of the current generator. The attenuator is followed by a rectifier which usually is an idealized diode rectifier based on a linear circuit. The last stage is an analog-to-digital converter and display.

1.1.2 Analog-to-digital converter The basic component of a digital multimeter is the analog-to-digital converter (ADC). The performance of the ADC determines the fastness, accuracy and interference immunity of the multimeter. ADC of the digital multimeter used in this work is basically a dual-slope ADC. Dual-slope ADC is the most common converter type in digital voltmeters, multimeters and in other slow measurement applications. The operation is slow compared to the other converter types but a very good linearity and interference immunity can be reached. The operation principles of the converter is shown in figures 18 and 19.

Voltage

Current

Current generator

AC/DC

DC

AC

Ohm.

A/D

Display

Voltage

CurrentResistance

Figure 17. Block diagram of a digital multimeter

In the beginning of the conversion the measured voltage UX is connected to the input of the integrator. Unknown voltage is integrated a constant time T1. Integration time is determined by the clock, counter and control logic of the converter. After the integration a negative reference voltage UR is connected to the input of the integrator. The reference voltage is integrated until the output voltage of the integrator UI has reduced to zero.

n

R

C

U

UR

reference voltage

Clock control logic

counter

integratorcomparator

X

digital output

UI

Figure 18. Dual-slope analog-to-digital converter

UI

t

T1 2T

12

3

Figure 19. The output voltage of the integrator UI at three different voltage levels.

Clock, counter and control logic measure the integration time until a comparator detects zero voltage. The measured time T2 is proportional to the measured voltage.

T TUU

X

R2

1= (1.1)

Because of the operation principle the accuracy of the converter is independent of the stabilities of the clock frequency and integrator time constant (however, they must be stable and unchanged the duration of the integration). Furthermore, a good attenuation of power line disturbance (at 50 Hz) can be reached if the integration time T1 is chosen to correspond to the period of the disturbance signal or its multiple.

1.1.3 Multimeter readout at AC-range Effective value (RMS-value) of an AC-voltage is determined as follows. Effective value of the AC-voltage (URMS) is equal to the DC-voltage value, which has the same average power to a resistive load as the studied AC-voltage. In case of AC-signals, effective value (URMS) can be used to calculate different parameters in stead of DC-values. For example, the current consumption of a 60 W bulb can be calculated with I=P/URMS. The instantaneous power of AC-voltage is

P t U tR

( ) ( )=2

, (1.2)

where U(t) is instantaneous voltage and R is load resistance. Average power is

P

U tR

dt

TAve

T

=∫

( )2

0 , (1.3)

where T is period. In case the signal is not periodic, the integration time T is chosen so that there will be no large deviation between many individual measurements. Average power can be used to calculate the effective value of the voltage (URMS):

U P RRMS Ave= (1.4) For example the effective value (URMS) of a sinusoidal wave is 1 2 times its

maximum value or 11,122

=π times the rectified average value of the voltage

signal. The response of the multimeter is usually based on the average value or on the effective value. Because the object is most often the effective value (URMS), an average value-based multimeter is adjusted to display effective value of sinusoidal signal by multiplying the average value by number 1,11. This kind of multimeters display correct effective value only for sinusoidal signals. However, in case of other wave types, the correct effective value can be calculated if the wave form is known. For example moving-coil multimeters and the most simple commercial multimeters (Metex M-4650) are typically average value based multimeters. Effective value based meters are for example moving iron multimeter (in electric power measurements) and specific digital multimeters that calculate the effective values with suitable integrated microcircuits. Fluke 8050 studied in this work displays the correct effective value. When measuring AC-signals, many multimeters do not take into account the DC-component of the signal (when AC-range of multimeter is selected). This means that multimeter is AC-coupled. Both multimeters in this work are AC-coupled. However, multimeters that measure the summed value of both AC-component and DC-component (AC + DC) does exist.

1.1.4 Measurement of small resistances When using a typical multimeter (Figure 17) the resistance of measuring cable is added to the measured resistance. When measuring small resistances (< 1 Ω) can cable and junction resistances have a remarkable influence. 4-wire measurement can be used to effectively eliminate the influence of unwanted resistances (Figure 20). The current through the measured resistance (R) is constant and independent of cable and junction resistances and the voltage meter measures only the voltage over the studied resistance. In this work HP 3468A or HP 34401A multimeter with 4-wire measurement option is used to measure a small resistance.

V

Junction and conductor resistances

R

I

Voltage meter

Measurementcurrent source

Figure 20. 4-wire measurement of a small resistance

1.1.5 Studied multimeters The studied Fluke is a three-and-half digit multimeter (maximum displayed value is 1999) and Metex M-4650 is a four-and-half digit multimeter. Both multimeters are based on the dual-slope ADC. In case of AC- and DC-signals, Fluke 8050 measures directly the correct effective value (true root mean square, TRMS), so that the displayed value is correct despite of the measured wave form. Metex, on the other hand, represents simpler technology. The value Metex displays is proportional to the rectified average value which is corrected by multiplying with the number 1,11 (in order to show the effective value of the sinusoidal signal). So, in case of other wave forms, the value Metex displays is different from the correct effective value. Both Fluke and Metex are AC-coupled, so when measuring in AC-mode, both multimeters display the value of AC-component only. The effective value of summed AC- and DC-signal can be calculated as

22

ACRMSDCRMS UUU += . (1.5)

1.2 Measurements Devices • Multimeter Fluke 8050 • Multimeter Metex M-4650 • Multimeter HP 3468A tai HP 34401A • Voltage source Mascot 0-30 V • Oscilloscope • Potentiometer • Function generator • "Black box", (gray in color) • Resistor test board

1.2.1 Measurement of current and voltage Connect the voltage source, resistor and two multimeters so that you can measure the voltage over the resistor and the current through the resistor. Adjust the voltage source to ca. 5 V. Calculate the resistance with the help of measurements.

1.2.2 Measurement of DC-voltage of a high-impedance circuit The measurement of the voltage of a high-impedance circuit is problematic because the multimeter introduces a load to the circuit. In our "black box" case (Fig 21.), the high-impedance circuit is modelled by a voltage source with high internal resistance RS. The voltage source is connected to the operational amplifier which has much higher input impedance Zin compared to the input impedance of a usual multimeter. The operational amplifier has unity gain and very small output impedance which is not effected by the internal resistance of the multimeter. Measure the output voltage of the operational amplifier with Metex. After that, measure the voltage of the "black box" voltage source with the Fluke meanwhile the Metex is still connected to the output of the operational amplifier. What value does the Metex display now? Use the voltage difference measured with Metex and calculate the RS .

A=1RS

E Zin

Figure 21. Black box

1.2.3 Measurement of AC-voltage Measure sinusoidal, triangular and square wave signals (f=100 Hz, unloaded Vpp=5 V) generated by function generator with both multimeters. (Do the measurement results change if both multimeters are connected simultaneously instead of one multimeter?) Add +2 V (DC-offset) to function generator output signal and repeat the measurements.

1.2.4 Current measurement, voltage drop of multimeter Measure the voltage over multimeters at the current of 100 mA. Use the range 0,2 A. Use one of the multimeters to measure current and the other one to measure voltage. The connections are shown in Figure 22. Change the multimeters and repeat the measurement. ATTENTION! Set the potentiometer to its maximum value before switching on the voltage source (in order to avoid short-circuit). Suitable voltage level is 5V.

Voltage source

V A

100 R

Figure 22. Measurement of the voltage drop of the current meter (ammeter)

1.2.5 4-wire measurement for small resistance Measure the small resistance with Fluke, Metex and HP multimeters (HP 4-wire measurement). How large is the junction resistance in the case of normal 2-wire measurement?

1.3 Questions 1.3.1 How large is inaccuracy of Fluke and Metex at range 200 V (in accordance

with manufacturer data sheets) when the measured voltage is: - 50 % of full scale, i.e. 100 V - 25 % of full scale, i.e. 50 V - 5 % of full scale, i.e. 10 V 1.3.2 Why does the voltage change (in section 1.2.2) when another multimeter is

connected to the input of the operational amplifier? Calculate the internal resistance RS. Input impedance of the operational amplifier is ca. 1012 Ω.

1.3.3 Use the voltages measured in section 1.2.3 by Metex and calculate correct

VRMS values. Take into account that Metex uses correlation coefficient which is suitable only for sinusoidal signal.

1.3.4 Compare the results in section 1.2.4 to the results given by the manufacturer . 1.3.5 Is it possible to find out (with Metex or Fluke) if the measured signal is DC-

voltage, AC-voltage or the sum of those.

Appendix: Notation ± 0.05% of reading + 3 digits means: • 0.05% of reading means 0,05% of the measured value. • 3 digits means change of three digits in the last displayed number. E.g. in Metex

at 200 mV range 3 digits is equal to 30µV. All the inaccuracies can be added directly together. Appendix 1.1 Metex M-4650 specifications 4. SPESIFICATIONS Accuracies are ± (% reading + No. of digits) Guaranteed for 1 year, 23°C ± 5°C, less than 75% RH. Warm up time is 1 minute. DC Voltage Range Accuracy Resolution 200 mV 10 µV 2 V 100 µV 20 V ± 0.05 % of rdg + 3 digits 1 mV 200 V 10 mV 1000 V ± 0.1 % of rdg + 5 digits 100 mV Input impedance: 10 Mohm on all ranges. Overload protection: 1000V dc or peak ac on all ranges. AC Voltage Range Accuracy Resolution 200 mV 10 µV 2 V 100 µV 20 V ± 0.5 % of rdg + 10 digits 1 mV 200 V 10 mV 750 V ± 0.8 % of rdg + 10 digits 100 mV Input impedance: >10 Mohm in parallel with <50 pF (ac coupled). Frequency range: 40 Hz to 400 Hz. Overload protection: 750 V rms or 1000 V peak countinuous on ac ranges, except 200 mV ac range (15 seconds maximum above 300 V rms). Indication: Average (rms of sine wave).

DC Current Range Accuracy Resolution 200 µA 10 nA 2 mA ± 0.3 % of rdg + 3 digits 100 nA 20 mA* 1 µA 200 mA 10 µA 2 A* ± 0.5 % of rdg + 3 digits 100 µA 20 A ± 0.8 % of rdg + 5 digits 1 mA * except 4630 and 4650 Overload protection: 2 A/250 V fuse. 20A range unfused. Maximum input current: 20 A (MAXIMUM OF 15 MINUTES). Measuring voltage drop: 200 mV. AC Current Range Accuracy Resolution 200 µA 10 nA 2 mA ± 0.8 % of rdg + 10 digits 100 nA 20 mA* 1 µA 200 mA 10 µA 2 A* ± 1.0 % of rdg + 10 digits 100 µA 20 A ± 1.2 % of rdg + 15 digits 1 mA * except 4630 and 4650 Overload protection: 2 A/250 V fuse. 20A range unfused. Maximum input current: 20 A (MAXIMUM OF 15 MINUTES). Frequency range: 40 Hz to 400 Hz. Indication: Average (rms of sine wave). Measuring voltage drop: 200 mV. Resistance Range Accuracy Resolution 200 ohm ± 0.2 % of rdg + 5 digits 0.01 ohm 2 Kohm 0.1 ohm 20 Kohm 1 ohm 200 Kohm ± 0.15 % of rdg + 3 digits 10 ohm 2 Mohm 100 ohm 20 Mohm ± 0.5 % of rdg + 5 digits 1 Kohm Overload protection: 500 V dc/ac rms on all ranges, except 200 ohm range (250 V dc/ac). Open circuit voltage: <1.2 V. Relative humidity: 0 to 75%, 0°C to 35°C on 2 Mohm, 20 Mohm 0 to 90%, 0°C to 35°C on all other ranges 0 to 70%, 35°C to 50°C

Appendix 1.2 Fluke 8050A Specification

Appendix 1.3 HP 3468A specifications

2 Signal spectrum measurements Goals of the work

• To study spectrums of periodic signals • To learn the most essential properties of spectrum analyzer

2.1 Signal spectrum A convenient way to study signals in frequency domain is to consider them as a superposition of sinusoidal signals of different frequencies. In most cases, the systems and instruments in nature and techniques are such that only sinusoidal stimulus gives a response of the same waveform, although signals are e.g. attenuated or delayed – the amount of attenuation and delay depending on signal frequency. Examples of this kind of instruments are electric circuits built of resistors, capacitors, and coils. Or, walls of buildings that attenuate acoustic waves of different frequencies in different ways, still preserving the sinusoidal waveform. (However, at higher signal levels walls have nonlinear response that leads to distortion of the sinusoidal waveform). Transistors and diodes, for example, are nonlinear components and thus make an exception. Anyway, in many cases, spectrum analyzer is a suitable instrument for studying signals in frequency domain. Bandpass filter of spectrum analyzer makes it possible to measure signals within a narrow frequency band. Center frequency of the bandpass filter is controlled by the analyzer. Usually the center frequency is swept over a certain frequency range repeatedly, and the signal level is measured simultaneously as a function of frequency. Thus, a spectrum of the measured signal is obtained, and displayed on the screen of the analyzer. Mathematically speaking, signals consist of infinite amount of sinusoidal components that are infinitesimally close to each other within the frequency band. Of course, when measuring, it is not possible to distinguish the frequency components that close to each other. Instead, the bandpass filter picks up sinusoidal waves within a narrow band, and all the waves contribute to the measured signal level. In other words, bandwidth of the bandpass filter determines the frequency resolution of the spectrum analyzer.

2.1.1 Sinusoidal wave This chapter concentrates on the special case of sinusoidal signal. Mathematically it would be possible to study any signal as a superposition of also others than sine functions. Then why does it come naturally to divide signals to sine components? One justification is that, in nature oscillators and systems reacting to oscillations usually resonate sinusoidally. Some examples of this are e.g. motion of a mass attached to a spring, harmonic motion of a pendulum (if the amplitude of the oscillation is not too large), and electric

oscillation in an LC-circuit. This is the reason why sinusoidal signal passes the medium without changing its waveform, while other signals are distorted. Next we will see why harmonic oscillators oscillate sinusoidally. State of oscillator will be solved as a function of time, after forcing it into a motion. As an example, let us consider a mass attached to a spring (mass of the spring is assumed to be zero). The force applied to the mass (by the spring) is given by F ky= − , where k is the elastic constant, and y is displacement of the mass

from the equilibrium position. Thus, the acceleration of mass m is − km

y t( ) ,

where the displacement is given as a function of time. On the other hand, we may write the acceleration as the second derivative of the displacement d y t

dt

2

2( ) . This leads to a differential equation of the form

d y t

dtkm

y t2

2 0( ) ( )+ = . (2.1)

Equation 2.1 has a general solution y t A t B t( ) cos sin= +ω ω , where ω is angular frequency of the oscillation, and ω 2 = k m/ . Constants A and B are obtained from boundary conditions, such as the values of velocity and displacement at time t = 0.

2.1.2 Fourier series of periodic signals A sinusoidal signal that is written in time domain as cos(ω 0 t), is described in frequency domain by a single spectral line at ω 0 . Non-sinusoidal, periodic function may be written as a superposition of sine functions at harmonic frequencies nω 0 (n = 1,2,3,...). This gives a line spectrum with spectral components at frequencies nω 0 , which mathematically correspond to the Fourier series of the signal. For a non-periodic signal, at certain conditions, the spectrum is given by the Fourier transform of the signal. In the following, only the case of periodic signal (and thus only the Fourier series) is discussed. The Fourier series gives us spectral components of a periodic signal u(t). That is, the signal is written as a sum of sine and cosine functions of different frequencies.

u t a a t a t a tb t b t b t

a a n t b n tn nn

( ) cos( ) cos( ) cos( ) ..sin( ) sin( ) sin ( ) ..

( cos( ) sin( ))

= + + + ++ + + +

= + +=

∞

∑

0 1 2 3

1 2 3

01

2 32 3

ω ω ωω ω ω

ω ω

(2.2)

a0 is amplitude of the DC component, and AC components are given by an and bn (n > 0). Fundamental, i.e. the lowest, frequency is ω π= 2 T where T is the signal period. Cosine functions and sine functions describe even and odd parts (in respect of time t = 0) of u(t), respectively. Sum of a cosine term and a sine term is a sine function that has a phase angle defined by the ratio of an and bn . In consequence, each spectral component has not only the amplitude, but also a phase.

2.1.3 Fourier integral Values for coefficients a0 , an , and bn are obtained by integrating the studied function, weighted with cosine and sine, over one period.

aT

u t dtT

T

02

21=

−∫ ( )

(2.3)

aT

u t n t dt nnT

T

= = ∞−∫

2 12

2

( ) cos( ) ( ..ω , ) (2.4)

bT

u t n t dt nnT

T

= = ∞−∫

2 12

2

( ) sin( ) ( ..ω , )

(2.5)

Terms 1/T and 2/T preceding the integrals are used for normalizing. That is, an in equation (2.4) equals to 1 if the function u(t) is cos( )n tω . Also, integral may be considered as an inner product. Using inner product, a period of the function is projected to sine and cosine components of each frequency. Thus, each value of inner product is a real number that indicates how much of each frequency component is contained in the function. Inner product of functions, e.g. the Fourier transform, corresponds to inner product (dot product) of vectors in geometry. FFT (Fast Fourier Transform) spectrum analyzers sample signals in time domain and use the Fourier transform to calculate the signal spectrum from the saved data.

2.1.4 Example: Fourier series of rectangular wave

tE

u(t)

tE

u(t)

T/2-T/2 T-T 0

T/2-T/2 T-T 0

a)

b)

Figure 23. a) Even and b) odd rectangular wave

Let us first calculate the Fourier series coefficients for the even rectangular wave shown in figure Error! Reference source not found.a). The coefficients, an and bn, can be calculated using equations (2.4) and (2.5): a0 equals to the time average of the signal, i.e. it gives the DC component. In the case of pure AC signal, its value is 0.

aT

u t nT

t dtnT

T

=

−∫

2 2

2

2

( ) cos π

dttT

nTEdtt

Tn

TEdtt

Tn

TE T

T

T

T

T

T∫∫∫

−+

+

−=

−

−

−

2

4

4

4

4

2

21)(22221)(2 πππ coscoscos

(2.6)

even for ,0

odd for ,4)1(2

sin2

sin22

sin22 2

1

n

nn

Ennn

TTn

E n

=

−=

+

+

=

−

ππππ

π

(2.7)

Both the rectangular wave of figure 23a) and cosine function are symmetric relative to time t = 0, i.e. they are even functions1. Thus, it is possible to calculate integral for example for the negative half of the period only, and multiply it then by factor of two to get the final result. 1 It should be noted that even or odd function relative to time t=0 is not the same thing as even or odd harmonic component, which refer to multiple frequencies of fundamental frequency.

On the other hand, bn equals to zero for every n. This comes from the fact that sine function is an odd function and the rectangular wave in figure 23a) is even – Integrals of negative and positive half periods thus have equal magnitudes of different signs, and they cancel out each other. The original rectangular wave in figure 23a) can now be re-constructed using sinusoidal waves given by the Fourier series. Using numerical values calculated for an, equation (2.2) gives:

u t ET

t Tt

Tt

( ) coscos cos

..=

−

+

−

4 23 2

3

5 2

5ππ

π π

(2.8)

If the function to be described is odd, the coefficients an equal to zero while bn:s have non-zero values. This gives a Fourier series representation for the signal of figure 23b):

u t ET

t Tt

Tt

( ) sinsin sin

..=

+

+

+

4 23 2

3

5 2

5ππ

π π

. (2.9)

If the time origin is chosen in such a way that the rectangular wave is neither even nor odd, both the an and bn coefficients have non-zero values when n is odd. Fourier series coefficients (up to n = 5) of the rectangular waves in figure Error! Reference source not found. are shown below, in figure 24.

f

e(f)

0 1/T 2/T 3/T 4/T 5/T

4Eπ 4E

π3 4Eπ5

Figure 24. Fourier series components of a rectangular wave build up a line spectrum where the amplitudes are given by coefficients an and bn. To get RMS values of the components, the amplitudes must be multiplied with 1 2 . Spectrum analyzer measures the RMS values of the spectrum components.

2.2 Noise White noise consists of thermal noise U (equations 2.10 and 2.11) and shot noise I (2.12), and its power is evenly spread over all the frequencies.

P = kTB (2.10)

U kTBR= 4 (2.11) where k = Boltzmann constant (1,38 x 10-23 Ws/K) T = temperature (Kelvin) B = bandwidth R = internal resistance of the noise source (resistor)

I qI BDC= 2 (2.12) where q is elementary charge (1,602 x 10-19C) and I is current through a potential gap (pn junction). Thermal noise is produced by random thermal motion of the charge carriers (e.g. electrons) that leads to arbitrary varying current flow between e.g. resistor ends. Shot noise is caused by statistical variation in the amount of charge carriers at different time moments, for example in a transistor junction. Also an additional noise contribution, so called 1/f noise, is present. 1/f noise arises from several different sources, and its power is spread over the frequency domain inversely proportional to n:th power of frequency (n varies from 0,9 to 1,3). Noise spectral density S(f) is given as a function of frequency, and it describes how the spectral components of noise are spread over the frequency domain. For example, thermal noise of a resistor has a constant noise spectral density (white noise is evenly spread over all the frequencies).

S f U BR kT( ) = =2 4 [W/Hz] (2.13) As an example, let us consider a model of operational amplifier where the noise sources can be described using voltage and current sources, and the noise power thus depends on an external resistance. Noise of the source is given as voltage noise density V Hz or, as current noise density A Hz . When the noise spectral density is known as a function of frequency, the total noise power can be calculated by integrating over the frequency range. In case of noise voltage, the voltage noise density must be squared before integrating. After that, square root of the integral is calculated to get RMS value of the noise voltage. This corresponds to sum of squares of the AC voltage components. RMS value of noise current is calculated in the same way.

2.3 Measuring spectrum of periodic signal Depending on the application, measurement equipment of different types is used to measure spectrum. In this chapter, three measurement instruments with different operating principles are introduced. - Selective voltage meter

- Each frequency component is measured separately using a tunable narrow bandwidth filter.

- Sweeping spectrum analyzer

- Input signal is mixed with local oscillator that can be swept in frequency.

- Contains an intermediate frequency filter at fixed frequency. - Spectrum is shown on a display. Y-axis indicates the measured voltage

and X-axis indicates the frequency. If the local oscillator frequency is e.g. 500 MHz, and the center frequency of the intermediate filter is 300 MHz, the analyzer is measuring either the frequency of 800 MHz or the frequency of 200 MHz.

- Is typically used at radio frequencies. - Digital spectrum analyzer

- Takes samples of the signal to be measured. - Processor of the analyzer calculates signal spectrum from the samples

using discrete Fourier transform (DFT). In practice, Fast Fourier Transform (FFT) is usually used. A minor drawback of the FFT is that number of the samples must be a power of two.

- Can be applied also for measuring spectrums of non-periodic signals. - Is typically used at audio frequencies. Network analyzer is an instrument that resembles spectrum analyzer, except that it also has an output in addition to the input. Output of the network analyzer is set to the same frequency as the bandpass filter, and the analyzer measures the amplitude and phase differences between the input and the output. Therefore, network analyzer is a suitable device for measuring e.g. frequency and phase responses of an amplifier. Signal reflection at the amplifier input or output can also be easily measured using network analyzer. In this laboratory work, a sweeping spectrum analyzer is used. Frequency resolution of the spectrum analyzer is set by intermediate frequency filter bandwidth. Figure Error! Reference source not found. describes how the intermediate frequency filter affects the measurement result.

f fa) b) c)

Figure 25. Effect of a bandpass filter to measurement result: a) response of the bandpass filter, b) ideally measured sinusoidal signal at frequency f, and c) the measurement result in practice.

If bandwidth of the filter is too large, it is not possible to make difference between two frequency components that lie close to each other. In that case, the bandwidth must be narrowed. However, if the filter bandwidth is about to be narrowed, the sweep time must be increased in order to allow the filter work properly. Thus, in practice, a suitable value for the filter bandwidth is given by the sweep time. The resolution bandwidth Br that can be obtained is

BBtrtot

s= (2.14)

where Btot is the frequency band that is swept over, and ts is sweep time. Some other spectrum analyzer properties that must be taken into account when performing measurements, are e.g. noise floor of the analyzer, distortions of preamplifier and mixer, and uncertainties of frequency and voltage references.

2.4 Measurements Equipment list

• Spectrum analyzer HP 8590B • Oscilloscope • Signal generator, output impedance 50 Ω, with variable pulse symmetry

– e.g. Hung Chang 8205A (SYM-control) • Noise generator • Band-reject filter

The first thing to do is to turn on the spectrum analyzer in order to allow the analyzer to warm up before the measurements. In this work, the frequencies to be measured are relatively small compared to the frequency span of the analyzer. Thus, while warming up, drifting of the 300 MHz reference oscillator of the analyzer may cause problems. Push PRESET to reset the analyzer settings.

The zero frequency (DC) of the spectrum analyzer may differ from the actual zero frequency by more than one MHz because it depends on the 300 MHz reference oscillator and on the center frequency of the intermediate frequency amplifier. One can verify the actual zero frequency e.g. by setting the center frequency on the display to 0 Hz (FREQUENCY center freq) and frequency span to 5 MHz (SPAN). Even if there is no signal connected to the analyzer, the actual zero frequency is shown as a high peak on the display. One can check the frequency of the peak using PEAK SEARCH or MKR keys, and tuning the knob. Frequency of the DC peak can be set to zero by selecting FREQUENCY freq offset, and after that inserting the desired frequency offset using front-panel keys. The numerical value of the frequency offset is obtained by inverting the frequency reading of the DC peak. After this procedure the DC peak is shown at zero frequency on the display. Repeat the procedure when necessary.

2.4.1 Spectrums of sinusoidal and rectangular waves Use a BNC ‘T’ adapter and two coaxial cables to connect the oscilloscope input to the signal generator output and to the input of the spectrum analyzer. Due to the 50 Ω input impedance, spectrum analyzer reduces the signal generator output voltage to approximately half of its open-circuit voltage. Using the oscilloscope, adjust the output signal of the signal generator according Fig. 27.

1 V

-1 V

1 µ s

U

t

Figure 27. Signal generator output

Measure the frequency components of the signal in figure 27 up to 10 MHz. Frequency span can be set for example by using FREQUENCY start freq and stop freq1. For the vertical axis of the spectrum analyzer display, use setting AMPLITUDE units = volts. To read out the frequency component values, use MKR key and the knob. If it appears to be difficult to measure the frequency components accurately, use AMPLITUDE ref lvl and the knob to adjust sensitivity.

Change the bandwidth control of the spectrum analyzer to manual mode (BW res bw auto/man) and measure the input signal with four different bandwidth settings. The analyzer automatically selects the sweep time. Write down on paper the sweep time, the bandwidth, and the frequency span. Use equation 2.14 to calculate the theoretical sweep times (re: Question 2.5.2). Set the bandwidth control of the analyzer back to the automatic mode using res bw auto/man. Select a sinusoidal waveform from the signal generator and measure its spectrum components up to 10 MHz.

2.4.2 Noise measurement There is a noise generator on the laboratory table. Apply a voltage of 12 to 15 V from the power supply to the noise generator, and connect the noise generator output to the spectrum analyzer using a cable with BNC connectors. Due to the characteristics of noise, amplitudes of the frequency components vary after every sweep. Thus, use BW video avg on/off to select averaging. Voltage noise spectral density is used to measure the noise voltage as a function of frequency [V/ Hz ], see paragraph 2.2. If the noise voltage at a certain frequency and the bandwidth of the spectrum analyzer bandpass filter are known, one can calculate the voltage noise spectral density. In practice, the resolution bandwidth well corresponds to the bandwidth of the bandpass filter. What is the voltage noise spectral density at 2.5 MHz? What would be the RMS value of the total noise voltage, assuming the voltage noise spectral density to be constant up to 1 GHz. Apply a band-reject filter between the noise generator and the spectrum analyzer. The filter has several stopbands. Measure the center frequencies (< 5 MHz) of the stopbands and calculate their differences. It is possible that one has to optimize the frequency span of the analyzer to find the minimums and measure them accurately.

2.5 Questions 2.5.1 Compare the measured spectrum of the rectangular wave to that

calculated in homework. If the measured spectrum differs from the calculated one, try to explain the differences.

2.5.2 Is equation (2.14) valid with different resolution bandwidth (res.bw)

settings? References: Engelson ja Telewski, Spectrum Analyzer Theory and

Applications, Artech House Inc. USA 1974. Mittaustekniikan perusteet opetusmonisteet 1993 (In Finnish)

Appendix 2.1 A paragraph from HP 8590B user’s guide

3 Frequency Counter Goals in this work

• Learn the structure of a frequency counter • Familiarize with capabilities of digital meters • Learn to handle measuring results with the help of mathematical

statistics

3.1 General Information Concerning Digital Meters Almost all digital meters return to measuring time (number of pulses) one way or another. The advantages of a digital meter compared to an analog one are: - probability of an error in reading decreases - position of the meter does not effect on the results3 - a more accurate result is usually obtained with a digital measuring

method - it gives a possibility to automate the measurements (many digital meters can be connected straight to a computer)

It is to be noticed when using a digital meter, that although the meter gives the result with many numbers, not all numbers are necessarily correct. One of the advantages of many digital meters is, that the measuring time can be modified. The measuring time can be chosen so, that the part of the random error is smaller than the part of the systematic error.

3.2 Frequency Counter

3.2.1 General Information With a frequency counter can be measured frequency, period, time difference of the pulses and ratio of the frequencies. With the frequency counter used in this measurement can only be measured frequency and period. Regardless of what quantity is measured at the time, the measurement is based on counting the pulses. Next we take a look at the two most important functions of the frequency counter, direct frequency measurement and measurement of period.

3In very specific measurements do not believe this. One very accurate counter was noticed to give different results in different positions: The frequency of the clock of a GSM base station was measured 13,000 000 01 MHz when the meter was horizontal and 13,000 000 09 MHz when vertical, which is also a very common position used in measurements. Turned upside down the meter showed 13,000 000 17 MHz. The change in results in different positions was many times greater than the drifting of the meters clock between the calibrations. The manufacturer answered to the inquiry, that gravity effects on all crystal oscillators, so that the meter needs to be calibrated in the same position, it will be used.

3.2.2 Direct Frequency Measurement The connection of the frequency counter in direct frequency measurement is in picture 28.

f m

T

N

f osk

Input Circuit

Gate Counter

Screen DividerOscillator

Picture 28. The connection of the frequency counter in direct frequency measurement.

In direct frequency measurement a pulse is created with the help of a frequency-change oscillator and a divider, that controls the gate so that the frequency to be measured gets into the counter, when the pulse is up. Number of the pulses that come into the counter is

N Tfm = ± 1 (3.1)

where fm is the frequency to be measured and T the measuring time. The factor of the uncertainty ±1 in the equation (3.1) comes from the fact, that the beginning of the pulse from the divider is in arbitrary phase compared to the frequency fm. Picture 29 clarifies the uncertainty.

T

N

= 4

= 5

N

Picture 29. The result of the frequency counter can vary ±1 pulse depending on the phase of the signal compared to the pulse on the gate.

The resolution of the frequency counter is ±1 pulses and the relative resolution is

= = 1∆ ∆f f N N Tfm m m( ) (3.2) The greater is the measured frequency and the measuring time, the better is the resolution. If the period is constant, some counters can measure the frequency even much better than the equation (3.2) let us assume.

3.2.3 Measurement of period Picture 30 shows the operating principle of the counter, when measuring period

Input circuit

Gate Counter

Oscillator Divider Screen

f m

T

N

f osk

m

T m

Picture 30. The connection of the frequency counter in the measurement of period.

In the measurement of period the number of the pulses from the frequency-change oscillator is counted in time Tm, that is made up of the measurable pulse sequence. In this case

N T fm osk = ± 1 (3.3) where Tm is the length of the measuring cycle and fosk the frequency of the frequency-change oscillator. The relative resolution is

∆ ∆T T N NT f

fnfm m

m osk

m

osk/ /= = =1 , (3.4)

where n is the number of periods contained in the measuring cycle and T n fm m= / .

From the equation (3.4) can be seen, that the longer is the measurable period (the lower frequency) and the greater is the frequency of the frequency-change oscillator, the better is the resolution. The frequency counter used in this work, has n =1000 at its maximum. Both in measurement of period and in direct frequency measurement the counters accuracy in the end is determined by the frequency stability of the frequency-change oscillator. In other words the better crystal oscillator is in the frequency counter, the better counter it is.

3.3 Measurements Equipments needed

• Function generator • Frequency counter Fluke • Multimeter 3468A • Potentiometer • Voltage-to-frequency converter • 10 V two-sided voltage source • Transformer

Read the appendix 3.1 of the frequency counter before starting the measurements.

3.3.1 Measuring the mains voltage and its period Connect the transformer to the digital voltmeter and to the frequency counter. Use measurement of period in frequency counter and choose settings so that the counter measures the length of 102 pulses. If there is an overflow –light on on the frequency counter, it means that the counter can’t show the most significant digits. The truncation remainder on the screen is still correct, which can be verified on another range, for example 101 pulses. Measure the mains voltage and its period ten times at intervals of ten seconds. Multiply the voltage readings by the voltage ratio of the transformer, when you get the true mains voltage. Calculate the mean and deviation from the results. Don’t forget units. The deviation is obtained from the equation (3.5).

sx x

n

in=

−

−

∑ ( )2

1 (3.5)

where s = estimate for the standard deviation σ (s → σ, when n → ∞ ) n = number of the measurements x = result of a measurement x = mean of the results. Mark also the relative deviation (= deviation/mean) on the paper.

3.3.2 Comparing direct frequency measurement and measurement of period

Measure the frequency of the function generator with frequency counter using both direct frequency measurement and measurement of period. Use the range 10 in measurement of period and 1 Hz in direct measurement. Measured frequencies are 100 Hz, 1 kHz, 10 kHz, 100 kHz and 1 MHz. Calculate (theoretical) relative resolution to each frequency both with measurement of period and with direct frequency measurement separately. Conclude from the results, when the direct measurement is better and when the measurement of period. There is more information about the characteristics of the frequency counters oscillator in the appendix.

3.3.3 Measuring linearity of the voltage-to-frequency converter Next we will study the linearity of the voltage-to-frequency converter. Make connections as in picture 31.

-10 V GND 10 V

-10 V GND 10 V

GND PLUS

MAA F/OUT

IN DVM

Frequency Counter

Figure 31. Connections of measuring of U/f-converter, when the operating voltage is ± 10 V

Adjust the voltages 1,2,3,4,5,6,7,8,9,10V in the U/f-converters input with the potentiometer. Measure the frequency corresponding every value of voltage. Mark down the exact values of frequency and voltage. Choose the measurement ranges of frequency and voltage so that the uncertainty of measurement is smaller than 5.10-4. Lets assume, that the U/f-converter satisfies equation

f = aU + b. (3.6) Calculate the coefficients a and b using linear regression. Linear regression consists of forming a line passing through a set of points, minimizing the sum of squared distances from the line to the points. Most scientific calculators manage to calculate the coefficients of linear regression. When the coefficients has been calculated (don’t erase the calculators memory before you have looked through the entire exercise), frequency can be calculated, when voltage is known. Because U/f-converter is nonlinear, the measured and calculated values differ from each other. Calculate the values of frequency fe with the formula fe = aUm + b for each measured voltage Um.

Mark down the difference of the measured and calculated frequency fm – fe on the table. The smaller the differences are, the more linear the U/f-converter is. If the differences are very small and are measured with many digits resolution, starts random variation to be visible in the results. The effect of the random variation can be reduced by repeating the measurement. The correlation coefficient can be used as a measure of linearity. Correlation coefficient is a number between zero and one. r=1 means perfect correlation and r=0 indicates that the quantities are completely independent. Another measure of linearity is residual deviation that is defined

sf f

nr

mi ein=

−

−

∑ ( )2

1. (3.7)

The residual deviation describes the average deviation of the calculated and measured results. Notice, that the deviation defined in equation (3.7) is the expression, that is minimized in linear regression. Calculate the residual deviation from the equation (3.7) or (3.8). There is a connection between the residual deviation sr and the correlation coefficient accordant with the equation (3.8).

s s rr f= −( )1 2 , (3.8)

where sf is the deviation of the frequency values and r is the correlation coefficient. Correlation coefficient can be really close to one, so when calculating the residual deviation all the significant numbers can be easily lost, if decimals are dropped between the calculations. Equation (3.8) can be interpreted so, that the output frequency has a standard deviation of sf without linear model. If a linear model is made, the deviation of

the frequency becomes smaller by a factor ( )1 2− r . The factor ( )1 2− r is a very good measure for example for the nonlinearity of the U/f-converter. One very common measure of nonlinearity is to express in per cent, how much the real value differs from the straight line at worst. The percentual value can be in relation either to the measured value at the point, where the measured value has the greatest deviation, or to the end point of the line.

3.4 Questions 3.4.1 How large is the change in input voltage of the U/f-converter that

corresponds to a frequency change the size of the residual deviation?

Compare the change in voltage to the inaccuracy of the voltage readings used in your calculations and consider, how big part of the residual deviation is due to the properties of the U/f-converter. Does some other part of the measurement set-up (for example the voltage source or the adjustable resistor) increase the value of the residual deviation ?

3.4.2 How great can the relative inaccuracy of the digital voltmeters voltage

reference be, so that the error in the least significant digit of the digital voltmeter (maximum reading is ±1999) is at most one?

3.4.3 When is it good to use direct frequency measurement and when

measurement of period, if a measuring time of one second is used in direct measurement and if the length of one period is measured in the measurement of period? Use equations (3.1) and (3.3). Calculate the boundary frequency (,where both methods give a result equally good), if the frequency of the counters own oscillator is 1 MHz.

Appendix 3.1 Specifications of the frequency counter Fluke 1900A and the switches on the front panel

4 Transducer measurements Objectives of this work

• Familiarize oneself with the different temperature sensors (platinum sensor, thermistor and thermocouples)

• Familiarize oneself with the use of strain gauges

4.1 Introduction Different physical quantities are often converted to an electrical signal with a transducer so that general electric measuring technology can be employed. In Table 4.1 various physical quantities and applicable types of transducers (sensors) are presented. Table 4.1. Applications of sensors

4.2 Grouping of sensors Sensors can be divided into the following four main groups by their operating principle: 1) analog sensors generating voltage or current 2) analog sensors with variable parameters 3) sensors generating pulses or frequency 4) digital sensors The first group consists mainly of sensors that do not need external power to operate. The second group consists of sensors mainly used in a bridge circuit, where the change of the impedance of the sensor generates a voltage. The borderline between the first and second group can be faint at times. Between the third and fourth group the differences are often more distinctive.

4.2.1 Thermoelectric sensors (thermocouples) Thermoelectric sensors are based on the temperature-dependent voltage generated over the junction of two different metals. In a closed electric circuit, one joint can never exist alone without the presence of another one, which should be kept in a stable temperature for reference. In Table 4.2 some of the most typical thermocouples are presented with their properties..

Table 4.2. Properties of thermocouples

Figure 32.The voltage of an iron-constantan (Fe-Ko) thermocouple as a function of the temperature difference.

In industrial use, the most widely utilized thermocouples are Cu-Ko, Fe-Ko, CrNi-Ni and PtRh-Pt.

4.2.2 Resistance temperature sensors When a greater accuracy and a larger voltage is desired compared to thermocouples, resistance temperature sensors are used. Their operating principles is their temperature dependent resistance. The most commonly used sensor is the Pt-100. It is a sensor made of platinum which has a nominal resistance of 100 Ω at the temperature of 0 °C. Platinum is the most utilized material for resistance temperature sensors and common in measurements requiring a high accuracy. The advantages of platinum sensors are their broad operating range of -250 °C to +962 °C, exceptionally good long-term stability even in high temperatures, linearity of the coefficient of thermal expansion, easy formability, and persistence against various chemicals. Also some other metals are used for the production of resistance temperature sensors. Temperature dependencies of various resistance temperature sensors are presented in Figure 33. The disadvantages of these sensors are their slow temperature response, large size and a more complicated measurement circuit (a bridge circuit is often used).

Figure 33. The temperature dependence of the resistance of platinum, copper, tungsten, nickel and a thermistor.

4.2.3 Semiconductor temperature sensors (thermistors) Thermistors are temperature sensors made of semiconductor materials. Like resistance temperature sensors, their operation is based on the temperature dependence of the resistance, which is typically about ten times greater and highly nonlinear. Thermistors are used in measurements where a high sensitivity is desired using only a simple electrical circuit. Thermistors are fabricated from metal-oxide powder by sintering. The powder is formed into the required shape and heated. Using adequate temperature and pressure re-crystallization takes place and a solid object is generated. After sintering, wires are attached to the sensor and it is covered by a metallic or glass layer for protection. The thermal coefficient of the most common sensors are negative, so that their resistance decreases as the temperature is increased. Such thermistors are called NTC-thermistors (Negative thermal coefficient). In addition to NTC-thermistors, also PTC-thermistors are produced. These thermistors have a positive thermal coefficient at a certain temperature range. As the temperature changes, the resistance of the thermistor changes rather strongly according to Equation

R R eTT T=

−

0

1 1

0β

, (4.1) where R0 is the resistance at a reference temperature T0 (in Kelvins), RT is the resistance at the temperature T and β is a coefficient that depends on the structure and manufacturing process of the thermistor. In general, β is of the magnitude of +3500 K. Solving R0 from Equation (4.1) with temperature approaching infinity, The following equation is obtained

RR

e T

0

0

= ∞−β , (4.2)

where R∞ is RT with the temperature approaching infinity. By taking the right hand side from Equation (4.2) and placing it to Equation (4.1), another equation is obtained which also is often used for describing the temperature dependence of the resistance of a thermistor.

R R eT T= ∞

β

, (4.3) where R∞ is the resistance of the thermistor as the temperature approaches infinity. Equations (4.1) and (4.3) are only approximations for the temperature dependence of the resistance of the thermistor. Therefore they can not be employed for accurate temperature determining. The temperature dependence of three thermistors are presented in Figure 34. The temperature dependence of a Pt-100 sensor is inserted to the same figure for comparison. The operating range of thermistors starts form near the absolute zero temperature to about 200°C. Thermistors offer high sensitivity, but their stability is not as good as with resistance temperature sensors. Ordinary selected mass resistances can be utilized as temperature sensors inside the range 4…100 K. Their temperature dependence is of the form

ln lnR K R C DT+ = + (4.4) Germanium temperature sensor is used at the temperature range 0...50 K as reference, because its hysteresis is very small (10-3 K) and its response time is very small.

Figure 34. Temperature dependencies of the thermistors 1,2 and 3.

4.2.4 Response of temperature sensors A temperature sensor indicates the correct temperature only when it has reached the temperature of its environment. The ability of a temperature sensor to follow changes of the ambient temperature depends of the sensors size and thermal resistivity. The response of a temperature sensor can be approximated by a first order transfer function and a dead-time. The transfer function is of the form

G s L s T s e sst( ) ( ) ( ) ( )= = +−τ τ0 1 (4.5) where L(s) is the LLLL-transform (Laplace) of the excitation, T(s) is the LLLL-transform of the response, τ is the time-constant and to is the dead-time. Figure 35 presents the measurand of a temperature sensor as a function of time when the sensor having a temperature T1 is inserted into a medium with a temperature T2. A sensor can be characterized with a equivalent circuit presented in Figure 36, where Tn is the ambient temperature and Ta is the temperature of the sensor. The dead-time is zero in this approximation. To calculate the warming or

cooling of a sensor, the same equation can be used as for capacitors C Tt

Pa∂∂

= ,

where C is the thermal capacity, t is the time and P is the thermal flow that heats the sensor. Time constant τ is RC.

0 τt

T1

T2

T2 - T1T1 + 0,63( )

t

T

Figure 35. Step-function response of the temperature sensor

Figure 36. Thermal equivalent circuit of the temperature sensor

Table 4.3. Corresponding electrical and thermal quantities

Electrical circuit Thermal circuit Quantity Symbol/Unit Symbol/Unit Quantity resistance R / Ω R / K/W thermal resistance current I / A P / W Power Voltage U / V T / K Temperature capacitance C / F C / J/K thermal capacity The thermal resistance of the temperature sensor can be determined with the following method. Measure the temperature with two different measuring currents. The product of the measuring current and voltage is the measuring power that raises the temperature of the sensor. If the ambient temperature Tn is kept constant, the thermal resistance R can be solved from

P T T RP T T R

a n

a n

1 1

2 2

= −= −

( )( )

. (4.6)

Parameters Ta1 and Ta2 are obtained from the calibration curve of the sensor. The ambient temperature Tn can also be solved form Equation (4.6). Note that

the unit of R is K/W. The thermal capacity C can be calculated if in addition the time constant is measured with a timer.

4.2.5 Strain-gauge sensors

Figure 37. Operating principle of a strain-gauge

The operating principle of a strain-gauge is based on the small resistance change in a thin film or wire as it is elongated or compressed. The relative resistance change (∆R R) can be expressed as a linear function of the relative length change (∆L L)

∆ ∆R R K L L= . (4.7)

If the volume of the wire or film is presumed to be constant in the deformation, the value of K is ideally 2. In reality the value differs slightly from this and in the case of semiconductor strain-gauges K can be even 100. The appropriate value is given in the sensors datasheet supplied by the manufacturer. The properties of the strain-gauges used in this work are K = 2,04 and R = 350 Ω. The sensor has a wire with a thickness of 25 µm winded to the pattern shown in Figure 6 and embedded inside a suitable plastic material. The size of the active area of the sensor can be from 1mm2 to 30cm2. Strain-gauges are also manufactured by etching the pattern to a paper- or Bakelite-backed metal-film. Strain-gauges produced by this method are thinner, more flexible, longer lasting and have a smaller hysteresis than their wire-based counterparts. The resistance of strain-gauges are usually about 100...400 Ω and the maximum permitted relative resistance change about 1-5 %. Two strain-gauges are presented in Figure 38. The temperature coefficient of the material used in the sensors can be tailored to near zero, but the thermal expansion will always remain. This can be compensated by utilizing two strain-gauges, one on each side of the object. These two sensors are placed in opposite branches of a bridge circuit, so that when one sensor is compressed and the other one is elongated the sensitivity of the measurement set-up is doubled. If both sensors are compressed or elongated at the same time no signal will be observed. In simple measurements a constant voltage can be applied across the bridge, but if a higher sensitivity is required lock-in techniques can be utilized. The strain-gauge is usually glued to the object to be measured with a suitable adhesive.

In this work two strain-gauges are used in opposite sides. However this is not always possible but two gauges can be utilized in other ways also if one of them can be made very sensitive to the measurand and the other one very insensitive.

4.3 Measurements Needed equipment

• Measuring computer with • 2 digital multimeters • Labview measurement software

• Temperature sensors: Pt-100, thermistor and a Fe-Ko thermoelement • Heating enclosure • Iron rod • 200 g weight • ±12 V power supply

Figure 38. Two strain-gauges

All the measurements are done with the computer, using the two multimeters with Labview. The first thing to do is to switch on the computer if it already is not. Next to the computer is a brief manual for using Labview and some advice for the labwork. If needed, the assistants will also help you get started. All the temperature sensors are labeled to ease their identification. The sensors are characterized using the heating enclosure that has a heating resistor and a cooling fan inside it. The sensors are to be inserted inside the resistor gently.

4.3.1 Measuring the time-constants The time-constants of the Fe-Ko thermoelement and of the calibrated Pt-100 resistance temperature sensor are to be determined using the heating enclosure. The sensors should be connected to the multimeter 1. Start the program “aikavakiot” (time-constants). Remove the sensors from inside the heating resistor. Switch the enclosure to OFF and connect the 12 V supply to it. Start the heating by selecting switching to HEAT and wait about 5 minutes for the temperature to rise. Do not wait much longer as by then the temperature has already stabilized to about 150° C.

Connect the Pt-100 to the multimeter 1. Ensure that the measuring type is two-wire (2W) resistance and the measuring range is 200 (200 Ω). Start running the program and insert the sensor in to the resistor as the first measurement point appears to the screen. Do not switch off the heating. The program takes a reading in 10 second intervals for a period of 3 minutes. Draw the measured curve to the measurement form and evaluate the time-constant. Withdraw the sensor from the enclosure, but be careful. The sensor is hot. Next, the time-constant of the Fe-Ko thermoelement is to be determined. Change the measuring mode to DC-voltage and connect the thermoelement to the multimeter 1. Set the range to 0,2 (0,2 V). Run the program and insert the thermoelement inside the resistor. The cold junction of the thermoelement is in the connector and is left at the ambient temperature. Draw the appearing graph to the response form and evaluate the time-constant from it. Start the fan in the enclosure by switching to FAN, so that the resistor and the sensors have time to cool down before the next measurement.

4.3.2 Comparing other sensors with the Pt-100 platinum sensor The resistance of the NTC-thermistor and the voltage of the Fe-Ko thermoelement are measured as a function of temperature. A calibrated Pt-100 sensor is used as a reference thermometer because of its linearity. The Pt-100 is connected to the multimeter 1 and the sensor to be measured to the multimeter 2. Close the program that was used in the previous measurement and start the program “anturivertailu” (sensor comparison). Wait a couple of minutes for the heating resistor to cool down. Comparing thermistor against Pt-100 Place the thermistor (NTC) in to the heating resistor together with thePt-100 platinum sensor, one from each side. The sensors should touch each others at the halfway of the resistor. Connect the sensors to the multimeters. Select suitable measurement ranges and check the scaling. For the thermistor, a suitable scaling for the graph is from 1 kΩ to 13 kΩ and the correct measurement range 20 kΩ (2W-resistance). Start running the program. The program displays the resistances of the Pt-100 platinum sensor and the thermistor. The program has also a button, that one can press to plot the value of the resistance of the thermistor to the position (x-value) defined by the resistance of the Pt-100. Start the heating and plot the current value whenever the resistance of the Pt-100 has changes about 2 Ω. This way the spacing of the samples will be about 5° C. When the Pt-100 sensor reaches a temperature of about 100° C (Pt-100 = 138 Ω), switch off the heating and start the fan. Repeat the measurement by sampling resistance values also during cooling in 5° C intervals. Stop the running of the program

when the resistance of the Pt-100 has reached its original value at room temperature. Plot the measured graph to the answer form. Comparing thermoelement against Pt-100 Replace the thermistor in the heating enclosure with the Fe-Ko thermoelement. Connect the thermoelement to the multimeter 2 and select DC-voltage for the type of measurement. Measure as previously plotting the values in 5° C intervals while heating and cooling. Draw the acquired graph to the answer form.

4.3.3 Strain-gauge measurements Strain-gauges are utilized commonly to measure deformation caused by stress, bending, pressure, torsion and weight. In this measurement strain-gauges are used to measure weight by measuring the bending of a thin steel rod. On both the upper and lower surfaces two strain-gauges are attached as presented in Figure 39. As a weight is attached to the end of the rod, are the strain-gauges at the upper surface elongated (resistance decreases) and the ones at the lower surface compressed (resistance increases).

Figure 39. Measuring torsion in the steel rod using strain-gauges.

The principle of the measuring circuit is presented in Figure 40. Connect the circuit to the ±12 V power supply. The circuit produces a regulated voltage of about 10 V across the bridge. Measure this regulated voltage with the multimeter 1 and connect the output of the instrumentation amplifier to the multimeter 2. Close the program that was utilized in the previous measurement and open a new program called ‘venymäliuskat’ (strain-gauges). The program measures and outputs the two measured voltages and their ratio, which should not suffer from the drift of the regulated voltage over the bridge. The program also plots the measured voltage in 0.5 s intervals. Wait a couple of minutes for the measured value to stabilize. Whenever the device is switched on the components start to warm up, especially the strain-gauges.

Figure 40. Diagram of the measurement circuit.

Changing the balance of the bridge circuit affects the output of the instrumentation amplifier. This output voltage is linearly dependent of the deformation of the strain-gauge, unless the maximum strain is exceeded (specified by the manufacturer). The input voltage of the amplifier as a function of the resistances of the strain-gauges can be expressed as

∆ ∆U RR

Uin Sup= , (4.8)

if the setup of Figure 40 is used. Uin is the amplifier input voltage, ∆R/R is the relative change of the resistance and USup is the supply voltage of the bridge. The relationship between the relative resistance change and the relative elongation (ε = ∆L/L) is obtained from Equation (4.7), if

Fl EW= ε (4.9) is applied for the torsion of the steel rod, where F is the force, E is the Young’s modulus, l is the perpendicular distance of the force form the attaching point (Fl is the torsion at the attaching point) and W is the bending resistance bh2/6, where b is the width of the rod and h is the thickness. The voltage change in the input of the amplifier is subsequently

∆ ∆U K FlEbh

Uin Sup= 62 . (4.10)

From literature, the Young’s modulus for steel E can be checked to be 20,6×1010 N/m2 and the manufacturer of the strain-gauges has given as the value of K to be 2,04. The values for l, b and h are written down next to the rod. Calculate from Equation (4.10) the relative change of the input voltage of the amplifier when a 200 g weight is attached to the rod (F=mg). Attach the weight and write down the amplified relative change of the voltage. Calculate the relative change at the input, when you know that the gain is 100. The calculated value and the measured value differ slightly from each other. This is because of uncertainty in the dimensions (l, b and h) of the rod, the value of K, the mass of the weight and in the Young’s modulus. Calculate a value for the Young’s modulus that would best fit with the measurement results. Use Equation (4.10) and the calculated Young’s modulus to estimate the weight of the pen use used to write down the measured results. You can also experiment increasing the sensitivity of the multimeter and try to measure very light weights.

4.4 Questions 4.4.1 Would increasing the supply voltage over the bridge circuit increase the

measurement accuracy or/and the measurement sensitivity? Justify. 4.4.2 Does the strain-gauge have a time-constant (delay)? 4.4.3 While comparing temperature sensors, did you notice a difference when

measuring while heating compared to measuring while cooling? Try to explain.

4.4.4 Derive Equation (4.8).

5 Oscilloscope XY-position Objectives

• To familiarize with the XY-measurement position, its applications and limitations.

• To get to know the properties of different components by studying their current-voltage curves.

5.1 Introduction Normally, oscilloscope is used for voltage measurement in time domain using time sweep. Oscilloscope is triggered to begin sweep and the voltage is drawn on the screen as a function of time. Sometimes user wants to measure voltage in some other domain than time. Such measurements can be for example diode current vs. diode voltage, transistor emitter current vs. base current and amplification of an amplifier.

x y

input outputamplifier

Figure 41. XY-position of an oscilloscope: amplification measurement

In addition to normal time sweep, most oscilloscopes have XY-position, where signal in channel 1 controls the horizontal (X) direction of the screen and signal in channel 2 controls the vertical (Y) direction of the screen. For example, when the amplification of an amplifier is to be measured, X-channel is connected to the input of the amplifier and Y-channel is connected to the output of the amplifier. If the amplifier is linear (distortionless), output is the input multiplied by a constant. Therefore there will be a tilted straight line on the screen, if alternating current is fed to the input. The slope of the line depends on the amplification and the sensitivity settings of the channels of the oscilloscope. If the amplifier has distortion, the amplification doesn't remain constant, and the resulting image on the screen will be a curve. If a rapidly changing signal is fed into the amplifier, an effect caused by its delay can be observed. When the

signal increases the curve is drawn on different position than when the signal decreases; an oval is formed eventhough there is no distortion. There is a phase shift between the signals caused by the delay.

5.2 Measuring the phase shift using the XY-position The phase shift can be measured with the oscilloscope. Situation where two sine waves with same frequencies but different phases are connected to X- and Y-channels of the oscilloscope is presented in Figure 42. For example

)sin( tPX ω= and )sin( ϕω += tPY , where PX and PY are the x- and y-coordinates of the curve on the screen, ω is the angular frequency (2π f), t is time and ϕ is the phase shift. The phase shift can be calculated from the points a and b. At point a the output is at its maximum and x = 0 at point b. Function PX is zero, when ωt = 0 or π. Since the signal has to be decreasing, ωt = π and

( ) 0sin == πxx cb (5.1) and

( ) ( )ϕϕπ sinsin yyy aab −=+= . (5.2) The phase shift ϕ can be calculated from (5.2). In Figure 42 it is negative (y-channel is delayed).

x

y

output maximum

inputmaximum

output value, when input is decreased to zero

a

b c

Figure 42. The phase shift between input and output

If the oval is formed by a dot moving clockwise, at point b the value of x is increasing, i.e. the phase of the x-channel is zero. Previous equations are changed into

( ) 00sin == xx cb (5.3) and

( )ϕsinyy ab = . (5.4) In the equations the angles are in radians, but in the results, for simplicity, they should be presented in degrees4. If the figure on the screen is a circle or a vertical oval, the phase shift is ±90°. If the oval is tilted to the left, the phase shift is over ±90°. The direction of the rotation is impossible to see with fast signals, and the sign of the phase shift is acquired for example by looking the signals in time domain. At frequencies over 100 kHz the phase shift measurement using the XY-position will produce false results because of the differencies in the vertical and horizontal amplifiers. In analog oscilloscopes this happens because of different electrical circuitries in vertical and horizontal sweep generators. The digital oscilloscopes don't have this problem, because their screens are based on normal television technology. Nevertheless, it is useful to check what is the capability of the oscilloscope. For example the HP digital oscilloscopes used in these laboratory works have an internal phase shift which prevents accurate XY-measurements at frequencies over 100 kHz.

yuu x

x y

measuredtarget

functiongenerator

R

+

-

+

-

Figure 43. Measuring current as a function of voltage

4 The reason for presenting the angles in radians and frequencies as angular velocities is propably the frequent need for derivations and integrations in electrical calculations. When derivating a sine function, an additional π/180° should be included: )360cos(360)180()360sin()( ftfftdtd °°°=° π . Also important Euler's formula )sin(cos yiyeeee xiyxiyx +==+ is valid only if radians are used.

5.3 Measuring current-voltage curve The current flowing through the measured target is obtained by using a small resistor R as in Figure 43. The current is calculated from the known resistance and the measured voltage. X-channel measures the voltage over the target. The resistor must be small compared to the impedance of the target, so that it won't cause error in the voltage readings. However, if the target impedance is so small, that resistor R would cause false readings, connection presented in Figure 44 must be made. Attention: In Figure 44 the current to the resistor R comes via a parallel connection between the target and the input impedance of the x-channel. Therefore this connection can't be used when the target has large impedance.

x y

"floating"signalgenerator

+-

+-

u x

targetmeasured

Ruy

Figure 44. Measuring current as a function of voltage (small target impedance)

Connecting the ground wires of the oscilloscope to the same point in between the the target and the resistor R may seem strange. This kind of connection is necessary because the channel grounds of the oscilloscopes are connected together (and furthermore via power line to the protective ground) and there must not be a potential difference on the ground connections. Y-channel has to be inverted to get the right image of the current-voltage curve. Usually the grounds of the function generators are connected to protective ground and the generator must be connected to the power outlet via isolation transformer. Another possibility is to use generator with symmetrical output.

5.4 Frequency sweep Spectrum- or circuit analyzers are normally used for frequency domain sweeps. Under some circumstances the frequency sweep should be made with an oscilloscope. Slightly simplified example of the observation of the wavelength of iodine-stabilized lasers at the Metrology Research Institute of the HUT using the XY-position follows.

x y z

laser with internal iodine cell

ramp generator

oscilloscope beam switch off

Photo detectorfrequency control 200MHz

5 MHz

ramp

voltage based frequency control

Figure 45. Monitoring laser frequency with an oscilloscope

Red light (633 nm) from a HeNe-laser is electromagnetic radiation whose frequency is 470 THz (THz is 1012 Hz). The frequency of the light is the speed of light divided by the wavelength. The frequency of the laser can be adjusted a few hundred MHz around the center frequency. The frequency is monitored via iodine absorbtion lines. Light travels inside the laser through a cell filled with iodine vapor. Iodine absorbs light at some wavelengths and the output power decreases. The X-channel of the oscilloscope and the laser frequency are controlled by a ramp generator in such a way that a certain point on the x-axis corresponds to certain laser frequency. On the upper end of the ramp the laser frequency is a few MHz higher than on the lower end. The repetition rate of the ramp is for example 100 Hz. Visible on the screen is a spectrum which is only a few MHz wide, practically a small portion of the iodine absorption spectrum. If there are iodine absorption lines on this portion of the spectrum, they are observed as decreased input power on the sensor, i.e. lower y-channel voltage on each absorption line. The frequencies of the absorption lines are natural constants, and certain line pattern on the screen tells the laser frequency. Using complicated frequency multiplier system some of the absorption line frequencies have been compared against atomic clock frequency of 9 GHz with 10 digit accuracy. The results of these comparisons are commonly available, and therefore laser frequency (and wavelength) can be very accurately adjusted to certain absolute values using the iodine cell.

5.5 Measurements Equipment

• Oscilloscope HP 54600A tai -B • 12 V double-sided voltage-source • RL-circuit • Current-voltage measurement board • Schmitt trigger

5.5.1 Phase difference To measure the phase difference, there is a coil-resistor circuit on the table (Figure 46). The internal resistance of the coil RL must be taken into account when analyzing the results. Borrow a multimeter and measure the values of resistors R and RL. From the signal generator, connect a sine-wave with an amplitude of 2,5 V to the ends of the coil-resistor circuit. Connect the signal generator to float (look for instructions on the workplace). Connect voltage uy to Y-channel and voltage ux to X-channel of the oscilloscope. Measure the phase difference between the channels with three different frequencies (8 Hz, 3 Hz and 1 Hz). Calculate the inductance of the coil at each frequency by using the measured resistance values and the phase differences of the voltages.

R R L L

u y

+-

u x Figure 46. Coil phase measurement.

5.5.2 Current-voltage curves You are about to measure the current-voltage curves of a resistor, a signal diode, a rectifying diode, two zener diodes, two LEDs and a base-emitter junction of a transistor. On the workplace there is a board where all the components are attached into. On the board there are also connectors for oscilloscope and floating signal generator. Certain component is selected by connecting the oscilloscope and the signal generator into right connectors. Measurement arrangement is similar to the one described in Figure 44. Resistor R (100 Ohms) is constant and used for determining the current running through the selected component. Remember to invert the Y-channel. Preceding measurement would have been possible to perform with an ordinary signal generator. Why the signal generator has to be floating in this

measurement? Set the signal generator for 100 Hz triangular or sine wave with an amplitude of 10 V. Make such a connection that the component to be measured is the resistor. Adjust the sensitivities of the channels of the oscilloscope so that the figure on the screen covers the largest possible screen area. Resistor From the resistor measurement you get an idea of the accuracy of this measurement method. The current-voltage curve of a resistor should be a straight line, whose slope is the inverse of the resistance. Measure the current and the voltage from both ends of the curve on the oscilloscope screen as accurately as you can. Calculate the resistance in both cases. Diode

Ideal diode is a component through which electrical current flows without resistance from anode to cathode. It doesn’t conduct at all if cathode has higher voltage than anode.

In real life, diode conducts properly only after the voltage between anode and cathode rises above threshold voltage (Figure 48). Simple measurement to determine the threshold voltage is difficult because the current starts to increase slowly. One approach is to fix the threshold current as 1 % of the maximum diode current (for signal diode it would be 0,5 mA). Real diode conducts also slightly from cathode to anode. The reverse current of a regular small circuit diode is few nanoamps and it stays quite constant regardless of the voltage. If a large reverse voltage is applied, a breakdown occurs and current increases rapidly as a function of the voltage.

0,0V 0,1V 0,2V 0,3V 0,4V 0,5V 0,6V 0,7V 0,8V 0,9V 1,0V0A

10mA

20mA

30mA

40mA

50mA

Cur

rent

Voltage

-10V -5V 5V

Cur

rent

Voltage

UZ

I Z

anode cat hode

Figure 47. Diode symbol

Figure 48. Current-voltage curves of diode (1N4153 at 25°C) and zener diode

Keep the 100 Hz 10 V sine wave from the signal generator. Measure the voltages of a signal diode, a rectifying diode, two zener diodes and a transistor at forward currents of 5 mA and 20 mA. Notice that the base-emitter junction of the transistor is also a diode. Breakdown with ordinary rectifying diodes occurs when the reverse voltage is hundreds or thousands of volts Zener diodes are built so that deliberate breakdown occurs at specific reverse voltage. Zener diodes are manufactured with different reverse breakdown voltages and they can be used as simple voltage references. The breakdown of the base-emitter diode of a transistor also occurs with low voltages because of e.g. thin base. The reverse voltage of a zener diode changes slightly as a function of current. Measure the reverse voltages U of the zener diodes and base-emitter junction of the transistor at reverse currents of 5 mA and 20 mA. Equivalent circuit of a

zener diode is presented in Figure 49. Calculate I

URZ dd= and the voltage of

the source in the equivalent circuit when the current I is 20 mA. RZ can be calculated by measuring the slope of the current-voltage curve around 20 mA. If the slope is calculated from the measurements at 5 mA and 20 mA, the result will be wrong because the 5 mA measurement isn’t on the linear part of the curve.

Rz

U-Rz I= U

I

Figure 49. Symbol of a zener diode and its low frequency equivalent circuit

Measure the forward voltages of the LEDs for example at 10 mA current and compare the results against the potential drops that are required an electron to emit a green photon (563 nm) or a red photon (635 nm). Electron charge is 1,602.10-19 As and the photon energy is hf, where h is Planck’s constant 6,626.10-34 J.s and f is the frequency of light. Increase the signal generator frequency up to 10 kHz and observe the curves of the different components. What unwanted phenomenom can be seen with the rectifying diode compared to the signal diode?

Reobserve the current-voltage curve of the resistor and increase the frequency. At what frequency the speed differences of the channels of the oscilloscope begin to interfere the measurements?

5.5.3 Hysteresis measurement Schmitt trigger is a circuit that has a two-state output. The circuit is voltage-controlled and it usually has hysteresis. Hysteresis is presented in Figure 50. It is the difference of the input voltages where the output changes its state.

input voltage

output voltage

hysteresis

outputamplitude

Figure 501. Hysteresis of an inverting Schmitt trigger

A measurement box with a three-state switch can be found on the work place. Circuitry when the switch is in position 3 is presented in Figure 51. Potentiometer R1 is used for adjusting input voltage of an operational amplifier, which should also be connected to X-channel of the oscilloscope. Feedback resistors R4 and R5 produce positive feedback. This means that when the input voltage of the operational amplifier is over some threshold value, the output voltage (measured with oscilloscope Y-channel) changes from one value to another. Circuitry also produces hysteresis.

15 V

-15 V

0 V

25k 180 270

22k

100k

y+

x+ x-

y-22uF +

- R1 R2 R3

R4

R5

Figure 51. Measurement box circuitry at switch position 3

Connect wires from ±15 V voltage source (+15V, 0V and -15V, initially switched off) to the measurement box. Connect wires from the outputs x+, x-,

y+ and y- to the oscilloscope. Turn on the voltage source and adjust the input voltage of the Schmitt trigger with R1. Measure the hysteresis and the amplitude of the output. References: John D. Lenk: Handbook of oscilloscopes, theory and

application, 1982. Jacob Millman: Microelectronics, 1979. Mittaustekniikan perusteet, opetusmonisteet 1993.

6 Electrical interferences Objective of the work

• To learn the different coupling mechanisms of electromagnetic interferences

• To learn how to avoid the coupling of electromagnetic interferences to the measurement systems

6.1 Origin of the electric interference Thunderstorms are the most important interference source in the nature. Other important sources are e.g. sunspots and background radiation of the space. Human based interferences can be generated with or without intent. Unintentional interferences are generated by e.g. 50 Hz power supply system, rotating machines, electric power distribution stations, relays, transformers, ignition devices, television and radio apparatus, fluorescent lamps, thyristors, high-frequency heaters, X-ray devices, diathermy machines and electric tissue burning devices. The purpose of the intentionally generated interferences is to radiate electromagnetic energy in to the environment. These are e.g. radar and telecommunication systems such as radio- and television transmitters as well as radiotelephones, beepers and electric keys. EMP-interference is electromagnetic radiation generated typically by nuclear explosions. The properties of the ElectroMagnetic Pulse depend on the altitude of the explosion as well as on the size of the atomic bomb.

6.2 Coupling mechanisms of electric interferences There are many ways how electric interferences can couple to the measurement circuit: 1. Capacitive coupling (high-impedance circuits) 2. Inductive coupling (conductor loops) 3. Resistive coupling (grounding wires and mains voltage cables) 4. Coupling of electromagnetic field (at radio frequencies) Note, that there is always simultaneously electric field and magnetic field despite of the origin of the interference field. This does not, however, apply in the DC-case. Although the interference field is always an electromagnetic field, it is normally referred to electromagnetic field only when the distance of the interference source to the object is much longer than several wavelengths of the interfering field (i.e. in the case of far field). If the distance is much less than the wavelength, the field is referred as a near field.

In the near field, it does not apply anymore that the ratio of electric field and magnetic field is 120 π Ω = 377 Ω as it is in the case of far field. If the near field interference is generated by a current loop, it is referred as a magnetic field interference and thus the field is so called low-impedance field, Z < 377Ω . This kind of interference is coupled inductively and it can be easily detected with a conductor loop. In case the interference voltage couples to a conductor with other end open, there will be generated an electric field interference in the near field. This interference is coupled capacitively. This kind of interference can be measured with a voltmeter with high input impedance equiped with a whip antenna. In this case the field impedance is Z > 377Ω . A metal casing gives a good shield against the electric field interferences, because the conducting surface will short circuit the electric field and therefore the electric field at the metal casing surface is zero. Because of the limited conductivity of the metal, an altering electric field will however penetrate into the metal a short distance, but typically every metal casing is much thicker than the penetration length. The metal casing should be mains grounded especially if the shielded electronics is mains grounded as well. E.g. in the 50 Hz power supply field the potential of the unshielded casing alters in the rhythm of the electric field. Thus the interference can be coupled capacitively from the casing to the electronics. Magnetic field interferences will go through an aluminum casing, because aluminum is not better magnetic conductor than air (relative permeability µr = 1). Iron is better magnetic conductor (µr = 5) and therefore the magnetic lines of flux of interfering field are conducted along the casing and only a fraction of the field can enter inside the casing. So called µ-metal has µr up to 100 000 and it can be used to have a good shielding against magnetic field.

6.2.1 Electromagnetic coupling Radio transmitters, radars and electric arcs are typical sources of interference of electromagnetic coupling, figure 52.

E

H

r >> λ

Interfered device

Radio antenna

Figure 52. The principe of electromagnetic coupling. The figure shows vertically polarized radio wave. The distance r is much larger than the wavelength, E is electric field amplitude and H is magnetic field amplitude.

6.2.2 Capasitive coupling The circuit diagram shown in figure 53 illustrates the interference in the signal cable induced by the mains cable. The reason for the interference is the capacitance between the mains cable and the signal cable. The interference is coupled through the capacitance to the measurement circuit.

R

R

s

i

C

C

1

2

Measuring device Measured device

U e.g. 230 V

C i

Figure 53. The principle of the capacitive coupling.

The capacitance can be calculated as

C la r r

r= πε ε02

1 2ln( ), (6.1)

C is the capacitance between the parallel conductors, l is the length of the parallel conductors, ε0 is permittivity of vacuum 8,85.10-12 F/m, εr is the relative permittivity of the media, a is the distance between the conductors and r1 and r2 are the radii of the conductors. The generated noise voltage in the measurement circuit is

( )Uj C

j C C C R RUh

i s i

=+ + + +

ωω

1

1 2 1 1. (6.2)

Capacitive noise currents are generated not only by coupling through conductors but also by possible filtering capacitors and by capacitances of coils in mains transformers. Capacitive coupling passes through the harmonics5 easier than the basic frequency. It is possible that the noise voltage is distorted in shape. The peaks in the line voltage caused by thyristors (rise time is small: 1 ... 10 µs) can esily enter in to the measurement circuit. Basically the circuit diagram in figure 53 forms a high pass filter.

6.2.3 Inductive coupling Conductor loops in measurement circuits are subjected to magnetic interferences, figure 54. Sources of such interferences are e.g. high-current cable the load of which alters or which is switched on and off. Alternating current causes a magnetic field to its environment.

H Irh =

2π, (6.3)

where Hh is the amplitude of the interfering magnetic field, I is the current in the interfering conductor and r is the distance from the conductor. When an alternating magnetic field goes through a conductor loop in the measurement circuit, a voltage is induced in to the loop Uh, which is connected in series with the measured voltage.

Uddt

AdHdt

Ar

dIdth

h h= = =Φ

µ µπ0 0 2

, (6.4)

where Φ h is interfering magnetic flux, A is projection of the interfered area normal to the flux and µ 0 is permeability of vacuum 4π.10-7 Vs/Am. If the resistances Rs and Ri are very small, there will be a current in the circuit which will generate a magnetic field that tries to compensate the change in the flux Φ h (and in the magnetic field Hh). In this case the voltage Uh, will not rise to as high level as the last part in the equation (6.4) would suggest.

5 Harmonics are multiple of the basic frequency. E.g. if the basic frequency is 50 Hz, then the second harmonic is 100 Hz, third harmonic is 150 Hz etc. Harmonics are generated by loads that distort the sinusoidal waveform of the signal. Such loads are e.g. rectifiers and fluorescent lamps, which have high current consumption at the peaks of the waveform.

I

R

R s i

s

A

H

U Area

Measured device Measuring device

Figure 54. The principle of the inductive coupling.

In the electric cables, the current typically propagates in the phase conductor to the device and comes back along the neutral conductor of the same cable. In this case the sum current is zero and the magnetic field generated around the cable is rather small. In the buildings, the sum current at the current supply of electric devices differs from zero if the body of the grounded6 device is in connection with the body of the building, figure 55. In the loop formed by final circuit and the metal body the building circulates a current I2, the magnitude of which depends on the ratio of the conductivity of the final circuit and the metal body of the building.

I1

I1

I2

+ I2

I2

I =

Metal parts of the building body: Water pipes, concrete reinforcement, etc.

~

PEN-conductor i.e. common shield- (PE)and neutral line (N)

fuseMain distributionboard

Final circuit

Mains lead

Grounding electrode = ca. 20 m noninsulating conductordug in the ground

Electric device

PEN

MetalbodyGrounding

Figure 55. Generation of the interfering current I2 .

The sum current will differ from zero if the current to ground through capacitances between the conductors, filter capacitors and transformer capacitances is remarkable. Also in the case of earthing in which the phase conductor is in contact with the building body, the sum current will differ from zero.

6 Protective earthing with common neutral and grounding conductors.

6.2.4 Resistive coupling The principle of the resistive coupling is shown in figure 56. Devices are neutralized. The current in neutral conductor is divided at point P to propagate along the shielding of the signal cable and neutral conductor.

R U s L s

I Z

R

0

~ I

Signal cable

P

Figure 56. The principle of resistive coupling.

When using asymmetric cable (coaxial cable), the noise current in the shield will cause a noise voltage which is summed directly to the signal voltage. The magnitude of the noise voltage depends on the magnitude of the noise current and on the cable coupling impedance. Coupling impedance is determined for an electrically short ( l << λ 4 ) coaxial cable as follows. There is a noise current Ih in the cable shield. A noise voltage Uh can be measured from the open end of the cable. The noise voltage corresponds to the voltage drop of the shield. The ratio of noise voltage and current (per length unit) is the coupling impedance.

Z UI lk

h

h= (6.5)

I

U h

h I h

central cable

shield

Figure 57. Coupling impedance.

6.3 Prevention of electric interference First of all, the aim is to eliminate the noise source. The location of the interfering device can be found out with measuring the strengths of electric and magnetic fields. If the spectrum of the noise is strong up to 150 kHz range (broadcasting range), there is a number of regulations that prohibit the use of

such devices. The noise source can be placed in a noise protected room, equip with filters or locate further away. Because there will always be some noise present, the electric devices must be designed so that they can stand well electric interferences. Electromagnetic compatibility means that device connections are compatible and do not disturb too much each other. Some manufacturers report that a device fulfils some MIL-standard based requirements of interference immunity tests. In these tests, a device is exposed to strong magnetic and electric fields. Furthermore, it is tested e.g. if a device fulfils the standards of interference coming from the mains cable. It is recommended to pay attention to these issues before purchasing equipment. An interference sensitive device in an industrial environment can be placed to such a place that has been measured to be low noise area. E.g. a concrete building attenuates remarkably and in cellar environment the noises can be attenuated enough. Notice, that in near field the interference coupling can be diminished by altering the distance, because in the case of high-impedance field the strength of electric field decreases as 1/r3 and magnetic field decreases 1/r2, where r is the distance from the source. Respectively, in the case of low-impedance field the strength of the magnetic field decreases as 1/r3 and electric field decreases as 1/r2. In far field the strength of both electric and magnetic fields decreases as 1/r. An extreme alternative is to place equipment into a shielded room.

6.3.1 Capacitively coupled interferences Capacitively coupled interferences can be prevented by metal casing, placing signal cables far away from power cables and avoiding long parallel lines, using shielded7 power cables, shielded signal cables (with two separately shielded casing if needed) and using static shield in mains transformers. A static shield is e.g. a protective earth grounded copper foil between coils of transformer. In this case the secondary coil sees the ground next it instead of the primary coil in which the voltage is altering between ± 400 V. Moreover, there can be used an additional signal ground which is isolated from the device body and which is switched to the protective earth only from one point.

6.3.2 Inductively coupled interference Inductively coupled interferences to signal cables can be prevented as follows. Signal cables are located far away from high-current cables and long parallel lines are avoided. Moreover, highly attenuating signal cables should be used: 7 A cable has a shielding which is made of metal or other conductive material. Shielding is connected typically to earth potential in order to get the protective effect.

Signal cables and grounding cables related to those are place close to each other (e.g. by using twisted pairs). In power applications totally protecting conductor systems are applied and thus neutral conductor is totally isolated from the ground and all protective earthing are connected to a separate grounding conductor which is earthed only at a main distribution board. In this case a situation described in figure 55, in which the sum current in feed cables is not zero.

6.3.3 Resistively coupled interference Interference based on resistive coupling can be prevented by using signal cables with low coupling impedance (several nested shieldings or a metal pipe as a shield) or by using separate (currentless) protective grounding conductor (5- or 3-wire system). In the case of symmetric cables, the resistive coupling interference can be avoided by using transformers or opto-couplers (combination of LED and phototransistor) in order to produce a galvanic isolation.

6.4 High frequency interference on low frequency devices

If the noise signal frequency is at the measurement device bandwidth, the noise influence to the measurement can be solved rather easily. E.g. when measuring 1 V AC-voltage with a root-mean-square detector, causes 0,1 V interfering frequency voltage 1 % inaccuracy to the measurement (root-mean-square detector sums voltages quadratic). If the interfering frequency is much larger than the upper limit frequency of the measurement device, there will be rectifying of the noise signal in the measurement device. Rectifying is caused by some nonlinear component of the measurement device. Worst of those are junctions of semiconductors, e.g. transistor base-emitter junction, ordinary diode etc. Somewhat more linear are e.g. FETs, vacuum tubes and poor junctions. Rather linear are e.g. mass and carbon-film resistors. A nonlinear component such as rectifier generates a DC-voltage relative to high frequency noise voltage amplitude. Because the noise voltage is typically not constant, there will be a low frequency component present as well. If the high frequency noise voltage enters to the base of a first transistor in a low frequency amplifier, it will be rectified just like in the case a diode detector. Thus, the generated DC-voltage drives that transistor. The negative feedback of the amplifier has typically no influence outside the used bandwidth, in other words, amplification and the operating point are changed and measurement accuracy suffers. The noise voltage that has entered the amplifier input effects also to AC-amplification through third order distortion factor. This effect can be eliminated with sufficient negative feedback.

If the noise voltage effecting on the nonlinear component is small (in the case of a diode less than 30 mV and of other components more), there exists a DC-voltage proportional to the square of the noise voltage. DC-voltage U0 can be calculated as

UU h

0

2

50=

mV, (6.6)

where Uh is noise voltage. E.g. 1 mV noise voltage generates 20 µV DC-voltage. When a measurement device is exposed to electrical interference, it is interesting to know how strong the interference can be in order not to cross the inaccuracy of e.g. 0,1 %, 1 % etc. If such comparable results were available, would the selecting of the right measurement device for a certain circumstances be much easier. It was notices in a typical measurement that some digital-voltage-meters and frequency counters were interfered (inaccuracy ~ 1 %) when the amplitude of the sinusoidal electric field was over 100 V/m at the frequency of 1 MHz. Respectively, some 10 ... 100 µT sinusoidal magnetic field was enough to generate interference at the frequency range of 10 ... 100 kHz. Case: Luotettavuusongelma säätöelektroniikassa Mittaustekniikan laboratoriossa on käytössä puolijohdelasereita, joiden aallonpituuden halutaan pysyvän paikallaan 10-8:n epätarkkuudella. Sen vuoksi laserdiodien läpi kulkeva virta pyritään pitämään stabiilina samoin kuin laserdiodien ja niiden alustana toimivan rakennelman lämpötilat. Lämpötilan stabilaattorielektroniikat perustuvat säätimiin, jossa säätöjännite määräytyy toisaalta asetusarvon ja toisaalta lämpötila-anturista saatavan takaisinkytkentäjännitteen avulla. Yllättäen havaittiin säätimien luotet-tavuudessa ongelmia. Erityisen haitallista oli laserin alustarakennelman lämpötilan vaeltelu ajoittain. Palautuminen oikeaan lämpötilaan kesti kymme-niä sekunteja hitaan aikavakion vuoksi. Kun havaittiin häiriöitä myös muissa laitteissa, alettiin epäillä ulkoista häiriötä. Kytkemällä antennina toimiva muutaman metrin pituinen johdin oskilloskooppiin tai spektrianalysaattoriin, havaittiin amplitudiltaan suuri, muutaman minuutin välein toistuva sekvenssi, jossa peräkkäin tuli signaaleja 14, 18, 21, 25 ja 28 MHz:n taajuuksilla. Kahdella viimeisellä taajuudella olevat signaalit aiheuttivat häiriöitä säätimiin. Häiriölähdettä etsittiin mittaamalla häiriön amplitudia laboratoriossa ja sen ympäristösssä oskilloskoopin avulla. Lopulta selvisi, että häiriön aiheuttaja oli teletekniikan laboratorion katolla oleva Suomen radioamatööriliiton 100 W:n tehoinen radiomajakka. Häiriön kytkeytymistavaksi arveltiin signaalin tasasuuntautuminen epälineaarisissa elementeissä säädinelektroniikan sisällä. Ei-toivottua tasajännitettä varautui todennäköisesti takaisinkytkentäpiirin kondensaattoriin häiriön keston ajan. Säädin muutti ohjausvirtaa virheellisen takaisinkytkentäsignaalin perusteella. Kaikki mittauskaapelit olivat

maadoitettuja koaksiaalikaapeleita. Huomattiin kuitenkin, että pahiten häiriin-tyneen säätöelektroniikan metallikotelo oli ollut kytkemättä maapotentiaaliin, minkä vuoksi se oli ollut muita alttiimpi häiriöille. Radiomajakan antenni siirrettiin sittemmin suurjännitelaboratorion katolle.

6.5 Examples 1. There is 1 kA 50 Hz continuous current in a conductor. In case of an interfernece the current may increase up to 100 kA in 10 µs. How large voltage is generated to a coil antenna at a distance of 10 m? The effective area of the antenna is 100 m2 (400 rounds á 0,25 m2). Assume that coil own capacitance is very small. (In practice the antenna is in resonance at 1 kHz with its own capacitance)

H Ir

=2π

(almost constant at

the coil) B H= µ0 flux density at the coil φ = BA flux through the coil

U Nt

NAr

Ith = =∂φ

∂µ

π0

2∆∆

a) f = 50 Hz, I = 1 kA i t ft( ) sin( )= ⋅ ⋅2 1 2 kA π , ∂∂

π πit

f ft= ⋅ ⋅2 1 2 kA 2 cos( ) , u t fth ( ) , cos( )= ⋅ ⋅2 0 63 2 V π , sinusoidal noise

voltage U h = 0,63 V .

b) ∆∆

It

= 100 kA10 sµ

, temporary noise peak

Uh max = 20 kV . 2. The peak value of 50 Hz electric field between laboratory roof and floor is Eh is 50 V/m. How large voltage is generated from a 1 meter long unshielded wire which is connected to a voltage meter with 10 MΩ:n input impedance as shown in figure 59? (Maximum value, vertical wire, thickness 1 mm)

H I

r V

A NA eff =

Ffigure 58. Mains cable and coil antenna

75 V

50 V25 V

0 V

10 M Ω h

l

katto

lattia

25 V

Figure 59. Unshielded wire in laboratory. Equipotential curves show situation in which the other conductor of the voltage meter is not connected to ground.

There is induced Ehl/2 voltage to an unloaded wire, where l is effective length of the antenna. In this case the voltage would be 25 V. Input impedance is formed by antenna capacitance relative to its environment Vertical wire capacitance relative to its environment is.

C l

dk

= ⋅

−

24 16, [m]

ln 21 [mm]

[pF] (6.7)

Wire capacitance is ca. 10 pF ie. Input impedance is ca.

12 50j

jπ Hz 10 pF

300 M⋅

= Ω .

Voltage division is ca. 1/30, and thus voltage is 0,8 V.

( ) ( )U

jh =

+

10

1025

2 2

M

- 300 M M V = 0,8 VΩ

Ω Ω

Note! Sphere capacitance gives in most cases good enough estimate for a capacitance of a certain body relative to its environment.

C r= 4πε (6.8)

3. Measurement circuit and null indicator are connected to each other with a 1 m long coaxial cable. Cable shielding resistance (interaction impedance) is 10 mΩ and resistance of connectors is also 10 mΩ. Devices are connected also to ordinary plug points. Electrical network has fuses of 10 A. How large 50 Hz noise voltage is generated in the worst case to the input of null indicator. Solution: Cable shielding resistance is 10 mΩ, when frequency is less than 1 MHz.

25 V

-j300M

10 M U h

Figure 60. Equivalent circuit

h/l k 0,01 0,42 0,1 0,345 1,0 0,207 10,0 0,144 ∞ 0,133

k

I

R

0

~

Coaxial cable

10 mΩ

Plug point Plug point

U h

l 0 R R

l R l R

l R

Measurement circuit

Null indicator

10 mΩ10 mΩ

10 mΩ 10 mΩ

10 mΩ

Figure 61. Measurement circuit and null indicator

The current through cable is

I RR R Rh

l k

=+ +

0

0 410 10 A = 10

10 + 40 + 10 A = 1,7 A

In this example, when R0 is 10 mΩ (depends on distance between plug points), U Ih h= ⋅ =30 50 m mVΩ . One gets noise voltage of 50 mV 50 Hz. So, there should be no current in shielding cables. A separate currentless shielding cable should be used.

6.6 Measurements Equipment:

• Oscilloscope • Current meter • Signal generator • Magnetic field antenna • Electric field antenna • Transmitter and receiver

The idea of this work is to study capacitive, inductive and resistive interference and their coupling to the system, which is composed of a transmitter, a receiver and a connecting signal cable. A microphone functions as a signal source in the transmitter circuit and a loudspeaker is used as an output in the receiver circuit. Typically some kind of measuring sensor is utilized as a signal source, but in this work the microphone and the loudspeaker are utilized to make it possible

to ´listen´ the interference. The transmitter and the receiver are independent devices and they are operated by mains current. A common ground plane for the equipment is formed with mains cables. Phenomena observed in this work occur also in the circuit boards and they have to be taken into account when designing electronics. The instruments are poorly designed in order to facilitate interference coupling to the system. To improve the interference sensitivity of the equipment (1) the signal is amplified only at the receiver and (2) the impedances of the transmitter and the receiver are high. By amplifying the signal at the receiver, all the interference coupled to the system is amplified at the same time. High-impedance input and output increase the equipment sensitivity for the capacitive coupling. The signal generator is utilized as an interference source in this work, but there is also other interference coupling to the system and they can be easily observed. The principle of the measurement set up is presented in figure 62. The signal is connected through a single amplifier from the microphone to the signal cable. The transmitter impedance has been increased by adding a 50 kΩ resistance to the amplifier output. The input resistance of the receiver is supposed to be extremely high. The capacitance between output/input and ground is about 100 pF, which are assumed to be connected in series with a 2 kΩ resistance at the transmitter and with a 3 kΩ at the receiver. This arrangement is presented in the fig. 64.

50 kA=1 A=100

Microphone Loudspeaker

BNC tooscilloscope

RECEIVERTRANSMITTER

Signal cable

Cover grounding

Current loop

Mains cable

Mains cableresistance

100 Ohm100 OhmGround cable Ground cable

Interfering currentinput

Interfering current input

Figure 62. The principle of the connections for interference measurements.

In this work the interference coupling to the different types of cables is studied and the capabilities of the cables to attenuate the interference are compared. The interferences are coupled equally to the system in all measurements. The coupling of the interference is described in the next paragraph. Read this paragraph carefully since you need the information in all measurements.

Interference coupling to the system

Each type of interference requires its own experimental arrangement. The capacitive interference is coupled to the system through an electric field antenna (fig. 63). The antenna is placed parallel under the signal cable.

Figure 63. Electric field antenna.

The idea of the capacitive coupling is presented in the figure 64. The signal generator ground is connected to the ground mat already inside the device thus the earth conductor needs not to be connected while measuring.

RECEIVER TRANSMITTERSignal cable

Ground

Signal generator

Capacita nce between signal cable and ground

50k

2k

100p

3k

100p

Figure 64. The principle of the capacitive coupling.

The inductive interference is coupled to the system through a magnetic field antenna (fig. 65). The antenna is placed next to the signal cable in the way that most of the flux of the antenna pass through the loop formed by the signal cable and the earth conductors. The position depends on how the transmitter and the receiver are positioned compared to the earth conductor. If the distance between the signal cable and the earth conductor is quite small (same or smaller than the size of the antenna), the most favorable place for the antenna is between the signal cable and the earth conductor. If the distance is longer, the most favorable place is next to the signal cable. The area of the magnetic field antenna is around 0.03 m2 and the number of turns is 125. At low frequency range the current intensity is determined by the voltage of the signal generator and the resistance of the antenna (50 Ω). A high frequency range the inductance of the antenna sets a limit to the current intensity. In practice the easiest way to obtain the current intensity is to use current meter.

Figure 65. Magnetic field antenna.

The resistive interference is coupled to the system by leading the interference current to the grounding as shown in figure 66. The interference current is thus coupled to the receiver. There is a connector in the cover of the equipment for the interference current connection. From the connector the interference current is coupled to the grounding through a resistance of 100 Ω. The resistance is added to the system to protect the equipment. Control with oscilloscope that the signal from the signal generator does not become distorted while measuring inductive and resistive interference. If the signal becomes distorted, the signal generator is overloaded and you should decrease the voltage. While measuring the resistive interference, the grounding is connected through the earth conductor of the signal generator and thus there is no need to connect the earth connection from the output.

Noisecurrent

RECEIVERTRANSMITTER

Ground

Signal generator

100 Ohm

NoiseVoltage

Figure 66. The principle of the resistive coupling.

Construction of the measuring set up and some general advice 1. Switch on the equipment and connect the transmitter and the receiver by

utilizing an unshielded signal cable. Switch on the microphone and the loudspeaker to make sure that they are working. After confirming that the equipment is working, you can switch off the microphone to ensure that the

microphone signal does not interfere with the measurement. Switch also off the loudspeaker in order that other people are not disturbed. You can however listen during measurement the sound of interference with different cables.

2. Connect the BNC-connector of the receiver to the oscilloscope. The

interference amplitude is measured by the oscilloscope. You can listen the interference coupling from the loudspeaker, but notice that you obtain a signal with the oscilloscope only when the loudspeaker is switched off.

3. Connect the signal generator to the other channel of the oscilloscope (utilize

T-connector at the signal generator). This channel is used to observe the functioning of the signal generator. Set the oscilloscope´s trigger at this channel since the measured signal is noisy and thus the triggering does not work well. You can improve the noisy signal by measuring average value with the oscilloscope.

4. Adjust the signal frequency (4 kHz) and the amplitude (20 Vpp (peak-to-

peak)). You can increase the amplitude during measurement to make it easier to measure weak interference. Be careful that the interference signal does not increase so much that the amplifier cuts off a part of the signal. Use frequencies specified in the answer sheet.

5. The intensity of current can be measured with the multimeter while studying

inductive and resistive coupling. Connect the signal generator from the other branch of the T-connector to the multimeter with BNC-banana-cable in such way that you can measure the current you are feeding to the magnetic field antenna or to the grounding. Connect the signal from the current meter to the antennas with a banana-banana-cable which can be found on the work place and which is particularly made for this laboratory work. With aid of this cable, the unintentional capacitive coupling can be avoided while measuring inductive and resistive coupling. (There are a grounded protective shield in this cable). The current meter can be switced on during measurements. Do not short circuit the signal generator with the current meter!

6. Pay attention to the following facts:

- The amplification of the receiver is 100. Thus the interference signal is hundredfold at the output.

- The voltage measured by the oscilloscope is peak-to-peak value, while the value obtained from the current meter is root-mean-square value.

- Due to the noise and high-frequency interference signals, the measurement signal is becoming broader in the vertical direction. Therefore the peak-to-peak value of the voltage have to be estimated as in figure 67.

Upp

Figure 67. Peak-to-peak value of the voltage have to be estimated.

6.6.1 Unshielded cable The measurement results obtained with the unshielded cable are used as a basis for other measurements. Measure the interference voltage amplitude with oscilloscope for each coupling mechanism (capacitive, inductive and resistive). Use frequencies specified in the answer sheet. Calculate on the grounds of the results the resistance of the earth conductor and the capacitance between the electric field antenna and the unshielded cable. Compare the capacitance with the value calculated in pre-laboratory exercises. What might cause the difference between these two values? Connect the interference current to the receiver while measuring the resistance of the earth conductor. Why does the resistance value differ from this value if the interference current is connected to the transmitter instead of the receiver? The calculation might be quite troublesome if using schema shown in the figure 64. To make the calculation easier, the resistance connected in series with the capacitor can be approximated to be very small and thus they do not have to be taken into account in the calculation. By using this approximation the capacitance can be calculated with the equation 6.2. Take into account that the measured voltages are absolute values and thus the capacitance can not be calculated directly with complex numbers since the values of the phase angles are not known. To further facilitate the calculation the capacitance between the antenna and the signal cable can be approximated to be much smaller than the intrinsic capacitances of the transmitter and the receiver.

6.6.2 Coaxial cable In the coaxial cable the signal cable is surrounded by a protective copper mesh. In some applications the coaxial cable is utilized even in the frequency range of 10 GHz in which case the copper mesh is replaced with a flexible tube. Replace the unshielded cable with the coaxial cable. Repeat same measurements than with unshielded cable by varying the way of grounding. 1) The ground connection of the coaxial cable is switched off, 2) the ground

connection is switched on at the receiver and 3) the ground connection is switched on at both ends. Why does the coaxial cable attenuate the capacitive coupling? Why inductive and resistive coupling are attenuated when the coaxial cable is grounded from both ends? Does the way of grounding have an influence on the amplitude of the desired signal?

6.6.3 Twisted pair cable In twisted pair cable two signal cables are twisted around each other and they are often surrounded by a protective metal mesh. The twisted pair is often in connection with a symmetrical switching which means that the same signal is sent into the both cables but in opposite phases. The principle of the symmetrical switching is presented in figure 68. Why does the symmetrical switching attenuate interference coupled to the system? The twisted pair cable and the symmetrical switching are generally utilized in the frequency range of 100 Hz and above.

U Out = A × (U1 - U2) +

- U

Differential amplifier U1

U2

Micro-phone

Twisted pair cable

Figure 68. Symmetrical switching.

Replace the coaxial cable with a twisted pair cable. By utilizing the twisted pair, the symmetrical switching is automatically used. Repeat the same measurements than with the coaxial cable. Be careful in measurements since the interference signals are probably very weak. It might be possible that with some coupling mechanism you can not measure the interference signal at all. Questions Why does the coaxial cable attenuate the interference signal? Compare different cables and their protection against interference on grounds of the results.

7 Measurements of optical telecommunication systems

Goals in this work

• Learn the properties of optical fibers and their measurements • Learn about led and laser as optical transmitters • Learn the limitations of fiber attenuation and dispersion on the data

transmission speed

7.1 Optical communications Optical communications has grown as very important technology as the volume of telecommunications has increased. The advantages of the use of optical fibers over conventional twisted pair copper cables or coaxial cables are low loss and huge bandwidth. The electrical signal transmitted in the fiber has to be transformed to light at the transmitting end and back to electrical signal after the fiber. The optical transmitters such as a led (light emitting diode) and semiconductor laser are nowadays available at a reasonable price. In this work the properties of optical fibers and optical transmitters and receivers are investigated within a short optical link.

7.2 Optical fiber Optical fiber is made of coaxial rods of glass. Light propagates in the core of the fiber the refractive index of which is higher than the refractive index of the surrounding cladding. Light is confined in the core by the help of total internal reflection between the interface of the core and the cladding. The material of the optical fibers is commonly fused silica (SiO2). Refractive index of fused silica can be changed by doping it with e.g. germanium (Ge). The fibers are roughly divided in two classes according to their properties. These classes are multi-mode and single-mode fibers. The refractive index profiles and measures of these fiber types are displayed in Figure 69. The outer diameter of the fiber is often 125 µm. Moreover, the fiber is coated with plastic to protect the glass. The diameter of the core of the fiber varies depending on the type of the fiber and on the wavelength of the light for which the fiber is optimized. Usually the diameter of the core is 9 µm for single-mode fiber and 50-62.5 µm for multi-mode fiber.

62.5 µm

~9 µm125 µm

n1

n2

Figure 69. Refractive index profiles and measures of step-index multi-mode fiber, graded-index multi-mode fiber and single-mode fiber. The difference in the refractive indices in the core and cladding is small, for example n1=1.4457, n2=1.45.

Often the refractive index profile in the fiber is step-like (step-index fiber). This profile can be either in a single-mode fiber or in multi-mode fiber. The refractive index of the multi-mode fibers can also be graded (graded index, GRIN), which improves the properties of the multi-mode fibers. The division of the fibers as single-mode and multi-mode is made according to the propagation mechanism of light in the fiber. The propagation paths in different fibers are displayed in Figure 70.

Step-index multi-mode fiber

Graded-index multi-mode fiber

Step-index single-mode fiber

Figure 70. Propagation in different fibers.

In multi-mode fiber the light pulse divides in components which propagate through the fiber with different paths having different lengths. These components arrive to the detector at different times due to difference in the length of the optical path. Different arrival times cause the broadening of the output pulse. In graded-index fiber the signal does not experience a total

internal reflection in the core-cladding interface but the path of the signal is varying smoothly. This kind of a fiber is in fact operating as a lens. This results in smaller difference in the arrival times of the pulses propagating with different paths and less broadening of the detected pulse. The properties of the single-mode fiber are superior to the multi-mode fiber. The diameter of the core of the single-mode fiber is so small that the light does not reflect through many paths but it propagates through one single path. In this case it is common to discuss about a fundamental mode of the fiber. The broadening of the detected pulse is negligible compared to multi-mode fiber. The phenomenon which causes the broadening of the optical pulses transmitted within fibers is called dispersion. The dispersion of the optical fiber is composed of the wavelength dependence of the material (wavelength dependence of the refractive index of glass) and dispersion of the waveguide (core of the fiber). By changing the core of the fiber the dispersion of the fiber can be tailored.

7.3 Attenuation of the optical fiber The power of the optical signal is often given in logarithmic units as dBm- (desibells/1mW). This unit is converted from the absolute Watt-units by calculating its ratio with 1 mW using the eq. (7.1)

)log(10)( 1)(

mWmWPdBmP ⋅= , (7.1)

where P(mW) is the power in milliwatts. We can directly calculate that 1 mW = 0 dBm ja 10 mW = 10 dBm. The reason for using the logarithmic scale is the simplification of the calculation of the link budget. The attenuation of the fiber is mainly caused by Rayleigh scattering and absorption. Rayleigh scattering is caused by a reflection from microscopic impurities or the small variations in the refractive index. The attenuation of the optical fiber as a function of wavelength is given in figure 71. The attenuation peak at a wavelength of 1.38 µm is caused by OH-ion absorption. The manufacturing process of new fibers is improved and this OH-absorption peak is lower. The wavelengths of the fibers often used are also marked in the figure. These wavelength windows are often referred as the 1st, the 2nd and the 3rd telecommunication window. Most common wavelength is 1.55 µm:n because at this wavelength an optical amplifier can be used.

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80

1

2

3

4

5

3.2.1.Infraredabsorption

OH- absorptionScattering

Atte

nuat

ion

[dB/

km]

Wavelength [nm]

Figure 71. Attenuation of the fiber as a function of the wavelength.

The power of the signal is attenuated also by fiber connectors and bends or twists along the fiber link.

7.4 Optical receivers and transmitters Optical transmitter is often a led or a laser diode. Both emitters are based on a semiconductor junction which emits light. This junction is formed by bringing together type p and type n semiconductors. The pn-junction emits photons when current is fed through the device. The optical power emitted by laser or led can be tuned by changing the current through the device. The electrical signal can thus be summed into the bias current of the device for modulation of the output power (see Figure 72).

Current

Opt

ical

pow

er

Threshold current

Bias-current

Modulation

Figure 72. Direct modulation of an optical transmitter (laser diode).

Emitted optical spectra of the laser and the led are very different. Light from the led is not coherent but it resembles broadband noise. Light from the laser often has higher power and its optical bandwidth is narrower. The optical spectra of the led and the laser applied in this work are displayed in Fig. 5.

Figure 73. Spectra of the led and the laser.

7.5 Power budget of the optical link Power budget refers to designing the system to operate reliably with adequate power at the receiver. Budgetting an optical link the quantities which are taken

into account: power of the transmitter, sensitivity of the detector (which means the minimum optical power at the receiver which is required for the link to operate), attenuation of the fiber and the connectors and dispersion induced limitations. Moreover a certain margin is added in the calculations to ensure reliable power level at the receiver. Calculation of a power budget of an optical link is outlined in Figure 74.

Transmitter Receiver0.5 dB 0.5 dB

Connector

Fiber

Power =-10 dBm

0.5 dB

Fiber

Connector Connector

Figure 74. Simple optical link.

Let us find out which is the maximum length of the fiber in the link of Figure 74. Sensitivity of the transmitter is –25 dBm and the margin is selected to be 5 dB. How long fibers are allowed when their attenuation is 2.7 dB/km? Let us write an equation describing the optical power of the link

ceiverMariginFibersConnectorsrTransmitte PLP Re=−⋅−− ααα , (7.2) where PTransmitter is the output power of the transmitter, αConnectors is the attenuation of the connectors, αFiber is the attenuation coefficient of the fiber, L is the length of the fiber and PReceiver is the minimum power allowed at the receiver. We will solve for L, which gives the maximum length of the fiber.

kmkmdB

dBdBdBmdBm

PPL

Fiber

ConnectorsceiverrTransmitte

15.3/7.2

55.12510

Re

=−−+−

=−−−

=

Marigin

ααα

(7.3)

Note: The units of optical power (dBm) and the units of attenuation (dB) can be directly subtracted and divided.

7.6 Dispersion of the optical fiber Dispersion refers to dependence of the refractive index of the optical fiber on the wavelength. Eventually this phenomenon leads to broadening of the optical pulses as they propagate through the fiber. Finally, the broadening of the pulses leads to overlapping of sub-sequential pulses and errors in their detection. The properties of pulses are often characterized by rise time and bandwidth. Rise time is defined as a time, which it takes from the pulse to increase from 10% of its final value to 90% of its final value. In case of multi-mode optical

fibers the measurement of the rise time of the signal can be used to characterize the useful bandwidth of the fiber. In this measurement a step function with a finite rise time, 0τ , is utilized. The rise time is determined form the properties

of the transmitter and the receiver. The total rise, sτ , time of the signal transmitted through the fiber can be evaluated from the relation

20

22 τττ += Fs , (7.4) where Fτ is the rise time of an infinitely short pulse through the fiber.

7.6.1 Bandwidth of the optical fiber The bandwidth of the optical fiber can be determined from the measured frequency response, temporal step response or from impulse response. Mathematically it can be shown that impulse response is a derivative of the step response and the frequency response is the Fourier-transform of the impulse response. It is often assumed that the impulse response of a multi-mode optical fiber follows a Gaussian function. In this case, a set of simple equations can be used to combine the bandwidth (BW) and the rise time τF

F

BWτ

48.0= . (7.5)

In the specifications of an optical fiber the product of the bandwidth and the length of the fiber is given in units of MHz·km. With the previous equation the product of the bandwidth of the fiber and the length is simply BW·L. The biggest allowed broadening is given as a fraction of the duration of the pulse. This fraction is given by the parameter γ, whose value is typically 0.2-0.25. In case of a Gaussian pulse the value of γ is exactly 0.25 in order to achieve a Bit- Error-Rate of BER=10-9. This implies that one of every 1 billion transmitted bits is incorrectly detected. It can also be shown that the duration of the pulse, τR, is determined by the rise-time of the pulse: τR=0.39 τF.

RTBR

τγ== 1

. (7.6)

With these equations the bit-rate (BR) length product can be defined BR·L. Let us illustrate the concept with 10 Mbit/s Ethernet connection. With this bit-rate the duration of a pulse is 100 ns and its maximum allowed broadening is 25ns. If we would like to transmit data with a multi-mode fiber whose BR·L is 200 Mbit/s·km at a wavelength of 850 nm the dispersion limited length of the fiber can be 20 km. If the data rate is increased to 1 Gbit/s the length of the fiber can be 200 m.

7.6.2 Dispersion The dispersion related rise time of the fiber can be divided into three components: material dispersion, modal dispersion and waveguide dispersion. Material dispersion is caused by the dependence of the refractive index of glass on the wavelength of glass. This is described by the parameter Dmat which is defined in proportion to wavelength and length of the fiber (for example, Dmat=10 ps/nm/km). Material dispersion causes a Gaussian impulse response with a width of τMaterial= DMaterial·∆λ·L, where ∆λ is the spectral width of the source (in wavelength) and L is the length of the fiber. Modal dispersion can be described with a similar manner with a parameter DModal, whose unit is ps/km, indicating that in this case the spectral width of the source is not affecting. The broadening of the pulse due modal dispersion is τModal= DModal·∆λ·L. Both of these contributions can be qubically summed.

222)( ModalMaterialtotR τττ += . (7.7)

When using a multi-mode fiber the waveguide dispersion is not wery significant. However, with single-mode fibers it can be applied in fabrication of fibers whose material dispersion is compensated with waveguide dispersion.

7.7 Measurements Measurement equipment Measurements are performed with equipment including a signal generator, a led, a laser diode and an optical receiver. The equipment is generally described in figure 75. In addition there are two spools of optical fibers which are numbered as #1 ja #2. The signal generator, the led, the laser and the optical receiver have BNC-connectors for connecting electrical signals. Optical fibers are connected with ST-connectors. NOTE: When you are connecting the optical fiber make sure that the connector is in correct angle and it is properly fastened. Do not use too much force when connecting the optical fibers!!

Optosci 000 000 000

1 2 3 4

Figure 75. Measurement equipment used in the work: 1 signal generator, 2 led, 3 laser, 4 receiver.

7.7.1 General instruction for making the measurements While making measurements of optical power take care not to touch or move the optical fiber connected for the measurement. Moving the fibers may cause clear variation in the detected power and lead to an erroneous measurement. The connectors of the fiber patchcords (1 meter long fibers) are numbered. When you are making the first measurement note which way they are connected between the transmitter and the receiver. Use the fiber the same way which will minimize the fluctuations in the optical power.

7.7.2 Characteristics of led and laser In the first measurement electrical current vs. optical power characteristics of led and laser are investigated. Connect the 1 meter long fiber between the led and the receiver. Adjust the bias current of the led between 0-100 mA and write the received power down to the answer sheet. Tune the current to 50 mA which will be use in the next experiments. Measure the optical power with this current setting. Repeat the previous measurement for the laser diode. Note: the optical power of the laser is much higher than the power of the led. Do not look directly to the tip of the fiber! Adjust the bias current of the led between 0-50 mA and write the received power down to the answer sheet. Tune the current to 37 mA which will be use in the next experiments. Measure the optical power with this current setting.

7.7.3 Attenuation of the optical fiber Next the attenuation of the optical fiber is measured. Measure the power of the laser after 1 meter fiber. Connect this fiber to the fiber spool #1 with a fiber adapter. Connect the other end of the fiber to the receiver and measure the power. Calculate the attenuation of the fiber spool #1 for laser light. Repeat the attenuation measurement for the fiber spool #2. Repeat the attenuation measurements with led as a transmitter.

7.7.4 Measurement of the length of the fiber In this measurement the length of the fiber will be determined from the phase shift between a short reference fiber and a long fiber of unknown length by utilizing the method described in preliminary exercise #2. Connect a BNC-T splitter between the signal generator (sinusoidal wave), the oscilloscope and the laser. First signal from the generator is connected to the laser. The other signal from the signal generator is connected into a channel 1 of the scope. Set the triggering of the scope to this channel and set the time division of the scope to 1 µs/div. Connect the laser to the receiver with the 1 meter fiber and connect the receiver signal to the channel 2 of the oscilloscope. Tune the frequency of

the signal and seek a point in the time axis where the phase of the signal remains unchanged when the frequency is tuned. Change the 1 meter long fiber to fiber spool #1. Again, seek a point in the time axis where the phase of the signal remains unchanged when the frequency is tuned. The time difference of these two measured time points can be utilized to determine the length of the fiber. Repeat the measurement of the length to the fiber spool #2. Calculate the attenuation constant (in dB/km) for the led and the laser with the length of the fibers you have just measured.

7.7.5 Bandwidth of the fiber Measurement in time domain Set the signal generator to square wave and connect it to the led. Connect the led to the receiver with the 1 meter reference fiber. Measure the rise-time of the signal (from 10% to 90%) for this combination of transmitter and receiver. Repeat the measurement of the rise-time to both of the fiber spools separately and also when the spools are connected. Determine the bandwidth of the system from the measured rise-times for different components and different lengths of the fiber. Calculate the bandwidth-length product (BW·L). Repeat the measurements for the laser diode. Measurement in frequency domain In this measurement, the bandwidth of the multi-mode fiber is repeated by utilizing a sinusoidal signal. Connect the signal generator to the led and use sinusoidal signal to modulate it. Connect the led to the receiver with the 1 meter reference fiber and measure the frequency response of the transmitter-receiver from frequency of 2MHz upto 22MHz. Repeat the measurement for the fiber spool #1, fiber spool #2 and to the combination of the two. Calculate the bandwidth of the fiber and the bandwidth-length product (BW·L).