Measurements &Testing (1)a

CSE 323a

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Grading Scheme

50 Semester work

50 Lab exam

50 Final exam

150 Total

Course webpage

http://ahmedalenany.webs.com/cse323a 2

1. Alan S. Morris, Measurement and Instrumentation Principles, Elsevier, 2001.

2. William Dunn, Introduction to Instrumentation, Sensors, and Process Control, Artech House, 2006.

3. William Bolton, Instrumentation and Control Systems, Elsevier, 2004.

4. Curtis Johnson, Process control instrumentation technology, Prentice-Hall, 6th edition, 2000.

References:

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Topics to be covered:

Topic ReferenceBasic electrical components (RLC) Dunn, Ch. 3Filters Dunn, Ch. 3Bridges Dunn, Ch. 3Signal conditioning Dunn, Ch. 4 & Johnson, Ch. 2Digital multi-meter & Oscilloscope Morris Ch.7Measurement system characteristics Bolton Ch. 1, Morris Statistical analysis of measurement errors Bolton, Appendix A, MorrisCurve fitting using linear regression Morris, Ch. 11

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Lecture 1: RLC

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• Are the three basic passive elements used in electrical circuits.

• Let us have a look at some useful slides from the course 6.091 offered at the Department of Electrical and Computer Science, MIT, available at:http://ocw.mit.edu/courses/electricalengineering-and-computer-science/

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Resistors, Capacitors, and Inductors

Resistors

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Resistors

• Used as loads in electrical circuits. • Resistor parameter: resistance, tolerance, and power

rating.• Standard values:

10 12 15 18 20 22 27 33 39 47 56 68 82.

• Common tolerances: ±5%, ±1%.• Resistor are color coded. 8

4-band Resistor Color Coding

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4-band, 5-band, 6-band Resistor Color Coding

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CapacitorsUsed as dc blocking devices, in level shifting, integrating, differentiating, filters, and delay circuits.

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Capacitors

• Capacitors range from 1 pF (10-12) to 100,000 µF (10-1).

• Typically, capacitors larger than 1 µF are polarized.

• All capacitors have maximum voltage ratings.

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Capacitors

• Standard values: 10 12 15 18 20 22 27 33 39 47 56 68 82

• Examples: 100pf, 180pf, 270pf, … , 1μF, 2.2μF, 4.7 μF, … 13

How to read puff capacitor codes?

Example: Capacitor marking: 104 = 10 x 104 pF = 105 x 10-12 F = 10-7 F = 0.1μF

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Inductors

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Inductors vary from a few µH (etched on a pcb) to Henries.

Inductors • Used as current

limiting devices.

• Found in relays, audio to electrical conversions, electromagnetic devices, light dimmers, and tuned circuits.

• They are also the basis for transformers and motors.

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3.2 Circuits with R, L, and C3.2.1 Voltage Step Input

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• When the current in the resistor is maximum, the voltage across it is maximum, given by E = IR. i.e. the voltage is said to be in phase with the current.

• For the capacitor, the voltage is zero when the current is maximum, and the voltage is a maximum when the current is zero. In this case, the voltage lags the current, or there is a phase shift between the voltage and the current of 90°.

• The voltage across the capacitor builds up exponentially, at a rate determined by the values of R and C.

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Step input to RL circuit

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• The voltage and current in the resistor are in phase. • However, in the inductor, the voltage leads the

current by of 90°.

• The voltage across the resistor increases exponentially, at a rate determined by the value of L and R.

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Time constant• In RC circuit, the voltage across the capacitor,

while charging, is given by:

where E is the source voltage.• and while discharging, is given by:

)1( /RCtC eEE

RCtC EeE /

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Time constant

• It is the time taken by the response to reach 63.2% of its full change.

• The time constant of RC circuit is given by RC, while for RL circuit, it is L/R.

• Practically, the response will complete its full change in 4 to 5 time constants.

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Time constant

• Applies not only to electrical circuits, but also to sensor outputs when there is a change in the measured variable.

• The output signal from the sensor changes exponentially, so that there is a delay before the sensor output reaches its final value.

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3.2.3 Sine-wave inputs

• E is the supply voltage, VR, VL, VC are voltage across resistor, inductor, capacitor.

• Assuming that the circuit is capacitive.

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• In series RLC circuit, the same current will flow through all three devices.

• When an ac sine wave is applied to RLC circuits, the same phase shift between voltage and current occurs as when a step voltage is applied:• IR and VR are in phase;

• IC leads VC by 90°;

• IL lags VL by 90°;

• That is, • VC and VL are 180° out of phase; and

• VC and VL are 90° out of phase with VR

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Vector addition

• Since the voltages and currents in capacitors and inductors are not in phase, they have impedance and not resistance.• Impedance and resistance cannot be directly added. • However, they can be combined using vectors.

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• The impedance (Z) of the ac circuit, as seen by the input is given by:

• Where

• The current flowing in the circuit can be obtained from Ohm’s Law, as follows:

222 )( CLR VVVE

22 )( CL XXRZ

fLX

fCX

L

C

2

,2

1

.Z

EI

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Example

What is the current flowing in the series RLC if R = 27 kΩ, C = 2.2 nF, L = 33 mH, E = 20V and the input frequency = 35 kHz?

mAZEI

kXXRZ

kfC

X

kfLX

CL

C

L

73.0)105.27/(20/

5.27]101.21025.7[)1027(][

1.210221035142.32

1

2

1

25.71035142.322

3

2332322

93

3

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Resonance• XL and XC are frequency dependent.

• As the frequency increases, XL and XC .

• A frequency can be reached where XL = XC , and the voltage across these components are equal, opposite, and cancel.• At this frequency, Z=R, E=IR, and the current is maximum. • This frequency is called the resonant frequency of the circuit.• At resonance:

29fC

fL

2

12 Hz

LCf

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• When the input frequency is below the resonant frequency XC > XL, the circuit is capacitive.

• Above the resonant frequency XC < XL, the circuit is inductive.• Plotting the input current against the input frequency

shows a peak at the resonant frequency as shown:

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What is the resonant frequency of the series RLC if R = 27 kΩ, C = 2.2 nF, and L = 33 mH? What is the current at this frequency?

The current can be obtained as (at resonance Z = R)

Example

kHz

LCf

7.181033102.2142.32

12

1

39

31mAR

EI 74.0

1027

203