Tc320 Lab Manual_2013

TCET 2102/TC 320 Analog and Digital Telephony 1

NEW YORK CITY COLLEGE OF TECHNOLOGY OF THE CITY UNIVERSITY OF NEW YORK

DEPARTMENT OF ELECTRICAL AND TELECOMMUNICATIONS ENGINEERING TECHNOLOGY

TCET 2102/TC 320 Analog and Digital Telephony

Laboratory Manual

Revised by Professor Jang January 2013

TCET 2102/TC 320 – Analog and Digital Telephony Laboratory Manual 2

Experiment # 1

dB Measurements for a Loaded Low Pass RC Filter First Order Butterworth

Objectives

1. Learn how to read, use and compare instruments that are dB/dBm-calibrated 2. Relate dB measurements to voltage measurements 3. Determine the cut-off frequency of an RC LPF using the difference in dB measurements 4. Evaluate the affects of instrument loading on frequency response 5. Use Thevenin’s Theorem to calculate a circuit’s loaded response 6. Use Audio Test Set, its functions, ranges and limitations; connections, switches, dials and indicator 7. Use VOM to read dB values, and how changing ranges affect the dB scale and input impedance

Equipment Audio Test Set (Electrodata) Analog Volt-Ohm Meter (VOM) (Simpson 260) Oscilloscope Digital Multi-meter (DMM) 10 kΩ ¼-watt Resistor 0.01 μF Capacitor Notes All dB measurements are referenced to 0.775Vrms, which equates to a meter calibration of 0 dBm (with an assumed load of 600 Ω). Actual loads are of no interest, as the experiment doesn’t measure dB power. The focus is the ratio of voltages, which equate to voltage in dB. The dB values of the voltage ratios are obtained as a result of taking the difference between dB measurements. The reference voltage in each reading cancels out of the equation; logarithmic properties are expressed:

Log A – Log B = Log (A/B) 20 Log (V2 / 0.775Vrms) – 20 Log (V1 / 0.775Vrms) = 20 Log (V2 / V1)

The frequency response for an RC Low Pass Filter or the First Order Butterworth Filter is:

V(f) / Vdc = 1 / √[12 + (f/Fc)2]

To find how the frequency “f” varies as a function of the tolerances and errors in the measurements, rearrange the equation as:

f = Fc * √[Vdc / V(f)]2 – 1 = 1 /(2πRC) * √[Vdc / V(f)]2 – 1 When f = Fc: [Vdc / V(f)]2 = (1 / 0.707)2 = 2 since at the cut-off frequency, V(f) = 0.707Vdc. Then f = Fc * (√2 – 1) = Fc. However, several uncertainties exist: a) the value of Fc = 1 /(2πRC) with R and C each having a tolerance; b) the measurements of the voltages are subject to error due to the meter inaccuracies; c) the precision of the readings by the observer. Since some of the readings are in dB, the method to equate errors between ± dB and the percentage of numerical values is stated as follows; a numerical value:

M ± E% is the same as M * (1 ± E / 100) In dB: 20Log [M * (1 ± E / 100)] = 20Log [M + 20Log (1 ± E / 100) = NdB ± error in dB. Therefore, given the dB


value N and the inaccuracy error in dB, the numerical value M and the error E in percentage can be found as follows: 10 NdB/20 = M and 10 ±error/20 = 1 ± E / 100 = result. Thus E = ± (1 – result) * 100. Converting numerical percent errors E into dB inaccuracies is then: 20Log (1 ± E / 100) = ± error in dB. Circuits

Figure 1 – Test Circuit

Figure 2 – VOM Impedance Test Circuit

V1

1.4 V 250 Hz 0Deg

R1

600 Ohm

R230kOhm

R312.5kOhm

R410MOhm

ATS

Rsource (ATS)

Impedance (ATS) Impedance (VOM) Impedance (DMM)

V1

1.4 V 250 Hz 0Deg

R1

600 Ohm

R330kOhm

R412.5kOhm

R510MOhm

R2

10kOhm

C10.01uF

Impedance (ATS) Impedance (VOM) Impedance (DMM)

ATS

Point BPoint A


Pre-calculations

1. Calculate the voltage value in dB at 2.8Vpp.

2. Determine the period of a 250 Hz waveform.

3. Assuming the VOM has an internal impedance of 5kΩ per volt, calculate the meter’s loading, RVOM in dB at the 2.5Vac range.

4. Assuming that ATS has an input loading affect, RATS in parallel with RVOM, calculate the voltage at the circuit

output Point B in Procedure Step 3 (b). The ATS has a source impedance, RGEN and voltage of 1Vrms. Assume near DC condition (Frequency = 0 Hz) condition with Vdc = 0 or that the capacitor is removed. The student is to find the values of RATS and RGEN from the ATS equipment manual.

5. Calculate the dB value at Point B using the 0.775 Vrms reference voltage.

6. Calculate the dBm value at Point B with an assumed load at Point B of 600Ω.

7. Calculate the dBm at Point B with an actual load at Point B of RVOM || RATS.

8. Calculate the cut-off frequency, Fc from Thevenin’s equivalent circuit:

Fc = 1 / (2π RTH * C)

where RTH = (10kΩ + Rgen of ATS) || RVOM || RATS

9. Calculate the voltage at Point B for the computed FC using voltage division. Where VB = [ ZLOAD / (ZLOAD + 10kΩ + RGEN)] × VGEN (rms) =VB. Reactance note: –jXC is parallel with| RVOM and RATS

10. Calculate voltage V(f) at Point B for f = FC, using the single-pole LPF voltage ratio formula:

11. Calculate the dB from the voltage at Point B for frequency Fc.

12. a) Calculate the dB difference between Pre-calculations # 11 and # 5

b) Show that the dB from the voltage ratio in Pre-calculation # 10 is equal to the value in # 12a): 20 × Log [V(f) / V(dc)]

13. Show that the frequency of approximately 250Hz is an adequate starting reference instead of DC (0Hz) for

determining the 3dB cut-off frequency, FC. This is done by showing that the dB difference between DC and 250Hz at the output, Point B is very small (compared to 3dB): 20 Log [V(f) / V(DC)]

14. From the dB value in Pre-calculation # 12 and the dB result of Pre-calculation # 13, find that V(Fc) / V(f = 250Hz) = 10(dB/20).

2

1

1

)(

)(

CF

fDCV

fV


Procedure Run I Step 1

a) Connect the Test Circuit as per Figure 1 leaving the ATS output terminal disconnected. Connect the ATS input terminal and VOM (2.5Vac range) to Point B.

b) Turn the ATS LEVEL knob completely counter-clockwise, and set the ATS switches (left to right): ON,

NORM, VAR, BRIDGE, LEVEL, and MONITOR.

c) Record the VOM ac impedance from the faceplate ____________ ac ohms/volt

d) Record the dB correction information from the VOM faceplate for each voltage range and calculate the correction:

Step 2

a) Connect the oscilloscope’s channel 1 and the DMM to the open circuit ATS output terminal as in Figure 1. Adjust the ATS output using the frequency knob between 250Hz and 275Hz. Set the LEVEL/FREQ switch to LEVEL mode and adjust the amplitude until approximately 1.0Vrms reads on the DMM; the reading should be approximately 2.8Vp-p on the oscilloscope.

b) Record ATS (dB) in MONITOR mode _________ dB

c) Record the oscilloscope channel 1 voltage: _______ pp (vertical boxes) × _______ volt/box = _______ Vp-p

d) Record the DMM value ________ Vrms e) Record the period on the oscilloscope: _______ (horizontal boxes) × ________ sec/box = _______ sec

Step 3: Set VOM to 2.5 Vac range and follow steps 3 & 4.

a) Connect the oscilloscope’s channel 1 to the circuit input at Point A, and connect the ATS output to the circuit input at Point A in Figure 2.

3.1 Record the DMM value _______ Vrms 3.2 Record the oscilloscope’s channel 1 voltage: _______ p-p (vertical boxes) × _______ volt/box = _______ Vp-p

3.3 Record the VOM readings _______ Vrms and _______ dB

3.4 Set the ATS MONITOR/NORM switch to NORM and record the value _______ dB

b) Connect the oscilloscope’s channel 2 to the circuit output at Point B, and connect the ATS input terminal to the circuit output at Point B in Figure 2.

3.5 Record the DMM value _________ Vrms

Range (volts) Correction (dB)


3.6 Record the oscilloscope channel 2 voltage:_______V p-p (vertical boxes) × _______ volt/box = ________ Vp-p

3.7 Record the VOM readings _________ Vrms and _________ dB

3.8 Set the ATS MONITOR/NORM switch to NORM and record the value _______ dB Step 4

a) Change LEVEL/FREQ mode to FREQ and slowly rotate the ATS frequency knob clockwise to increase the frequency, or counter-clockwise to decrease the frequency until the ATS shows a reading in the NORM mode of the MONITOR/NORM switch of 3dB less than the dB value in Step 3.8. Record the ATS value ________ dB Record the VOM value ________ dB

b) Switch the ATS to FREQ mode to record the frequency ________ Hz c) Record the period on the oscilloscope:______ (horizontal boxes) × ________ sec/box = _______ sec

Step 5: Set VOM to 10 Vac range and follow steps 5 & 6.

a) Connect the oscilloscope’s channel 1 to the circuit input at Point A, and connect the ATS output to the circuit input at Point A in Figure 2.

5.1 Record the DMM value _______ Vrms 5.2 Record the oscilloscope’s channel 1 voltage: _______ p-p (vertical boxes) × _______ volt/box = _______ Vp-p

5.3 Record the VOM readings _______ Vrms and _______ dB


b) Connect the oscilloscope’s channel 2 to the circuit output at Point B, and connect the ATS input terminal to the circuit output at Point B in Figure 2.

5.5 Record the DMM value _________ Vrms 5.6 Record the oscilloscope channel 2 voltage:_______V p-p (vertical boxes) × _______ volt/box = ________ Vp-p 5.7 Record the VOM readings _________ Vrms and _________ dB


Step 6

a) Change LEVEL/FREQ mode to FREQ and slowly rotate the ATS frequency knob clockwise to increase the frequency, or counter-clockwise to decrease the frequency until the ATS shows a reading in the NORM mode of the MONITOR/NORM switch of 3dB less than the dB value in Step 5.8. Record the ATS value ________ dB Record the VOM value ________ dB

b) Switch the ATS to FREQ mode to record the frequency ________ Hz c) Record the period on the oscilloscope:______ (horizontal boxes) × ________ sec/box = _______ sec


Questions

1. Calculate the dB value from the Scope’s Vp-p result in Step 2c. ____________dB Calculate the dB value from the DMM’s Vrms result in Step 2d. ____________dB Compare it with the dB value in Pre-calculation #1.

Note: db based on 0.775 Vrms = dBm based on assumed 600 ohm load.

2. Calculate the frequency from the oscilloscope’s measurement in Step 2e. ____________Hz 3. Repeat the calculation for Question # 1 with the DMM and oscilloscope readings taken in Steps 3d; compare

it with the dB value in Pre-calculation # 1.

4. Calculate the cut-off frequency, FC = 1 / (2π RC) where R = (10kΩ + Rgen of ATS) || RVOM || RATS Rvom = (faceplate ohms/volt) (VOM range) RATS = Rgen = student to find in ATS manual

5. Find Fc and V(f)/V(DC) at 0 Hz, 250 Hz, and 3.36 kHz from Fig.2 in Steps 3 & 4. 6. Find Fc and V(f)/V(DC) at 0 Hz, 250 Hz, and 2.35 kHz from Fig.2 in Steps 5 & 6.

7. Explain any differences between each result in Questions # 5 and 6, and any deviations in the results from expected values such as 0.707 and –3dB.


Lab Experiment # 1 – Computer Simulation

dBs and the RC Low Pass Filter Objectives

1. Verify the observations and results obtained in the laboratory. 2. Obtain a broader aspect of frequency response measurement. 3. Expand the understanding of the ways apparent dBm/dB measurements are used to determine voltage dB.

The Student is to use Multisim for simulating and exploring the laboratory experiment. Equipment

Multisim software Circuit Description:

See Figure 2. The circuit consists of a RC-LPF (10kΩ and 0.01 μF) fed from a 600Ω source impedance. The measurement instruments are a VOM (simulating the Simpson VOM), a Scope (simulating the Scope). Bode Plotter (which was not included in the Lab Experiment). Although in the experiment the ATS input measuring circuit was included, here we have alternative means to determine dB values. However, the loading effect of the ATS has been replaced by a 30kΩ fixed resistor.

The loading effect of VOM is accomplished by the properties settings for the VOM, which is 12.5kΩ simulating the 2.5 VAC range. The VOM’s dB meter calibration reference is set at 0.775 Vrms for simulating the 2.5 VAC range. Note that when we will simulate the VOM’s 10 VAC range, the meter resistance will be set for 10 × 5000 Ω/V = 50kΩ. The dB calibration reference for the 10 VAC range will be set to 0.775 V × 10 V/2.5 V = 3.1 Vrms. This has the effect of requiring a 20log10(10/2.5) = +12 dB correction factor.

Instead of the ATS generating source, we used the Multisim Function Generator. This was chosen for

convenience, as well as to easily provide a rectangular waveform to demonstrate the circuit transient response to signals in the Time Domain. From this information, the correspondence to the Frequency Domain can easily be demonstrated.

The settings of the Function Generator for the frequency analysis will be set to correspond to the Lab

Experiment values. Namely 250 Hz and at the – 3 dB cutoff frequency. The cutoff frequency will be determined quickly through the use of the Multisim AC Analysis feature. This program sweeps the frequencies based on a selected range, regardless of the Generator’s setting. The amplitude of these signals will remain as the Generator’s setting. The amplitude will be set to correspond to the experiment 2.8 Vp-p. Note that the Function Generator panel shows amplitude in peak value as opposed to rms. Simulation Results: AC Analysis:

Before going further, two characteristic about the Multisim AC Analysis program must be stated. First, the source amplitude is that of the ac source in Vrms. However, the Function Generator’s amplitude is set for peak values. This program treats the set value as rms. Therefore, for convenience the generator was set to 1.0 V and 2.0 V in two runs of this program.

The second characteristic is that this program calculates dB levels referenced to 1.0 Vrms. As a result, the graphs


show dB values that are off from the standard meter calibration values, which are referenced to 0.775 Vrms and 0 dBm for 600Ω loads. It can be easily shown that the difference between the level is

20log10(1.0/0.775) = 2.214 dB in going from 1.0 to 0.775. The analysis shows that the –3dB Cutoff Frequency occurs at 3.3 KHz. Aside from measuring the amplitude

response with the graph cursors to find the –3dB point, a quick determination can be accomplished by locating the –45 degree phase shift for a RC LPF. The student should examine the graphs, which show the voltages and dB levels (off by 2.2 dB from a 0.775 reference) at the circuit output B. Scope and VOM Analysis:

The waveforms show channel 1 at the generator with a 2.8 Vp-p, corresponding to the 1.4 Vpeak (1.0 Vrms) generator setting. Then there are the channel 2 waveforms shown for point B. These are in fair agreement with the VOM voltage readings at B for the 250 Hz and 3.3 KHz conditions.

At 250 Hz: Scope Vp-p = 1.4 V: VOM Vrms = 0.45; AC Analysis graph Vrms = 0.45 At 3.3 KHz: Scope Vp-p = 0.9 V: VOM Vrms = 0.316; AC Analysis graph Vrms = 0.320 The dB/dBm VOM readings agreed with the graphs with the 2.2 dB adjustment. At 250 Hz: VOM dB = – 4.75 V: AC Analysis graph dB = – 6.94 + 2.2 = – 4.74 At 3.3 KHz: VOM dB = – 7.52 V: AC Analysis graph dB = – 9.9 + 2.2 = – 7.7 Note: How close the change in dB is to 3 dB. Also: 20log(0.45/0.775) = – 4.75 dB and 10log[(0.45)2/600]/0.001 = – 4.72 dB 20log(0.32/0.775) = – 7.68 dB and 10log[(0.32)2/600]/0.001 = – 7.68 dB

Other Results: Bode Plot: Other measurements were obtained using a Bode Plotter, which gave corresponding results. In this case, the dB values are based on the voltage ratio between two points. These were set for Vgen and point B. Since the generator remains constant and point B changes with frequency, the Cutoff Frequency can be found by locating the frequency that corresponds to a –3dB change. Time Domain: One run was done with the generator set for a rectangular waveform. This allowed for the evaluation of the transient circuit response in the Time Domain. Rise Time (Tr) = 2.2•R•C; (Rise Time) × (Cutoff Frequency) = 0.35 Tr = 2.2•4.8kΩ•0.01•10–6 = 105.6•10–6 = 0.1056 msec Tr •FC = (105.6•10–6) • (3.3kΩ) = 0.349 The Scope waveform showed a Tr = 1.1 msec. Then 1.1 ms • 3.3 KHz = 0.363 Changing VOM Range: Another run was done to evaluate the effects of changing the VOM to the 10 VAC range. This showed the Cutoff Frequency to change to 2.4 KHz and the dB levels referenced to 3.1 Vrms (10/2.5 • 0.775). The dB values are then 20log10(0.775/3.1) = – 12 dB from the 0 dBm reference condition. As an example: The VOM showed – 16.97 dB at 2.4 KHz and – 13.86 dB at 250 Hz. This is a –3dB difference, but the dB/dBm values referenced to 0.775 are – 16.97 + 12 = – 4.97 and – 13.86 + 12 = – 1.86 dB; still – 3dB The student is strongly invited to examine the various figures of this simulation. The Student is urged to do and explore the Multisim simulation with different RC values.


Experiment # 2

604Ohm_1%

10.0kOhm_1%

10nF

30kOhm_5%

XFG1

XSC1

A B

G

T

XBP1

IN OUT

XMM1

Scope

VOM

ATS 30 kΩ

0.6 kΩ

10 kΩ

0.01 μF

Bode Plot

Function Generator

Figure 2. RC Low Pass Filter


Experiment # 2

Two-Ports and Decibels Attenuator, Insertion Loss and Impedance Matching Networks

Introduction: Two-Port Networks: Many analog telephone circuits and functions can be described and analyzed through the use of Two-Port Networks (also known as two-terminal pair). These networks can be passive or active. Many of the passive networks fall into a category of circuits that can be called Transmission Circuits for Telephone Communication. Circuits that are in this category are: filters, Transformers, Equalizers, Attenuators, Impedance matching & transforming networks, Phase shifters and Transmission Lines. The basic advantage of this approach is that complex networks can be combined for the analysis and synthesis of larger systems. A network model can be defined by a set of equations. The parameters of these equations can be calculated from an analysis of the actual network; or simply measured from the circuit’s driving point impedances at the input and output ports for open and/or short circuit conditions. These measured values and/or parameters can be used to synthesize simple equivalent circuits, which can then be compared against the defining equations. Decibels: Decibel (dB) is one of the most used measurement units in communications. The dB is a logarithmic expression of ratios. There are several reasons for the use of the dB. First of all, it is logarithmic. This allows evaluating and plotting large variations of values with equal resolution in each subrange of numbers. An example of this is gain as a function of frequency. Many performance evaluations require multiplication and division: cascading of networks (amplification and attenuation), evaluating insertion loss, gain margin & loop gain in feedback systems. These are much easier to evaluate using addition and subtraction of dBs. In addition, many physical phenomena’s and human sensations are logarithmic. Examples of these are acoustic and vision. It also turns out that the original Transmission Unit for describing a loss in power in a standard cable for one mile is closer to 1 dB. Also, the minimum discernability in human hearing is 1 dB at 1 KHz, with a doubling of loudness perception for every 10 dBs. Objectives

1. Designing, analyzing and measuring networks using the two-port concept. 2. Learn the relationship between two-port parameters and equivalent circuits. 3. Verify the circuit values through various measurement approaches: ABCD and Z parameters, open-circuit,

short-circuit and image-impedance, and the use of the Reciprocity Theorem. 4. Measure and compare attenuation and insertion loss. 5. Illustrate the relationship between dB and dBm for voltage, current and power, and when to use corrections

for dBm measurements. 6. Learn to use the voice frequency meter (VFM) and audio test set (ATS) 7. Illustrate cascading two-port networks 8. Compare the T network to the minimum loss L-Pad resistance network.

Discussion This manual is the main reference for this experiment. Recommended reading:

Introductory Circuit Analysis Robert Boylestad Z, Y and H Parameters, Reciprocity Theorem

MicroSim P-Spice Circuit Analysis John Keown (3rd ed) ABCD, Z and H parameters; two-


port networks, transmission Communications Roddy & Coolen (4th ed) T and L-Pad attenuators Analysis, transmission and filtering of signals

Javid & Brennar Two-port networks, equivalent circuits, image-impedance matching

Passive and active networks can be modeled with 2-input and 2-output terminals (each pair per port) and a set of parameters. These parameters relate the voltages and currents at the two ports. Several popular representations of networks with linear, passive and bilateral components:

Open-circuit impedance Z-Matrix Parameters Short-circuit Admittance Y-Matrix Parameters Cascade ABCD Matrix Parameters Scattering Matrix Parameters Hybrid H-Matrix Parameters

By using network theorems, passive, linear and bilateral two-port networks can be represented by equivalent “T”or “Pi” circuits. For some symmetrical conditions, a lattice equivalent is preferred. The same type two-port T and Pi network can represent a distributed-parameter circuit transmission line, or a lumped-parameter network such as: attenuator, impedance matching, equalizer, or filter. Although the design formulas can be derived through circuit analysis, as in Roddy & Coolen’s book for Symmetrical Ts and L-Pads, a classical approach has been used here. This method is applicable to both symmetrical and non-symmetrical networks, filters and transmission lines, and utilizes formulas that contain hyperbolic functions. However, only an introductory definition in terms of eθ is required for Tanhθ, Sinhθ, and in terms of Loge(Ln) is required for the inverse formula Tanh-1 K = θ. Many lower level texts avoid hyperbolic functions at the expense of limiting the student’s understanding. Since the amount of knowledge of hyperbolic math needed is extremely small and the benefit to the student is large, it is worth the time and effort to take this approach. The student will gain the ability to design and analyze these circuits from a point of view that leads to a simpler and faster procedure. The student will also gain the ability to read and better understand more of the literature pertaining to the topics of networks and transmission lines. Attenuation and Insertion Loss: Attenuation is the loss (voltage, current or power) between input and output of the inserted network. Insertion loss is the loss at the load due to inserting the network (output without the network to the output with the network). For symmetrical networks, attenuation equals insertion loss. Many signal sources have output levels for optimum signal/noise ratios, or for other reasons that are too large for the load circuit or measuring instrument. It is then necessary to use lower levels to maintain acceptable S/N ratios, or to be within the load circuit input range. A solution for this situation is to incorporate a switch-able attenuator pad or several sections that can be cascaded (ladder network). Actually, all passive networks inserted between a source and a load cause attenuation or insertion loss. Many concepts in this experiment are applicable to other types of telephonic transmission networks, including transmission lines, filters, LC matching and equalizer. Another application is to set up a logarithmic or dB reference for measurements, since attenuators can be selected in calibrated dB steps.


Matching: Matching is desired to obtain maximum power transfer from source to load. In the audio (lower) frequency range, iron core transformers are used, and in the higher ranges of RF, air core transformers and LC “L” circuits are used. In these narrow, higher bands, the network insertion losses are very small. At higher frequencies, matching is accomplished using transmission line sections and waveguide techniques. For conditions requiring very wide band frequencies ranging down to DC or near DC, a pure resistive network may be required. A typical application would be matching a generator or load to a transmission line. The objective would be a “match” to prevent reflections, more so than to obtain maximum power transfer. A problem that arises is the loss in power and signal attenuation or insertion loss. A solution that’s used is the minimum loss L-Pad. Two types of matching:

Iterative-matched Input impedance Zin to the matching network equals the load Zload, and the network’s output impedance Zout equals the source Zgen.

Image-matched Input impedance Zin to the matching network equals the source Zgen, and the network’s output impedance Zout equals the load Zload.

Equipment Variable 0-5Vdc Source, 100 mA 2 digital multi-meters (DMM) Audio Test Set (ATS) Oscilloscope Voice Frequency Meter (VFM) 20dB insertion loss non-symmetrical 600Ω-to-50Ω T-network 30dB attenuator symmetrical 600Ω T-network 10dB attenuator symmetrical 600Ω T-network 600Ω-to-50Ω resistive L-Pad

TCET210/TC320 – Analog and Digital Telephony Laboratory Manual

14

Parameter Conversions

TABLE EQUATIONS Condition Verification AD – BC = 1 Parameter

T-Circuit Value

Cascade ABCD Value

Open-Circuit Z Value

Za = Z1oc – Zc

A/C – 1C

Z11 – Z12

Zb = Z2oc – Zc

D/C = 1/C

Z22 – Z12

Zc = √Z1oc (Z2oc – Z2sc) ≡ √Z2oc (Z1oc – Z1sc)

1 / C

Z12 or Z21

A = V1 / V2 when I2=0

(Za + Zc) / Zc

Z11 / Z12

B = V1 / I2 when V2=0

(ZaZb + ZaZc + ZbZc) / Zc

(AD – 1) / C

[Z11Z22 / Z12] – Z12

C = I1 / V2 when I2=0

I / Zc

1 / Z12

D = I1 / I2 when V2=0

(Zb + Zc) / Zc

Z22 / Z12

Z11 = V1 / I1 when I2=0

Za + Zc

A / C

Z22 = V2 / I2 when I1=0

Zb + Zc

D / C

Z12 = V1 / I2 when I1=0 ≡ Z21 = V2 / I1 when I2=0

Zc

1 / C

Z1oc

Za + Zc

A / C

Z11

Z1sc

Za + (ZbZc) / (Zb+Zc)

B / D

[Z11Z22 – (Z12)

2] / Z22 Z2oc

Zb + Zc

D / C

Z22

Z2sc

Zb + (ZaZc) / (Za+Zc)

B / A

[Z11Z22 – (Z12)

2] / Z11 Z11 = √Z1ocZ1sc

√[Za+Zc][Za + (ZbZc) / (Zb+Zc)]

√(A/C)(B/D)

√(Z11)(Z11Z22-Z12

2) / Z22

Z12 = √Z2ocZ2sc

√[Zb+Zc][Zb + (ZaZc) / (Za+Zc)]

√(D/C)(B/A)

√(Z22)(Z11Z22-Z12

2) / Z11

Zimage1

√Z1ocZ1sc

√(A/C)(B/D)

Z11

Zimage2

√Z2ocZ2sc

√(D/C)(B/A)

Z12

K = √Z1scZ1oc ≡ √Z2ocZ2sc

√(ZaZb+ZaZc+ZbZc) / (Za+Zc)(Zb+Zc)

√(BC) / (AD)

√(Z11Z22 – Z12

2) / Z11Z22


15

Wiring Diagrams

Zc19.8

Za

650

Zb

37.3 1

2 4

3

PORT 2PORT 1

Figure 1a: 20dB Insertion Loss 600 ohms to 50 ohms

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1b: Setup & Determine A

DC3 V U1

DC 10M3.000 V+

-

2

U2DC 10G0.089 V

+

-

4

0

Rload50

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1c: Setup & Determine C

DC3 V

U2DC 10G0.089 V

+

-

4

0

U1

DC 1e-0094.479m A

+ -3

2


16

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1d: Setup & Determine B

DC3 V

U2DC 10M3.000 V

+

-

3

U1DC 1e-0091.569m A

+

-

0

4

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1e: Setup & Determine D

DC3 V

U2DC 10M3.000 V

+

-

U1

DC 1e-0094.525m A

+ -

52

U3

DC 1e-0091.569m A

+ -03

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1f: RECIPROCITY THEOREM

DC3 V

3

0

2

U1DC 1e-009-1.569m A

+

-

U2DC 10M3.000 V

+

-


17

Z1oc = Zin with PORT 2 open

Z1sc = Zin with PORT 2 shorted

Z2oc = Zout with PORT 1 open

Z2sc = Zout with PORT 1 shorted

Zimage 1 = Zin with Zload=Zout=50 ohms across PORT 2

Zimage 2 = Zout with Zsource=Zin=591 ohms across PORT 1

Zc19.8

Za

650

Zb

37.3 1

2 4PORT 2PORT 1

Figure 1g: Setup & determine Open-ckt, Short-ckt & Image Imped

0

Rload50

Rsource591k

Zin--> Zout-->

Zc19.8

Za

650

Zb

37.3 1

PORT 2PORT 1

Figure 1h: Setup & Determine Attenuation & Insertion Loss

Rsource

600

Rload50

Vsource

1.5 V 1kHz 0Deg

3

ATS Output

!v

!

U1AC 10M0.558 V

+

-

XSC1

A B

G

T

0

U2AC 10M7.743m V

+

-

Connect ATS & VFM

to read dB/dBm first

at port 1 & then 2

0

XMM1

0

2 4

Ω


18

ZAa

580

ZAb

587

ZBa

346

ZBb

316

ZAc37.6

ZBc445k

U1

DC 1e-0098.097m A

+ -

U2DC 10M0.304 V

+

-

DC5 V

532 4

PORT B-2PORT A-2

PORT B-1PORT A-1

600 ohm to 600 ohm

40 dB Attenuation/Insertion Loss

Figure 2a: Determine Z11-total & Z21-total

6

U3

DC 10M5.000 V

+

-

1

0

ZAa

580

ZAb

587

ZBa

346

ZBb

316

ZAc37.6

ZBc445k

U1

DC 1e-0098.097m A

+ -

U2DC 10M0.304 V

+

-

DC5 V

53 4

PORT B-2PORT A-2

PORT B-1PORT A-1

600 ohm to 600 ohm


Figure 2b: Determine Z22-total & Z12-total

U3

DC 10M5.000 V

+

-

261

0

ZAa

580

ZAb

587

ZBa

346

ZBb

316

ZAc37.6

ZBc445k

U2AC 10M0.507 V

+

-

53

PORT B-2PORT A-2

PORT B-1

PORT A-1

600 ohm to 600 ohm


Figure 2c: Determine Attenuation / Insertion Loss

U3

AC 10M9.815m V

+

-

ATSsource1 V 1kHz 0Deg

ATS

600 7

ATS Output

!v

Rload600

U1AC 10M0.021 V

+

-

XMM1

61 4

0

445 Ω

445 Ω

445 Ω


19

Ra

583

Rc62.5

Rload50

ATS

600

ATSsource

1 V 1kHz 0Deg

3

PORT 1 PORT 2

U1AC 10M0.504 V+

-

U2

AC 10M0.023 V

+

-

1

Figure 3: DEtermine Minimum Resistive L-PAD

ATS Output

2

0

!V

Procedure Run 1 – 600/50 Mismatched Network 20dB IL A) For the network of Figure 1a, measure the resistance in each branch:

Za (Ω) Zb (Ω) Zc (Ω)

B) ABCD Parameters: V1 = A * V2 + B * I2 and I1 = C * V2 + D * I2

Each frequency would produce a different set of ABCD values. This circuit is designed for dc (0Hz) to higher frequencies using resistive parts. The measurements will be performed using a dc voltage source. The higher the source value, the better the meter reading, however, component damage may occur.

1. Set up the network as per Figure 1b.

2. Connect the dc voltage to Port 1 and select a voltage value between 1-3 volts.

3. Open Port 2 (Figure 1b): V1 =________ Vrms V2 =_________ Vrms 4. With Port 2 open (Figure 1c): I1 =________mA V2 =_________Vrms

V2 values should remain the same

5. Short Port 2 through the ammeter (Figure 1d): V1 =________ Vrms I2 =_________ mA V1 should be the same level as Step b

6. With short, without ammeter at Port 2 (Figure 1e): I1 =__________ mA

In the low impedance circuit of Port 2, measuring current I2 may be difficult due to the meter’s internal impedance. This impedance may alter the circuit impedance resulting in a current reading error. Two methods available to overcome this problem are:


20

a) Place a low value resistor in the circuit path and measure the voltage across it with a high-

impedance oscilloscope or DMM. The (expected current) * (resistor) must be a high enough voltage to see.

b) Use the Reciprocity Theorem: interchange current and voltage sources.

7. Set the dc voltage generator at Port 2 to the same voltage level as V1 in Step B3. 8. Short Port 1 through the ammeter (Figure 1f): I2 = ________ mA

C) Open-circuit and Short-circuit Measurements

1. Measure the open-circuit and short-circuit values from each port (Figure 1g) with an ohmmeter:

Open-circuit (Ω) Short-circuit (Ω)

R1

R2

D) Image-Matched Impedance

1. Connect Rload (50Ω) across Port 2 and measure at Port 1 (Figure 1g): Zin = _________Ω 2. Without load, connect a 600Ω resistor across Port 1 and measure

at Port 2: Zout = _________Ω E) Attenuation

1. Replace the dc source at Port 1 with the ATS generator with 600Ω source impedance (Figure 1h). 2. Connect a 50Ω load to Port 2 and the oscilloscope to Ports 1 and 2. 3. In the open-circuit condition, set the ATS output to approximately 1.0Vrms at 1kHz, and record

voltages and decibel levels (dB/dBm) at Ports 1 and 2:

Port 1 Port 2

DMM (Vrms)

VFM (dB/dBm)

Oscilloscope (Vpp)

ATS (dB/dBm)


21

F) Insertion Loss 1. In the open-circuit condition, disconnect the network and verify the ATS output is set to 1.0Vrms and 1kHz

as in Step E3. 2. Connect the ATS output directly to the 50Ω load and record voltage and dBm at Port 2:

Port 2

DMM (Vrms)

VFM (dB/dBm)

Oscilloscope (Vpp)

ATS (dB/dBm)

Procedure Run 2 – 600/600 Matched Network 40dB IL A) Set up the symmetrical cascaded network as in Figure 2a (matching 600Ω to 600Ω with a total attenuation

or insertion loss of 40dB); measure the resistance in each branch:

Port A (Ω) Port B (Ω)

Za

Zb

Zc

B) Open-circuit Z Parameters: V1 = Z11 * I1 + Z12 * I2 and V2 = Z21 * I1 + Z22 * I2

1. Connect the dc voltage source to Port A-1 with Port B-2 in an open-circuit condition (Figure 2a). Set the voltage to 5.0Vdc; record:

VA-1 (Vdc)

VB-2 (Vdc)

IA-1 (Adc)

2. Connect the 5.0Vdc source to Port B-2 with Port A-1 in an open-circuit condition (Figure 2b):

VB-2 (Vdc)

VA-1 (Vdc)

IB-2 Adc)


22

C) Attenuation

1. Replace the dc source at Port A-1 with the ATS generator. Connect a 600Ω load across Port B-2 (Figure 2c).

2. In an open-circuit condition, set the ATS output to approximately 1.0Vrms at 1kHz. 3. Measure and record the voltage and dB/dBm at Ports A-1 and B-2. Use the ATS and/or the VFM for

dB/dBm readings, and the DMM for rms voltage: DMM (Vrms) ATS (dB/dBm) VFM (dB/dBm)

Port A-1

Ports A-2 and B-1

Port B-2

D) Insertion Loss

1. Disconnect the network and verify the ATS output in the open-circuit condition is the same as in Step C2. Connect the ATS output directly to the 600Ω load; measure across the load:

DMM (Vrms) ATS (dB/dBm) VFM (dB/dBm)

Port B-2

Procedure Run 3 – 600/50 Mismatched Network (Resistive L-Pad) A) For the network of Figure 3, measure the resistance in each branch:

Ra (Ω) Rc (Ω)

B) Impedance Matching; set the L-Pad as per Figure 3 to image-match the 600Ω source to the 50Ω load. C) Attenuation; repeat Step 1E and measure:

DMM (Vrms) ATS (dB/dBm) VFM (dB/dBm)

Port 1

Port 2

D) Insertion Loss; repeat Step 1F and measure: DMM (Vrms) ATS (dB/dBm) VFM (dB/dBm)

Port 2


23

Questions Run 1 – 600/50 Mismatched Network 20dB IL

1. Aside from component damage, why is the exact generator voltage not important? Refer to Step B2. 2. Given that all the components are 250mW or more and the impedance levels are 600 and 50 ohms,

what is the allowable maximum generator voltage? 3. Using measured resistance values: Za, Zb and Zc, calculate: Z11, Z12, Z21, Z22 and ABCD parameters

to the third-decimal place using T-Circuit Values and Open-Circuit Z Values from the Table Equations; show calculations. Using the Condition Verification formula, AD – BC = 1, confirm the theoretical calculations.

4. Using experimental results, calculate ABCD parameters to the third decimal place; show calculations.

Compare to the theoretical results by calculating the percentage difference:

| P1 – P2 | / [(P2 + P1) / 2] • 100% 5. Confirm the experimental results by using the Condition Verification formula, AD – BC = 1. 6. Using Cascade ABCD Values from the Table Equations and experimental results, calculate: Z1oc, Z2oc,

Z1sc, Z2sc and Zimage1 and Zimage2; show calculations. Compare to the theoretical results by calculating the percentage difference.

7. Determine dBm at the generator; show calculation. 8. Determine dB of the circuit; show calculations. 9. Determine the Voltage Attenuation; show calculations. 10. Determine the Power Attenuation; show calculations. 11. Determine the Insertion Loss; show calculations.

Run 2 – 600/600 Matched Network 40dB IL

1. Using experimental results, calculate ABCD parameters; show calculations. Derive Parameter B from the Condition Verification formula.

2. Calculate the Insertion Loss; show calculations:

a) With the network b) With the network at Port B2 c) With the network at Port A1 d) With the network at Ports A2/B1 e) Total Insertion Loss (A1 – B2) f) Confirm Total Insertion Loss (A1 – A2/B1) + (A2/B1 – B2)


24

Run 3 – 600/50 Mismatched Network (Resistive L-Pad)

1. Determine Voltage Attenuation at Ports 1 and 2, and Total Voltage Attenuation; show calculations. 2. Determine Power Attenuation; show calculation. 3. Determine Insertion Loss; show calculations.


25

Experiment # 3

Introduction to MATLAB

Objectives 1. Learn a comprehensive introduction to fundamental MATLAB programming. 2. Lear basic MATLAB function commands. 3. Familiarize with basic the MATLAB features – notations and operations. 4. Learn to write the simple script files and function files in MATLAB. 5. Obtain MATLAB as an application tool for data manipulation and plotting.

Equipment Computer: MATLAB 5.3 Run 1 – Pre-Lab In this first week, the pre-lab will be extremely short and very easy. Although we will not be testing out your ability to do a Blackboard on-line quiz, please make sure that you read through the information below to coming to lab. 1.1 Overview MATLAB will be used extensively in all the labs. The primary goal of this lab is to familiarize yourself with using MATLAB. Here are three specific goals for this lab:

1. Learn basic MATLAB commands and syntax, including the help system. 2. Write and edit your own script files in MATLAB, and run them as commands.

3. Learn a little about advanced programming techniques for MATLAB, i.e., vectorization.

1.1 Movies: MATLAB tutorials On the Blackboard course page, there are a large number of real-media movies on basic topics in MATLAB, e.g., colon operator, indexing, functions, etc. Look for the link with the movie film icon if it is available. 1.2 Getting Started After logging in, you can start MATLAB by double-clicking on a MATLAB icon, typing matlab in a terminal window, or by selecting MATLAB from a menu such as the START menu under Windows-XP. The following steps will introduce you to MATLAB.

(a) View the MATLAB introduction by typing intro at the MATLAB prompt. This short introduction will demonstrate some of the basics of using MATLAB.


26

(b) Run the MATLAB help desk by typing helpdesk. The help desk provides a hypertext interface to the MATLAB documentation. The MATLAB preferences can be set to use Internet Explorer as the browser for help. Two links of interests are Getting Help (at the bottom of the right-hand frame), and Getting Started which is under MATLAB in the left-hand frame.

(c) Explore the MATLAB help capability available at the command line. Try the following:

help

help plot help colon %< - - - a VERY IMPORTANT notation help ops help zeros help ones lookfor filter %< - - - keyword search Note: it is impossible to force MATLAB to display only one screen-full of information at once by issuing the command more on).

(d) Run the MATLAB demos: type demo and explore a variety of basic MATLAB commands and plots.

(e) Use MATLAB as a calculator. Try the following: pi*pi – 10 sin(pi/4) ans ^ 2 %< - - - “ans” holds the last result

(f) Do variable name assignment in MATLAB. x = sin (pi/5); cos(pi/5) %< - - - assigned what? y = sqrt(1 – x*x) ans

(g) Complex numbers are natural in MATLAB. The basic operations are supported. Try the following: z = 3 + 4i, w = -3 + 4j real (z), imag (z) abs([z, w]) %< - - - Vector constructor conj (z + w) angle (z) exp (j*pi) exp(j*[pi/4, 0, -pi/4])

Run 2 – Warm-up 2.1 MATLAB Array Indexing

(a) Make sure that you understand the colon notation. In particular, explain in words what the following MATLAB code will produce

jk1 = 0 : 6 jk1 = 2 : 4 : 17 jk1 = 99 : -1 : 88 ttt = 2 : (1/9) : 4 tpi = pi * [ 0:0.1:2];

(b) Extracting and/or inserting numbers in a vector is very easy to do. Consider the following definition of xx:


27

xx = [ zeros(1, 3), linspace(0, 1, 5), ones(1, 4) ] xx (4:6)

size (xx) length (xx) xx(2 : 2 : length (xx))

Explain the results echoed from the last four lines of the above code.

(c) Observe the result of the following assignments: yy = xx; yy(4 : 6) = pi*(1 : 3)

Now write a statement that will take the vector xx defined in part(b) and replace the even indexed elements (i.e., xx(2), xx(4), etc) with the constant π π. Use a vector replacement, not a loop.

2.2 MATLAB Script Files

(a) Experiment with vectors in MATLAB. Think of the vector as a set of numbers. Try the following: xk = cos(pi*(0:11)/4) %< - - - comment: compute cosines

Explain how the different values of cosine are stored in the vector xk. What is xk(1)? Is xk(0) defined? NOTES: the semicolon at the end of a statement will suppress the echo to the screen. The text following the % is a comment; it may be omitted.

(b) (A taste of vectorization) Loops can be written in MATLAB, but they are NOT the most efficient way to get

things done. It’s better to always avoid loops and use the colon notation instead. The following code has a loop that computes values of the cosine function. (The index of yy() must start at 1.) Rewrite this computation without using the loop (follow the style in the previous part).

yy = [ ]; %< - - - initialize the yy vector to be empty for k=-5:5 yy(k+6) = cos(k*pi/3) end yy

Explain why it is necessary to write yy(k+6). What happens if you use yy(k) instead?

(c) Plotting is easy in MATLAB for both real and complex numbers. The basic plot command will plot a vector y versus a vector x. Try the following:

x = [-3 –1 0 1 3]; y = x.*x – 3*x; plot(x, y) z = x + y*sqrt(-1) plot (z) %< - - - Complex values: plot imag vs. real

Use help arith to learn how the operation xx.*xx works when xx is a vector; compare to matrix multiply.

(d) Use the built-in MATLAB editor (on Windows-XP), or an external one such as EMACS on UNIX/LINUX, to create a script file called mylab1.m containing the following line:

Instructor Verification (separate page)


When unsure about a command, use help.


28

tt = -1 : 0.01 : 1; xx = cos(5*pi*tt); zz = 1.4*exp(j*pi/2)*exp(j*5*pi*tt);

plot(tt, xx, ‘b-‘, tt, real(zz), ‘r--‘), grid on %< - - - plot a sinusoid

title(‘TEST PLOT of a SINUSOID’) xlabel(‘TIME (sec)’)

Note: Do not save this file or any of your MATLAB files to the local hard disk. Your computer account contains a private networked directory where you can store your own files. However, I recommend you save all MATLAB files to your floppy disk. Explain why the plot of real(zz) is a sinusoid. What is its phase and amplitude? Make a calculation of the phase from a time-shift measured on the plot.

(e) Run your script from MATLAB. To run the file mylab1 that you created previously, try mylab1 %< - - - will run the commands in the file type mylab1 %< - - - will type out the contents of mylab1.m to the screen Run 3 – Manipulating Sinusoids with MATLAB Now you’re on your own. Include a short summary of this Section with plots in your Lab report. Write a MATLAB script file to do steps (a) through (d) below. Include a listing of the script file with your report.

(a) Generate a time vector (tt) to cover a range of t that will exhibit approximately two cycles of the 2500 Hz sinusoids defined in the next part, part (b). Use a definition for tt similar to part 2.2(d). If we use T to denote the period of the sinusoids, define the starting time of the vector tt to be equal to –T, and the ending time as +T. Then the two cycles will include t=0. Finally, make sure that you have at least 25 samples per period of the sinusoidal wave. In other words, when you use the colon operator to define the time vector, make the increment small enough to generate 25 samples per period.

(b) Generate two 2500 Hz sinusoids with arbitrary amplitude and time-shift.

x1(t) = A1cos(2π(2500)(t – tm1)) x2(t) = A2 cos(2π(2500)(t – tm2))

Select the value of the amplitudes and time-shifts as follows: Let A2 be equal to your age and set A1 = 1.2A2. For the time-shifts, set tm1 = -(37.2/M)T and tm2 = (41.3/D)T where D and M are the day and month of your birthday, and T is the period.

Make a plot of both signals over the range of –T ≤ t ≤ T. For your final printed output in pat (d) below, use subplot(3,1,1) and subplot(3,1,2) to make a three-panel subplot that puts both of these plots in the same figure window. See help subplot.

(c) Create a third sinusoid as the sum: x3(t) = x1(t) + x2(t). In MATLAB this amounts to summing the

vectors that hold the values of each sinusoid. Make a plot of x3(t) over the same range of time as used in the plots of part (b). Include this as the third panel in the plot by using subplot(3,1,3).

(d) Before printing the three plots, put a title on each subplot, and include your name in one of the titles. See

help title, help print and help orient, especially orient tall.



29

3.1 Theoretical Calculations Remember that the phase of a sinusoid can be calculated after measuring the time location of a positive peak, if you know the frequency.

(a) Make measurements of the “time-location of a positive peak” and the amplitude from the plots of x1(t) and x2(t), and write those values for Ai and tmi directly on the plots. Then calculate (by hand) the phases of the two signals, x1(t) and x2(t), by converting each time-shift tmi to phase. Write the calculated phases φi directly on the plots. Note: when doing computations, express phase angles in radians, not degrees!

(b) Measure the amplitude and time-shift of x3(t) directly from the plot and then calculate the phase (φ3) by

hand. Write these values directly on the plot to show how the amplitude and time-shift were measured, how the phase was calculated.

(c) Now use the phasor addition theorem. Carry out a phasor addition of complex amplitudes for x1(t) and

x2(t) to determine the complex amplitude for x3(t). Use the complex amplitude for x3(t) to verify that your previous calculations of A3 and φ3 were corrected.

3.2 Complex Amplitude Write one line of MATLAB code that will generate values of the sinusoid x1(t) above by using the complex-amplitude representation: x1(t) = ReX ejωt Use constants for X and ω.


30

Laboratory #3 TCET 2102/TC 320 Analog and Digital Telephony

Instructor Verification Sheet

Turn this page to your Instructor before end of your lab period.

Name: __________________________________ Date of Lab: _____________ Part 2.1 Vector replacement using the colon operator: Verified: __________________ Date/Time: ____________________ Part 2.2(b) Explain why it is necessary to write yy(k+6). What happens if you use yy(k) instead?

Verified: __________________ Date/Time: ____________________

Part 2.2(d) Explain why the plot of real (zz) is a sinusoid. What is its amplitude and phase? In the space below, make a calculation of the phase from time-shift.

Verified: __________________ Date/Time: ____________________


31

Experiment # 4

Attenuation and Insertion Loss of Telephone Transmission Lines With and Without Loading Utilizing Computer Simulations

Objectives 1. Illustrate and analyze the relationships between a transmission line’s attenuation constant (alpha),

attenuation and insertion loss. 2. Illustrate and compare how inductive loading affects the attenuation and insertion loss. 3. Illustrate and compare the effects of distributed inductive loading to the effects of lumped-circuit coil

loading:

a. Illustrate the validity of Campbell’s formula for short sections at lower frequencies b. Illustrate that loaded coil transmission lines exhibit LCL low pass filter cut-off characteristics

4. Compare Loss versus Frequency characteristics due to impedance-matched terminations and realistic

terminations. 5. Illustrate and evaluate the use of an equivalent T two-port (lumped component) circuit to simulate a short

section of a transmission line, with and without loading coils. 6. Learn important features of computer aided circuit analysis through the use of:

c. Matlab for generating frequency response graphs, which illustrate and compare transmission line

loss performance d. Multisim (Electronic Work Bench) to plot frequency response curves from implementation of the

simulation program Equipment Computer: Matlab 5.3, Multisim 7.0 Matlab script file, tlcompara112.m Multisim file (optional) The lab is divided into two experimental procedures:

A) Matlab B) Multisim

Discussion I A) MATLAB Several graphs will be generated that illustrate the comparative attenuation and insertion loss characteristics for sections of a transmission line with various loading conditions:

No additional inductance Added distributed inductance Added loading coil inductance

The Matlab program uses two types of circuit models:


32

Transmission_Line

1813.82 m 0.17161

R1

600

L1

44mH

L2

44mH

R20.6k

V1

10 V 60 Hz 0Deg

XBP1

IN OUT

Bode Plotter

1. Model 1 (Figure 1) uses the complete general formula for a transmission line, with and without reflections.

See “Transmission Line in the Voice Band”, Page 6. The Matlab formulas for Model 1 have been derived from the basic transmission line formulas with reflections given in the handout.

All cable-distributed parameters are programmable, so any twisted pair, gauge or coaxial type line can be simulated at any length. Cable values must be entered on a per-unit-distance (mile) basis, and the Length, in miles, is entered separately. The program formulas include lumped loading coil resistance and inductance. Both loading coil and additional distributed inductance characteristics are obtained from programmed coil values. The formulas automatically provide solutions for both situations. The entered coil values are treated as distributed parameters in one set of equations, and as lumped-circuit coil values in another set of equations. Attenuation and insertion loss curves for both the added distributed inductance transmission line and the lumped-circuit loading coil transmission line are provided by the same coil data.

For loading, the total inductance and resistance for the given section length must be used for the coil values. A zero loading is obtained by programming zero values for the coil. If the added inductance is included in the value of the cable-distributed inductance, then it must be entered on a per-unit-distance basis and the coil values must be set to zero, resulting in performance curves for the high-distributed inductance line for Model 1 only. For a comparison of distributed loading versus lumped-circuit loading, program the total additional inductance and resistance into the coil values. The program makes allowances for source impedance and load-side termination impedance. These terminations can be set for characteristic impedance matching. The impedance-matched condition is that of a line terminated in its characteristic impedance.

However, the low inductance transmission line in the voice band exhibits complex characteristic impedance that varies with frequency. This is not an attainable termination. The further a line section is from the source or load termination end, the closer the terminations to that section approach the characteristic values. This program simulates:

Middle sections (matched terminations at both ends) End sections (matched one end and a practical and realistic value at the other end) Short line (practical and realistic values at both ends)

The high inductance line has a fixed-value, characteristic impedance (usually for telephone lines of 600-1000 ohms); therefore, for the added or loaded inductance cases the selected matched impedance is a realistic condition.

Figure 1 – Transmission Line with Loading Coil


33

The realistic values that equate to these impedances approach Zo

where Lline-per-unit-distance = Lcable-per-unit-distance = Lcoil / Unit distance in miles: Zo = √ [(Lline-per-unit-distance) / (Cline-per-unit-distance)]

The published attenuation and insertion loss curves that compare unloaded to coil-loaded lines are based only on the matched impedance situations. The formulas are configured to solve for attenuation and insertion loss in dB from the same set of input data. The result of the Matlab program produces frequency response curves for attenuation and insertion loss. Figure 3 (matched terminations and no loading) and Figure 4 (matched terminations and loading) are other conditions that can be run in the experiment.

Formulas for Zo, Gamma, Alpha and Beta are based on a section of transmission line that extends to infinity in both directions, from the source end to the load end. Terminations that match the characteristic impedance result in no reflections from that termination. This is equivalent to the line being continuous to infinity at that point.

For these conditions, the gain is:

e – gamma • length = e –alpha * length • e –jBeta • length

The magnitude of attenuation is: e +alpha • length

The attenuation in dB:

8.686 • alpha • length 2. Model 2 (Figure 2) is based on the equivalent symmetrical T-circuit. The program equations are formed so

that by programming Model 1 values automatically programs Model 2 values. The selection of matched terminations automatically set Model 2 for image-matched conditions. However, since the T is a lumped-circuit equivalent of a short section of a transmission line, it cannot simulate the added distributed inductance condition. The T will always act as a LCL low pass filter at the cut-off frequency and above.

This situation is the same as the coil-loaded condition of a transmission line section. The T exhibits the distributed high inductance transmission line section characteristics in the lower frequency range, but contains the cut-off characteristics of the coil-loaded transmission line section.

At low inductance conditions and in the frequency range of interest for short lengths, the T exhibits the same performance as a distributed low inductance transmission line section without loading coils.


34

V1

1 V 1000 Hz 0Deg

Rsource600

R2

155.6

R3

155.6

Rload600

L1

44.54mH

L2

44.54mH

C195.4nF

XSC1

A B

G

T

XBP1

IN OUT

Model 2 formulas can be found in the Appendix.

Matlab Procedure Run 1 – Matched Terminations without Added Inductance Select File, Open, Select 31/2 Open file TCET2102_Lab4 Select file, Exit, Select file, Run Enter 300, then 10000 frequencies Enter 20 for number of data points Termination type: select 1 for matched conditions Transmission line data: choose the 24-gauge wire Select 1.136-mile line length Choose NO LOADING coil values: L = 0 and R = 0 Click on the graph window to view results Click on the graph Legend box and drag the graph to the upper left corner Label the graph for the conditions programmed Since the conditions of the results may be identical, six curves may appear as one Run 2 – Matched Terminations with Added Inductance Repeat all values in Run 1 except use values of an H-88 loading coil for coil inputs; assume coil resistance is 7Ω. Run 3 – Realistic Terminations without Added Inductance Repeat Run 1 except select 0 for realistic termination and use 600Ω for both source and load sides (choose L = 0). Run 4 – Realistic Terminations with Added Inductance Repeat Run 2 except use the realistic 600Ω terminations for the source and load. Run 5 – Realistic Terminations without Added Inductance at 4 miles Repeat Run 3 at 4 miles Run 6 – Realistic Terminations with Added Inductance at 4 miles Repeat Run 4 at 4 miles

Figure 2 – T-circuit with Loading Coil


35

Model 1 Legend Transmission line with only distributed inductance

Attenuation = 0 points Insertion loss = + points

Transmission line with loading coils

Attenuation = * point Insertion Loss = x point

Current Attenuation = points Model 2 Legend

Attenuation = solid line Insertion loss = dashed line

Discussion II B) MULTISIM Figures 1 and 2, Transmission Line and T-Circuit are used to simulate realistic terminations. In these simulations the circuits are drawn and instruments are connected to record the circuit responses at selected nodes. 1. Figure 1. The transmission line section is drawn with series lumped inductors and resistors at each end (one

half value on each side). Transmission line parameters are edited through the dialog box. Double-click the transmission line symbol on the schematic. Values can be edited to simulate a telephone transmission line at any length. Set the length window equal to the cable section length in meters. All line parameter values must be entered on a per-meter basis. Conversion Identities

a) [(section length in miles) • (5280 ft/mile) • (0.3024 m/ft)] b) [(cable parameter per mile) • (1/5280 ft/mile) • (3.3069 ft/m)]

For high-distributed inductance, edit the line inductance to a high value per meter. For loading coil transmission line performance, set each coil value to the Total Coil Value for the desired length divided by two. Each response type is obtained separately:

a) edit the cable inductance parameter to the higher values and set the coil values to zero (Lcoil and Rcoil) b) set the total coil values (Lcoil and Rcoil) to half-values on each side and edit the cable parameters to

their normal per-meter values

2. Figure 2. The T is programmed by setting the lumped-circuit components from the component dialog box; only lumped-circuit characteristics are attainable. For short sections, the T will exhibit the same performance characteristics of a transmission line with and without loading coils, but the T and the distributed high inductance line are equivalent only at frequencies below cut-off. This model requires programming the combined values of the line and coil.


36

R and L value

cable value per unit distance (miles) • section length (miles) + total coil value (for the section)

C and G values (usually ignored) cable value per unit distance (miles) • section length (miles)

The simulation program provides:

AC Analysis Voltage versus Frequency curves at selected nodes

Frequency range (Hz) and voltage range (dB) are programmed by clicking on the graph icons in the tool bar.

Bode Plotting Gain or Attenuation versus Frequency curve This device is connected with its input at the circuit’s output (load) and with its output at the circuit’s input (loading coil input node). The plotter will generate an attenuation plot. It will be required to set the Bode instrument’s measurement values for frequency range (100 to 10000 Hz), and for voltage range (0 to +10 or +20 dB).

Attenuation in dB

20 Log (Vin / Vout) = 20 Log (Vin / 0.775) – 20 Log (Vout / 0.775)

Attenuation in dB can also be calculated from the AC Analysis curves by subtracting the dB value of the voltage at the load termination node from the dB voltage value at the loading coil input node. Values should be calculated for several frequencies above and below the cut-off frequency. Cut-off can be identified at the point when the load voltage drops 3dB below the dB value at 300Hz. This should occur when D, the coil length separation is equal to the section length:

FC = 1 / [(π √(Lcoil • Ccable • D)] dB values in the AC Analysis are negative and reference to 1.0Vrms instead of 0.775Vrms. Each graph can be corrected by:

Actual dB = 20 Log [(V / 1.0) * (1.0 / 0.775) = 20 Log (V / 1.0) + 20 Log (1.0 / 0.775)

Actual dB = Graph value in dB + 20 Log (1.0 / 0.775) = Graph value in dB + 2.22dB However, the difference between curves eliminates the reference. Therefore, all that is required is taking the dB difference. The attenuation is [–dB minus (–dB)] resulting in +dB attenuation. It is possible that at some frequencies the attenuation may be a negative dB value meaning a voltage gain, as a result of L and C resonance effects.


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Insertion Loss in dB

20 Log (Vload without network / Vload with network) Both terms are referenced to the same voltage source, Vsource:

20 Log (Vload without network / Vsource) – 20 Log (Vload with network / Vsource) Where 20 Log (Vload without network / Vsource) = 20 Log [Rload / (Rload + Rsource)]. This is the –6dB with resonance effects, when Rload = Rsource. If the resistances are unequal, the dB value of 20 Log [Rload / (Rload + Rsource)] should be used instead of –6dB. 20 Log (Vload with network / Vsource) is the dB difference between the load voltage in dB and the source voltage in dB. Multisim AC Analysis curves are referenced to 1.0Vrms and the source is taken at 1.0Vrms. Therefore, the source is 0dB; the insertion loss:

–6dB – (negative dB value from the load voltage curve – 0dB) equals

–6dB – negative dB value from the load voltage curve Multisim Procedure Run 1 – Transmission Line with Loading Coil Inductance

Select circuit file, 24ga lossy

Set/change labels on circuits as in Figure 5 and 6 Left click on component twice to set/change any component label Use component dialog box or text box to add labels to components If Lcoil is H-88, then set each coil separately to 44 (the unit, mH is pre-programmed). Verify/set Rsource and Rload to 600Ω each Left-click on the transmission line, select default and line 1 Left-click edit

24-gauge Convert to meters Length of coil separation = 1.136 miles

Resistance R = 274Ω/mile

Inductance L = 0.95mH/mile

Capacitance C = 0.084μF/mile

Conductance G = 1.219μS/mile

Click OK, then OK again Click cable from red to black Program Bode Plotter; click plotter to enlarge it for programming Set vertical for LOG, F = 20 dB and 1= 0dB Set horizontal LOG, F = 10 kHz and 1 = 100 Hz


38

Select circuits and then schematic options Wiring tab: enable Auto Route, drag, and always Reroute Grid tab: enable show and use Show/hide tab: enable Labels, Models, References, Values, Nodes and keep parts bin positions Analysis Left click on the Analysis icon; click AC Analysis Set Start Freq = 100 Hz, set End Freq = 10 kHz Sweep = Decade No of Points = 100 Vertical scale = Decibel Nodes for display: Add nodes at source voltage Input to input coil (between Rsource and Coil) Input to cable and load termination Click simulate, a graph should appear Click square box icon to enlarge graph; select the AC Analysis tab if necessary Click lower graph (phase plot); click grid icon on tool bar; the lower graph should show a grid pattern

Click the upper graph (voltage), click grid icon Click the paper-and-pen icon to set the graph values Click the icon with the colored horizontal lines; the node values appear for each curve Title: TL-24ga-H-88coil-1.136mi-AC-Analysis Click table for left axis tab Label: Voltage dB Axis: enable check mark, pen size = 0, select black Scale: Decibel dB Range: Minimum = -40 (choose a value that gives a good ability to read the curves) dB Range: Maximum = 0 Divisions should be set so the desired value of each scale division is fixed and gives enough resolution to the curve. For the –40dB range, 8 divisions give 5dB per division. Frequency = 1, Precision = 1, Scale = 1 Select the bottom axis tab Label: Frequency Axis: enable check mark, pen size = 0, select black Hz Range: Minimum = 100 Hz Range: Maximum = 10000 or 20000 Division for the LOG scale of frequencies is best at 9: Freq = 9, Scale = 1 Click the lower graph to select phase settings and proceed as above. It is ok not to set up the phase plot. Click the Bode tab and set the data for the Bode graph by clicking the graph first Click the grid icon and the paper-and-pen icon Title: TL-24ga-H-88coil-1.136mi-Bode-Attenuation Select left axis tab Label: Attenuation Loss dB Scale: Decibel Hz Range: Maximum = 20


39

Hz Range: Minimum = 0 Divisions for 5: Freq = 1, Precision = 0, Scale = 0 Select bottom axis tab Label: Frequency Scale: Logarithmic Hz Range: Maximum = 10000 Hz Range: Minimum = 100 Divisions for 9, Freq = 9, Precision = 0, Scale = 1

Multisim Run 2 – Transmission Line without Loading Coil

Repeat Run 1 with the inductance of the coils set to zero. Multisim Run 3 – T Section with Loading

Set component values for the 24-gauge line. T arm values are each half of the total value, and the cable and coil values are added together. The model is that of the lumped-circuit (conductance, G is usually not included). The values in per-mile must be multiplied by the coil separation in miles. After computing the component values, follow the Analysis procedure as in Run 1.

Set each coil arm:

(RTotal / 2) and (LTotal / 2)

LTotal = (Lline • coil separation) + Lcoil

RTotal= (Rline • coil separation) + Rcoil

Set the center leg:

Cline • coil separation

Multisim Run 4 – T Section without Loading

Repeat Run 3 setting the following component values:

Set each coil arm:

½ • (cable inductance, Lline per mile) • (section length in miles) Set each resistive arm:

½ • (cable inductance, Rline per mile) • (section length in miles)

Set the center leg:

(Cline per mile) • (section length in miles)


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Matlab Questions 1. Which Runs and Graphs show curves that relate the circuit attenuation directly to the attenuation constant,

where Loss = 8.686 • alpha • length?

2. Why is a middle line section approach with terminations equal to its characteristic impedance? 3. Why does the condition of high inductance or high frequency equate to using realistic values for the

terminations? 4. What are the effects on cable attenuation due to adding distributed inductance? 5. In terms of cable attenuation, how does adding lumped-circuit inductive loading differ from additional

distributed inductive loading? Compare at both the lower frequency range and higher frequency range. 6. Why are insertion loss and attenuation curves in Graphs 1 and 2 basically the same? 7. A transmission line’s equivalent circuit for a short section at low frequencies is reduced to an equivalent

circuit of lumped components. Therefore, adding coil loading is the same as increasing the cable’s equivalent lumped-circuit values. This is then a circuit’s approach to the validation of Campbell’s mathematics. Campbell’s formula showed that for short distances between loading coils, the coil value is added on a per-unit-distance basis directly to the cable parameter. This is especially true when evaluating the propagation constant and the attenuation constant.

Compare the equivalent T section to the transmission line section; compare each in both the lower frequency range and the higher frequency range, and the cut-off region:

a. Low inductance T to low inductance line b. High inductance T to coil-loaded line c. High inductance T to distributed loaded line

8. Identify deviations in Campbell’s theory from the graphs. 9. Using the Approximation formula for a low inductance cable section with matched impedance, calculate

alpha:

alpha = √ [(ω • Rline-per-mile • Cline-per-mile) / 2]

10. Calculate the attenuation constant, 8.686 • alpha • length at frequencies: 300, 500, 1000, 2000 and 4000 Hz 11. Plot the results, Loss = 8.686 • alpha • length as Graph 1 where l is the section length. Explain how the

calculated curve may differ. 12. Using the Approximation formula for an added inductance cable section, calculate alpha:

alpha = [(Rline-per-mile / 2) • √ (Cline-per-mile / Ltotal-per-mile) + (Gline-per-mile / 2) • √ (Ltotal-per-mile) / Cline-per-mile)]

13. Calculate the attenuation, 8.686 • alpha • length 14. Plot the result for 8.686 • alpha • length onto Graph 2 as a horizontal line –the agreement in the low

frequency range. 15. Calculate the cut-off frequency, Fc; plot this value onto Graph 2 as a vertical line:

Fc = 1 / [(π √(Lcoil • Ccable • D)]


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16. Calculate the attenuation above the cut-off frequency for frequencies 4000 Hz and 5000 Hz and plot onto

Graph 2:

alpha = cosH-1 [2 (f/Fc)1/2 – 1] or

Let K = 2 (f/Fc)1/2 – 1, then alpha = Ln [( K + √(K2 – 1)] 17. Compare the attenuation and insertion loss performance for the realistic termination graphs (Runs 3 and 4);

note only the differences. 18. Compare the matched termination graphs to the realistic termination graphs; what are the basic differences? Multisim Questions 1. From Run 1 graphs, calculate the attenuation at 500Hz (the frequency at which the Bode curve shows

minimum attenuation), and at the 3dB frequency and at 4000 Hz. 2. Compare the calculated results in Question 1 to the results from the Bode attenuation curve. 3. Calculate the insertion loss at the same frequencies as in Question 1. 4. Compare the insertion loss values to the attenuation values; explain any differences. 5. Compare Questions 1 and 3 results to the Matlab graph in Run 4, Realistic Terminations with Added

Inductance. 6. Compare the curves from Run 3, T Section with Loading to the curve generated in Run 1, Transmission Line

with Loading Coil Inductance; note the differences; explain possible causes.


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Figure I: (Run I) Matched Terminations without added inductance

Figure II: (Run II) Matched Terminations with added inductance


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Figure III: (Run III) Realistic Terminations without added inductance

Figure IV: (Run IV) Realistic Terminations with added inductance


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Figure V: (Run V) Realistic Terminations without added inductance at 4 miles

Figure VI: (Run VI) Realistic Terminations with added inductance at 4 miles


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Figure I: (Run I) Transmission Line with Loading Coil Inductance

Figure II: (Run II) Transmission Line without Loading Coil Inductance


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Figure III: (Run III) T Sectin with Loading Coil Inductance


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Figure IV: (Run IV) T Sectin without Loading Coil Inductance


48

Experiment # 5

Telephone DC Local Loop with TLS Objectives

1. Learn to use standard telephone equipment to trace signals to the main distribution panel, including the use of the telephone line simulator.

2. Measure and determine DC resistance under various operating conditions. 3. Measure and determine DC equivalent circuit of the local loop. 4. Measure the DC signaling loop-start.

Equipment

Telephone Line Simulator (TLS) Black Box Corporation Model TS215A RJ-11 line cords Breakout box DC power supply Tone generator 66 Punch-down (PD) block Line-aid amplifier Variable resistor (decade box) Main Distribution Frame (MDF) panel Digital multi-meter


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Run 1 – Trace and Identify Wiring Figure 1 Main Distribution Frame / Punch Down Block

MDF Board

66 Block Brunch

RJ-11 Cord

RJ-11 Cord

Telephone Set

Recepticle Box/Breakout Box

Ring(-)

Tip(+)

Ring(-)

Ring(-)

Tip(+)

Tip(+)

T

R

Tone Generator

A) Trace the wiring

1. If connected, disconnect the telephone line cord from the RJ-11 box. 2. Use the Tone Generator and Craft Test Set to trace the wiring from the bench’s PD block to its corresponding

PD block on the MDF. Record pin numbers and wire color codes at each end. 3. Trace the wiring using the Inductive Amplifier (Line-Aid) to the PD block connected to the PBX trunk line.

Record the pin numbers and wire colors. B) Identify the Tip and Ring

1. If the connection from the 66 PD block to the MDF does not provide 48Vdc +/- 10% Tip-to-Ring, then skip to Run 2.

2. Use the Tone Generator, a red LED will illuminate when the black lead is on Tip and the red lead is on Ring. Record the Tip and Ring pins and wire colors at the bench PD block and at the bench RJ-11 box.

3. Repeat B1 using the Craft Test Set; black lead on Tip will illuminate green and reverse will light red.


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Run 2 – DC Equivalent Circuits of the Local Loop Figure 2 Local Loop

Start-up Procedure

1. The TLS power cord should be disconnected. Using an RJ-11 line cord, connect an RJ-11 receptacle box to the TLS.

2. Connect a second RJ-11 box to the first box by cross-connecting wires (red to green and green to red). This step is necessary, as the RJ-11 cord causes a cross-connection of the Tip and Ring voltages from the TLS to the RJ-11 box.

3. Connect a 0.08-inch pin probe into the TLS chassis ground reference jack (back panel). 4. Jump the ground probe to a laboratory ground point (any Earth ground point including trunk conduit pipe). 5. Current flows from the TLS Tip to the telephone, or to the TLS Ring from the telephone. Connect a DC

ammeter (or DMM with dc current < 200mA range) to the Ring-side (in series with the telephone and the RJ-11 box).

6. Place the variable resistor (decade box) in series with the ammeter (ring side). Reconnect the line cord. Set the variable resistor to minimum resistance, or zero.

7. Connect the TLS power cord to the AC power outlet. 8. Toggle front panel switch to ON, then OFF, then MAN/RING. Hold the switch in MAN/RING mode until

the POWER LED illuminates and then release the switch. 9. In the ON-HOOK condition (open-circuit), connect the telephone to the second RJ-11 receptacle box.


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Run 2, continued A) Tip and Ring Voltages

1. Use the Tone Generator to identify the Tip and Ring. The red LED will illuminate when the black lead is on Tip and the red lead is on Ring. Record the Tip and Ring wire colors at the RJ-11 box connected to the telephone.

2. If skipped Step B1 in Run 1, repeat the above step using the Craft Test Set; black lead on Tip will illuminate green and reverse will light red.

3. Measure and record the open-circuit DC voltages:

ON-HOOK (open-circuit)

Tip to Ring (Vdc)

Tip to Ground (Vdc)

Ring to Ground (Vdc)

B) Telephone DC Resistance due to TLS

1. In the OFF-HOOK condition (closed-circuit), measure and record the voltage, Tip-to-Ring. 2. If it’s necessary to use the same meter to measure voltage and current, disconnect the line cord from the RJ-

11 box to the TLS before changing meter positions (from box end to TLS). Current flows from the TLS Tip to the telephone, or to the TLS Ring from the telephone. Connect a DC ammeter (or DMM with dc current < 200mA range) in series with the telephone and the RJ-11 box. Reconnect the line cord to the RJ-11 box. The ammeter should read 0.00mA.

3. In the OFF-HOOK condition, the ammeter should read 0-30.0mA; record the current. C) Thevenin DC Equivalent Circuit

1. If it’s necessary to use the same meter to measure voltage and current, disconnect the TLS before changing meter positions. Reconnect the TLS to the RJ-11 box. In the OFF-HOOK condition (closed-circuit), measure and record the voltage Tip-to-Ring and compare to the value in Step B1; there should be no change in voltage.

2. Measure and record DC voltages:

OFF-HOOK (closed-circuit)

Tip to Ground (Vdc)

Ring to Ground (Vdc)

3. Confirm the total Thevenin equivalent TLS resistance, R = Vopen-circuit / Iclosed-circuit by placing a jumper wire

(short) across the Ring-to-Tip on the RJ-11 box. Record the current. D) Loop Ground Location To determine if the Local Loop ground is located on the battery (source) side or the load (telephone line) side of the Tip-side source resistor (ballast RB1):

1. Place a jumper wire across Tip-to-Ring and record the voltage from Tip-to-Ground. Zero voltage indicates the ground is on the telephone line side of RB1. Any other value than zero indicates the ground is on the source side of RB1.


52

Run 3 – Local Loop DC Signaling Characteristics Refer to Figure 2 and the start-up procedure. A) Loop Start Current and Local Loop Length

1. Set the variable resistor to zero. 2. Go on-hook then off-hook, listen for dial tone and hang up. 3. Increase the variable resistance to maximum and repeat Step A2; there should be no dial tone. 4. Keep listening to the phone while decreasing the variable resistance value until the dial tone reappears.

Record the DC current and voltage at the variable resistor, and record the resistance value at this point. Note: the TLS specifies loop current ≥ 15mA.

5. Reduce the variable resistor to 0Ω. 6. Go on-hook and then off-hook; there should be a dial tone followed by a reorder tone. 7. Increase the variable resistance until the phone goes off. This condition can be determined by blowing into

the microphone and not detecting a sidetone (feedback of sound in the earpiece). Record current. The TLS specifies ≤ 10mA.

Run 4 – Non-Linearity of the Telephone Set Resistance

1. If it’s necessary to use the same meter to measure voltage and current, disconnect the TLS before changing meter positions. Reconnect the TLS to the RJ-11 box.

2. Turn off the DC power supply and connect it to the RJ-11 box (TLS side): positive to Tip and negative to Ring.

3. Set the variable resistor to maximum resistance. 4. Set the DC power supply knob at 0Volts and turn on. Raise the voltage slowly to 3.0V. 5. Go off-hook. The ammeter should read a low current; record this value. 6. Raise the voltage slowly to 30.0V. The ammeter should read less than 5mA; record this value. 7. Set the variable resistance until the voltage across the telephone is 3.0V; record the current. 8. Change the variable resistor value to 15.0V in 2.0V increments; record the current at each interval.


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Questions 1. Knowing that the chassis ground is connected in some manner to the TLS source voltage, is the ground

connected at the Tip-side, Ring-side or somewhere between (split battery connection)? 2. Explain the current flow direction. 3. Calculate the telephone’s DC resistance. 4. Calculate the equivalent resistance in each wire leg looking back into the TLS. Use voltage values from Run 2:

Step C2 voltage across telephone (off-hook) Step B1 or C1 voltage Tip-to-Ring (on-hook) Step B3 current in the circuit (off-hook) Question 3 telephone DC resistance

RB1 + RB2 = RTotal = [Vtip-ring (on-hook) – Vtip-ring (tele off-hook)] / I (tele off-hook) RB1 = Rsource(tip-side) = Vtip-ground(tele off-hook) / I (tele off-hook) RB2 = Rsource(ring-side) = RTotal – Rsource(tip-side)

Vring-ground(tele off-hook) = I (tele off-hook) * Rsource(ring-side) – Vtip-ring(on-hook) Vtip-ring(on-hook) = I * Rsource(ring-side) + Rsource(tip-side) + Rtelephone

5. Calculate the equivalent Rsource of the TLS and compare it to the result from Question 4. In theory, the TLS

simulates a central office (CO) or PBX. Source resistors (ballast) of a CO or PBX are typically 200Ω in each leg. The TLS output resistance may be larger to include the effects of local loop wiring.

On-hook voltages from Run 2 Step A3 would be divided by the corresponding off-hook currents: Tip-to-Ring, Tip-to-Ground, and Ring-to-Ground. These calculations result in the source resistance (Thevenin’s equivalent impedance) in each leg of the TLS output circuit. Note: 0/0 is indeterminate, but RB2 = RTotal – RB1.

RB1 + RB2 = RTotal = V tip-ring (on-hook) / I tip-ring (off-hook)

RB1 = V tip-ground (on-hook) / I tip-ground (off-hook)

RB2 = V ring-ground (on-hook) / I ring-ground (off-hook)

6. Explain how the method in Run 2 Step D determines the ground location. 7. Draw the complete DC Thevenin equivalent circuit of the TLS. 8. Calculate the resistance using the voltage and current from data in Run 3 Step A4. 9. Calculate the local loop cable length that the resistance in Question 8 represents for 26-gauge and 19-gauge wire. 10. Plot the volt-ampere and telephone resistance curves with voltage as the independent X-axis. 11. Draw the load line on the volt-ampere curve for the condition of the Tip-to-Ring voltage (on-hook) and the

Thevenin equivalent resistance found in Run2. 12. Compare the curve intersection point, voltage and current to the values of voltage and current measured in Run 2,

Steps B1 and B3. 13. Find the telephone resistance from the resistance curve for the load line points of Question 12 and compare the

value to the telephone resistance calculated in Run 2 (Question 3).

You may use the following MATLAB program TCET2102_Lab5 to plot and answer Questions 10-13.


54

Telephone DC Resistance MATLAB program: This program calculates and plots the volt-amp and DC resistance characteristics from the data measurements taken in the laboratory. Enter the number of voltage-current data point pairs 7 x =

0 0 0 0 0 0 0 y =

0 0 0 0 0 0 0 For data point pair 1 Enter voltage 3.1 Enter current in milliamps 2.5 For data point pair 2 Enter voltage 4 Enter current in milliamps 8.1 For data point pair 3 Enter voltage 4.3 Enter current in milliamps 9.1 For data point pair 4 Enter voltage 5 Enter current in milliamps 13 For data point pair 5 Enter voltage 5.9 Enter current in milliamps 23 For data point pair 6 Enter voltage 7 Enter current in milliamps 39 For data point pair 7 Enter voltage 10.1 Enter current in milliamps 82


55

Enter the polynomial degree of fit 2 To plot the telephone resistance curve, enter 1 r1

1.0e+003 *

1.6400 0.4938 0.4725 0.3846 0.2565 0.1795 0.1232 Enter the polynomial degree of fit for resistance 3 Load Lines To plot a load line, enter 1. To stop use 0 Assume Rballast 1 & 2 inside C.O. = 400 ohms Enter wiring resistance Kohms from C.O. to Tel. 1.3 Enter C.O. battery voltage, V open circuit 51 To plot a load line, enter 1. To stop use 0 Assume Rballast 1 & 2 inside C.O. = 400 ohms Enter wiring resistance Kohms from C.O. to Tel. .6 Enter C.O. battery voltage, V open circuit 51 To plot a load line, enter 1. To stop use 0 To plot the telephone resistance vs. current, press 1 Enter the polynomial degree of fit for curve 2 t =

2.5000 8.1000 9.1000 13.0000 23.0000 39.0000 82.0000 c = 1.0e+003 *

0.0005 -0.0508 1.1791 t_fine = Column 1 through 12

0 5 10 15 20 25 30 35 40 45 50 55 Columns 13 through 21

60 65 70 75 80 85 90 95 100


56

To calculate ratios of telephone DC resistance to line Resistance + telephone resistance, press 1. To stop = 0 Read the resistance from either plot 2 or 4 at the voltage or current values determined from the intersection of the Load Lines and the volt-amp curve Plot 3 Enter determined telephone resistance 250 Enter resistance for selected Load Line 1300 Tel. Res. / (Tel. Res. + Line Res.) =

0.1613 To calculate another ratio, press 1. Stop press 0 Read the resistance from either plot 2 or 4 at the voltage or current values determined from the intersection of the Load Lines and the volt-amp curve Plot 3 Enter determined telephone resistance 250 Enter resistance for selected Load Line 600 Tel. Res. / (Tel. Res. + Line Res.) =

0.2500 To calculate another ratio, press 1. Stop press 0

1.3 kΩ

0.6 kΩ

Use Log plot

Use Log plot


57

Experiment # 6

AC and Tone Local Loop Signaling Characteristics Objectives

1. Study the local loop AC and tone signaling characteristics 2. Learn How to measure and record the 90Vrms offset ringing signal from oscilloscope observations 3. Learn how to measure the properties of the progress tones 4. Learn how to measure the properties of the telephone’s address signals (DTMF) 5. Learn how to use the telephone line simulator (TLS) to provide signaling functions

Equipment

(2) touch-tone telephones (electronic) with RJ-11 cords Optional: classical Bell-500 telephone (pulse-dialing) Telephone Line Simulator (Black Box Corporation, model TS215A or equivalent) Ground lead with 0.08-inch pin (for TLS ground socket) RJ-11 line cord with RJ-11-4 connectors (to RJ-11 receptacle box from TLS) (2) RJ-11 receptacle boxes Audio Test Set (Electrodata Inc. or equivalent): AC signal generator 250Hz to 4kHz, 0-2Vrms, 600Ω Rout Voice Frequency Monitor (Electrodata Inc. or equivalent): +6dB to –50dB true RMS Oscilloscope with 1:1 and 10:1 probes Analog or digital ammeter 0mA to 100mA Digital multi-meter (non-true RMS, AC/DC volts 0.2V to 200V, 200Ω to >10MΩ, AC/DC current 0.2mA to > 200mA Screwdrivers (flat and Philips head) (4) jumper leads with alligator clips

Notes:

1. Reference the instructor’s handouts, “The Local Loop and Signaling” and “The Telephone Set”. See See “TC320 Equipment Manual”, TS215A manual, course textbook and class notes for telephone operation, TLS operation and other equipment.

2. (4) touch-tone phone sets are connected to the TLS directly through the RJ-11 receptacles and RJ-11 telephone cords. An alternate connection may be implemented: each phone at its bench is connected through an RJ-11 connection box to a 66-punch down (PD) block with two wires (tip and ring), which are color-coded. Each bench PD block is connected to a corresponding PD block on the MDF with corresponding pins and colors through a trunk cable. All the PD blocks corresponding to each bench are cross-connected to a single PD block, which is connected to the TLS.

3. Answer all questions after procedures are completed and all the data has been recorded. Show answers, calculations and diagrams in the Q&A section of this experiment. Be sure to reference each response to the procedure or additional questions.

4. Conclusions should respond to the objectives with concrete examples. Deviates from the ideal concepts should be explained. Limitations and practicalities of implementing the test and alternative techniques should be discussed.

5. Report format: folder cover with title and squad names; table of contents with page numbers; procedure with data (use the handout procedure sheets, do not retype); answers to questions (do not repeat the questions); conclusions.


58

Procedure Run 1 – Ringing waveform measurements Caution: must be taken since this test involved high voltage, 90Vrms. Before proceeding with this run, obtain the instructor’s advice, observation and permission to proceed.

1. Connect the circuit as per Figure 1; insert figure here.

2. Connect the 10:1 probe from the oscilloscope to the telephone. Place the probe on the RING pin (red wire) on the RJ-11 receptacle to the telephone, and the probe ground on the TIP pin (green wire). Note: the probe ground may also be left unconnected. The lab instructor should check the connections before proceeding.

3. The instructor shall demonstrate and program some additional features:

a) Program the second line number for each phone to have continuous ringing. b) Lift off-hook line 1 with all other lines: 2, 3 and 4 on-hook and dial **99##*23#30#0# # then dial 02

*23#30#0# # c) repeat for lines 3 and 4

4. Set the oscilloscopes’ vertical scale for 5.0 volts/box and the time base for 5 or 10 ms/box. Set the

oscilloscope’s DC ground level for the horizontal centerline.

5. One squad should not call the other unless directed by the instructor. Each squad is to call itself on the phone connected to the RJ-11 receptacle box. Phone numbers: For squad 1, dial 101 and dial 102, and for squad 2, dial 103 and dial 104.

6. From physical observation, record the ringing cadence (on-time and off-time duty cycles).

7. An unusual characteristic of the TLS is that it may generate the ringing signal by digital simulation of the

analog sine wave. The TLS’ offset level during the ringing-off interval is also unusual. Record the waveform:

peak positive number of boxes

peak negative number of boxes

volts per box

probe ratio 10:1

time per box

one period of the waveform

DC level offset during signal on and signal off

8. Lift the handset, say “hello” to your caller. The ringing should stop and the caller should hear you and hang

up. Repeat the call and have the caller hang up again. Verify: ringing will stop and the call is again terminated.

9. Dial as before to the second number. This shall cause a continuous ringing allowing the waveform to be

drawn. Draw the waveform exactly as it appears on the scope, and the gradual boxes for amplitude and time, and the scale settings.

10. Reverse the probe connections, oscilloscope on the ring pin. Have you phone called. Record your

observations and draw the waveform again.


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Run 2 – Progress Tone Measurements Discussion

The progress tone easiest to measure is the Dial Tone, since it is on for approximately 20 seconds. The other tones have on-off duty cycles, which make measurements difficult unless a storage scope or digital sampling is used. However, the TLS makes it possible to program a continuous mode. All of these signaling tones are composed of two or more superimposed sinusoidal waveforms of different frequencies. When viewing any of these signals on a scope, the pattern appears to be a random varying waveform.

However, for the case where there are only two sinusoids of equal amplitude and close frequency (relative to 0Hz), the pattern can be made to appear as double sideband suppressed carrier (DSB-SC) waveform with careful triggering and a proper time base selection.

Refer to Young, chapter 8. Refer to B.F. Wilensky observation (figures on next page) For two approximately equal signals with close frequencies F1 and F2, a DSB-SC with envelope frequency FM = (F2 – F1) / 2 appears to be modulating a modulated signal of frequency Fc = (F2 – F1) / 2 with Fc >> FM Letting ω1 = [(ωc – ωm)t] and ω2 = [(ωc + ωm)t], the DSB-SC nature of the tones with two frequencies can be explained as follows:

2 cos (ωT) cos(ωct) = cos [(ωc + ωm)t] + cos [(ωc – ωm)t] Therefore, by measuring the periods of the modulating envelope Tm and modulated Tc waveforms, the frequencies of the two signals can be approximated: F1 = Fc – Fm and F2 = Fc + Fm. Note that the produce of the cos terms, the cos ωmt terms acts as an amplitude envelope of the cos ωct term when ωc is >> ωm. As an example: F1 = 500, F2 = 550, then Fc = 525 and Fm = 25. This shows that the carrier will go through 525/25=21 cycles for each modulator cycle. If the frequencies are far apart then the waveform will appear as a sinusoid riding on top of another sinusoid. Scope figure here? Note that the scope measurement will only be approximate due to the difficulty in the lack of precision in reading the carrier frequency. Another factor that affect the result is unequal signal amplitudes. A better way to determine the frequencies is to use a spectrum analyzer. Measuring power in dBm of two sinusoids or complex waveforms The spectrum analyzer is also a good way to determine the power levels. However, dBm measurements using a true RMS reading instrument such as an ATS will be more than adequate. Note that a typical voltmeter is an average or peak reading device. Therefore, RMS voltage and dBm results are inaccurate when reading complex signal combinations. The voltage that a true RMS reading instrument such as an ATS will show:

Vrms total = √ (V1rms)2 + (V2rms)2 dBm = 10 Log [(Vrms total)2 / (600 * 0.001)]

A determination of the envelope amplitude on the scope can be used to calculate the power and dBm of the dial tone. It should be recognized that due to the AC balance to ground of the network, it is best to do measurements differentially floating with respect to ground. The ATS provides this feature, while the scope will create a short around the TIP-side resistance (probe on RING will measure ring-to-ground bypassing the power lost in the TIP-side of the transmission line and the TIP-side of the ballast resistor). From the produce of two sinusoids, we have sideband amplitudes that are half the total amplitude of the amplitude of the modulated waveform. It is assumed that R = 600Ω; if not, the dBm correction must be applied:


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10 Log (600 / Ractual) From the oscilloscope:

(Vpp envelope / 2) * (.707) / 2] = Vrms sideband1 = Vrms sideband2

Power = [(Vrms sideband1)2 / R] + [(Vrms sideband2)

2 / R] If the dBm of each individual sinusoid were measured, the total dBm must be found from converting back (from

the antilog) to the Vrms values and combining as above. dBm values cannot be added, but can be subtracted to

give power dB whereas dB values can be added or subtracted.

Run 2 Procedure 1. Do not connect the scope ground. Using the phone connected to the RJ-11 receptacle, connect a 1:1 probe from

channel 1 to the RING wire. 2. Adjust the scope for 0.5 volts/box or less as required, and 0.5 ms/box or as required 3. The phone should be on-hook and connected. Lift the handset and observe the waveform and record the period,

Tm of the modulation envelope (the zero-crossings (valleys) are best to use. See Figure next page. 4. Record the envelope peak-to-peak amplitude. 5. Readjust the scope controls to obtain more detail for the modulated waveform. It is not necessary to maintain the

DSB-SC waveform; see next page. Record the period, Tc of the modulated signal. 6. Hang up the handset. 7. Connect the ATS or equivalent and the DMM (set for AC voltage) across the phone Tip-to-Ring; record the dBm

and AC voltage. 8. Lift the handset and dial another phone, which should not be answered; allow it to keep ringing. Observe the

waveform on the scope. 9. Repeat Step 8 with the other phone off-hook.


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Run 3 – Dual-tone Multiple Frequency (DTMF or touch-tone) Discussion; refer to handout notes Procedure 1. Measure and record the following waveforms at the RJ-11 receptacle. Lift the handset of the specially marked

phones and obtain a dial tone. Record values from the three instruments for each:

a Press any single button on the dial pad b Press any two buttons that are diagonal c-f Press two buttons in the same row for each of the four rows g-i Press two buttons in each column for each of the three columns

Procedure ATS (dBm) ATS (freq) DMM (Vrms) Scope (Vpp) Scope (period) a

b

c

d

e

f

g

h

i


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Questions 1. Why is the probe connected as per Run 1 Step 2? 2. From Run 1 measurements, calculate the frequency, DC peak maximum and minimum offset voltages from the

theoretical 90Vrms waveform superimposed on the open-circuit DC voltage. Compare your calculations to the observed scope values. See the figures in the literature or handout.

3. Explain why there is an offset during the signal. Use circuit analysis to prove your explanation. 4. What happened when the probe connections were reversed in Run 1 Step 10? Note the DC current path from the

source side of RB1 to scope ground at the RING-side of the telephone. 5. Why was a 10:1 probe used? 6. Calculate the two frequencies F1 and F2 that make up the dial tone. Use concepts and formulas given in the

Discussion. Compare the results to the values in the literature or handout, “Local Loop” and “The Telephone Set”.

7. List the other progress tones and their frequencies and duty cycles (cadences). 8. Calculate the dBm value from the results of the scope measurements in Run 2 Step 4. Use the concepts and

formulas given in the Discussion. Calculate the dBm value from the results of the voltage reading from the DMM in Run 2 Step 7. Compare both of these calculations to the ATS reading in Run 2 Step 7.

9. Comment as to the characteristics of the waveform in Run 2 Step 8 and its differences from the 90Vrms ringing

signal recorded in Run 1. How does this waveform compare to the literature? 10. Comment about the differences between the busy signal and the ring-back signal. 11. Compare each row and column frequency measured in Run 3 to the frequencies in the literature. Are the

measured values within the frequency limits of the DTMF specifications? 12. Calculate the total dBm from the individual tones measured in Run 3, Steps c-f and compare to the total dBm

values obtained from Step a. 13. For the dual-tone of a single pressed button, explain any differences between the dBm calculated from the DMM

voltage and the dBm measurement from the ATS.


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Experiment # 7

Voice, Sound, Noise and AC Impedance Objectives

1. Study the characteristics of sound and voice: wave shape, frequency, power and response 2. Learn how to measure noise an signal-to-noise 3. Learn how to measure and determine the AC impedance of a telephone 4. Learn how to operate the Audio Test Set 2

Equipment

(2) touch-tone telephones (electronic) with RJ-11 cords Optional: classical Bell-500 telephone (pulse-dialing) Telephone Line Simulator (Black Box Corporation, model TS215A or equivalent) Ground lead with 0.08-inch pin (for TLS ground socket) RJ-11 line cord with RJ-11-4 connectors (to RJ-11 receptacle box from TLS) (2) RJ-11 receptacle boxes Audio Test Set (Electrodata Inc. or equivalent): AC signal generator 250Hz to 4kHz, 0-2Vrms, 600Ω Rout Audio Test Set 2 (ATS2) (Electrodata Inc.) Voice Frequency Monitor (Electrodata Inc. or equivalent): +6dB to –50dB true RMS Oscilloscope with 1:1 and 10:1 probes Analog or digital ammeter 0mA to 100mA Digital multi-meter (non-true RMS, AC/DC volts 0.2V to 200V, 200Ω to >10MΩ, AC/DC current 0.2mA to > 200mA 500Ω resistance (two, 1kΩ ½-watt resistors in parallel) 50Ω resistance (two, 100Ω ½-watt resistors in parallel) Screwdrivers (flat and Philips head) (4) jumper leads with alligator clips

Notes:

1. Reference the instructor’s handouts, “The Local Loop and Signaling” and “The Telephone Set”. See “TC320 Equipment Manual”, TS215A manual, course textbook and class notes for telephone operation, TLS operation and other equipment.

2. Four (4) touch-tone phone sets (two per squad) are connected to the TLS directly through the RJ-11 receptacles, and RJ-11 telephone cords.


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Run 1 – Voice Sounds A) Single tone simple whistle

This is a two-phone set-up. Call another phone and have it answered before connecting instruments.

1. With the scope ground unconnected, connect the scope only at the calling phone’s RING pin. 2. Connect the ATS input: black lead to the talker’s telephone TIP and red lead to the talker’s RING. 3. Connect the VFM black lead to the listener’s TIP and the VFM red lead to the listener’s RING. 4. Connect two DMM’s (AC voltage), one at the talker and one at the listener. 5. Someone whistles into the talker’s phone at a normal sound level, while someone else listens at the other

phone. Record all readings simultaneously: ATS (dBm) ATS (freq) VFM (dBm) DMM (Vrms) Scope (period)

Talker

Listener

B) Continuous Complex Tones

1. Repeat Step A with a sustained sound, “ahhh” instead of the whistle. Record values simultaneously: ATS (dBm) ATS (freq) VFM (dBm) DMM (Vrms) Scope (period)

Talker

Listener

2. Repeat Step A with another sustained sound, “oooo”. Record values simultaneously:

ATS (dBm) ATS (freq) VFM (dBm) DMM (Vrms) Scope (period)

Talker

Listener

Run 2 – Responses to Sound A) Loudness Evaluation


1. Connect the ATS output to the talker’s telephone TIP (ATS black lead) and ring (ATS red lead). 2. Connect the ATS input and the VFM (black lead to the listener’s TIP and the red lead to the listener’s

RING). 3. Set the power level at the TIP and RING of the listener’s telephone to –8dBm at 1004Hz. 4. The listener should be listening. At both phones, cover the microphone to prevent any sound pickup. Adjust

the ATS output until the listener feels the sound level is normal. Record the listener’s ATS and VFM power readings in dBm.

5. Increase the output until the listener feels the sound level has doubled. Record the dBm at the listener. 6. Return to the original level and then decrease the ATS output until the loudness is half of the level of that

considered to be normal. Record the dBm at the listener. B) Sensitivity Evaluation


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1. Repeat setup in Run 2A Steps 1-4. Record the dBm at the listener. 2. Adjust the ATS output clockwise so the listener just perceives a noticeable increase in sound. Record the

dBm at the listener. 3. Decrease the ATS output counter-clockwise until the listener just perceives a decrease in sound. Record the

dBm at the listener.

Run 3 – Signal and Nose A) Signal-to-Noise Sensitivity.

1. Repeat setup in Run 2A Steps 1-4. 2. Turn the ATS level completely counter-clockwise to eliminate all input sound. A squad member should

listen at the listener’s phone to confirm the 1004Hz signal cannot be heard. However, the listener should be aware of some type of noise or disturbance. If necessary, create some noise at the talker’s phone. Record the noise at the listener’s end in dBm.

3. Slowly increase the ATS output to 1004Hz until the listener feels the noise is not noticeable and only perceives the 1004Hz signal. Record the signal dBm level.

Run 4 – Sound Resonance (Optional)

This is a two-phone set-up. Disconnect the ATS output leads from the talker’s TIP and RING, Place the talker’s telephone microphone next to the ATS sound speaker’s output.

1. Connect an oscilloscope at the listener’s end. Set the ATS output level for –8dBm at the listener’s end. Vary

slowly the ATS frequency from 250Hz to less than 3.5kHz. Record the signal amplitude variations (maximum and minimum) versus frequency.

Run 5 – AC Impedance Discussion – test method

Refer to Figure X. In order to control the DC current levels and void interference from the PBX or CO, a variable DC power supply is used to simulate the Local Loop DC current source. Aside from noise and signal disturbance, the PBX or CO would add parallel loading. The DC current should be varied to see how biasing affects the AC impedance.

The 500-1000Ω fixed value resistor limits the source current and simulates the Local Loop and ballast

resistance. The 50Ω resistor allows the current to be measured as a voltage drop, and it is placed TIP-side since this provides a ground point that is compatible with the oscilloscope ground. The scope is AC coupled on both cannels to block the DC voltage values from swapping the AC observation.

The ATS or equivalent is used to simulate AC signals at realistic voltage levels and allows the necessary audio

frequency range variation. The ATS has a 600Ω output resistance and is DC isolated to at least 25Vdc (more than the off-hook voltage across the telephone).

Procedure


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Connect the circuit per Figure X (page 74 of original manual)

1. With the telephone handset off-hook, set the current Idc by varying the DC power supply. Record the DC voltage across Ring-to-Tip.

2. Set the ATS for approximately – X dBm and verify that the voltage is XVpp on the scope. Keep the ATS AC voltage constant across the telephone for all the frequency and DC current levels.

3. Vary the frequency for each DC current setting according to the chart below. Record the voltage peak-to-peak values for oscilloscope channel 2.

4. Record the phase shift difference between channels 1 and 2 waveforms. 5. Repeat Step 4 for AC voltages corresponding to 0dBm (0.775Vrms). 6. Calculate the magnitude1, Ztel1 and phase angle θtel from the data recorded. 7. Plot a graph, Ztel1 and θtel versus frequency for each current level.


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Run 5 Data Sheet

Frequency (Hz) 400 1000 2000 3000 3500 4000 Vdc (Tip-to-

Ring)

2.2Vpp AC, 0dBm at 600-

ohms

Idc = 40mA

Vpp channel 2

Time channels 1 and 2

Idc = 25mA

Vpp channel 2


1.0Vpp AC, -6.8dBm at 600-

ohms

Idc = 40mA Vpp channel 2


Idc = 25mA

Vpp channel 2



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Questions

1. Calculate the dBm from each DMM voltage reading and compare against the ATS and VFM dBm readings.

2. Calculate the frequency from the scope period reading and compare against the ATS reading.

3. Calculate the power dB loss from the ATS and VFM readings (talker to listener).

4. Convert the ratio voltages of the DMM readings to dB and compare it to that calculated from the difference in dBm readings of the ATS and VFM.

5. In Run 1B, repeat the above questions and compare the differences between Run 1 Steps A and B.

6. Compare and explain the wave shapes of the whistle and “ahhh” sound.

7. Comment on the dB value obtained in Run 2 Step A to double loudness from Run 2 in comparison to the

theoretical values for the perceived sound doubling. The student shall research the theoretical values.

8. Comment on the dB result obtained in Run 2 Step B to perceive a change in sound in comparison to the theoretical value. The student shall research the theoretical values.

9. What is the signal-to-noise in dB from Run 3? The student shall determine the theoretical value for

acceptable audio signal-to-noise in dB.

10. Why does the response have peaks and valleys with frequency from Run 4?

Documents

Tc320 Lab Manual_2013