ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
SIGNAL TRANSMISSION LABORATORY
EE 442
(revised version)
Winter 2007
1
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
SIGNAL TRANSMISSION LABORATORY
Page
Acknowledgements
Personal Laboratory Notebook and The Laboratory Report…………………………....0-1
Lab A: Time Domain Transmission Line Analysis…………………………………….A-1
Lab B: Sinusoidal Steady-State Transmission Line Analysis…………………………..B-1
Lab 1: The Network Analyzer ………………………………………………………… 1-1
Lab C: Transmission Line Reflection Coefficient, Impedance and the Smith Chart…..C-1
Lab 2: Impedance Measurements by /2 and /4 Lines ………………………………. 2-1
Lab 3: Transmission Line Parameters ………………………………………………… 3-1
Lab 4: Use of the Smith Chart for Line-Length and Line-Loss Corrections …………... 4-1
Lab 5: The Slotted Line Technique for Load Impedance Measurements ……………... 5-1
Lab 6: Impedance Matching by the Single-Stub Tuning Method ……………………... 6-1
Lab 7: Impedance Matching by the Double-Stub Tuning Method ……………………. 7-1
Lab D: Impedance Matching with Single- and Double-Stub Tuning…………………..D-1
Lab E: Introduction to Electrical Performance Analysis of Printed Circuit Boards …..E-1
Acknowledgements
The Signal Transmission Laboratory Manual was initially developed in 1984 by Dr.
Shien-Yi Ming to incorporate the donation of eight HP 8754A network analyzers into the
laboratory curriculum. The manual allowed Cal Poly students to use network analyzers
in their study of transmission lines, and was used for EE 353, a concurrent laboratory
course for the signal transmission line lecture course, EE 313. The next major revision of
the manual was performed by Dr. Dean Arakaki His revision of the EE 353 lab manual
was used for was used for the 2003-05 catalog curriculum revision for the
electromagnetic courses. The new signal transmission laboratory course was designated
EE 442, a laboratory taken concurrently with the new designated lecture EE 402. In
anticipation of new revisions for addressing the theory of transmission lines first in the
presentation of the two lecture sequence (EE 335 and EE 402) and a curriculum change
to allow the laboratory to be taken concurrently with the first electromagnetic lecture
course EE 335, Dr. Jim Harris revised the manual by developing the five labs A thru E.
This revision incorporated the donation in Fall 2006 of ten new 200MHz digital
oscilloscopes (DSO 3202A) from Agilent Technologies and anticipated the 2007-09
catalog revised laboratory course EE 375 to be taken concurrently with EE 335. This
Winter 2007 revision of the Signal Transmission Laboratory Manual has benefited from
the comments the Microwave and Photonics Technical Area Committee and of a number
of faculty teaching the new laboratory projects including Dr. Xiaomin Jin and Dr.
William Schaffer. It is expected that this manual will continue to be revised and updated
as new equipment is donated to the microwave laboratory to replace the old components
and network analyzers, and the current six workstations are increased to eight, allowing
the number of students per group to be reduced from three to two.
Respectively submitted,
Jim Harris
1/8/07
PERSONAL LABORATORY NOTEBOOK AND THE LABORATORY REPORT
Personal Bound Laboratory Notebook:
Each student enrolled in this laboratory class should document their experience in EE 442
in a personal bound notebook, using the format and knowledge that they have gained in
other Cal Poly laboratory courses. This notebook will not be graded. However, this
personal bound notebook (8 ½ x 11 grid paper recommended) will be used as the only
reference when taking the lab final for this course. In addition, this experience will
continue the development of the documentation of laboratory experiences for all Cal Poly
graduates. Remember - the criteria for your documentation in this notebook is that a peer
could use the contents to reproduce your results with the identical equipment. Please
refer to the write-up at the end of this section for some notes on the format and content of
this notebook (and the report).
The Laboratory Report:
The laboratory report developed after the completion of each lab activity is the main
product of the team's work that is used for evaluation of performance. Writing effective
technical reports is a valuable skill that will enhance your professional career.
The purpose of the laboratory report is to describe the measurement procedure, lab
results, and analysis procedure, and to interpret and discuss the results. The conclusions
indicate the knowledge gained by completing the experiments.
There is no one best format for all technical reports, but the following format is
recommended:
Title and date
Lab team members
Purpose
Equipment
Include ID numbers
Procedure
Circuit diagrams for all measurements taken, with variables defined on diagram
Describe measurement procedures used so a peer could repeat
Chronological record of what was accomplished, including any problems
Record all measurements directly: either separately, in a table, or with a graph; follow
format for tables and graphs presented in the write-up at the end of this section
Include formulas for all calculations with one sample of actual values used
Note all problems encountered
Index the documentation with any numbering used in the manual, if appropriate
Conclusions
Comparison of the expected outcomes of the experiment, derived from theory or
computer simulation, to measured values. One way to compare multiple data sets is to
plot theoretical prediction and experimental data on one graph using different line styles
to distinguish each data set.
A critical part of the conclusion is error analysis. Comparison between theoretical and
experimental results will not always result in perfect agreement. …
Individual paragraphs from each of the team members: A thoughtful, reflective
paragraph which discusses what has been learned during this laboratory experience,
which is signed and
dated.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Time Domain Transmission Line Analysis
Lab A
Purpose: This project introduces the student to the time domain response of transmission lines. The effects
of time (or propagation) delay caused by a transmission line to the step response of a five different loads
will be investigated: matched, mismatched, open circuit, short circuit, and parallel RC. The results will be
discussed in the context of the performance of practical digital circuits. The step response of each load will
be investigated in three ways: using a simulation with PSpice, a mathematical analysis, and a measurement
circuit. For each case, the results of each investigation will be compared.
EE 402 Text
References:
Iskander, Magdy F.; Electromagnetic Fields and Waves; Waveland Press; 2000
Chapter 7, especially sections 7.1-9
Equipment:
HP 3312 Function Generator
Agilent DSO3202A Oscilloscope
2 8m RG 58A/U cable
3 short (around 30 cm) RG 58A/U cables
2 BNC Tees
1 BNC to double banana adapter
BNC-double banana: 50 ohm load resistor; 10 ohm resistor; open circuit; short circuit, parallel RC load (50
ohm and 160 pF)
PSpice on workstation computer
Discussion:
In this experiment, we will use a technique first presented in your lower division circuits laboratory to
observe the step response of a circuit. The technique is to use an appropriately chosen squarewave to
periodically repeat a positive step input to a circuit. Note that a positive DC offset is applied to the
sqaurewave so that the squarewave appears to just be a positive pulse. Then only the positive portion of the
squarewave is observed; however, nothing prevents observation of the effects of the second half of the
squarewave. The period T of the squarewave is determined so that the step response of the circuit is
essentially in steady state at a time T/2, i.e., half the period. This technique allows the periodic voltages
observed with an oscilloscope to be the complete step response. The same basic technique is used to
provide the input voltage waveform for a PSpice simulation (see the template code below).
The unique feature of this project is that with relatively inexpensive, low performance instrumentation and
a long transmission line (16m), we can show the time domain effects of wave propagation, i.e., the step
response of a circuit with propagation delay under different loading conditions. The observed voltages
present the same phenomena as a practical circuit which has dimensions commensurate with the
wavelength of its signals, dim ~ λ = vp / f, where dim is the dimension of the circuit, λ is the wavelength in
the media of the circuit, vp is the velocity of propagation in the media of the circuit, and f is the frequency
of the signal (voltage). In this project the transmission line is an RG 58 A/U which has a velocity of
propagation of about 2 x 108 m/s, which yields a propagation delay of about 80 ns for a 16m cable. Thus
with a 60MHz scope and a 1 MHz squarewave function generator (and properly chosen values for the RC
load to get a reasonable time constant), the effects of the propagation delay can be measured.
Note that the characteristic impedance of the RG 58A/U is 50 ohms. The output impedance of the HP
3312A function generator also is 50 ohms, so the source (function generator) is matched to the transmission
line. This follows because the small length of transmission line (about 30 cm) which connects the function
generator to the oscilloscope also is RG 58 A/U and is matched to the source. The effect of the loading of
the oscilloscope output impedance (parallel 1 Mohm and 14 pF) also is negligible as the time constant due
to the output impedance and connecting transmission lines is estimated to be less than 1ns, and therefore
too small to observe. The effect of the oscilloscope impedance can be simulated though.
Part I (Prelab): PSpice Simulation
Using PSpice, simulate the following circuit for five cases using PROBE to display V(2) and V(3):
a) 50 ohm matched load
b) 10 ohm mismatched load
c) open circuit
d) short circuit
e) parallel RC load (50 ohm and 160 pF)
For each case, provide a copy of the PROBE output for V(2) and V(3), and a one paragraph description of
why the waveform for V(2) has the shape presented in the simulation. Also, to prepare for the experiment
read the Part II (laboratory project), and in particular, review the Exp A Analysis notes. The Exp A
Analysis notes presents a mathematical model for the step response of the transmission line circuits that
students will be asked to use to predict and to understand the phenomena observed.
FG
SCOPE
FF
TL RG 58A/U (16m)
LOAD
d
V(2)
V(3)
Figure 1 Transmission Line Measurement Circuit
Use the following template PSpice code to construct your simulation:
*ee 442 exp A time domain analysis tl_rc
*parallel rc load 50 ohm and 160 pF
vg 1 0 pulse(0 1 0 1ns 1ns .5us 1us) ;0 to 1V pulse, 0 delay, 1ns rise/fall time, 0.5us width, 1us period
rg 1 2 50
t1 2 0 3 0 z0=50 td=80n
;lossless TL: input 2 0, output 3 0, Zo=50ohms, time delay 80ns
r1 3 0 50
c1 3 0 160p
.tran 0.1n 500n 0 0.1n
;transient analysis 0.1ns print step, 500 ns duration,
;tstart=0 (initial print value), tmax=0.1 (max internal step size)
.probe
.end
Part II (laboratory project)
a) Matched 50 ohms Load:
1. The simulation and analysis will now be verified with measurements. Construct the transmission line
circuit given in Figure 1. Use V(2) as the channel 1 input and trigger; connect the first Tee on the scope
channel 1 connection. Connect the banana load with 50 ohm resistor directly to the first Tee (no
transmission line), and observe the voltage V(2) for an input voltage of 1 MHz square wave with 1.0 Vpp
and +500mV DC offset. Provide a sketch of the voltage V(2).
2. Connect the matched load with a 16 meter transmission line, and connect V(3) to channel 2 of the scope
(use the second Tee). Using the same input voltage, observe the voltages V(2) and V(3) for each case.
Provide sketches of the voltages V(2) and V(3) on the same figure.
3. Use the analytic form presented in the analysis to provide sketches for the voltages V(2) and V(3).
Compare the results of the simulation, analysis, and measurement; how close are they?
Discussion: Notice that with a matched load, the reflection coefficient of the load Γ L = 0, and the value of
the reflected (negative going) wave is zero. However the delay observed can have a deleterious effect on
the performance of a synchronous (clocked) digital circuit. The delay in the signal can impact the
satisfaction of the set-up time requirement for flip-flops. Variable delays caused by different length signal
traces can cause clock skew, where the edge of a clock waveform will occur at different times for different
flip-flops. Also, the maximum delay limits the minimum clock period that can be used, i.e., the period
must be larger than the maximum delay for correct synchronous signal interpretation.
b) Mismatched 10 ohms Load:
1. Connect the banana load with 10 ohm resistor directly to the first Tee (no transmission line), and observe
the voltage V(2) for the same source voltage. Provide a sketch of the voltage V(2).
2. Connect the mismatched load with a 16 meter transmission line, and connect V(3) to channel 2 of the
scope (use the second Tee). Using the same input voltage, observe the voltages V(2) and V(3) for each
case. Provide sketches of the voltages V(2) and V(3) on the same figure.
3. Use the analytic form presented in the analysis to provide sketches for the voltages V(2) and V(3).
Compare the results of the simulation, analysis, and measurement; how close are they?
Discussion: Notice that with a mismatched load, the reflection coefficient of the load Γ L = -0.66, and the
value of the amplitude of the reflected (negative going) wave is -0.33V. Now there is not only a delay in
the response for V(3) at the load, but there is a reflected wave that affects the V(2) waveform at the source.
Hence, the waveform voltage at V(2) does not remain constant at 0.5V, and after the reflected wave arrives,
has another value (what is it?). Note that this case is only an example of a mismatch load, and that other
values of a load resistance not equal to Zo will cause different values for V(2) in the steady state. This
change could affect the interpretation of the digital logic level at the source and at the load, and hence give
rise to improper circuit performance.
c) Open Circuit Load
1. Connect the open circuit load directly to the first Tee (no transmission line), and observe the voltage
V(2) for the same source voltage. Provide a sketch of the voltage V(2).
2. Connect the open circuit load with a 16 meter transmission line, and connect V(3) to channel 2 of the
scope (use the second Tee). Using the same input voltage, observe the voltages V(2) and V(3) for each
case. Provide sketches of the voltages V(2) and V(3) on the same figure.
3. Use the analytic form presented in the analysis to provide sketches for the voltages V(2) and V(3).
Compare the results of the simulation, analysis, and measurement; how close are they?
Discussion: The open circuit load shows the effect of a time delay of about 80 ns. The initial V(2) is the
positive going wave only. The change in the value of voltage at the load demonstrates the creation of the
negative going wave; note that ΓL = 1, i.e., the positive and negative voltage wave are equal. Notice what
happens at the source after the reflected wave arrives. At this point in time, the transmission line is in
steady-state, i.e., it has a constant voltage. On a printed circuit board, the effect observed can be caused by
a trace that is not connected, leading to spurious values. However, the effect can be used to advantage; the
PCI bus interface used in PCs uses an open circuit at each end of the bus to increase the voltage level of the
signal lines through the use of the reflected wave from the open circuits.
d) Short Circuit Load
1. Connect the short circuit load directly to the first Tee (no transmission line), and observe the voltage
V(2) for the same source voltage. Provide a sketch of the voltage V(2).
2. Connect the short circuit load with a 16 meter transmission line, and connect V(3) to channel 2 of the
scope (use the second Tee). Using the same input voltage, observe the voltages V(2) and V(3) for each
case. Provide sketches of the voltages V(2) and V(3) on the same figure.
3. Use the analytic form presented in the analysis to provide sketches for the voltages V(2) and V(3).
Compare the results of the simulation, analysis, and measurement; how close are they?
Discussion: Notice the delay in obtaining a value of the voltage at the source of 0V; again, there is a
transient response before the steady-state values are observed for the transmission line. A PCB trace which
is shorted to ground will have the same behavior. The reflection coefficient of the load is ΓL = -1, i.e., the
negative voltage wave is the negative of the positive voltage wave. This leads to the steady-state value of
current (short circuit current) which is limited by the value of the function generator output impedance
which is 50 ohms and which is matched with the characteristic impedance of the transmission line, Z o = 50
ohms.
e) Parallel RC load
1. Connect the banana parallel RC load with 50 ohm and 160 pF directly to the first Tee (no transmission
line), and observe the voltage V(2) for the same source voltage. Note that the load resistor is matched to Zo
and the time constant is much less than the transmission line delay. Provide a sketch of the voltage V(2).
2. Connect the parallel RC load with a 16 meter transmission line, and connect V(3) to channel 2 of the
scope (use the second Tee). Using the same input voltage, observe the voltages V(2) and V(3) for each
case. Provide sketches of the voltages V(2) and V(3) on the same figure.
3. Use the analytic form presented in the analysis to provide sketches for the voltages V(2) and V(3).
Compare the results of the simulation, analysis, and measurement; how close are they?
Discussion: The parallel RC load is a model for a matched load which has a parasitic capacitance connected
in parallel to it. All connections (nodes) on a PCB comprise a two conductor system, which is a capacitor;
a typical rule of thumb is that there are 1 pF at every node due to this effect. This intrinsic parasitic
capacitance effect is a fundamental limitation for the input to any electronic circuit, and was recognized by
Bode in the 1930's. Notice that the load has the same voltage waveform whether it is connected to the
transmission line or directly. For the case of this load, the analysis shows the form of the negative voltage
wave, and its subsequent effect on the source voltage for this step response. The effect of the negative
going wave on the source voltage is a glitch; after a delay, the voltage at the source goes briefly to zero, and
then returns to the steady-state value for the transmission line. Obviously, this behavior in a digital circuit
could cause erroneous results. The design of synchronous digital circuits address this possibility by
specifying when signals are sampled, generally at the edge of a clock signal (which occurs only during a
relatively short period of time) – it doesn't matter what the signal does at other times. Asynchronous
circuits on the other hand have to deal with this problem in very clever ways.
Note: Don't forget to end your report with the individual thoughtful, reflective paragraphs discussing what
has been learned from the experiment.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Sinusoidal Steady-State Transmission Line Analysis
Lab B
Purpose: This project will introduce the student to the sinusoidal steady-state response of
transmission lines. The effects of time delay caused by a transmission line (or propagation delay)
to the sinusoidal input and the determination of the sinusoidal steady-state response of five
different loads will be investigated: matched, mismatched, open circuit, short circuit, and parallel
RC. The results will be discussed in the context of the performance of practical circuits. The
sinusoidal steady-state response of each load will be investigated in three ways: using a
simulation with PSpice, an analysis, and a measurement circuit. For each case, the results of each
investigation will be compared.
EE 402 Text
References:
Iskander, Magdy F.; Electromagnetic Fields and Waves; Waveland Press; 2000
Chapter 7, especially sections 7.10-13
Equipment:
HP 3312 Function Generator
Agilent DSO3202A Oscilloscope
2 8m RG 58A/U cable
3 short (around 30 cm) RG 58A/U cables
2 BNC Tees
1 BNC to double banana adapter
BNC-double banana: 50 ohm load resistor; 10 ohm resistor; open circuit; short circuit, parallel
RC load (50 ohm and 160 pF)
PSpice on workstation computer
Discussion:
In this project, you will use a technique first presented in your lower division circuits laboratory
to observe the sinusoidal steady-state response of a circuit. The technique is to observe the
response of a sinusoidal input voltage with an oscilloscope to determine the amplitude and phase
using the time base measurement of the oscilloscope to convert the time difference between two
sinusoids at the same frequency to a phase difference. The same basic technique is used for a
PSpice simulation (see the template code below). However, you will use the PSpice transient
analysis which will allow you to see the complete response, which will consist of a transient part
before the response begins the steady-state part. The circuit you will use is shown below, and as
in the Lab A you will investigate five different loads. You will use the PROBE output to display
the source voltage, V(2), the voltage at the midpoint of the transmission line, V(3), and the load
voltage, V(3), for each of the five different loads.
The unique feature of this project is that with relatively inexpensive, low performance
instrumentation and a long transmission line (16m), we can show the time domain and frequency
domain effects of wave propagation, i.e., the sinusoidal steady-state response of a circuit with
propagation delay under different loading conditions. The observed voltages present the same
phenomena as a practical circuit which has dimensions commensurate with the wavelength of its
signals, dim ~ λ = vp / f, where dim is the dimension of the circuit, λ is the wavelength in the
media of the circuit, vp is the velocity of propagation in the media of the circuit, and f is the
frequency of the signal (voltage). In this project the transmission line is an RG 58 A/U which has
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a velocity of propagation of about 2 x 108 m/s, which yields a propagation delay of about 80 ns
for a 16m cable. Thus with a 60MHz scope and a 10 MHz sinusoidal voltage from the function
generator (and properly chosen values for the RC load to get a reasonable impedance), the effects
of the propagation delay on the phase of the sinusoidal voltage can be measured.
Note that the characteristic impedance of the RG 58A/U is 50 ohms. The output impedance of
the HP 3312 function generator also is 50 ohms, so the source (function generator) is matched to
the transmission line. This follows because the small length of transmission line (about 30 cm)
which connects the function generator to the oscilloscope also is RG 58 A/U and is matched to
the source. The effect of the loading of the oscilloscope output impedance (parallel 1 Mohm and
14 pF) also is negligible, and therefore too small to observe. The effect of the oscilloscope
impedance can be simulated though.
Part I (Prelab): PSpice Simulation
Figure 1 Transmission Line Measurement Circuit
Using PSpice, simulate the following circuit for five cases using PROBE to display V(2), V(3),
and V(4):
a) 50 ohm matched load
b) 10 ohm mismatched load
c) open circuit
d) short circuit
e) parallel RC load (50 ohm and 160 pF)
For each case, provide a copy of the PROBE output for V(2), V(3), and V(4); annotate the display
to indicate the load simulated. Note that all the waveforms are in steady-steady after 160 ns.
That is, the source is matched and after the reflected voltage reaches the source end, there is no
more reflections added to the transmission line voltage and the sinusoidal voltages remain
constant in amplitude and phase with respect to each other (just like that oscilloscope display in
your circuits lab did). Using the input sinusoid as the reference, use the PROBE output to
measure the amplitudes of each of the three voltages, and measure the time difference between
V(2) as the reference sinusoid and V(3) and V(4). Then calculate the phase difference, again
using V(2) as the reference, using the fact that the phase can be calculated from 2*pi*f* td, where
td is the time difference and f=10MHz, and the phase units are in radians. Then review the
sinusoidal steady-state analysis of a transmission line with various loads presented in the
mathematical analysis, and calculate the phasor voltages V(2), V(3), and V(4). Note that you will
have to use the expression for V(z) to calculate V(3). Also note that you will have to relate the
40ns delay for each transmission line into an equivalent phase difference using the expression
2*pi*f* td again. Note that the phasor for V(2), the source, will not have a phase of 0 degrees for
the analytic calculation, and therefore you will have to subtract this calculated phase angle from
the phasors V(3) and V(4) to get the corresponding phases differences. In the analysis, there are
terms like exp(-jβz) for z=l and z=l/2 where l is the length of the transmission line and β is the
phase constant for the transmission line. With the time delay for the length l of the transmission
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line given by T=l/u, where u is the propagation velocity of the transmission line and with β=ω/u,
terms like βl and βl/2 are equal to ωT and ωT/2, respectively. Referencing the phasor voltages to
the source voltage V(2), summarize your results in a table which presents the phasor amplitude,
time difference and corresponding phase with respect to V(2) for each of the three voltages from
the measurements from your PROBE simulation and those derived from the analytical
calculation. Comment on any discrepancies that occur (the two values should be very close).
Use the following template PSpice code to construct your simulation:
*pspice Lab B sinusoidal steady state tl_ac_rc
*parallel rc load 50 ohm and 160 pF
vg 1 0 sin (0 1v 10meg)
;VO=0V offset, VA=1V amplitude, 10MHz frequency
rg 1 2 50
t1 2 0 3 0 z0=50 td=40n
;lossless TL: input 2 0, output 3 0, Zo=50ohms, time
delay 40ns
t1 3 0 4 0 z0=50 td=40n
;lossless TL: input 3 0, output 4 0, Zo=50ohms, time
delay 40ns
r1 4 0 50
c1 4 0 160p
.tran 0.1n 300n 0 0.1n
;transient analysis 0.1ns print step, 300ns duration,
;tstart=0 (initial print value), tmax=0.1n (max internal step size)
.probe
.end
Part II (laboratory project)
a) Matched 50 ohms Load:
1. The simulation and analysis will now be verified with measurements. Construct the
transmission line circuit given in Figure 1. Use V(2) as the channel 1 input and trigger; connect
the first Tee on the scope channel 1 connection. Connect the banana load with 50 ohm resistor
directly to the first Tee (no transmission line), and observe the voltage V(2) for an input voltage
of 10 MHz sine wave with 1.0 Vpk.
2. Connect the matched load with a 16 meter transmission line, and connect V(4) to channel 2 of
the scope (use the second Tee). Using the same input voltage, provide sketches of the voltages
V(2) and V(4). Determine the amplitudes and time difference, and the phasor representation for
the two voltages V(2) and V(4), i.e., the complex number that represents the amplitude and phase
of each.
3. Compare the phasor results of V(2) and V(4) (amplitude, time difference, and phase difference)
of the simulation, analysis, and measurement; how close are they?
Discussion: Notice that with a matched load, the reflection coefficient of the load Γ L = 0, and the
value of the reflected (negative going) wave is zero. However the delay observed due to the
transmission line is equivalent to a phase shift of the output voltage of the transmission line
relative to the input voltage of the transmission line.
b) Mismatched 10 ohms Load:
1. Connect the banana load with 10 ohm resistor directly to the first Tee (no transmission line),
and observe the voltage V(2) for the same source voltage.
3-
2. Connect the mismatched load with a 16 meter transmission line, and connect V(4) to channel 2
of the scope (use the second Tee). Using the same input voltage, provide sketches of the voltages
V(2) and V(4). Determine the amplitudes and time difference, and the phasor representation for
the two voltages V(2) and V(4), i.e., the complex number that represents the amplitude and phase
of each.
3. Compare the phasor results of V(2) and V(4) (amplitude, time difference, and phase difference)
of the simulation, analysis, and measurement; how close are they?
Discussion: Notice that with a mismatched load, the reflection coefficient of the load ΓL = -0.66,
and the value of the amplitude of the reflected (negative going) wave is -0.33V. Now there is not
only a delay in the response for V(3) at the load, but there is a reflected wave that affects the V(2)
waveform at the source. Hence, the waveform amplitude voltage at V(2) does not remain at
0.5V, and after the reflected wave arrives, has another value (what is it in the steady-state?). Note
that this case is only an example of a mismatch load, and that other values of a load resistance not
equal to Zo will cause different values for V(2) in the steady state
c) Open Circuit Load
1. Connect the open circuit load directly to the first Tee (no transmission line), and observe the
voltage V(2) for the same source voltage.
2. Connect the open circuit load with a 16 meter transmission line, and connect V(4) to channel 2
of the scope (use the second Tee). Using the same input voltage, provide sketches of the voltages
V(2) and V(4). Determine the amplitudes and time difference, and the phasor representation for
the two voltages V(2) and V(4), i.e., the complex number that represents the amplitude and phase
of each.
3. Compare the phasor results of V(2) and V(4) (amplitude, time difference, and phase difference)
of the simulation, analysis, and measurement; how close are they?
Discussion: The open circuit load shows the effect of a time delay of about 80 ns. The initial
V(2) is the positive going wave only. The change in the value of voltage at the load demonstrates
the creation of the negative going wave; note that ΓL = 1, i.e., the amplitude of the positive and
negative voltage waves are equal. Notice what happens at the source after the reflected wave
arrives. At this point in time, the transmission line is in steady-state, i.e., it has a constant
voltage. On a printed circuit board, the effect observed can be caused by a trace that is not
connected, leading to spurious values. However, the effect can be used to advantage; the PCI bus
interface used in PCs uses an open circuit at each end of the bus to increase the voltage level of
the signal lines through the use of the reflected wave from the open circuits.
d) Short Circuit Load
1. Connect the short circuit load directly to the first Tee (no transmission line), and observe the
voltage V(2) for the same source voltage.
2. Connect the short circuit load with a 16 meter transmission line, and connect V(4) to channel 2
of the scope (use the second Tee). Using the same input voltage, provide sketches of the voltages
V(2) and V(4). Determine the amplitudes and time difference, and the phasor representation for
the two voltages V(2) and V(4), i.e., the complex number that represents the amplitude and phase
of each.
4-
3. Compare the phasor results of V(2) and V(4) (amplitude, time difference, and phase difference)
of the simulation, analysis, and measurement; how close are they?
Discussion: Notice the delay in obtaining the steady-state value of the amplitude voltage at the
source; again, there is a transient response before the steady-state values are observed for the
transmission line. Note the phase shift in the steady-state value of V(2) with respect to the initial
sinusoidal voltage phase for V(2) due to the transmission line. A PCB trace which is shorted to
ground will have the same behavior. The reflection coefficient of the load is ΓL = -1, i.e., the
negative voltage wave is the negative of the positive voltage wave. This leads to the steady-state
value of current (short circuit current) which is limited by the value of the function generator
output impedance which is 50 ohms and which is matched with the characteristic impedance of
the transmission line, Zo = 50 ohms.
e) Parallel RC load
1. Connect the banana parallel RC load with 50 ohm and 160 pF directly to the first Tee (no
transmission line), and observe the voltage V(2) for the same source voltage. Note that the load
resistor is matched to Zo but the impedance of the RC load is not equal to Zo.
2. Connect the parallel RC load with a 16 meter transmission line, and connect V(4) to channel 2
of the scope (use the second Tee). Using the same input voltage, provide sketches of the voltages
V(2) and V(4). Determine the amplitudes and time difference, and the phasor representation for
the two voltages V(2) and V(4), i.e., the complex number that represents the amplitude and phase
of each.
3. Compare the phasor results of V(2) and V(4) (amplitude, time difference, and phase difference)
of the simulation, analysis, and measurement; how close are they?
Discussion: The parallel RC load is a model for a matched load which has a parasitic capacitance
connected in parallel to it. All connections (nodes) on a PCB comprise a two conductor system,
which is a capacitor; a typical rule of thumb is that there are 1 pF at every node due to this effect.
This intrinsic parasitic capacitance effect is a fundamental limitation for the input to any
electronic circuit, and was recognized by Bode in the 1930's. Notice that the load has the same
voltage waveform whether it is connected to the transmission line or directly. For the case of this
load, the analysis shows the impedance adds a phase shift in addition to the transmission line
delay, and there is a reflected wave. The effect of the negative going wave on the source voltage
is a phase shift; after a delay, the phase of the voltage at the source shifts. Obviously, this
behavior could cause erroneous results.
Note: Don't forget to end your report with the individual thoughtful, reflective paragraphs
discussing what has been learned from the experiment.
5-
6-
7-
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
The Network Analyzer
Lab 1
Purpose
To become familiar with the operation and capabilities of a Network Analyzer (HP
8754A) for transmission and reflection measurements.
References
HP 8754A
HP 8502A
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Tranmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WO3
Open-Circuit Termination
GR 874-WN3
Short-Circuit Termination
GR 874-W50B
50  Termination
GR 874-G10
10 dB Attenuator
GR 874-FXXXX
Low-Pass Filter (XXXX = cutoff-frequency in MHz)
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Part I: Transmission Measurement Calibration of the HP 8754A Network Analyzer
1) Connect the HP 8754A to the HP 8502A Test Set as shown on the next page.
A) HP 8754A Network Analyzer Settings
1) Polar A/R: toggles between complex plane display of the reflection coefficient (over
the defined frequency range, see below) and a linear display of gain and/or phase vs.
frequency. Depress button to obtain polar display. Set origin for polar plots: Press
Polar Center button and adjust position of origin. Release to obtain linear display.
2) Freq: select center. Center of linear display (horizontal axis) corresponds to the
displayed frequency.
3) Sweep: auto/fast, knob controls sweep speed (turn clockwise to display solid line).
4) Video Filter: turn off (limits bandwidth of sweep frequency).
5) Tuning: initially set to 750 MHz.
- 1 --
HP 8754A
Network Analyzer
RF Out R
A
B
Transmitted
Incident
Equal
Length
Lines
Reflected
HP 8502A
Test Set
RF In
R
A
Test
Port
DUT
Device
Under
Test
Figure 1: Configuration for Transmission Measurement
6) Markers: set to 50 MHz spacing. Note: with sweep width set to full range (4 – 1300
MHz) and markers off, one marker will remain at the displayed frequency.
7) Output dBm: set to < 0 dBm to avoid saturating the R, A, and B inputs.
8) Intensity: turn clockwise until trace can be seen.
9) Focus: self-explanatory.
10) Stability: N/A
11) Reference positions (Ch 1 and 2): set to desired locations. Release reference buttons
to take measurements.
12) Channel 1:
a) Offset: press button to allow for corrections.
b) Select B/R (‘thru’) measurement.
c) Sensitivity: set to 10 dB/div.
13) Channel 2:
a) Offset: press button to allow for corrections.
b) Select Phase B/R measurement (green button).
c) Sensitivity: set to 45 o/div (green scale).
The above channel settings enable a simultaneous display of dB magnitude and phase for
the device under test (DUT).
2-
B) Transmission Measurement Calibration of the HP 8754A Network Analyzer
1) Connect the RF Output of the HP 8754A to the Fluke 7220A frequency counter (50 
input) and calibrate the HP 8754A frequency display; initially use 750 MHz.
2) Set the RF Input Attenuation knob for the HP 8502A Test Set to 0 dB.
3) Connect a ‘thru’ for the device under test (DUT).
4) Set CRT display on HP 8754A to linear (release polar A/R button), sweep: auto, fast,
knob turned to right, output dBm: set to < 0 dBm.
5) Channel 1: select B/R, set reference wheel to 0, press offset button and adjust until
the Ch. 1 reference level is obtained (calibrates magnitude level to the DUT plane).
6) Channel 2: select Phase B/R, set reference wheel to 0, press offset button and adjust
until the Ch. 2 reference level is obtained (calibrates phase level to the DUT plane).
Part II: Transmission Measurements
1) Replace ‘thru’ with a 10 dB pad (GR 874-G10); initially use 750 MHz..
2) Copy CRT display on the HP 8754A. For any CRT display, record gain and phase
separately, if desired.
3) Reset sweep width to 200 MHz and copy CRT display.
4) Reset sweep width to entire range (4 – 1300 MHz) and copy CRT display.
5) Replace 10 dB pad with a low-pass filter (GR 874-FXXXX).
6) Reset Freq to 500 MHz or 1000 MHz (as appropriate), widen sweep width (try 500
MHz), and adjust Ch. 1 and 2 reference levels to fit responses within CRT display.
Determine the filter’s corner frequency, roll-off slope (dB/dec), and sketch the CRT
display.
7) Replace low-pass filter with a 20 cm air line (GR 874-L20) using a frequency of 750
MHz and copy CRT display. Calculate expected phase shift and compare to
measurement.
8) Reset sweep width to entire range (4 – 1300 MHz) and copy CRT display. Calculate
expected phase slope (deg/MHz) and compare to measurement.
Part III: Reflection Measurement Calibration of the HP 8754A Network Analyzer
A) HP 8754A Network Analyzer Settings
1) Polar A/R: Depress to obtain polar display.
2) Freq: select center.
3) Sweep: auto/fast, knob controls sweep speed (turn clockwise to display solid line).
4) Video Filter: turn off (limits bandwidth of sweep frequency).
5) Tuning: set to 750 MHz.
6) Sweep Width: set to 0.
7) Markers: turn off (disabled in polar display).
8) Output dBm: set to < 0 dBm to avoid saturating the R, A, and B inputs.
9) Intensity: turn clockwise until trace can be seen.
10) Focus: self-explanatory.
11) Stability: N/A
3-
12) Reference positions (Ch 1 and 2): N/A in polar display.
13) Channel 1:
a) Offset: press button to allow for corrections.
b) Select A/R (reflection) measurement.
c) Sensitivity: disabled in polar display.
14) Channel 2:
a) Disabled in polar display.
B) Reflection Measurement Calibration of the HP 8754A Network Analyzer
1) Connect the RF Output of the HP 8754A to the Fluke 7220A frequency counter and
calibrate the HP 8754A frequency display, if necessary.
2) Connect the HP 8754A to the HP 8502A Test Set as follows:
HP 8754A
Network Analyzer
RF Out R
A
B
Incident
Reflected
Equal
Length
Lines
HP 8502A
Test Set
RF In
R
MM &
FF
“Thru’s”
A
Test
Port
DUT
Device
Under
Test
Figure 2: Configuration for Reflection Measurement
3) Set the RF Input Attenuation knob on the HP 8502A Test Set to 0 dB.
4) Connect a pair of female-female and male-male ‘thru’ adapters between the R port on
the HP 8502A and its cable. This will compensate for the phase delay caused by the
distance between the test port and the actual short position. The RF signal traverses
this distance twice: once from the test port to the short position and from the short
4-
position back to the test port (where it effectively enters port A). Hence, two ‘thru’
adapters electrical lengths are used to compensate for the phase measurements.
5) Connect a short (GR 874-WN3) for the device under test (DUT).
6) Adjust Ch. 1 offset to obtain a magnitude of 1.
7) Adjust Ch. 1 line length to obtain phase of 180o. May also require an adjustment of
the Ch. 2 reference wheel: use Ch. 1 line length to fine tune.
Part IV: Reflection Measurements
Discussion on measurement procedure: Remember that Z(z) = Zo (1 + Γ(z)) /(1 - Γ(z)) is
the relationship between the reflection coefficient at a location Γ(z) and the impedance at
a location Z(z) for a transmission line with z=0 at the load and Zo is the characteristic
impedance of the transmission line. Also remember that the boundary condition at z=0,
the position on the transmission line which we used to calibrate the network analyzer
with the short circuit, requires that Z(0) = ZL since the voltage and current are continuous
at z=0. Also note that Zo is the characteristic impedance of the measurement system, i.e.,
the test set for the network analyzer, which is 50 ohms. Because Γ(0) = ΓL, then
ZL = Zo (1+ ΓL)/(1-ΓL), where Zo is the 50 ohms of the test set.
1) Replace short with unknown load (GR 874-M or 874-ML); open the "can" and record
the value of the lumped parameter resistor using its color code.
2) Record the value (magnitude and phase) of the reflection coefficient for the unknown
load, i.e., Γ(0)=ΓL. Convert this reflection coefficient to its corresponding
transmission line impedance at the location of the reflection coefficient, Z(0); this
impedance is the measurement of the actual load impedance, ZL.
3) Replace the unknown load with a 50  termination (GR 874-W50B) and repeat step
#2 above. Discuss what you observe in this case for Γ(0)=ΓL and ZL.
5-
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Transmission Line Reflection Coefficient, Impedance and the Smith Chart
Lab C
Prelab
Read Section 7.13 of text.
Purpose
To understand the relationship between reflection coefficient measurements and the
measurement of transmission line impedance and electrical length, and the use of the
Smith Chart to facilitate the calculation of transmission line circuits impedances and
reflection coefficients, and to use /2 and /4 lines as measurement aids and to verify
transmission line theory for /2 and /4 lines.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WO3
Open-Circuit Termination
GR 874-WN3
Short-Circuit Termination
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-LK10
10 cm Adjustable Air Line (35 cm to 45 cm)
GR 874-LK20
20 cm Adjustable Air Line (60 cm to 80 cm)
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Theory
Modifying equation (7.69) in the text for lossless transmission lines:
Z  jZo tan l 
Z in (l )  Z o L
Z o  jZ L tan l 
the input impedance for a transmission line /2 long is
(1)
1-
Zo
Zin
ZL
Z in  Z L
/2
For transmission lines /4 long,
Zin
Zo
ZL
Z in 
Z o2
ZL
/4
Procedure
Part I: reflection coefficient, transmission line impedance, and smith chart
1) Choose an operating frequency between 500 MHz and 800 MHz, and calibrate the
network analyzer (setting the sweep width to 0) for reflection measurements by
connecting the HP 8502A to the HP 8754A as shown in Figure 2 of Lab #1 for reflection
measurements and using the short circuit for a load following Part III of Lab #1.
2) Connect the unknown load and measure and record the reflection coefficient, (ΓL)direct,
and then use the smith chart to calculate the load impedance, (ZL)direct.
3) Insert the 20 cm air line between the unknown load and the test set, and then measure
and record the input reflection coefficient of the resulting circuit, (ΓL)20 cm.
4) Using the Smith Chart, use a short for a load to estimate the electrical length of the
transmission line, length as measured in units of wavelength, Lλ. Annotate the smith
chart with sufficient information so that a peer will understand your procedure for
obtaining the electrical length from a short circuit load.
5) Using the value of your input reflection coefficient (ΓL)20 cm and the length of the
intervening transmission line Lλ, analytically calculate the load impedance,
(ZL)20 cm analytical.
6) Using the Smith Chart, determine the reflection coefficient of the unknown load
(ΓL)20 cm smith and provide an estimate of the unknown load impedance, (ZL)20 cm smith;
annotate the smith chart with sufficient information so that a peer will understand your
procedure for obtaining the estimated load impedance.
Part II: Reflection Measurements using /2 line
1) Connect the HP 8502A to the HP 8754A as shown in Figure 2 of Lab #1 for
reflection measurements. Set sweep width to 0.
2) Use the same frequency chosen in Part I and calibration settings.
3) Connect an adjustable air line (GR 874-LK10L or 874-LK20L) to the test port of the
HP 8502A.
2-
4) Terminate the line with a short (GR 874-WN3). Adjust the length of the air line to
obtain a –1 display on the CRT (may require additional fixed-length air lines). This
sets the length to a multiple of a half-wavelength.
Note: the adjustable lines have a locking clamp which can be used to fix the length.
Loosen the clamp for adjustment and tighten when the correct length has been found.
5) Replace the short-circuit termination with the unknown load (GR 874-M or 874-ML).
Record the reflection coefficient (polar display, magnitude and phase).
6) Convert the reflection coefficient into the actual load impedance, (ZL)λ/2.
Assume Zo = 50 .
Part III: Reflection Measurements using /4 line
1) Retaining the same frequency and calibration, replace the unknown load with an open
termination (GR 874-WO3). Adjust the length of the air line to obtain a –1 display on
the CRT (may require additional fixed-length air lines). This sets the length to an odd
multiple of a quarter-wavelength.
2) Replace the open with the unknown load (GR 874-M or 874-ML) and record the
position of the reflection coefficient (polar display, magnitude and phase).
3) Convert the reflection coefficients obtained into the actual load impedance, (ZL)λ/4.
Assume Zo = 50 . Compare to the value obtained in Part II and explain any
discrepancies.
Part IV: Propagation Velocity
1) Replace the adjustable air line with a fixed-length 20 cm line (GR 874-L20) and
terminate the line with a short (GR 874-WN3).
2) Adjust the signal frequency of the HP 8754A to obtain a –1 display on the CRT. This
sets the length of the line to /2.
3) Compute the propagation velocity Vp using the formula Vp = f. Compare to c.
Suggestion: use the transmission line set up in Part II (adjustable air line plus possibly
fixed air line to get /2), and measure the length of the line from the calibration plane to
the short circuit to estimate the length of /2, hence .
Note: The above Part IV procedure leads to a frequency that is different from the one
used to calibrated the network analyzer, and hence can lead to values of Vp > c; this is a
good exercise for the students to appreciate the limitations of the measurement procedure,
i.e., explain the error.
Report Conclusion: Compare the estimate calculations of the unknown impedance:
(ZL)20 cm analytical, (ZL)20 cm smith, (ZL)λ/2, and (ZL)λ/4, with the value obtained with the direct
measurement (ZL)direct, ; use a table to summarize your results. State possible sources of
error for any differences. Also, open the "can" and record the value of the lumped
parameter resistor (use the color code), and comment on why the value of ZL is not the
value of the resistor. In addition, comment on any error obtained for the measurement of
Vp.
3-
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Impedance Measurement by /2 and /4 Lines
Prelab
Read Section 7.13 of text.
Lab 2
Purpose
To use /2 and /4 lines as measurement aids and to verify transmission line theory for
/2 and /4 lines.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WO3
Open-Circuit Termination
GR 874-WN3
Short-Circuit Termination
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-LK10
10 cm Adjustable Air Line (35 cm to 45 cm)
GR 874-LK20
20 cm Adjustable Air Line (60 cm to 80 cm)
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Theory
Modifying equation (7.69) in the text for lossless transmission lines:
Z  jZo tan l 
Z in (l )  Z o L
Z o  jZ L tan l 
the input impedance for a transmission line /2 long is
Zin
Zo
/2
ZL
(1)
Z in  Z L
For transmission lines /4 long,
Zin
Zo
ZL
Z in 
Z o2
ZL
/4
Part I: Reflection Measurements using /2 line
7) Connect the HP 8502A to the HP 8754A as shown in Figure 2 of Lab #1 for
reflection measurements. Set sweep width to 0.
8) Choose an operating frequency between 500 MHz and 800 MHz and calibrate for
reflection measurements as per Part III of Lab #1.
9) Connect an adjustable air line (GR 874-LK10L or 874-LK20L) to the test port of the
HP 8502A.
10) Terminate the line with a short (GR 874-WN3). Adjust the length of the air line to
obtain a –1 display on the CRT (may require additional fixed-length air lines). This
sets the length to a multiple of a half-wavelength.
Note: the adjustable lines have a locking clamp which can be used to fix the length.
Loosen the clamp for adjustment and tighten when the correct length has been found.
11) Replace the short-circuit termination with the unknown load (GR 874-M or 874-ML).
Record the reflection coefficient (polar display, magnitude and phase).
12) Convert the reflection coefficient into the actual load impedance. Assume Zo = 50 .
Part II: Reflection Measurements using /4 line
4) Replace the unknown load with an open termination (GR 874-WO3). Adjust the
length of the air line to obtain a –1 display on the CRT (may require additional fixedlength air lines). This sets the length to an odd multiple of a quarter-wavelength.
5) Replace the open with the unknown load (GR 874-M or 874-ML) and record the
position of the reflection coefficient (polar display, magnitude and phase).
6) Convert the reflection coefficients obtained into the actual load impedance. Assume
Zo = 50 . Compare to the value obtained in Part I and explain any discrepancies.
Part III: Propagation Velocity
4) Replace the adjustable air line with a fixed-length 20 cm line (GR 874-L20) and
terminate the line with a short (GR 874-WN3).
5) Adjust the signal frequency of the HP 8754A to obtain a –1 display on the CRT. This
sets the length of the line to /2.
6) Compute the propagation velocity Vp using the formula Vp = f. Compare to c.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Prelab
Read Section 7.10 of text.
Transmission Line Parameters
Lab 3
Purpose
To determine the transmission line parameters for an RG-8U cable.
References
EE 402 Text
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
HP 8754A
HP 8502A
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WO3
Open-Circuit Termination
GR 874-WN3
Short-Circuit Termination
RG-8U Cable
Fittings & Accessories
Smith Charts
Theory
Below is the representation for the measurement circuit with the definition of the
variables used in the analysis.
z = -l (reference plane)
Zom
Zo
network analyzer
end
Γm <-> Zm
z=0
low loss transmission line
Zin(-l)
load
Note that Zom = 50 ohm is the characteristic impedance of the network analyzer, and Γm is
the measured reflection coefficient at the reference plane determined by the calibration
procedure. Zin(-l) is the transmission line impedance at z = -l and is equal to Zm because
of the boundary conditions. Therefore, Zin(-l) = Zm = Zom (1 + Γm)/(1 - Γm). The
measurement calculations for the low loss transmission line follow the analysis below.
Modifying equation (7.68) in the text for lossy transmission lines (   0 ):
Z in (l )  Z o
Z L  Z o tanh l 
Z o  Z L tanh l 
(1)
The input impedance of a transmission line of length l terminated in a short-circuit has
the value
Z inshort  Z o tanh l 
(2)
For the same line terminated in an open-circuit, the input impedance is given by
Z inopen  Z o coth l 
(3)
where  =  + j,  = propagation factor,  = attenuation factor (Np/m),  = phase factor
(rad/m). Multiplying equation (2) by (3) yields,
Zo  ZinshortZinopen
(4)
Dividing equation (2) by (3) results in,
tanh l  
Z inshort e 2l  1

Z inopen e 2l  1
(5)
Solving for the exponential in (5),
1
e 2l 
Z inshort
Z inopen
Z inshort
1
Z inopen
and taking the natural logarithm of both sides of (6) yields,
(6)
short

 1  Z in
Z inopen
1 
l  l  jl  ln 
2 
Z inshort
1


Z inopen








(7)
Defining
Z inshort
1
Z inopen
x
Z inshort
1
Z inopen
(8)
and solving for  in (7) yields,

1
ln  x 
2l
(9)
Solving for  in (7),

1
anglex   2n
2l
(10)
where n is the number of periods in the smith chart for the length of the low loss
transmission line at the frequency of the measurements.
Part I: Reflection Coefficient Measurements
1) Connect the HP 8502A to the HP 8754A for reflection measurements as shown in
Figure 2 of Lab #1.
2) Set the HP 8754A to 35 MHz and calibrate for reflection measurements as per Part III
of Lab #1.
3) Connect one length of the RG-8U cable (about 1.8m in length) to the test port of the
HP 8502A Test Set; record the ID# of the cable, and use a ruler to measure its
physical length.
4) Terminate the cable with a short (GR 874-WN3) and record the reflection coefficient
(polar display).
5) Determine the value n in equation (10):
a) Reduce the frequency setting on the HP 8754A to zero (cursor should be close to
-1 ). At zero frequency, the electrical length of the cable is 0.
b) Slowly increase the frequency up to the test frequency and note the number of full
revolutions on the display. This is the value n: the electrical length of the cable at
the test frequency is n full half-wavelengths.
6) Replace the short with an open termination (GR 874-WO3) and record the reflection
coefficient (polar display).
7) Convert the reflection coefficients obtained in steps #4 and #5 above into Z inshort and
Z inopen using a Smith Chart. Note each calculated impedance is Zin(-l) for the
appropriate load and that Zom = 50 .
8) Repeat steps #2 (cal only), and #3 through #7 for a frequency of 1000 MHz.
[optional 8)] Repeat steps #2 (cal only), and #3 through #6 above for a frequencies of 500
MHz through 1000 MHz in steps of 100 MHz. For step #7, use a computer program to
compute Z inshort and Z inopen from the measured reflection coefficients.
Part II: Computation of Transmission Line Parameters
1) Calculate Zo, , and  for all frequencies using equations (4), (9), and (10),
respectively. A computer program may be used to facilitate these calculations.
2) Compute the propagation velocity of the transmission line Vp at each frequency and
then the velocity factor for the cable using
velocity factor 
propagation velocity on transmissi on line
velocity of light in free space
(11)
3) Calculate the distributed component values L and C using the relations
   LC
Zo 
L
C
(12)
(13)
4) Compare the calculated parameters Zo, , , L, and C for all frequencies and justify
any discrepancies. Include a derivation for  and  using equations (6) and (8).
Present the results in a table for both frequencies: 35 MHz and 1000MHz, for
comparison, and note the effect on the performance of the cable as the frequency is
increased. What does this difference in performance imply for the limitations on the
use of the cable as a lossless transmission line?
5) In Part I, step 5b, why does the trace rotate in the clockwise direction as the frequency
is increased?
Discussion of results for 35 MHz and 1000MHz:
These measurements at the two frequencies demonstrate that as frequency increases, the
transmission line performance changes from a lossless model of behavior to a lowloss
model of behavior. Using this concept, a check can be made on the calculations of the
transmission line parameters as follows:
1. α35 ~ α1000/10
2. β35~ β1000/30
3.
4.
5.
6.
|Γsc|~|Γoc| and (angle of Γsc) + (angle of Γsc) ~ (180 degrees)mod
(Zo)35 ~ (Zo)1000
(L,C)35~(L,C)1000
(Vp)35~(Vp)1000
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442 Use of the Smith Chart for Line-Length and Line-Loss Corrections
Lab 4
Prelab
Read section 7.12 in text.
Purpose
To learn Smith Chart techniques to correct for line-length and line-loss errors caused by
transmission lines.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WN3
Short-Circuit Termination
GR 874-M or ML
Unknown Load (component mount)
RG-8U Cable
Use same cable (#ID) as used in Lab 3
Fittings & Accessories
Smith Charts
Part I: Reflection Coefficient Measurements
1) Connect the HP 8502A to the HP 8754A for reflection measurements as shown in
Figure 2 of Lab #1.
2) Set the HP 8754A to 35 MHz and calibrate for reflection measurements as per Part III
of Lab #1.
3) Connect the same RG-8U cable used in Lab 3 (use the ID# to determine) to the test
port of the HP 8502A Test Set and terminate the cable with a short (GR 874-WN3).
Record the reflection coefficient (polar display).
4) Plot the reflection coefficient on a Smith Chart and find the electrical length in
wavelengths and return loss of the cable in dB.
5) Replace the short-circuit termination with the unknown load (GR 874-M or 874-ML).
Record the reflection coefficient (polar display), +cable.
6) Remove the RG-8U cable and connect the unknown load directly to the test port of
the HP 8502A Test Set. Record the reflection coefficient (polar display), load.
7) Plot the reflection coefficients obtained from steps #5 and #6 on a Smith Chart. Apply
line-length and line-loss corrections to +cable and compare to the actual reflection
coefficient, load.
8) Convert both the corrected and actual reflection coefficients into the load impedances
ZL(corrected) and ZL(actual), respectively. Assume Zo = 50 .
9) Repeat steps #2 (cal only), and #3 through #8 above for a frequency of 1000 MHz.
Part II: Conclusions
Compare the pairs of values for  and ZL computed at 35 MHz and 1000 MHz.
Determine length and loss errors in  and dB, respectively, and comment on any
discrepancies. Present the results in a table for both frequencies. Again, note that the
performance of the transmission line changes as the frequency increases; discuss the
transition from a lossless model to a lowloss model to explain this change in behavior.
.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
The Slotted Line Technique in Impedance Measurements
Lab 5
Prelab
Read sections 7.15-16 in text.
Purpose
To learn the use of the slotted line in impedance and SWR measurements.
References
EE 402 Text
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
GR 874-LBA or LBB Slotted Line Operating Manual
HP 415B
Standing Wave Indicator Operating Manual
Equipment
GR 874-LBA or LBB Slotted Line
HP 415B
Standing Wave Indicator
Fluke 6060B
RF Signal Generator
GR 874-WN3
Short-Circuit Termination
GR 874-D20
Adjustable Stub (26 cm to 46 cm)
GR 874-M or ML
Unknown Load (component mount)
RG-8U Cable
Fittings & Accessories
Smith Charts
Part I: SWR Measurement Calibration of the GR 874-LBA or LBB Slotted Line and HP
415B Standing Wave Indicator
A) HP 415B Standing Wave Indicator Settings
1) Input Selector: set to Xtal, 200 k (this is the type of detector used on the slotted
line)
2) Range: 30 dB position
3) Bolo Bias Current: N/A when selector is set to Xtal.
4) Meter Scale: Normal (black scale). Allows measurement of SWR from 1 to 
(expanded scale only allows a maximum of 1.3: this is for precision measurements on
well-matched lines).
5) Gain: to be adjusted while taking measurements. Initial setting: turn completely in the
clockwise direction.
2
6) Indicator: shows detected power (square-law detector: indicator  E  P )
B) Fluke 6060B RF Generator Settings
1) Parameter data entry: press function key (i.e.: Freq, Ampl, AM, etc.), enter value,
then press unit (i.e.: MHz/V, dBm, etc.)
2) Set Freq to 500 MHz, Ampl to 0 dBm, and AM to 50%.
3) Press INT AM and select 1000 Hz by pressing the 400/1000 key. The INT AM key
turns on the amplitude modulation function (internally triggered). The AM setting
specifies the duty cycle of the waveform.
C) SWR Calibration and Measurement Procedure
1) Connect the Fluke 6060B, adjustable stub (GR 874-D20), and short (GR 874-WN3)
to the slotted line (GR 874-LBA or LBB) as follows:
HP 415B
SWR Meter
GR 874-D20
Adjustable Stub
Fluke 6060B
RF Signal
Generator
probe
Zo
Load
GR 874-LBA or LBB Slotted Line
Figure 3: Configuration for Slotted Line Measurements
2) Adjust probe position on the slotted line until the HP 415B detects a peak. This may
require adjustment of the stub (GR 874-D20) length.
3) Adjust stub (GR 874-D20) length for maximum deflection on the HP 415B SWR
meter. Simultaneously adjust the gain knob to avoid ‘pinning’ the SWR indicator
needle. Note: the stub length adjustment is very sensitive. The proper length improves
the match from the slotted line to the probe which enhances power transfer to the
SWR meter.
4) Adjust the gain dial to obtain a needle deflection at exactly SWR=1. Verify that the
peak has been found by moving the probe along the slotted line around the peak
position and resetting to SWR=1 if necessary.
5) To measure SWR, move the probe to the minimum power position (left deflection)
and note SWR. For a short-circuit termination, the SWR should be very high
(theoretically infinity).
Part II: Wavelength and Load Measurement using the Slotted Line
1) Record two adjacent voltage minimum positions l1 (nearest the load) and l2 in cm on
the slotted line.
2) Replace the short with the unknown load (GR 874-M or ML) and measure the SWR.
Note: must recalibrate for SWR measurement (set to SWR=1 at the peak power
position).
3) Record the position d1 of the voltage minimum between l1 and l2.
4) Repeat steps #1 through #3 above for frequency intervals of 50 MHz to 700 MHz.
Part III: Computation of the Wavelength and Load Impedance
1) Calculate the free-space wavelength in cm for the frequencies specified in step #4 of
Part II above.
2) Calculate the distance between two voltage minimums (l1 and l2) and compare to the
expected value.
3) Plot the SWR circle on a Smith Chart for each frequency tested.
4) Compute the distance between the load and voltage minimum between l1 and l2
produced by the unknown load (l = distance between l1 and d1).
5) Beginning at the voltage minimum point on the SWR circle, move along the circle in
the WTL direction the distance l in  to obtain the reflection coefficient at the load
plane. Alternatively, the distance between l2 and d1 can be used in which case the
movement along the SWR circle should be in the WTG direction. Repeat for all
frequencies.
6) Convert the load plane reflection coefficient to the actual load impedance. Repeat for
all frequencies.
7) Measure the load impedance with the network analyzer at all frequencies for
comparison purposes.
8) Compare the calculated load impedances to the values measured by the network
analyzer at all frequencies and discuss results.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Impedance Matching by the Single-Stub Tuning Method
Lab 6
Prelab
Read section 7.14 in text.
Purpose
To match a load impedance to a transmission line using the single-stub matching
technique.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WN3
Short-Circuit Termination
GR 874-WO3
Open-Circuit Termination
GR 874-L10
10 cm Fixed-Length Air Line
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-LK10
10 cm Adjustable Air Line (35 cm to 45 cm)
GR 874-LK20
20 cm Adjustable Air Line (60 cm to 80 cm)
GR 874-D20
Adjustable Stub (26 cm to 46 cm)
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Smith Charts
Part I: Reflection Measurements and Single-Stub Matching
1) Connect the HP 8502A to the HP 8754A for reflection measurements as shown in
Figure 2 of Lab #1.
2) Select a frequency between 500 MHz and 800 MHz and calibrate the HP 8754A for
reflection measurements as per Part III of Lab #1.
3) Replace the short-circuit termination with the unknown load (GR 874-M or 874-ML)
and record reflection coefficient (polar display). Use a Smith Chart to convert to load
impedance.
4) Use a Smith Chart and the load impedance information obtained in the previous step
to calculate the required lengths and locations of a single short or open-circuit
matching stub for both possible solutions. Select realizable configurations with
respect to the adjustable and fixed length air line lengths (see equipment list above).
5) Insert the stub lines terminated with short (GR 874-WN3) or open circuit loads (GR
874-WO3) and series lines. Adjust the stub length and location to the design lengths
calculated in step #4 above for both solutions. Record the return loss and VSWR.
Determine the bandwidth for both solutions within which the return loss is greater
than 10 dB.
Part II: Conclusions
1) Show all details of the load impedance determination in step #3 of Part I above.
2) Show all details of the single-stub design procedure described in step #4 of Part I
above. Include Smith Chart diagrams.
3) Discuss the return loss and VSWR for both solutions. Was one design better than the
other? Why?
4) Determine which of the two designs yields the widest bandwidth and why.
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Impedance Matching by the Double-Stub Tuning Method
Lab 7
Prelab
Read section 7.14 in text.
Purpose
To match a load impedance to a transmission line using the double-stub matching
technique.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WN3
Short-Circuit Termination
GR 874-WO3
Open-Circuit Termination
GR 874-L10
10 cm Fixed-Length Air Line
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-LK10
10 cm Adjustable Air Line (35 cm to 45 cm)
GR 874-LK20
20 cm Adjustable Air Line (60 cm to 80 cm)
GR 874-D20
Adjustable Stub (26 cm to 46 cm)
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Smith Charts
Part I: Reflection Measurements and Double-Stub Matching
1) Connect the HP 8502A to the HP 8754A for reflection measurements as shown in
Figure 2 of Lab #1.
2) Select a frequency between 500 MHz and 800 MHz and calibrate the HP 8754A for
reflection measurements as per Part III of Lab #1.
-
3) Replace the short-circuit termination with the unknown load (GR 874-M or 874-ML)
and record reflection coefficient (polar display). Use a Smith Chart to convert to load
impedance.
4) Use a Smith Chart and the load impedance information obtained in the previous step
to calculate required lengths for a double-stub design (both solutions) with two stubs
terminated with open-circuit, short-circuit, or a combination of open and short-circuit
loads. Account for the distance between the load and the first T adapter. Choose one
of the fixed-length or adjustable air lines for the g=1 circle rotation. Select realizable
configurations with respect to allowable air line lengths (see equipment list above).
5) Insert the stubs and adjust both stub lengths to the lengths calculated in step #4 above
for both designs. Record the return loss and VSWR. Determine the bandwidth for
both solutions within which the return loss is greater than 10 dB.
Part II: Conclusions
1) Show all details of the load impedance determination in step #3 of Part I above.
2) Show all details of the double-stub design procedure described in step #4 of Part I
above. Include Smith Chart diagrams.
3) Discuss the return loss and VSWR for both solutions. Was one design better than the
other? Why?
4) Determine which of the two designs yields the widest bandwidth and why.
-
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Revised Lab 6 and 7
Lab D
The intent of these revised procedures is to complete labs 6 and 7 with one report in the three
hours of lab, i.e., you will turn your lab report in at the end of the lab. The reports will be graded
and returned before the Lab Final period. Note that there will be lab time allocated to
preparation for the lab final and to completing student evaluations. The smith charts required for
each of the designs for the prelab will be checked at the beginning of the lab. Measurement of
distances is very important in the construction of your designs, and you should consult with the
instructor if you have questions.
Prelab:
1. Read Lab 6 Impedance Matching by the Single-Stub Tuning Method and Lab 7 Impedance
Matching by the Double-Stub Tuning Method in your EE 442 manual.
2. Review section 7.14.2 and example 7.14 in your text for single-stub matching.
3. Review section 7.14.3 and example 7.15 in your text for double-stub matching.
4. For the measured value of your load impedance ZL at 600 MHz (use the value measured in Lab
#1, and check load ID# for measurements to verify design):
a) design a single-stub matching network for ZL using a smith chart; annotate the smith chart with
sufficient information so that a peer can understand your design (include a diagram to define your
variables). Refer to Lab 6 for details.
b) design a double-stub matching network for ZL using a smith chart; annotate the smith chart
with sufficient information so that a peer can understand your design (include a diagram to define
your variables) Refer to Lab 7 for details.
References
EE 402 Text
HP 8754A
HP 8502A
Magdy Iskander, Electromagnetic Fields and Waves, Waveland
Press, 2000
Network Analyzer Operating Manual
Transmission/Reflection Test Set Operating Manual
Equipment
HP 8754A
Network Analyzer
HP 8502A
Transmission/Reflection Test Set
Fluke 7220A
Frequency Counter
HP 11851A
RF Cable Kit
GR 874-WN3
Short-Circuit Termination
GR 874-WO3
Open-Circuit Termination
GR 874-L10
10 cm Fixed-Length Air Line
GR 874-L20
20 cm Fixed-Length Air Line
GR 874-LK10
10 cm Adjustable Air Line (35 cm to 45 cm)
GR 874-LK20
20 cm Adjustable Air Line (60 cm to 80 cm)
GR 874-D20
Adjustable Stub (26 cm to 46 cm)
GR 874-M or ML
Unknown Load (component mount)
Fittings & Accessories
Smith Charts
-
Lab Procedure:
1. Verify your value of ZL with a measurement before beginning (use 600 MHz as before). If the
measured value has an error greater than 5% from the assumed value for your design, then notify
the instructor for further instructions.
2. Construct your single-stub design making sure to use an adjustable airline to realize your
design, and then:
a) measure its input Γ with the network analyzer
b) calculate its VSWR
c) "tune" your design by adjusting the stub to get the smallest value of VSWR, i.e., smallest value
of return loss and record the corresponding frequency, which is the center frequency f0.
d) for the "tuned design", measure the -10dB bandwidth, i.e., the frequency above and below 600
MHz for which the return loss is -10dB, f1 and f2.
Discussion on measuring -10dB bandwidth: Refer to the figure below. Remember that
VSWR = (1+|Γ|)/(1-|Γ|) and that |Γ| = 0 implies that (VSWR)min = 1 which in turn implies that |Γ|
= -∞ dB, i.e., matched load conditions.
e) insert a 10 cm airline between the load and the matching network, and tune the stub to get the
lowest value of VSWR, and record it.
3. Construct the double-stub design making sure to use adjustable airlines between the load and
the stubs to realize your design, and then:
a) measure its input Γ with the network analyzer
b) calculate its VSWR
c) "tune" your design by adjusting both stubs to get the smallest value of VSWR, i.e., smallest
value of return loss and record the corresponding frequency, which is the center frequency f0.
d) measure the -10dB bandwidth of the "tuned" design using the same procedure used for the
single stub measurement to obtain f1 and f2.
e) insert a 10 cm airline between the load and the matching network, and tune the stubs to get the
lowest value of VSWR, and record it
4. In your conclusion, discuss the merits of each design and present a table that compares the two
"tuned" matching designs with respect to:
a) tuned load VSWR and bandwidth
b) tuned 10 cm adjusted load VSWR
Don't forget your individual thoughtful, reflective paragraphs that discuss what you have learned.
-
ELECTRICAL ENGINEERING DEPARTMENT
California Polytechnic State University
EE 442
Introduction to Electrical Performance Analysis of Printed Circuit Boards
Lab E
Purpose: This project introduces the student to the analysis of the electrical performance of printed circuit
boards. This analysis uses the principles investigated in Lab A, Time Domain Analysis of Transmission
Lines, and in Lab B, Sinusoidal Steady-State Analysis of Transmission Lines. The time domain step
response and the frequency domain sinusoidal steady-state response of the electrical performance of a
printed circuit board can be modeled using transmission lines and lumped parameter elements. This
investigation of wave propagation on a printed circuit board uses the same technique used in Labs A and B,
the use of long transmission lines and inexpensive, relatively low frequency instrumentation to observe the
effects of time (or propagation) delay on the interconnect signal lines of a printed circuit board. This
introduction studies the performance of the connection of signal lines (traces) on a printed circuit board,
which is emulated by the behavior of interconnected transmission lines and lumped parameter elements.
The results will be discussed in the context of the performance of practical circuits. Both the time domain
step response and frequency domain sinusoidal steady-state response are investigated in two ways: using a
simulation with PSpice, and a measurement circuit. For each response, the results of each investigation
will be compared.
EE 402 Text
References:
Iskander, Magdy F.; Electromagnetic Fields and Waves; Waveland Press; 2000
Chapter 7, especially sections 7.1-9
Review the results of Lab A and Lab B
Equipment:
HP 3312 10 MHz Function Generator
Agilent DSO3202A Oscilloscope
3 RG 58A/U cables (each 8m)
2 short (around 30 cm) RG 58A/U cables
4 BNC Tees
3 BNC barrels
1 BNC male to male
2 BNC to double banana adapter
2 BNC-double banana with 50 ohm load resistor
PSpice on workstation computer
Discussion:
Printed circuit boards (PCBs) are used to implement electronic circuits. A combination of lumped
parameter elements (e.g., R, L, C, voltage and current sources) and distributed parameter transmission line
elements are used to model PCB circuits to analyze performance. At high frequencies, i.e., frequencies for
which the wavelength of the signal is comparable to the length of the traces that connect the chips mounted
on the PCB, the distributed parameter transmission line model can be used to model the behavior of the
signal traces; for example, see figure 1. If the signal of interest is 3 GHz, then the wavelength in free space
will be 10 cm (about 4 inches), and the actual wavelength for the PCB trace will be less - hence even more
comparable to the actual dimension of its length. Within the chips, the integrated circuit typically will have
line widths, and hence transistor and circuit component features, on the order of less than a micro, which is
less than the wavelength in the media, i.e., circuit dimension = 10 -6 << 10-1 = wavelength in media (λ).
Therefore, within the chip lumped parameter circuit elements can be used to model the circuit behavior.
Between the chips on the PCB, since the dimension of the signal traces are on the order of the wavelength
in the media, the distributed parameter transmission line model can be used to analyze circuit behavior.
In this lab, the prelab will use PSpice to simulate the performance of a circuit which consists of both
lumped parameter and distributed parameter elements. There are two circuits that will be studied: two
transmission lines with a parallel connected 50 ohm resistor between them, and a three transmission lines
circuit with one transmission line connected to two transmission lines in parallel (all the transmission lines
-
have a characteristic impedance of 50 ohms). As will be observed, the behavior of the source single
transmission line and one of the parallel matched parallel transmission lines can be determined by replacing
the other parallel matched transmission line with a parallel connected 50 ohm resistor. This can most easily
be explained by the fact that both of the matched parallel transmission lines do not have a reflected wave.
Note however that the source single transmission line does have a reflected wave, and therefore does not
represent a matched load to the source. For each circuit studied, the step response and the sinusoidal steady
state response are simulated and analyzed.
Figure 1 Printed Circuit Board Example Circuit
Part I (Prelab): PSpice Simulation
Review your results of Labs A and B, particularly the prelab PSpice simulation code. Modify it
accordingly, and use a transient analysis duration of 300 ns, which should be sufficient to observe the full
step response behavior as well as the complete sinusoidal response (transient and the beginning of the
sinusoidal steady state response). Refer to figure 2. Simulate the step response and the sinusoidal
response for each of the two circuits presented in figure 2. The first case is the step response and the
second case is the sinusoidal response. The terminating load for each case is 50 ohms, i.e., matched
conditions for each transmission line. Each of the 8m RG 58 A/U lines can be model with a characteristic
impedance of 50 ohms and a time delay of 40 ns.
For the step response and for the sinusoidal response: for the circuit in figure 2a`provide a copy of the
PSpice code and on one figure a copy of the PROBE for V(2), V(3), and V(4), and for the circuit in figure
2b a copy of the PSpice code and on one figure a copy of the PROBE output for V(2), V(3), V(4), and
V(5),. For each case, provide a one paragraph description of why the waveform for V(2) has the shape
presented in the simulation. Also, answer the following questions:
1. Why can the circuit in figure 2a be used to model the behavior of V(2) for the circuit of figure 2b?
2. What is the average power delivered to each of the loads in figure 2b? Note that the transmission lines
are lossless.
3. Can the reflected wave in the source transmission line be removed by choosing different terminating
loads on the two parallel transmission lines, i.e., is it possible to matched the source with two appropriate
parallel transmission lines with loads?
4. What happens to the average power for the loads if more than two matched parallel transmission lines
are connected to the source transmission line? Note that a matching network at the junction of the two
transmission lines to the source transmission line can be used to maximize the power to each load.
-
Figure 2 Transmission Line Measurement Circuits
Part II (laboratory project)
A. Lumped Parameter and Transmission Lines Circuit (figure 2a):
a) Step response
1. The simulation for a circuit with two transmission lines connected with a 50 ohm resistor in parallel
between them will now be verified with measurements. Before constructing the lumped parameter and
transmission lines circuit given in Figure 2a, connect the first BNC Tee to the scope channel 1 connection
so that V(2) will be used as the channel 1 input and trigger. Connect the banana load with 50 ohm resistor
directly to the first Tee without any transmission line, and observe the voltage V(2) for an input voltage of
1 MHz square wave with 1.0 Vpp and +500mV DC offset. Use the oscilloscope features to capture the
display of the voltage V(2) for your report.
2. Construct the circuit shown in Figure 2a using a matched load of 50 ohms; use two BNC tees at the
connection between the two transmission lines, one for adding the 50 ohm resistor in the connection
between the two transmission lines, and the other one to measure V(3) on channel 2 of the scope. Use
another BNC tee to connect the 50 ohm load, and to provide access to V(4) to be measured on channel 2 of
the scope. Using the same input voltage, observe the voltages V(2), V(3) and V(4) (note that either V(3) or
V(4) can be measured at one time). Capture the displays of the voltages V(2), V(3) and V(4) from the
oscilloscope for your report.
3. Compare the step response results of the simulation and measurement; how close are they?
Discussion: Notice that with a matched load, the reflection coefficient of the load Γ L = 0, and the value of
the reflected (negative going) wave in the second transmission line is zero. However, the voltage at the
load is not equal to the initial positive wave in the first (source) transmission line due to the parallel 50 ohm
-
resistor. Therefore, there is a reflected wave at the source. If the reflected wave is large enough and of the
correct sign, then the logic value at the source end could be complemented.
b) Sinusoidal response
1. Using the same circuit (figure 2a), disconnect the transmission lines and connect the banana load with 50
ohm resistor directly to the first Tee (no transmission line), and observe the voltage V(2) for an input
voltage of 10 MHz sinusoidal wave with a 1.0 Vpeak. Use the oscilloscope features to capture the display
of the voltage V(2) for your report.
2. Disconnect the 50 ohm banana resistor, and reconnect the transmission lines. Using the same input
voltage, observe the voltages V(2), V(3) and V(4) (note that either V(3) or V(4) can be measured at one
time). Capture the displays of the voltages V(2), V(3) and V(4) from the oscilloscope for your report.
3. Compare the sinusoidal response results of the simulation and measurement; how close are they?
Discussion: Again, the second transmission line is matched with no reflected wave, but the steady state
amplitude is decreased. If the input signal was a clock signal, then there would be two effects caused by
this circuit: time delay (clock skew) and a decrease in load (clock) voltage.
B. Multiple transmission lines circuit and loading (figure 2b)
a) Step response
1. The simulation for a circuit with one transmission line loaded with two matched transmission lines
connected in parallel will now be verified with measurements. Before constructing the multiple
transmission lines circuit given in Figure 2b, connect the first BNC Tee to the scope channel 1 connection
so that V(2) will be used as the channel 1 input and trigger. Connect the banana load with 50 ohm resistor
directly to the first Tee without any transmission line, and observe the voltage V(2) for an input voltage of
1 MHz square wave with 1.0 Vpp and +500mV DC offset. Use the oscilloscope features to capture the
display of the voltage V(2) for your report
2. Construct the circuit shown in Figure 2b using matching loads of 50 ohms; use two BNC tees at the end
of the source transmission line, one for connecting the two parallel load transmission lines, and the other
one to measure V(3) on channel 2 of the scope. Use the barrels to connect the 50 ohm loads with one of the
BNC tees to provide access to V(4) or V(5) as the situation requires for its measurement on channel 2 of
the scope. Using the same input voltage, observe the voltages V(2), V(3), V(4), and V(5) (note that either
V(3), V(4), or V(5) can be measured at one time). Capture the displays of the voltages V(2), V(3), V(4),
and V(5) from the oscilloscope for your report. Note that if you observe no measurable difference between
V(4) and V(5), then you can state something like “difference between V(4) and V(5) less than 5 mV”
stating your estimate of the maximum voltage difference; this estimate value should not be discernable in
the captured display, i.e., one display can represent both voltages.. .
3. Compare the step response results of the simulation and measurement; how close are they?
Discussion: Notice that with a matched load, the reflection coefficient of the load Γ L = 0, and the value of
the reflected (negative going) wave in the two load end transmission lines is zero. However, the voltage at
the either of the loads is not equal to the initial positive wave in the first (source) transmission line due to
the loading of the parallel matched transmission lines. Further, the results at the source V(2), the
connection V(3), and each load V(4) or V(5) is the same as the results with Part A. This means that the
circuit can be analyzed by replacing one of the parallel matched transmission lines by an equivalent circuit
of a 50 ohm lumped parameter element with respect to the values of the other source voltage V(2),
connecting voltage V(3), and either of the load voltages V(4) or V(5). This is an important observation for
simplifying the analysis of a PCB which has multiple parallel signal trances.
B. Sinusoidal response
1. Using the same circuit (figure 2b), disconnect the transmission lines and connect the banana load with 50
ohm resistor directly to the first Tee without any transmission line, and observe the voltage V(2) for an
input voltage of 10 MHz sinusoidal wave with a 1.0 Vpeak. Capture a display of the voltage V(2).
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2. Disconnect the 50 ohm banana resistor, and reconnect the transmission lines. Using the same input
voltage, observe the voltages V(2), V(3), V(4), and V(5) (note that either V(3), V(4), or V(5) can be
measured at one time). Provide displays of the voltages V(2), V(3), V(4) and V(5).
3. Compare the sinusoidal response results of the simulation and measurement; how close are they?
Discussion: The same observation with respect to equivalent circuits for the matched transmission lines
applies to the sinusoidal case. As for the step response, each of the load transmission lines is matched with
no reflected wave, but the steady state amplitude of the load is decreased. If the input signal was a clock
signal, then there would be two effects caused by this circuit: time delay (clock skew) and a decrease in
load (clock) voltage. With more clock signal traces with loads equal to the source impedance (50 ohms),
there would be more pronounced decreases in the load voltage, i.e., less clock power delivered. These two
phenomena are a big issue in the design of large synchronous digital chips such as FPGAs.
Conclusions
1) Discuss the overall comparison of the simulation results and the measured results.
2) Discuss the use of lumped parameter equivalent circuits for matched transmission lines, and its
applicability to the analysis of PCB circuit behavior.
Don’t forget the individual thoughtful, reflective paragraph from each lab group member at the end of your
report.
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