MULTIMEDIA UNIVERSITY
FACULTY OF ENGINEERING
LAB SHEET
ELECTROMAGNETIC THEORY
EMF2016
MW2 – IMPEDANCE MEASUREMENT AND MATCHING
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EXPERIMENT MW2:
IMPEDANCE MEASUREMENT AND MATCHING
OBJECTIVES:
a) To measure the normalized impedance of an unknown load.
b) To perform impedance matching using a slide-screw tuner and Smith Chart.
APPARATUS:
Klystron Source
Klystron Power Supply
Isolator
Slotted-line probe detector
SWR measurement amplifier/meter
Slide-Screw Tuner
Attenuator
Short-circuit Plate x 2
BNC coax cable x 1
Spanner
INTRODUCTION:
The ratio between the electric and the magnetic fields at a particular point along a
waveguide is defined as the impedance at that point. It may be denoted as Z = E / H = R +
jX. If there is no reflected wave, this ratio is the same at all points along the line. The
standing wave ratio (SWR) will be unity. In this case, the load absorbs all the incident
energy and is said to be matched to the characteristic impedance Zo of the waveguide. If a
reflected wave is present, causing a standing wave, then the impedance will vary
periodically with distance along the transmission path. It is therefore necessary to specify
the plane to which the impedance is defined when measuring an unknown impedance. It
can be shown that the relationship between SWR, reflection coefficient , and the
impedance Z at any point on the line be given by
Z - Zo
 = 
Z + Zo
1 + 
SWR = 
1  
= Z / Zo
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Smith Chart (see Appendix A) is usually used to analyze the values of R and X at
any distance along the transmission line. On Smith Chart, impedance values are normalized
with respect to the characteristic impedance Zo. Complete circles in the chart are curves of
constant resistance R/Zo. Incomplete circles which are at right angles to the complete
circles are curves of constant reactance jX/Zo. Thus, every point in the chart specifies a
normalized impedance Z/Zo=(R+jX)/Zo. The impedances at various points along the
waveguide lie on a circle with its centre at the centre of the Smith Chart. This circle is often
called the circle of constant mismatch (or the SWR circle). When the load is equal to Zo,
there is no mismatch and the radius of the SWR circle will be zero. The impedances at
various distances from a point (where the impedance is known) can be established by
moving around the SWR circle through the appropriate angles. The point where the SWR
circle crosses the horizontal axis on the right-side of Smith Chart (i.e. R/Zo + j0)
corresponds to a point of maximum electric field in the standing wave pattern. It also gives
the VSWR, since at this point the normalized resistance value is equal to the VSWR (i.e.
R/Zo = VSWR). The point at the opposite end of the horizontal diameter (on the left-side
of Smith Chart) corresponds to a point of minimum electric field and has impedance Z =
(1/VSWR) + j0.
To measure an unknown impedance, the SWR (=So) of the device connected to a
slotted-line waveguide and the position of one minimal point xo is determined (see Fig-1).
A circle corresponds to R+j0 where R=So is drawn on the Smith Chart. After that, the
unknown device is substituted by a short circuit plate. Two successive minimum points, x1
and x2, are noted. Twice the distance between them is the guide wavelength g. One of the
minimum points is used as reference. Let d = (xo - x1) / g. The impedance at the input
terminal of the unknown device can be found on the constant mismatch circle at a distance
d from the point of minimum electric field towards load if d  0; otherwise towards
generator. It should be noted that the impedance along the line is equal to the load
impedance at any integral number of half-wavelengths from the load.
Plane of
load
Emax2
minimum with
load, Emin2
xo d
x2
g / 2
x1
Fig 1 : Illustration to Impedance Measurement.
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When the load doesn’t match with the transmission line impedance, the reflected
energy is usually lost as heat and, in some cases, may destroy the source amplifier. It may
also cause a wide variation in performance when the condition is disturbed by, for example,
temperature change or signal frequency drift. Therefore, it is usually desirable that the load
accepts all the RF energy or additional impedance matching network can be incorporated
to the line in order to minimize the amount of energy reflected to the generator. In the case
of waveguide, a slide-screw tuner which consists of a slotted waveguide section and a
movable metal rod penetrating through the slot can be used for this purpose. A variable
capacitive susceptance is introduced in parallel to the transmission line by varying the
tuner’s protrusion depth.
A convenient feature of Smith Chart is that, if the normalized impedance is
represented by one point Z, then the normalized admittance (reciprocal of impedance) is
found by simply moving to the opposite end of the diameter through Z on the constant
mismatch circle. The admittance Y = G + jB changes along the waveguide according to the
values represented by the circle. A point Y1 can be found where the conductance G is equal
to the characteristic admittance Yo. If the susceptance at this point has a negative value (ie.
-jB), a slide-screw tuner can be used to add a susceptance +jB in parallel with Y so that the
combined susceptance will be zero and the resulting admittance Y’ will simply become Yo.
There may be a standing wave in the waveguide section between the tuner and the load but,
as far as the source generator is concerned, no part of the incident wave is reflected.
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PREPARATION
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Conduct background study about the experiment, e.g. read the lab sheet.
Bring log book for recording observations and results.
Bring scientific calculator.
Bring Smith Charts.
Bring a pair of compasses.
PROCEDURE:
CAUTION 1: The RF power levels in the following experiments are not harmful,
but a human eye may be damaged by low level of radiation. DO NOT LOOK
INTO THE WAVEGUIDE at any time when the equipment is on.
CAUTION 2: Klystron tube gets extremely HOT when it is operated and must
not be handled by hand.
A. Experiment Setup and Tuning (30 minutes)
The experimental setup (see Fig. 2) is similar to the setup used in MW1. The main
difference being a slide-screw tuner is inserted in between the transmission line and the
load. The slide-screw tuner allows a metal rod to protrude into the waveguide introducing
a shunt capacitance at the point of protrusion. The shunt capacitance introduced is
proportional to the depth of protrusion. It is used to perform impedance matching in this
experiment.
A1. The experiment setup is pre-assembled by the lab technician. Familiar yourselves
with the experiment setup and components.
A2. Seek the lab instructor assistance to tune the setup for optimal operation (see MW1
Appendix).
SWR
Meter
Klystron
Power Supply
Diode
Detector
Short
Circuit
Variable
Attenuator
Slide Screw
Tuner
Slotted Line
Fig. 2: MW2 Experiment Setup
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Isolator
Reflex
Klystron
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Note:
 Do not disturb the repeller voltage, slotted-line probe’s depth, and tuning gear beyond
this point. Else, the setup needs to be re-tuned.
 You may and indeed need to adjust the SWR meter gain, the slotted-line probe’s
position and the attenuator setting.
 Make your measurements at the central part of the slotted-line; avoid the two ends.
 All measurement readings have to be in the correct precision. Please make it a habit.
 Make your own tables of observations. Make it a habit too.
Evaluation A: (cognitive – knowledge, level 1)
i. Please make sure you know all components of the setup and their functions. You may
consult the lab instructor if necessary.
ii. Request for evaluation when you are ready.
B. Determine the Normalised Load Impedance (50 minutes)
B1. Replace the load (attenuator and short-circuit) by a short circuit plate. You need
spanners; borrow them from the lab technician. Do not turn off the Klystron Power
Supply. Do not look into the waveguide. Do not lose the screws.
B2. Move the slotted-line probe along the waveguide to locate two successive points of
minimum power*. Record the positions of these two points, x1 and x2. Determine the
waveguide wavelength g .
* The SWR meter used in the setup is a power meter with SWR scales on it (see MW1
Introduction). Power increases from left to right side of the scales.
The SWR meter has 3 gain knobs, one 10 dB step fixed gain knob (the big knob) and
two variable gain knobs (the smaller concentric knobs, one on top of another, for fine
and coarse gain adjustment, respectively)
As the slotted-line probe is moved towards the point of maximum power, the SWR
meter will show that power is increasing (pointer swing to right). As the probe reaches
the maximum and then moves away from the maximum, the SWR meter will show that
power reaches a maximum and then decreases (pointer swing to a rightmost point and
then swing to left). The minimum point can be determined in a similar way. Adjust the
SWR meter’s gain if necessary to have a decent deflection (swing) on the meter and to
avoid overdriving the meter.
B3. Restore the load. Do not turn off the Klystron Power Supply. Do not look into the
waveguide. Make sure the joints are tight, e.g. cannot be displaced by hand.
B4. Set the attenuator to 1.1 mm (about 6 dB return loss).
B5. Move the detector probe along the waveguide to locate the point of maximum power.
Henceforth, for convenience, it will be referred to as the maximum point (or
minimum point for minimum power).
B6. Adjust the gain of the SWR meter so that its reading is 0 dB on the bottom scale (i.e.
full scale deflection). Do not overdrive the SWR meter.
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B7. Move the probe to locate a minimum point (any minimum point). Record its position,
x0 . Read and record the SWR from the SWR meter**.
** There are 5 scales on the SWR meter. From the top, the first two are meant for the
“Expand” mode (Not used, the meter should have been preset to “Normal” mode).
Third and fourth are linear scales. The third scale is used when the maximum and
minimum are observed using the same gain setting. The fourth scale is used when the
minimum is observed using a step-gain 10 dB higher than that of the maximum. The
fifth or the bottom scale is a log scale (dB). Difference in step-gain between the
maximum and minimum should be added to the reading on the log scale to obtain the
SWR in dB.
B8. Calculate d = (x0 – x1) / g .
B9. Using the measured SWR, draw the SWR circle on a Smith Chart.
B10. Locate d on the “TOWARD LOAD” scale of the Smith Chart (if d < 0, use the
“TOWARD GENERATOR” scale instead). Hereafter, it is referred to as point E, see
Appendix B.
B11. Draw a straight line that passes through point E and the centre of the Smith Chart,
and crosses all the circles. There are two intersections between this line and the SWR
circle. The normalized load impedance zL is given by the intersection nearest to point
E. The farther intersection gives the normalized load admittance yL. With the aid of
the resistance/conductance grids and reactance/susceptance grids, read zL and yL. See
Appendix A and B.
Evaluation B: (psychomotor – complex overt response, level 5)
i. Tabulate your measurements and draw on the Smith chart.
ii. Be ready to demonstrate how the measurements were done.
iii. Request for evaluation when you are ready.
C. Impedance Matching Using Smith Chart (20 minutes)
C1. The line drawn in Step B11 also makes two intersections with the “TOWARD
GENERATOR” scale. Record the distance d1 on the “TOWARD GENERATOR”
scale (irrespective of the sign of d) for the farther intersection. See Appendix B.
C2. Determine the point y1 where the SWR circle intersects the unity constant resistance
circle. There are two intersections; use the one with negative susceptance. Draw a
line from the center of the Smith Chart, through y1, to the outer most circle. The line
will intersect the “TOWARD GENERATOR” scale. Record the distance d2 on the
“TOWARD GENERATOR” scale at the intersection point. See Appendix A and B.
C3. Calculate d = (d2 - d1)g
d is the distance from the load terminal towards generator where the input
conductance G will be equal to the characteristic admittance Yo.
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Evaluation C: (cognitive – application, level 3)
i. Draw on the Smith chart.
ii. Request for evaluation when you are ready.
D. Verify and Fine Tune Impedance Matching Conditions (60 minutes)
D1. The slide-screw tuner (hereafter referred to as tuner) acts as a variable shunt
capacitor. For impedance matching, it should be placed d from the load terminal.
Note that d is measured from the load towards generator. d computed from Step
C3 may not give a practical position to insert a tuning screw. In that case, add an
integral number of half-wavelengths (ng/2) to d in order to determine a practical
position to insert a tuning screw. Record the distance Do = d + ng/2 from the load,
where the tuning screw is to be inserted.
D2. Position the tuner at distance Do from the load terminal. The distance between the
load terminal and the beginning of the vernier scale on the tuner is 50 mm.
D3. Measure the SWR before impedance matching (see Steps B5 to B7). Henceforth, it
will be referred to as the initial SWR.
D4. Increase the tuner (not slotted-line probe!) protrusion depth slowly until there is a
noticeable change in the meter reading. Re-measure the SWR at this point.
D5. If the new SWR is less than the initial SWR, proceed to step D6. Otherwise, there
were errors in impedance matching calculations and Do is not correct. Move the tuner
to the left or right (without disturbing the protrusion depth and choose a direction
with ample movement space) 2 mm at a time. Re-measure the SWR after every
movement. The SWR will eventually drop to a minimum and rises again. Reduce the
movement step when you are close to the minimum. Locate this point of SWR
minimum.
D6. At this point, you should have a new SWR less than the initial SWR.
D7. Increase the tuner protrusion depth slowly until there is a noticeable change in the
meter reading. Re-measure the SWR.
D8. Repeat step D7. As the tuner protrusion depth increases, the SWR will drop to a
minimum and rises again. Reduce the movement step when you are close to the
minimum. Locate this point of SWR minimum.
D9. If the new SWR is less than 1.1, proceed to step D10. Otherwise, further fine tuning
is required. With the protrusion depth intact, change the tuner position slowly and
locate the point of SWR minimum. Then, with the position intact, change the tuner
depth slowly and locate the point of SWR minimum. Repeat and alternate the position
and depth tuning until the SWR is less than 1.1.
D10. Record the final SWR = S1 achieved, the position D1 of the tuner, and the protrusion
depth p.
Evaluation D: (psychomotor – adaptation, level 6) [40 marks]
i. Tabulate your results.
ii. Be ready to demonstrate the impedance matched state.
iii. Request for evaluation when you are ready.
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APPENDIX A
reactance/susceptance grids
“TOWARD GENERATOR” scale
SWR circle
unity constant
resistance/conductance circle
centre
0 + j0
SWR
resistance/conductance grids
Intersections with
the unity circle
“TOWARD LOAD” scale
http://www.sss-mag.com/pdf/smithchart.pdf
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APPENDIX B
SWR circle
d1 (25)
yL
d
zL
E
y1 (26)
d2 – d1
d2 (26)
http://www.sss-mag.com/pdf/smithchart.pdf
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http://www.sss-mag.com/pdf/smithchart.pdf
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