MULTIMEDIA UNIVERSITY
FACULTY OF ENGINEERING
LAB SHEET
ELECTROMAGNETIC THEORY
EMF2016
MW1 – MICROWAVE FREQUENCY AND SWR MEASUREMENTS
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EXPERIMENT MW1:
MICROWAVE FREQUENCY AND SWR MEASUREMENTS
OBJECTIVES:
1.
2.
3.
4.
5.
To demonstrate standing wave pattern developed along a waveguide.
To make direct SWR measurements using an SWR meter.
To make indirect SWR measurements using the Double Minimum Method.
To make a direct frequency measurement using a cavity wavemeter.
To make an indirect frequency measurement via a waveguide wavelength
measurement.
APPARATUS:
Klystron Source
Klystron Power Supply
Cavity Wavemeter
Isolator
Slotted-line probe
SWR meter
Variable attenuator
Short-circuit plane
BNC coax cable x 1
INTRODUCTION:
At radio frequencies (RF) and microwave frequencies, signals must be viewed
as waves instead of currents and voltages. One of the reasons is the wavelength becomes
very short that the current at one point of a long conductor is not the same as that at
another point. As a result, the ordinary Circuit Theory can no longer be used for the
analysis of transmission lines that have a physical dimension greater than 1/10 of the
signal wavelength. This kind of problems can be solved using Electromagnetic Theory.
The electromagnetic field at any point on a transmission line may be considered
as the sum of two traveling waves: the incident wave propagates from the generator and
the reflected wave from the load. These give rise to a standing wave along the line due
to constructive and destructive interference, as shown in Fig. 1. The electromagnetic
field strength varies periodically with distance. The maximum field strength Emax is
found where the two waves add in phase, and the minimum Emin where the two waves
add in opposite phase. The Voltage Standing Wave Ratio (VSWR or just SWR) is
defined as the ratio of the maximum to the minimum field strength along the line, as
given in Eq. (1). It is a parameter used to describe the size of standing wave or the
strength of reflected wave relative to that of incident wave. The SWR will be higher
(i.e. larger peaks and nulls in the standing wave pattern) if there is more wave power
reflected from the load end. The magnitude and phase of the reflected wave are related
to the load impedance which is generally a complex value. Thus, the SWR and the
positions of constructive and destructive interference depend upon the load impedance.
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Power
Emax2
Emin2
Distance
g / 2
Fig. 1: Standing wave pattern
For a waveguide system, the SWR can be measured using a slotted-line method.
A short length of wire, acting as a probe, protrudes into the waveguide through a
longitudinal slot to couple to the electric field confined within the waveguide. A small
fraction of power is picked up and detected by a diode detector connected to the other
end of the probe. By sliding the probe along the longitudinal slot, the maximum power
Pmax and minimum power Pmin can be measured. The SWR is then given by
SWR 
E max
Pmax

Pmin
E min
or
20 log 10 SWR  Pmax (dBm)  Pmin (dBm)
(1)
(2)
In normal operation, the diode detector gives a voltage which is proportional to
the electromagnetic wave power (or square of the electric field strength). This is the
case if the power is small enough to allow the diode detector to work in its “square-law”
region. The probe must not protrude too deep into the waveguide so that the power
picked up by the probe is small. This is also necessary to ensure that the field
distribution in the waveguide is not significantly disturbed.
An SWR meter can be used to give direct readings of SWR. A simple one
consists of a power meter with SWR scales on it. One way to establish an SWR scale
on a power meter is to make Pmax a known constant using a variable gain amplifier. A
convenient constant for this purpose is the full scale value of the power meter. With
Pmax made constant, there is a one-to-one conversion between Pmin and SWR, and SWR
values can be marked on the power meter in place of the power values. Fig. 2 shows an
example SWR meter. There is a power scale and an SWR scale on the meter. To use
the SWR scale, one has to first set Pmax to the full scale value, 1 W in the example, with
the aid of a variable gain amplifier. Then, Pmin is measured. The SWR will be
SWR 
Pmax

Pmin
1
Pmin
(3)
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Note that this is exactly the relationship between the power and SWR scales. In other
words, the SWR can be read directly from the meter at the point of P min, no further
division is necessary.
0.4
0.2
0.6
0.8
1.0
0
2.2
1.6
1.3
Power (W)
SWR
1.1

1.0
Fig. 2: An example SWR meter
For the case where the SWR is high (for example, SWR > 3), the null points of
the standing wave pattern along the waveguide may have very low field strength. The
probe depth can be increased so that a sufficiently high meter deflection can be obtained
at the minimum power point. However, this will deform the field when the probe is
moved to the maximum power point. Also, the large electric field strength at the
maximum point may cause the diode detector to operate out of the “square-law” region.
The above problem can be overcome using the “Double Minimum Method”. In this
method, one measures the distance between the points where the detector output is
double the minimum field strength, as illustrated in Fig 3. It can be shown that the SWR
is given by:
SWR 
E max
1
 1
E min
sin 2 d / g


Power
d
Emax2
2Emin2
Emin2
3 dB
Distance
g / 2
d1
d2
Fig. 3: The Double Minimum Method
(4)
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A wavelength is defined as the distance between two successive points with the
same phase on a waveform. An electromagnetic wave is reflected from one
waveguide’s wall to another as it propagates along a waveguide As a result, the apparent
longitudinal wavelength is different from the free-space wavelength, as shown in Fig.
4. The relationship between the apparent longitudinal wavelength or simply waveguide
wavelength g and the free space wavelength o is given by:
1

2
o

1

2
g

1
(5)
c2
where c is the cutoff wavelength for the particular mode of propagation. For an
electromagnetic wave with freespace wavelength equals to c, g will be infinitely long,
which means that no field variation occurs along the waveguide. A wave with freespace
wavelength equals or larger than c would not be able to propagate through the
waveguide (in the particular mode of propagation) and therefore c is called the cutoff
wavelength (for the particular mode of propagation). For the usual TE10 dominant mode
operation of a rectangular waveguide, c = 2a with ‘a’ being the broad-face dimension
of the waveguide.
waveguide’s wall
equiphase
wavefront
o
plane wave
propagation
g
the longitudinal
direction
Fig. 4: Waveguide wavelength
Eq. (5) provides an indirect way of measuring the signal frequency. The
waveguide wavelength g can be measured as twice the distance between two
successive minimum points of the standing wave pattern. Using Eq. (5), the free space
wavelength can be calculated. The frequency f can be determined using the relationship
u = fo, where u is the speed of light in the waveguide medium. For an air-filled
waveguide, u = 3  108 m/s.
Frequency can also be measured using a variable size resonant cavity known as
cavity wavemeter. A resonant cavity is made of a rectangular or circular waveguide
with both ends short-circuited. A cavity wavemeter is coupled to a waveguide by a
small hole. Because the hole is small, the cavity wavemeter can normally absorb only
a tiny fraction of the energy propagating in the waveguide. At a certain cavity size, a
standing wave can be set up and sustained between the cavity walls. When this happens,
the cavity will absorb a larger fraction of power from the waveguide system, which
results in a progressive building up of the the standing wave within the cavity. This in
turn causes a small dip in the power in the down-stream of the waveguide system. In
this condition, the cavity is said to be in resonance with the signal frequency. The
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resonant frequency can be calculated by solving Maxwell’s equations with the
dimensions of the cavity defining the boundary conditions. Varying the cavity size will
alter the resonant frequency. Some cavities are marked in frequency for direct
measurement reading. Others come with calibration charts so that the frequency can be
read off the charts. It is important to note that resonant frequency is not unique. There
are numerous resonance modes, each gives rise to a different resonant frequency. A
solution to this problem would be to use only the dominant resonant mode (lowest
resonant frequency), to search for the resonance from the smallest cavity size and
gradually increasing its size, and to read from the first resonance occurrence.
In the following experiments, you will trace out the standing wave pattern
developed along a waveguide. You will make direct and indirect SWR measurements
using an SWR meter and the Double Minimum Method, respectively. Also, you will
make direct and indirect measurements of the signal frequency using a cavity
wavemeter and Eq. (5), respectively.
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PREPARATION
 Conduct background study about the experiment, e.g. read the lab sheet.
 Bring log book for recording observations and results.
 Bring scientific calculator.
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 get extremely hot when it is operated and must
not be handled by hand.
A) Experiment Setup and Tuning (30 minutes)
Fig. 5 shows the experimental setup. It mainly consists of a microwave source (Klystron
source), a transmission line (slotted-line), and a variable load (variable attenuator and
short-circuit termination). An isolator is used to protect the source from reflected power.
The cavity wavemeter is for direct frequency measurement. Further details about the
components are given in the Appendix.
SWR
Meter
Klystron
Power Supply
Diode
Detector
Short
Circuit
Variable
Attenuator
Slotted Line
Cavity
Wave Meter
Isolator
Reflex
Klystron
Fig. 5: Slotted-line measurement setup
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
Appendix).
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.
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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) The Standing Wave Pattern (40 minutes)
B1. Set the attenuator’s micrometer setting to 1.1 mm (this corresponds to about 6 dB
return loss, i.e. reflected power is 6 dB below the incident power).
B2. Move the probe along the slotted-line 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).
B3. Adjust the gain of the SWR meter* so that its reading is 1 dB on the bottom scale
(an arbitrary value close to but not full scale deflection so that you can observe
the pattern peak). Do not overdrive the SWR meter.
B4. Move the probe along the slotted-line to locate and record the positions of
maximum and minimum points.
B5. Record your observations of power variation along the slotted line.
* The SWR meter used in the setup is a power meter with SWR scales on it (see
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.
Evaluation B: (psychomotor – complex overt response, level 5)
i. Tabulate your measurements.
ii. Be ready to demonstrate the standing wave pattern.
iii. Ask for evaluation when you are ready.
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C) Measure SWR Using an SWR Meter (30 minutes)
C1. Set the attenuator’s micrometer setting to 1.5 mm (about 12 dB return loss).
C2. Move the probe along the slotted-line waveguide to locate the maximum point.
C3. Adjust the gain of the SWR meter so that it has full scale deflection at the
maximum point (0 dB on the bottom scale).
C4. Move the probe to locate the minimum point. Read and record the SWR from the
SWR meter**.
C5. Set the attenuator to 1.1 mm (about 6 dB return loss). Repeat steps C2. to C4.
C6. Set the attenuator to 0.5 mm (about 2 dB return loss). Repeat steps C2. to C4.
** 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.
Evaluation C: (psychomotor – complex overt response, level 5)
i. Tabulate your measurements.
ii. Be ready to demonstrate how the measurements were done.
iii. Ask for evaluation when you are ready.
D) Measure SWR Using The Double Minimum Method (40 minutes)
D1. Set the attenuator to 0 mm (about 0 dB return loss).
D2. Move the probe along the waveguide to locate two successive minimum points.
Adjust the SWR meter gain if necessary to have a decent deflection at the
minimum points. Record the positions of these two points (x1 and x2). Determine
the waveguide wavelength g (see Introduction).
D3. Set the attenuator to 1.1 mm (about 6 dB return loss).
D4. Move the probe along the waveguide to locate the minimum point.
D5. Adjust the SWR meter gain to obtain a reading of 3 dB on the bottom scale (the
power is 3 dB below that at 0 dB).
D6. Move the probe to the left of the minimum point until the detected power
increases to 0 dB (this point has power 3 dB (= double) more than the minimum,
see Fig. 3). Record the probe position, d1.
D7. Move the probe to the right of the minimum point until the detected power
increases to 0 dB. Record the position d2.
D8. Calculate the SWR using Eq. (4).
D9. Set the attenuator to 0.5 mm (about 2 dB return loss). Repeat steps D4. to D8.
Evaluation D: (psychomotor – complex overt response, level 5)
i. Tabulate your measurements.
ii. Be ready to demonstrate how the measurements were done.
iii. Ask for evaluation when you are ready.
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E) Frequency Measurement (20 minutes)
E1. Using the waveguide wavelength g from Experiment D, calculate the free-space
wavelength o using Eq. (5). The inner dimensions of the waveguide are a =
2.2870 cm and b = 1.0160 cm. Calculate also the frequency fo = c / o .
E2. Set the attenuator to > 2.8 mm (> 20 dB return loss).
E3. Adjust the SWR meter gain to have a decent deflection on the meter.
E4. Starting with the cavity wavemeter dial set to maximum clockwise, unscrew the
dial slowly. Initially there will be little effect on the SWR meter reading. At one
point, cavity resonance causes a noticeable dip*** in signal power (so is the meter
reading). Read the resonant frequency fo’ of the cavity wavemeter at this point.
***
In some cases, the power dip is small. Though small, the dip is noticeable if
monitored closely. A quick approach to locate the dip is to rotate the wavemeter
at moderate speed while closely monitoring the meter deflection. When a
suspect dip is found, rotate the wavemeter forward and backward about the
suspect dip to verify.
Evaluation E: (psychomotor – complex overt response, level 5)
i. Tabulate your measurements.
ii. Be ready to demonstrate how the measurements were done.
iii. Ask for evaluation when you are ready.
F) Discussions (homework)
1. Compare the SWR measurements you obtained from the SWR meter (Experiment
C) and that from the Double Minimum Method (Experiment D).
2. Estimate return losses from the SWR measurements (see Appendix). Discuss
whether the estimated return losses are consistent with the given attenuator settings.
3. Compare the frequency measurements fo and fo’ .
4. Discuss the sensitivity of error in fo to error in slotted-line-probe position
measurements (e.g. what is the frequency error if position measurement has 0.1 mm
error?)
Evaluation F: (cognitive – analysis, level 4)
i. Write a summary of this lab experiment. The lab report should include
a. An introduction section to explain the theory behind the experiment.
b. An experimental setup section to explain how the experiment was
conducted.
c. A results and discussions section to present and discuss the results.
d. A conclusion section to conclude the experiment.
ii. Do not copy anything from this lab sheet. Plagiarism is strictly prohibited.
iii. Submit the lab report to the lab technician within 7 days from the day the
experiment was conducted. Late submissions are subjected to penalty.
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APPENDIX
Initial setup and tuning
The setup in Fig. 5 needs to be tuned for optimal signal strength before use. This
includes tuning the Klystron source’s repeller voltage for maximum output power, the
tuning gear and the source’s modulation frequency and amplitude for maximum
reception at the SWR meter. This should be done >30 minutes before use.
1.
2.
3.
4.
5.
6.
Set up the equipment as shown in Fig 5.
Set the cavity wavemeter dial to maximum clockwise.
Set the SWR meter input setting to ‘XTAL LOW’.
Set the slotted-line probe’s depth to 0.5 mm.
Set the attenuator to > 2.8 mm (> 20 dB return loss).
Make sure that the SWR meter is in the “normal” deflection mode (set by the
smaller dial at and on top of the step-gain knob).
7. Switch on the Klystron power supply (with internal modulation active) and SWR
meter.
8. Adjust the SWR meter’s gain until a significant deflection appears on the meter.
9. Adjust the repeller voltage knob for maximum reception at the SWR meter.
10. Adjust the tuning gear of the slotted-line probe for maximum reception at the SWR
meter.
11. Adjust the modulation frequency and amplitude for maximum reception at the SWR
meter.
12. At this stage, the SWR meter should give a good deflection at gain settings of 30 to
40 dB. If necessary, increase the slotted-line probe’s depth to achieve the stated
condition. Make sure that a full deflection can be obtained by adjusting the vernier
gain knob.
Isolator
An isolator is a non-reciprocal device, which attenuates waves propagating in one
direction and on the other hand causes negligible attenuation for waves propagating in
the opposite direction. Such a device is, therefore useful in transferring power from a
microwave generator to the load with negligible loss and at the same time ensuring all
reflections from the load end are completely absorbed by the time they reach the
generator. This is important to ensure that the frequency stability and output power level
are not affected by the load variation.
The isolator must be connected in the proper direction. An arrow, which indicates the
forward (lossless) direction, usually comes with the label on the device.
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Variable Attenuator
An attenuator can be constructed by placing a resistive card (made of lossy material) at
the centre of a waveguide section at which the electric field strength is the highest for
TE10 mode. A fraction of the microwave will be absorbed, with the remaining power
transmitted. The resistive card is tapered at both ends to maintain a low VSWR. A
variable attenuation can be realised by varying the position of the resistive card across
the waveguide broad dimension. If the device is terminated with a short-circuit plane,
a variable load impendence can be emulated for which the return loss is equal to twice
the attenuation level (in dB). For example, if attenuation is 3 dB, then
Return loss   20 log   6dB
where  is the reflection coefficient
  0.50 .
And,
SWR 
1   1  0.50

 3.01
1   1  0.50
wave propagation
Tapered resistive card
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Cavity Wavemeter
A cavity resonator is a rectangular or circular waveguide with both ends short-circuited.
A given resonator can have an infinite number of resonant modes, and each mode
corresponds to a definite resonant frequency. The mode having the lowest resonant
frequency is known as the dominant mode. When the frequency of the wave signal is
equal to a resonant frequency, a standing wave will be set up in the cavity.
high-order
mode
moving
plunger
dominant
mode
The cavity resonator can be used as a frequency meter. A moving plunger in the cavity
gives a variable resonant frequency. If the cavity is coupled to a waveguide system, a
small amount of energy will be extracted through the coupling hole only if the resonant
frequency is tuned to the frequency of the waves. At other frequencies, it will have no
effect. An absorption-type cavity wavemeter acts by absorbing a small amount of the
microwave power at its resonant frequency causing a small dip in the indicated power
in the waveguide system. The transmission-type wavemeter acts as a high-Q bandpass
filter. The power extracted by the cavity is coupled to an output waveguide or detector.
Calibration against some standard frequencies is usually performed and a calibration
chart or a direct-reading scale can be produced to relate the cavity size to resonant
frequency.
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Slotted-line Probe
The electromagnetic field at any point along a transmission line may be considered as
the sum of two travelling waves; the incident wave generated by the source, and the
returned wave reflected by the load. The interference between the two travelling waves
gives rise to a standing wave. The maximum field strength is found where the two
waves add in phase, and the minimum is encountered where the two waves add in
opposite phase. The distance between two successive minimum field points
corresponds to one half the guide wavelength g. The Voltage Standing Wave Ratio
(VSWR) can be determined by taking the ratio of the maximum field strength Emax
over the minimum Emin .
Variable shortcircuit tuner
slotted
waveguide
A
SWR
Meter
The electric field strength along the waveguide can be probed using a slotted-line
section. A short length of wire (electric probe) is inserted so as to couple to the electric
field in the interior of the waveguide. The probe is mounted on a carriage, which slides
along the slot. The field ‘picked up’ by this probe may be detected by a diode detector.
By moving the probe along the slot, a sampling of the E-field variation can be
performed. Usually the probe protrusion into the waveguide is adjustable so that
coupling is variable. The deeper the protrusion, the larger will be the detected output.
However, the shortest length of the probe is preferred because the deeper the protrusion
the greater will be the perturbation of the probe to the fields within the waveguide. In
some designs, a tunable stub assembly is cascaded with the probe so as to maximise the
detector output. In addition, this tuning also serves to minimise the small loading effect
(i.e. shunt capacitance and resistance) of the probe on the transmission line circuit.
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Microwave Diode Detector
When microwave voltage is applied across a diode (pint-contact diode or Schottkybarrier diode), a DC current is produced. If the microwave is AM modulated, the output
current will be the modulating signal with a frequency span from DC up to a few MHz.
The current is proportional to the microwave power. This is true if the diode is operating
in the ‘square law’ region of the non-linear I-V characteristic curve at which the
incremental current I is proportional to the square of the incremental voltage V across
the diode. The applied signal level must be low enough to prevent saturation. Otherwise,
the diode will operate in the linear region and the current will instead be proportional
to the applied voltage. In order to obtain maximum output, the impedance of the
detector should be matched to the characteristic impedance of the transmission line. In
the case of a standing wave indicator, this is usually accomplished by using a movable
coaxial short circuit known as the stub the matching tuner.
SWR Meter
The output from a diode detector is usually very low in amplitude. A high gain tuned
amplifier is incorporated in the SWR meter to amplify this detected signal prior to the
displaying meter. The bandpass response of the tuned amplifier shall be set at the
modulating signal frequency range. Tuning of the centre frequency and the bandwidth
may improve the signal selectivity.
Square law characteristic ( I o  KVs2 ) of the detector is usually assumed, and the SWR
meter scales are then calibrated such that the needle deflection is proportional to the
microwave power ( P  Vs2 R  K ' I o ). The gain of the amplifier may be adjusted
subject to the range of signal level being measured so that the reading is within the
meter scales.
Klystron Source
There are basically two types of Klystron tubes: reflex-type and single-transit-type. The
reflex Klystron is generally used in microwave oscillators. A highly focused beam of
electrons passing through the cavity gap will be accelerated or decelerated by the
induced current on the cavity. The alternate action of increasing and decreasing the
electron velocity will modulate the electron beam into varying dense and sparse of the
electrons referred to as electron bunches. This electron bunching mechanism is also
called intensity modulation or velocity modulation. At the exit chimney of the cavity
gap, a high negative electrostatic potential on the repeller will stop the movement of the
electrons, turn them around and send them back through the cavity gap. As the repelled
electrons re-enter the cavity, they give up their energy. Their volume charge due to
bunching will be phased such that it reinforces the next wave of bunched electrons. As
a result, this energy serves as a regenerative feedback to sustain the oscillation at the
resonant frequency of the cavity. This is the case if the repeller voltage is set such that
the electrons complete their travel through the gap, turn around, and back through the
gap in three-quarter cycle of the RF waveform. In other words, the Klystron tube will
oscillate only if the repeller voltage is properly set within certain voltage ‘windows’.
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Switching the repeller voltage in and out of the operating region will produce an overmodulated AM waves in the form of the square pulses. The oscillation frequency may
be altered by turning the compression set screw that changes the cavity size.