CEVA, HEVA: measurements on waveguide link
3. Measurements on waveguide link
3.1 Introduction
In a waveguide, electromagnetic wave propagates by the phase velocity vf. The phase velocity
depends on the shape and the dimensions of the transversal cross section of the waveguide, on
parameters of environment inside the waveguide (permittivity, losses) and on frequency. The phase
velocity of the dominant mode TE10 of the rectangular waveguide is
vf 
c
1   0 2a 
(3.1)
2
Here, a is the width of the waveguide, c is velocity of light and 0 = c/ f is the wavelength in free
space (vacuum). If the phase velocity is known, the wavelength in a waveguide can be computed
g 
vf
(3.2)
f
If the waveguide is excited by a wave of a frequency which is lower than the cutoff frequency of the
waveguide, the wave is reflected back to the source from the input of the waveguide, and no energy
passes the waveguide. The cutoff frequency can be computed according to
2a   0 
c
f
(3.3)
If the waveguide is not terminated by the matched load, a part of energy is reflected back to the
source, and a standing wave is formed in the waveguide. The distance of neighboring minima of the
standing wave is
x 
g
2

vf
(3.4)
2f
The distance of neighboring maxima of the standing wave is the same.
The standing wave can be described by the standing wave ratio (SWR). SWR is a ratio of the
amplitude of the standing wave in maximum and in minimum
PSV 
U max
U min
(3.5)
If the load is perfectly matched (no energy is reflected back to the source), PSV = 1. If the load is
perfectly unmatched (all the energy is reflected back to the source), PSV  .
Magnitude of the reflection coefficient can be computed from PSV
 
PSV  1
PSV  1
(3.6)
If losses in the waveguide are negligible, the magnitude of the reflection coefficient stays constant
along the whole transmission line. Phase of the reflection coefficient on the load is
 0    2
2
g
xm
(3.7)
where xm is the distance of the minimum of the standing wave from the load.
- 3.1 -
CEVA, HEVA: measurements on waveguide link
If the end of the waveguide is shorted, the first minimum of the standing wave is in the
distance g/2 from the short end. Considering (3.7), the phase on the load is (0) = 3. Reflection
coefficient at the end of the waveguide is (0) = 1. Field intensity in minimum is Umin = 0 and
PSV   according to (3.5).
3.2 Measurement method
The measurement set consists of a microwave generator G, a variable attenuator A and a
waveguide link with a waveguide R100 (rectangular cross section). Voltage at the output of a diode
detector is measured by a millivolt-meter mV (Fig. 3.1).
mV
G
A
linka
Z
Fig. 3.1 Measurement setup.
The sliding unit of a link contains a probe, which is sensing electric field in a waveguide,
a resonator and a detector. The detector transforms a high-frequency voltage induced in the probe to
a direct (or low-frequency) voltage which can be simply measured. Sliding the unit along the
waveguide, the output voltage of the detector varies in relation to the field intensity in the position
of the probe. Using the scale on the link, we can determine positions of minima and maxima of the
standing wave. Considering the value given by the meter (after the correction of the non-linearity),
standing wave ratio can be computed.
For measuring wavelength of the waveguide, the waveguide should be terminated by the short
circuit because minima of the standing wave are very sharp then. The first minimum of the standing
wave is in the position of the short circuit and other minima are repeating with the period g / 2.
An unknown load can be characterized by the reflection coefficient (0) Magnitude of the
reflection coefficient can be computed from the measured standing wave ratio SWR (relation 3.5).
Phase of the reflection coefficient can be determined from the shift of the positions of the minima of
the standing wave with respect to positions of the short-ended waveguide (see relation 3.7).
3.3 Tasks
1.
Positions of minima of the standing wave on a short-ended waveguide are measured, and their
distance is computed. Wavelength in the waveguide is determined and is compared with the
computed wavelength.
2.
For given loads (a horn antenna, an open waveguide), we determine standing wave ratio and
reflection coefficient (both the magnitude and the phase) on the load. Matching of measured
loads should be evaluated.
3.
Output voltage of the detector is measured between the minimum and the maximum of the
standing wave when the waveguide is terminated by the short circuit. Calibration chart of the
detector is drawn and is used for the verification of the measurements of loads in the task 2.
- 3.2 -
CEVA, HEVA: measurements on waveguide link
3.4 Comments on measurements
In order to detect the voltage by a low-frequency millivolt-meter, a microwave generator has
to generate a signal with an amplitude modulation. The modulation depth can be arbitrary since
does not influence accuracy of measurements (30 % is recommended). When adjusting and
calibrating the generator, instructions available in the lab have to be followed.
During the measurement, the generator should not be influenced by changes of loads. The
attenuator A (Fig. 3.1) is therefore conceived as a cascade of two attenuators. The first attenuator
(closer to the generator) does not need being scaled; its attenuation protects the generator. The
second attenuator is used for measurements. For an accurate adjustment of the attenuation, we use
a linear scale (black) and the correction curve. An auxiliary scale in dB (red) can be used for
verifications and an inaccurate determination of the attenuation.
1
2
3
Obr. 3.2 Sliding unit with probe, resonator and detector: (1) screw for adjusting the depth
of inserting the probe, (2) screw for tuning resonator to resonance, (3) screw for
sliding the unit along the link.
In a wider wall of the waveguide, a groove is drilled so that the probe can be inserted into the
waveguide so that the electric field can be sensed. The depth of inserting the probe into the
waveguide can be changed by the screw 1 at the top of the probe (Fig. 3.2). In case of a deeper
insertion, field in the waveguide is deformed and results of measurements are distorted. Therefore,
the depth of the insertion should not be changed.
The unit is sliding by the screw 3 along the link. The position of the unit is measured on a
scale. A voltage induced in the probe excites the cavity resonator. The resonator has to be tuned to
the resonance by the screw 2 in the center of the probe. The resonance is indicated by the maximum
value on the millivolt-meter. The value of the signal should be limited by the attenuator so that the
voltage at the input of the millivolt-meter from 10 mV to 30 mV in the maximum.
When measuring the wavelength in the waveguide, the link is terminated by the short circuit
and positions of minima of the standing wave are determined along the whole link. In order to
increase the accuracy, an average distance between neighboring minima is computed and used for
determining the wavelength.
When measuring the reflection coefficient of a load, the load replaces the short circuit at the
end of the link, and positions of minima of the standing wave are determined. The shift of the
positions of minima with respect to the short circuit determines the value xm in (3.7) to be used for
computing the phase of the reflection coefficient. If minima are shifted towards the generator, the
value of xm is positive.
Magnitude of the reflection coefficient is computed from SWR using (3.6). Computations are
complicated by the non-linearity of the detector (the value at the output of the detector does not
linearly depend on the high-frequency signal in the position of he probe). The influence of this non-
- 3.3 -
CEVA, HEVA: measurements on waveguide link
linearity can be eliminated by exploiting the meter at the output of the detector as an indicator of a
given value:
 The probe is shifting to the minimum. A proper value on the meter is adjusted by the
attenuator, and the attenuation of the attenuator is recorded.
 The probe is shifting to the minimum. The attenuation of the attenuator is increased so that
the meter can indicate the same value.
 The standing wave ratio is computed SWR (v dB) as a difference of attenuations of the
attenuator.
Non-linearity of the detector does not play any role because the meter indicated the same value of
the signal in the position of the probe.
In the described measurement procedure, values on the meter in the maximum and the
minimum with the same attenuation of the attenuator should be recorded. These values can be used
for the verification of SWR with the calibration chart of the detector.
If extensive measurements are planned, the calibration chart of the detector should be
measured. The calibration chart is the dependence of the high-frequency voltage at the output of the
probe Uvf and the low-frequency voltage Udet, which is detected by the meter. The calibration chart
Uvf = f( Udet) is used when correcting the non-linearity of the detector.
When measuring the calibration chart, the link is terminated by the short end (the standing
wave is harmonic). The probe is sliding to proper positions xi and values on the meter Udet are
recorded. The value of the high-frequency signal in the position of the probe is computed
considering the harmonic dependency of the standing wave
 2


U vf  U sin 
xi  x0 
 g



Here, x0 is the position of the minimum on the short-ended link and U is the constant of
proportionality.
During the measurement, we record Udet from the low-frequency meter, and the calibration
chart is used to obtain a corresponding Uvf / U. When evaluating SWR according to (3.5), we
compute the ratio of voltages, and the constant of probability U vanishes.
3.5 Processing results in MATLAB
When measuring the wavelength in the waveguide, positions of six minima has to be
determined x(1), x(2) to x(6). Consequently, we compute the average value of distances
between two neighboring minima
lam = 0;
for n=1:5
lam = lam + (x(n+1) – x(n));
end
lam = lam / 5;
Now SWR of a given load is going to be computed. We measured the standing wave ratio SWR (in
dB) as a difference of attenuations of the attenuator in the minimum and the maximum of the
standing wave PSV_dB. The values of SWR is sufficient to be recomputed from decibels to absolute
measures SWRdB = 20 log (SWR); i.e.
PSV = 10^(PSV_dB / 20);
- 3.4 -
CEVA, HEVA: measurements on waveguide link
Substituting SWR to (3.6), the magnitude of the reflection coefficient can be computed
rho = (PSV – 1) / (PSV + 1);
We measured that the first minimum of the standing wave is in the distance x_min from the end of
the waveguide. Substituting to (3.7), we can compute the phase of the reflection coefficient on the
load
phi = pi + 4*pi*x_min/lam;
% result in radians
Now, the calibration chart is going to be created. The position of the probe y(n) and the detected
voltage Udet(n) is measured in 10 points between the minimum and the maximum; n=1:10. The
corresponding high-frequency voltage can be computed as follows:
for n=1:10
Uvf(n) = Udet(10) * sin( 2*pi*( x(n)-x(1)) / lam);
end
The dependence Udet on Uvf is shown in a chart
plot( Udet, Uvf);
That way, results of measurements are processed.
- 3.5 -