EXPERIMENT 2
SWR MEASUREMENTS
OBJECTIVE
To become familiar with basic slotted line SWR measurements and the use of the SWR-meter.
THEORY
The electromagnetic field at any point of a transmission line (e.g. a waveguide) may be considered
as the sum of two traveling waves: the incident wave propagates from the generator, the reflected
wave propagates toward the generator. The reflected wave is set up by reflection of the incident
wave from a discontinuity on the line or from a load impedance not equal to the characteristic
impedance of the line. The magnitude and phase of the reflected wave depends upon the amplitude
and phase of the reflecting impedance. The magnitude also depends upon the losses on the line.
On a lossy line the reflected and incident waves will be attenuated. If the line is uniform and
infinitely long, there will be no reflected wave. The same is true for a line of finite length that is
matched, i.e. has a load impedance equal to the characteristic impedance of the line. The presence
of two waves traveling in opposite directions gives rise to standing waves along the line. The
electric fields vary periodically with distance. The maximum field strength is found where the two
waves add in phase, and the minimum where the two waves add in opposite phase. The Voltage
Standing Wave Ratio (VSWR or SWR or S) on a transmission line is defined as the ratio between
the maximum and the minimum field strength along the line.
SWR =
Vmax | Vi | + | Vr |
=
Vmin | Vi | − | Vr |
(2-1)
Figure 2-1 shows the voltage standing wave patterns for different load impedances. The distance
between two successive minima (or maxima) is half the wavelength on the transmission line. The
ratio between the electric field of the reflected and the incident wave is called the voltage reflection
coefficient, Γ, which is a complex number, in general. In an ideal transmission line the phase of Γ
varies uniformly with position. If there are losses on the line, the amplitude of Γ will also vary with
position on the line.
From Figure 2-2 it can be proven that,
Γ = Vr/Vi = (Z-Z0)/(Z+Z0)
(2-2)
where Z is the impedance at some distance along the line. The reflection coefficient at the load
itself is,
ΓL = (ZL - Z0)/(ZL+Z0)
(2-3)
The magnitude of the reflection coefficient is related to the SWR as follows,
|ΓL| = (SWR- 1)/(SWR+1)
(2-4)
The limits of ΓL and SWR are
Perfect match
Perfect mismatch
|ΓL|
0
1
SWR
1
∞
There are several methods for measuring SWR with a slotted line. In the slotted line, a small part
of the electric field is sampled by a diode (crystal) detector via a probe inserted in the waveguide.
In the most straightforward method, the SWR can be read directly on the SWR-meter connected to
the diode (crystal) output. This method is accurate only when: 1) the probe depth is small enough
not to disturb the field in the waveguide, 2) the diode (crystal) operates in the "square-law" region,
e.g. the output voltage is proportional to the input power. When the SWR is high, the probe depth
must be increased if a reading is to be obtained at a voltage minimum. This will, however, cause:
1) field deformation when the probe is at a voltage maximum and perhaps 2) so much power is
incident on the diode (crystal) that it does not operate in the square-law region. One method to
overcome the effect of probe loading is the “3dB-method". In this method, one measures the
distances between the points where the diode (crystal) output voltage (proportional to the RF
power) is twice the minimum. See Figure 2-3. The SWR is given by
SWR = 1 +
1
(2-5)
π ( d1 − d 2 )
sin
λg
2
The effect of detector variations from square-law is overcome in the “Calibrated-Attenuator”
method. In this method the diode (crystal) output at a maximum is made equal to the output at a
minimum by means of an attenuator placed between the generator and the slotted line. The
difference in the attenuator settings (A2-A1) in db yields the SWR,
A2 - Al - 20 log (SWR)
(2-6)
where Al is the attenuator setting at a minimum, and A2 is the attenuator setting at a maximum.
The accuracy here is determined by the accuracy of the attenuator, (a precision attenuator is
recommended) and the probe loading effect.
PROCEDURE
General
1.1 Set up the equipment as shown in Figure 2-4. In this setup, the combination of Attenuator 2
and the short circuit load yield a variable impedance load whose return loss is dependent on the
setting of Attenuator 2 (as will be seen as the experiment progresses).
1.2 Set Attenuator 1 (Precision Attenuator) to 0 dB, and Attenuator 2 to 20dB.
1.3 Set signal generator for nominal 1mW (0 dBm) output with 1KHz square wave modulation at
a frequency of 9 GHz (or other convenient frequency).
1.4 Adjust gain of the SWR meter for on-scale deflection.
1.5 Move the probe along the standing wave detector. Note that the deflection changes very little;
i.e. the transmission line is well matched.
Measurement of low and medium SWR
2.1 Set Attenuator 2 at 10 dB. This corresponds to a reflection coefficient of 20dB which is
equivalent to an SWR of 1.22. This is found using |ΓL|= 10-A/20 and SWR = (1 + |ΓL|)/(l - |ΓL|).
2.2 Move the probe along the standing wave detector to a maximum deflection of the meter.
2.3 Adjust the SWR-meter gain until meter indicates 1.0 on the Normal (black) SWR scale.
2.4 Move the probe to a minimum. NOTE: Do not change anything else (generator power or
SWR meter controls).
2.5 Read the SWR on the scale. Record this value in Table 2-1.
ATTENUATION
5
7
10
12
SWR
Table 2-1. The SWR-meter method
2.6 Repeat the steps 2.2 to 2.5 for Attenuator 2 settings of 5dB, 7dB, and 12dB.
2.7 From the attenuator settings calculate the SWR (Eqn. 2.4 or the equation in Step 2.1) and
compare with the measured values from Table 2-1.
Measurement of High SWR. The "3dB Method"
(Double minimum method)
3.1 Set Attenuator 2 to 1 db.
3.2 Move the probe along the standing wave detector until a minimum is indicated.
3.3 Adjust the SWR-meter gain to obtain a reading of 3dB (lowest scale on the SWR meter).
3.4 Move the probe to the left on the standing wave detector until full scale deflection is
obtained (0 db on lowest scale of the SWR meter). Note and Record the probe position, dl in
Table 2-2.
3.5 Repeat step 3.4 but this time move the probe to the right. Note and Record probe position,
d2.
d1
(mm)
d2
(mm)
Table 2-2 "The 3-dB method"
First minimum
Second
(mm)
minimum
(mm)
λg
(mm)
SWR
3.6 Lower the range on the SWR meter, then set Attenuator 2 to 0 dB. Measure the distance
between two successive minima. Twice this distance is the guide wavelength, λg.
3.7 Calculate the SWR using equation (2-5).
QUESTIONS
1. Explain why successive minima of a standing wave pattern are separated by a half
wavelength.
2. Figure 2-1 shows various standing wave patterns. The capacitive and inductive loads shown
have losses (resistive components). If no losses existed at the load, what would the patterns look
like?
3. Which attenuator setting gave the largest SWR?