How To Determine The Vswr And The Reflection Coefficient; Formulas - Hameg HZ547 Manual

How to determine the VSWR and the reflection coefficient

The VSWR bridge HZ57 allows the measure-
ment of the voltage standing wave ratio (VSWR)
and the reflection coefficient of 50 ohm devices.
Typical objects are e.g. 50 ohm attenuators, load
resistors, am-plifiers, cables, mixers, frequency
selective devices. The frequency range is 100 kHz
to  GHz.
The return loss measurement requires a HF-
signal generator and a hf-receiver and is possible
for discrete frequencies. If it is necessary to extend
the measurement over greater frequency ranges
it will be advantageous and time saving to select
a spectrum analyzer with a tracking generator
instead.
The return loss is determined by the difference of
the results of two measurements: first measure-
ment with the DUT terminal open or short-
circuited, i.e. total mismatch, second measure-
ment with the device under test connected to the
DUT terminal.
The measurement result from a total mismatch
is achieved thus:
1. Connect the signal source (signal generator
or tracking generator) to the N connector IN.
. Connect the OUT terminal of the bridge to the
input of the receiver or spectrum analyzer.
. Leave the DUT terminal open which equals
total mismatch.
The spectrum analyzer will indicate the amplitude
of the reflected signal from OUT. This result must
be registered or stored in the reference memory.
Function: „Store A to B (A>B)" of the spectrum
analyzer. Then switch the spectrum analyzer to
the operating mode „A minus B (A – B)".
Continue by connecting the device under test to the
DUT terminal. Now the reflected energy (100 % in
the previous measurement) will depend upon the
properties of the DUT, in general the reflected en-
ergy will be lower than before, again measured by
the spectrum analyzer which will now indicate the
algebraic difference between both measurements
in dB which is the desired return loss.
Of course, an ideal 50 ohm load will not reflect
any energy, the return loss will become infinite. In
reality more than appr. 0 dB are hard to achieve.
0 dB means that 99% of the energy will be absor-
bed by the DUT and only 1% will be reflected.
Once the return loss has been determined use
table 1 to read the REFLECTION COEFFICIENT
and the VSWR. This table is also available on top
of the bridge.

Formulas

Calculations:
a = Return Loss [dB]
r = Reflection coefficient of the DUT
s = VSWR
Z = System impedance = 50 ohms
o
Z = Impedance of the DUT
r = 10
s = – – – – – –
Example:
Return loss as indicated on the spectrum
analyzer = 0 dB
VSWR = 1.
Reflection coefficient = 0.1 = 10 %.
REFLECTION COEFFICIENT
VSWR
V S W R - M e a s u r i n g b r i d g e
-0,05 · a
1+ IrI
1+ r
s = – – – – – – Z
1 – IrI 1 – r
Subject to change without notice
o
DUT
50
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