Determining Voltage Standing-Wave Ratios
June 1954 Radio & Television News
voltage standing wave ratio (VSWR) is a fairly common and simple operation
these days with readily available and relatively inexpensive test equipment.
Inserting a power meter in series with a signal to measuring the incident
and reflected power, or even simpler, inserting a bidirectional power
coupler in series with the signal and measuring the difference between
the forward and reverse ports is a routine matter for even modestly
equipped laboratories, Ham shacks, or field operations. Simply plug
the two values into the following equation for the answer: VSWR=(1
+ β)/(1-β), where β=√(Prev/Pfwd). What if
all you have is an oscilloscope, then how would you make the measurement?
Actually, the calculation is even simpler because you use the ratio
of the peak incident and reflected waves, but making the measurement
requires more work. This article presents one way to get the job done.
Comparison Methods for Determining
Voltage Standing-Wave Ratios
By J. F. Sterner
Fig. 1. Bench setup showing arrangement of transmission line
for VHF work. Coaxial line is wrapped around box on the left.
Tube Department, Radio Corporation of America (RCA)
A simple method for matching a load to a transmission line or for
determining if a load is correctly matched.
A combination of
high-quality television test equipment such as a sweep generator, a
high-gain oscilloscope, and a demodulator probe or detector provides
a quick and accurate means for matching impedances, determining voltage
standing-wave ratios, and measuring line attenuation. The technique
described in this article is based on the observation and measurement
of voltage standing-wave ratios to determine impedance matches. A good
match between a component or circuit under test and a transmission line
results in a VSWR approaching one. If the VSWR is not close to one,
the circuit or component may be replaced by pure resistive loads having
various values until the VSWR obtained with the original setup is duplicated;
the impedance of the component or circuit may then be determined by
direct measurement of the substitute resistive load.
The Comparison Method
Fig. 2. Pattern produced by shorted line.
Fig. 3. Test equipment arrangement for determining impedance
match by VSWR.
Fig. 4. Simplified block diagram shows the arrangement of test
equipment for matching a transmission line to all antenna.
Fig. 5. (A) Detector circuit for use with test equipment shown
in Fig. 1. (B) A detector circuit for a balanced input.
Fig. 6. Oscilloscope pattern produced by a 300-ohm line terminated
by 330·ohm resistor.
Fig. 7. How a television calibrator is coupled to the input
end of transmission line.
Fig. 8. Tube loading effect across the antenna circuit of a
TV tuner. The tuner presents a good match to the antenna over
the passband as indicated by the two marks. This is the condition
with the filaments turned on and "B+" applied to the circuit.
Trace with the power removed from the tuner and the reactive
components of the tuner circuit less tube grid loading causing
a mismatch. This shows that the input transformer is properly
designed for the type of tube used in this circuit, i.e., the
grid circuit applies a resistive component across the antenna
transformer so as to effect a good match from the 300-ohm input
to the tube.
The complete physical
arrangement of a suitable combination of test equipment is shown in
Fig. 3. The output cable of the RCA WR-59C sweep generator is coupled
to one end (input end) of the transmission line. The sweep generator
must have good linearity and a constant output voltage over its frequency
range. The input of an RCA WG-291 demodulator probe or a simple detector
is connected to the same end of the line. The output of the demodulator
or detector is fed to ·the vertical input terminals of the RCA WO-56A
oscilloscope. The scope used in this method must have good linearity
and good sensitivity.
If the impedance of the load and the characteristic
impedance of the line are equal, the voltage which appears across the
demodulator or detector is independent of the frequency.1
In other words, if there is a perfect match between the load and the
line, the voltage does not change as the generator sweeps through its
When the load impedance differs from the characteristic
impedance of the line, however, the voltage across the detector or demodulator
varies with a change in frequency. The amplitude of this variation is
a function of the reflected voltage.
If the line is shorted
at the output end, highest impedance appears across the input end of
the line at frequencies at which the length of the line is an odd number
of quarter-wavelengths. At these frequencies, therefore, maximum voltage
develops across the demodulator or detector. Lowest impedance and minimum
voltage appear at frequencies at which the line is an even number of
quarter-wavelengths. Fig. 2 shows a typical pattern which may be observed
on the oscilloscope. The number of voltage peaks in the waveform is
directly proportional to the frequency swing of the generator and the
length of the line.
This shorted-line method may be used to
measure reflected voltage over a wide range of frequencies, provided
that the vertical-amplifier gain control of the oscilloscope is adjusted
initially so that the peak-to-peak amplitude of the waveform is equal
to ten divisions on the screen of the scope. If the cable is then terminated
by a load, the vertical distance between the maximum and minimum peaks
of the waveform represents the reflected voltage. For example, a waveform
having an amplitude of one division represents a reflected voltage equal
to ten percent of the incident voltage over the range of frequencies
Attenuation in the line may also be measured, provided
the sweep generator has blanking of the sweep oscillator so that a zero
base line can be observed on the scope. If there are no losses in the
line, the reflected wave equals the incident wave, and the voltage minimum
is coincident with the zero base line. The distance from the zero base
line to the voltage minimum therefore provides a measure of the attenuation
due to losses in the line. Care must be used in this method to prevent
the existence of any large degree of reactance at the short itself.
To make an effective short for 300-ohm line, it is convenient to strip
back the line about one-half inch and twist the leads together. For
coaxial lines, it is better to strip back the inner polyethylene insulation
about one-quarter inch and short the outside braid directly to the inner
When measurements are made at VHF, the transmission
line should be 75 to 100 feet long. 300-ohm line may be wound around
a cardboard box, a packing carton, or any low-dielectric form. The spacing
between the turns should be equal to or greater than the width of the
line being used, as shown in Fig. 1. Coaxial cable may be placed in
any convenient location without regard to spacing between turns.
For most applications in which the frequency is below 216 megacycles,
the detector or demodulator used in the measurements may be an RCA WG-291
demodulator probe or a simple detector such as that shown in Fig. 5A.
An alternate detector for balanced input is shown in Fig. 5B. Either
of these detectors may be constructed on a phenolic board 1/16-inch
The entire test setup may be checked by the connection
of a 1/4-watt or 1/2-watt carbon resistor, having the same value as
the line impedance, directly across the termination or output end of
the line. The line connection to the resistor leads must be made in
the area directly adjacent to the body of the resistor. The pattern
observed on the screen of the oscilloscope should be similar to that
shown in Fig. 6. It may be necessary to try several resistors having
the same nominal value as the line before a good match is obtained because
of variations in the resistance values and in the characteristic impedance
of the line due to manufacturers' tolerances. When a good match has
been obtained, the characteristic impedance of the line may be determined
by measurement of the resistor.
Use of Comparison Method
The application of this method to the determination
of impedance matches can best be illustrated by an example. If it is
desired to determine the match of a 300-ohm transmission line to a television
tuner, the tuner is connected as the load in the arrangement shown in
Fig. 3. In this case, because the effect of the match is limited to
a bandwidth of 4.5 megacycles, a television calibrator such as the RCA
WR-39C is used in conjunction with the sweep generator and the oscilloscope.
The calibrator is loosely coupled to the input end of the line. See
The sweep generator is set to the same frequency as
the television tuner. Fig. 8 shows typical traces produced on the screen
of the scope, representing a good match and a mismatch, respectively.
The efficiency of the match may be determined from the standing-wave
ratio, as follows:
Efficiency = (VSWR-1)/(VSWR+1) where:
VSWR = E2/E1
E2 = peak
of reflected wave
E1 = valley of reflected wave
A similar arrangement may be used to determine the transformation
ratio of a matching transformer. The primary of the transformer is connected
as the load, and resistors are substituted across the secondary until
a VSWR of unity is obtained.
This arrangement is also useful
in the matching of a transmission line to an antenna. In the case of
a two-element array, for example, the sweep generator and demodulator
are connected to the same end of the line as the receiver or transmitter,
and the antenna is connected as the load. A good match is obtained by
adjustment of the spacing between the two elements of the antenna to
give a VSWR as close to unity as possible. See Fig. 4.
described in this article is simple, and the instruments are readily
available. Accuracy of the method is within ten percent of that obtained
using a slotted-line technique. The engineer or technician willing to
spend the few minutes necessary to set up the equipment will find this
method extremely useful.
1. Bauer, John A.; "Special Applications of Ultra-High-Frequency
Wide-Band Sweep Generators, "RCA Review, Sept. 1947
Posted September 23, 2013
Copyright: 1996 - 2024
BSEE - KB3UON
RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling
2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas
and reference material while performing my work as an RF system and circuit design engineer.
The Internet was still largely an unknown entity at the time and not much was available
in the form of WYSIWYG
All trademarks, copyrights, patents, and other rights of ownership to images and text
used on the RF Cafe website are hereby acknowledged.
My Hobby Website: AirplanesAndRockets.com