Poor impedance matching
between the source and load has been the cause of many poor performance issues ever
since the wavelength of the transmitted signal became less than the length of the
interconnecting line. A generally accepted rule of thumb is that when the line is
more than about a tenth of the wavelength of the highest frequency, impedance matching
is probably required lest standing waves cause problems. An impedance mismatch causes
part - or maybe all - of the incident signal to be reflected back towards the source.
That results in part of the signal not being transferred to the load, and the rest
is dissipated as heat and/or radiated as an electromagnetic wave. In some circumstances
the reflected signal can cause damage to the source because the reflected voltage
can be much greater than the output circuit can withstand. VSWR is not just a concern
for transmitters since a severe impedance mismatch from the antenna to a receiver
can result in not being able to pick up the weakest of signals. For a long time
VSWR was only of concern to radio type circuits, but once the frequency of digital
circuits began exceeding the 1/10th wavelength point all of a sudden digital PCB
designers needed to adopt controlled impedance methods.
Determining Voltage Standing-Wave Ratios
Fig. 1 - Bench setup showing arrangement of transmission line
for v.h.f. work.
By J. F. Sterner
Tube Dept., Radio Corporation of America
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 v.s.w.r. approaching one. If the v.s.w.r. is not
close to one, the circuit or component may be replaced by pure resistive loads having
various values until the v.s.w.r. 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.
Fig. 2 - Pattern produced by shorted line.
Fig. 3 - Test equipment arrangement for determining impedance
match by v.s.w.r.
Fig. 4 - Simplified block diagram shows the arrangement of test
equipment for matching a transmission line to an 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 a transmission line.
The Comparison Method
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 frequency range.
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 per-cent of the incident
voltage over the range of frequencies covered.
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 conductor.
When measurements are made at v.h.f., 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 RGA 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 thick.
Fig. 8 - Tube loading effect across the antenna circuit of a
TV tuner. (Top) 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. (Bottom) 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 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 out-put 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
RGA 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 Fig. 7.
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 = (v.s.w.r.-1)/(v.s.w.r.+1)
where: v.s.w.r. = 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 v.s.w.r. 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 v.s.w.r. as close
to unity as possible. See Fig. 4.
The technique described in this article is simple, and the instruments are readily
available. Accuracy of the method is within ten per-cent 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 January 6, 2021