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Keysight Technologies
Impedance Matching in the Laboratory
University Engineering Lab Series - Lab 4

Application Note
Introduction

The reception and transmission of small signals into amplifier stages and the transmission of large,
powerful signals into loads both require careful attention to minimizing losses. At RF and microwave
frequencies reflections of the propagating wave can drastically undermine the efficiency of transmit-
ted power or the signal-to-noise ratio of transmitted information. Proper matching of impedances is
needed to minimize these reflections and insure that any signal which reaches a load is actually ab-
sorbed by that load as useful power. Proper impedance matching is a fundamental skill that is central
to all RF and microwave engineering. The ability to design and execute proper impedance matches
is a crucial and highly sought skill which can make or break a career as well as a specific design. The
mathematical elements of impedance matching have already been investigated using SPICE and other
tools such as the Smith chart. In this lab, some practical laboratory approaches to the problem of
impedance matching will be examined. Network analyzers are the essential tool for assessing and tun-
ing an impedance match. Impedance matching is often viewed as a difficult art because impedance
matching involves an interplay of measurements and design calculations. However, there are devel-
oped methods, and mastering these is essential to RF and microwave engineering.
03 | Keysight | mpedance Matching in the Laboratory, University Engineering Lab Series - Lab 4 - Application Note

A quick overview
Consider first the following problem. A load resistance of RL = 10 is to be fed by a
Z0 = 50 transmission line. If the line were directly connected to the load, this would
produce a reflection of = -0.667, which means that the load only absorbs ||2 = 0.555
of the incident power, and the other 1 - ||2 = 0.445 fraction gets reflected back to the
generator. The voltage standing wave ratio (VSWR) for this situation is 5.00, indicating
deep standing waves which will make the line impedance very sensitive to its length and
potentially cause problems for the generating source.

One approach to this problem is to add a series matching resistance of Rsm = 40 , which
will bring the total of Rsm + RL equal to Z0 , as shown in figure 1. This indeed creates a
perfect impedance match between the load and the line, with the reflection coefficient
now reduced to = 0. However, the introduction of Rsm reduces the power that the load
RL receives. Since these two resistances are in series, the load RL only receives 1/5 of the
power leaving the transmission line. The matching network of Rsm thus introduces a huge
insertion loss of 10 log (5.0) = 7.00 dB.

Rsm = 40
Z0 = 50 RL = 10

transmission matching
load
line network
Figure 1. Insertion of a series matching resistance when RL < Z0

Next, consider a load resistance of RL = 75 which needs to be matched to the same
Z0 = 50 transmission line. Directly connecting the load to the line would produce a
reflection coefficient of = +0.200 and a VSWR = 1.50. In this case, a parallel match-
ing resistance of Rpm = 150 could be added to reduce the effective load impedance to
match to the line, as shown in figure 2. Note that 150 || 75 = 50 . Again, this creates
a perfectly matched situation, but the introduction of the parallel matching resistance
allows the actual load RL to only receive 2/3 of the power leaving the transmission
line. In this case, the parallel matching resistance Rpm introduces an insertion loss of
10 log (1.5) = 1.76 dB.

Z0 = 50 Rpm = 150 RL = 75

transmission matching
load
line network
Figure 2. Insertion of a parallel matching resistance when RL > Z0

In both of the above cases, the introduction of a series or parallel matching resistance
created a perfect impedance match, and an important benefit of this matching is that it
is frequency independent. Although significant power loss is an obvious drawback. Resis-
tive elements can be used for broadband matching, but at the expense of power or signal
loss, which can often be significant.

In many cases, the range of frequencies is restricted to a narrow band, and this can
allow the use of reactive elements, that is, inductors and capacitors, to achieve low loss
impedance matching over that range. Simply adding a single reactive element in series or
04 | Keysight | mpedance Matching in the Laboratory, University Engineering Lab Series - Lab 4 - Application Note

parallel to a load impedance can cancel any reactive component of the load, but it can-
not bring an arbitrary load impedance to equal the desired Z0 = 50 . To handle arbitrary
load impedances with both real and imaginary parts, an additional degree of freedom is
required, and this is most easily achieved through the use of an L-network which involves
two reactive elements.

The synthesis of these L-networks involves some computations for which the Smith chart
is a very handy tool for mapping out the matching strategy and getting initial values for
these elements. In practice there will be parasitic elements which may not have been
accounted for, as well as other inaccuracies which will cause the final match to be imper-
fect. The overall procedure for matching a load to a line first involves a measurement of
the load impedance. Once that is known, a matching strategy can be developed to guide
the calculation of the matching elements. These will be nominal values which should
be close to the needed values, but perhaps still not exact. Achieving a finer degree of
matching then involves adjusting these matching element values while monitoring the
reflection coefficient of the line. Thus, some ability to fine tune the matching network
is often required. A network analyzer is the preferred tool for both measuring the initial
impedance of the load as well as monitoring the reflection coefficient so that it can be
nulled out by fine tuning of the matching network.

A Smith chart is a polar plot of the reflection coefficient , so that the point at the origin Im()
corresponds to = 0, the case for zero reflections and perfect impedance matching of a
load to the transmission line. The objective of impedance matching is therefore to land
a bullseye in the center of the Smith chart for the range of frequencies that need to be
matched, as shown in figure 3. The great advantage of the Smith chart is that after it has
been mastered, it provides a very intuitive way of understanding the load and line inter-
actions and of designing proper impedance matching networks. One can assess a situ- Re()
ation on a Smith chart and very quickly learn what is possible, easy, or difficult, versus
performing brute force "what if" calculations, many of which might lead to dead ends.

ZL = Z0
A computational example will next be developed to illustrate the procedure for synthe- =0
sizing an L-type matching network. Suppose that the load is a complex impedance of
ZL = 20

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