34 High Frequency Electronics
High Frequency Design
BROADBAND MATCHING
An Introduction to Broadband
Impedance Transformation
for RF Power Amplifiers
By Anthony J. Bichler
RF Micro Devices, Inc.
T
his paper discusses
broadband impe-
dance-transform-
ing techniques specific for
radio frequency power
amplifiers. Single and
multiple Q matching
techniques are demon-
strated for broadband performance; here the
reader will understand the importance of a
load impedance trajectory relevant to load
pull contours.
Introduction
When analytically defining radio frequen-
cy circuits, a common approach incorporates
admittance or impedance. Admittance, which
is symbolized by Y, is defined in terms of con-
ductance G and an imaginary susceptance
component, jB. Admittance is often useful
when defining parallel elements in a network
and is expressed by the complex algebraic
equation Y = G + jB.
Impedance, the mathematical inverse of
admittance, is symbolized by Z and consists of
a resistive component R in units of ohms and a
reactive or imaginary component jX. Together
in a series complex expression they define
impedance as Z = R + jX. Impedance in this
rectangular form is often used in industry to
define a power device’s optimal source or load.
For linear systems, the condition for maxi-
mum power transfer is obtained when the
impedance of the circuit receiving a signal has
an equal resistance and an opposite reactance
of the circuit sending the signal. In the math-
ematics of complex variables, this relationship
is known as the complex conjugate. The com-
plex conjugate of a complex number is
obtained by simply reversing the sign of the
imaginary part. Here Z* denotes the complex
conjugate of Z; thus, for linear systems the
condition for maximum power transfer is
when Z
Load
= Z
Source
*, or: Z
L
= Z
S
*.
As the frequency of operation changes for
Z
S
, relative to its parasitics, the value of the
resistive component can substantially change
as well as the value of the imaginary compo-
nent. Transforming a standard system
impedance to present a driving point load
impedance Z
L
that maintains a complex con-
jugate relationship to the source impedance
change over frequency is the most challenging
aspect of broadband design.
Note: The linear condition for maximum
power transfer is often traded for other per-
formance parameters such as efficiency or
gain. For this tradeoff the load impedance will
not hold a conjugate relationship; however, the
challenge of maintaining a load for this per-
formance parameter over a broadband will
generally remain the same.
A Review of Smith Chart Fundamentals
Philip H. Smith introduced the Smith
Chart in Electronics Magazine on January
1939, revolutionizing the RF industry [1, 2].
This chart simplified complex parallel to
series conversions graphically and, for the
first time, provided intuitive transmission line
solutions.
The Smith Chart is a graphical reflection
coefficient system with normalized conformal
mapping of impedance or admittance coordi-
nates, as shown Figure 1 and 2, respectively.
Reflection coefficient is often referred to as
gamma and is symbolized by the Greek letter
Γ. Gamma in its simplest form is defined as
This tutorial article reviews
impedance matching
principles and techniques,
as they are applied to
power device matching
in amplifier circuits
From January 2009 High Frequency Electronics
Copyright © 2009 Summit Technical Media, LLC
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