AN215A Datasheet, PDF (1/11 Pages) –

MOTOROLA
SEMICONDUCTOR
APPLICATION NOTE
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AN215A
RF SMALL SIGNAL DESIGN
USING TWO-PORT PARAMETERS
Prepared by: Roy Hejhall
INTRODUCTION
Design of the solid-state, small-signal RF amplifier using
two-port parameters is a systematic, mathematical proce-
dure, with an exact solution (free from approximation)
available for the complete design problem. The only sources
of error in the final design are parameter variations resulting
from transistor parameter distributions and strays in the
physical circuit. Parameter distributions result from limits in
measurement and random variations among identically
designed transistors.
The purpose of this paper is to provide, in a single working
reference, the important relationships necessary for the
complete solution of the RF small-signal design problem
using two-port parameters.
The major portion of the report presents design equations
in terms of admittance parameters. A section on design with
scattering parameters is also included.
This paper is based on work by Linvill1, Stern2, and
others. Those who may wish to consider the derivations of
some of the expressions should refer to the bibliography.
This report assumes that the reader is familiar with the
two-port parameter method of describing a linear active
network. Several references are available on this sub-
ject.1,2,6,8,11,12
It has also been assumed that a suitable transistor or
other active device for the task at hand has been selected,
and that two-port parameters are available for the frequency
and bias point which will be used. Device selection will not
be covered as a separate topic in this report; rather, a
thorough understanding of the material in the report should
provide the designer with the tools he needs to select
transistors for a particular small-signal application.
The equations given in the text of this report are applicable
to the common-emitter, common-base, or common-collector
configuration, if the applicable set of parameters (common-
emitter, common-base, or common-collector parameters) is
used. Equations for the conversion of the admittance or
hybrid parameters of any configuration to either of the other
two configurations of the same parameter set are given in
the appendix.
While directed primarily toward circuit design with
conventional bipolar transistors, two-port network theory has
the advantage of being applicable to any linear active
network (LAN). The same design approach and equations
may therefore be used with field effect transistors7,9,
integrated circuits10, or any other device which may be
described as a linear active two-port network.
Finally, various parameter interrelationships and other
data are given in the Appendix.
GENERAL DESIGN CONSIDERATIONS
Design of the RF small-signal tuned amplifier is usually
based on a requirement for a specified power gain at a given
frequency. Other design goals may include bandwidth,
stability, input-output isolation, and low noise performance.
After a basic circuit type is selected, the applicable design
equations can be solved.
Circuits may be categorized according to feedback
(neutralization, unilateralization, or no feedback), and
matching at transistor terminals (circuit admittances either
matched or mismatched to transistor input and output
admittances). Each of these circuit categories will be
discussed, including the applicable design equations and the
considerations leading to the selection of a particular
configuration.
STABILITY
A major factor in the overall design is the potential stability
of the transistor. This may be determined by computing the
Linvill stability factor1 C using the following expression:†
y12 y21
C=
(1)
2g11 g22 – Re (y12y21)
When C is less than 1, the transistor is unconditionally
stable. When C is greater than 1, the transistor is potentially
unstable.
The C factor is a test for stability under a hypothetical
worst case condition; that is, with both input and output
transistor terminals open circuited. With no external
feedback, an unconditionally stable transistor will not
oscillate with any combination of source and load. If a
transistor is potentially unstable, certain source and load
combinations will produce oscillations.
Although the C factor may be used to determine the
potential stability of a transistor, the conditions of open
circuited source and load which are assumed in the C factor
test are not applicable to a practical amplifier. Consequently
it is also desirable to compute the relative stability of actual
amplifier circuits, and Stern2 has defined a stability factor
k for this purpose. The k factor is similar to the C factor except
that it also takes into account finite source and load
admittances connected to the transistor. The expression for
k is:
2 (g11 + Gs) (g22 + GL)
k = _{y12y21 + Re (y12y21)}
(2)
†Re _{(y12y21) = Real part of (y12y21)}
RF Application Reports
1
© Motorola, Inc. 1993
Copyright of Motorola. Used by Permission.