IEEE Solid-State Circuits Magazine - Winter 2016 - 50

where the linear values are all normalized to the same value by setting a 1 = 1. The slope gain goes to
zero most rapidly, since this is most
sensitive to the actual waveform distortion. Both ratiometric gains can
never get to zero when the amplifier is operating usefully. When the
slope power gain gets to zero, this
signifies the onset of output power
saturation, which corresponds to
maximum output waveform distortion as shown in Figure 11.
All four of these gain metrics are
used in lab work, usually (and unfortunately) completely interchangeably
with the single descriptive word gain.
For example, standard RF engineering practice is to describe the power
gain of a stage as the difference in
the decibel power measured at the
output and input of the stage. Using
capital letters for decibel and lower
case for linear measures of gain and
signal power, this becomes
G = POUT - PIN
= 10 log 10 ^p OUTh
- 10 log 10 ^p INh

(8)

= 10 log 10 ^g RPh .

Thus, gain calculated by decibel differences between output power and
input power is a ratiometric power
gain result.
Regarding all of these gain metrics
and their use in standard RF laboratory practice, the following list presents common situations:
■ Measuring
g m and calculating g m R L: transconductance is
directly readable from a curve
tracer (such as the venerable
Tektronix 576) and has units
dI/dVGS . Resistor R L has units
V/I, and since the resistor IV characteristic does not compress, the
units dVDS /dI also apply. Multiplying these together provides
the net units dVDS /dVGS, which
means that this is slope gain. This
is the gain metric that is directly

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applicable to circuit stability
determination and is the most
representative of waveform distortion. When bipolar transistors
are used, the most appropriate
corresponding forms are based
on the slope gain bR L: a transresistance with units dVCE /dI B .
■ Measuring
voltage waveforms
on an oscilloscope: the common
practice of observing the input
waveform on one oscilloscope
trace, the amplifier output waveform on another trace, and then
dividing the trace measurements
point by point gives units of V/V.
This measurement technique
provides ratiometric gain.
■ Using a spectrum analyzer and a
signal generator: linearity of any
RF stage is often checked by stepping the output power from a signal generator in 1-dB steps and
then measuring the output signal
power step on a spectrum analyzer
to see if it also takes 1-dB steps.
This method is related to a slope
power gain measurement because
it relates change of output power
to change of input power.
■ Using a power meter or spectrum
analyzer: this is the measurement described by (8), measuring
the applied input power and the
resulting output power and taking their ratio (equivalently the
decibel difference). As mentioned
above, the result is a ratiometric
power gain measurement.
Clearly, when reporting any gain
measurement, it is vitally important
to fully describe the gain metric
used, to avoid all possible ambiguity,
and also to particularly allow readers to follow the scientific method
and repeat the measurements that
are reported.
When considered as the threeport circuits they really are, more
aspects of amplifier performance
and behavior become evident. When
used as two ports, these additional

IEEE SOLID-STATE CIRCUITS MAGAZINE

performance aspects generally have
little importance. But when the power supply is varied for any reason
during amplifier operation, particularly to improve energy efficiency
and/or reduce power consumption
for other reasons, these additional
characteristics become very important to know about and understand.
This is particularly true for the discussion in Part 6 of this series.

references

[1] E. McCune, "A technical foundation for
RF CMOS power amplifiers-Part 1," IEEE
Solid-State Circuits Mag., vol. 7, no. 3, pp.
81-85, Summer 2015.
[2] E. McCune, "Operating modes of dynamicpower-supply transmitter amplifiers,"
IEEE Trans. Microw. Theory Tech., vol. 62,
no. 11, pp. 2511-2517, Nov. 2014.
[3] E. McCune, "A technical foundation for
RF CMOS power amplifiers-Part 2," IEEE
Solid-State Circuits Mag., vol. 7, no. 4, pp.
75-82, Winter 2015.
[4] E. McCune, Dynamic Power Supply Transmitters. Cambridge, U.K.: Cambridge
Univ. Press, 2015.
[5] S. C. Cripps, RF Power Amplifiers for Wireless Communications, 2nd ed. Norwood,
MA: Artech House, 2006.

About the Author
Earl
McCune
(emc2@wirelessandhighspeed.com) received his
B.S. from the University of California, Berkeley, his M.S. from Stanford University, and his Ph.D. from
the University of California, Davis.
His experience in RF circuits, signals, and systems spans more than
40 years. He cofounded two Silicon
Valley startups: one doing direct
digital synthesis beginning in 1986,
which merged with Proxim in 1991,
and the second, Tropian, doing
switch-based RF transmitters beginning in 1996, which was acquired by
Panasonic ten years later. He has 74
issued patents in the United States.
He has authored two books, Practical Digital Wireless Signals and Dynamic Power Supply Transmitters.
He has been an IEEE Microwave Theory and Techniques Society Distinguished Lecturer since 2013.

http://www.sandhighspeed.com

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Winter 2016