IEEE Solid-State Circuits Magazine - Winter 2016 - 49

This is called the slope gain of
the amplifier and is designated as
g s to avoid ambiguity. As was used
to define the absolute resistance of
the amplifier supply input, there is
a similarly defined gain that is the
direct ratio of the output signal
divided by the input signal,
y
y-0
g R ^x h / =
x
x-0
a 1 + a 2 x + a 3 x 2 + ... x # x c
y max
.
=*
x 2 xc
x
(5)
This is called the ratiometric gain
of the amplifier and is designated as
g R to avoid ambiguity. The relationship between slope gain and ratiometric gain for any transfer function
is illustrated in Figure 12.
The gain metrics of (4) and (5) have
several differences and one very important similarity. The similarity is
that when the amplifier remains in
L-mode and away from compressed
operation, the values of g R and g S
are identical. This coincidence has allowed all amplifier designers, including myself, to get lazy about our use
of the term gain, as long as linear operation is intended. But as the importance of energy efficiency increases,
that forces the amplifier design to operate transistors nonlinearly [1], and
this fortunate convenience no longer
applies. With modern amplifier designs, it is now important to unambiguously refer to the gain metric that
is being used at any and all times.
This same approach applies to
the power transfer function. By similarity, we also have the slope power
gain g SP

= a 12

(6)

Clipping

PSAT

and the ratiometric power gain g RP
-1

y2
P
0
R
= 2L .
g RP ^x h / OUT
PIN - 0
x
R IN

(7)

Cut-Off

Figure 11. Waveform clipping at the
amplifier output by saturation and cut off at
the transistor stops all voltage increases, but
power continues to increase as the waveform transitions from sinusoidal to square.

Comparisons among these four
gain metrics are shown in Figure 13,

1.2
Normalized Output (V)

dy
dx
a 1 +2a 2 x +3a 3 x 2 +... x # x c
='
.
x 2 xc
0
(4)

g S ^x h =

y2
m
RL
2
dc x m
R IN
R L = R IN ,

dPOUT
g SP ^x h /
=
dPIN

dy
dx

1
0.8

y-0
x-0

0.6
0.4
0.2
0

0.0

0.5
1.0
1.5
Input (V, Normalized to P1dB)

2.0

Figure 12: Definitions of ratiometric and slope gains for any transfer function. The voltage transfer function is used in this example, but the same principles apply to the power
transfer function.

1.2

Amplitude Characteristic

where D (x) is a collection of all the
higher-order terms and represents
distortion of the output signal. The
gain metric mentioned above is the
first derivative of the voltage transfer function

Transfer Function

1
0.8
0.6
gR

0.4
gS

0.2
0

gRP

gSP
0.2

0.4

0.6

0.8

Input (V)

Figure 13: A comparison of the four voltage and power gain metrics for an amplifier. All
gain metrics are similar (shown here as equal) when the amplifier operates linearly. With
the onset of compression, these gain metrics diverge and tell an amplifier designer different
things about what the amplifier is doing.

IEEE SOLID-STATE CIRCUITS MAGAZINE

W I N T E R 2 0 16

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