IEEE Solid-State Circuits Magazine - Winter 2016 - 48

I_PA (A)

R_PA

4
3.5
3
2.5
2
1.5
1
0.5
0

ro = 10,000
ro = 100
ro = 10
0

1
2
3
Envelope Voltage
(a)

4

1.2
1
0.8
0.6
0.4
0.2
0

0

1
2
3
Envelope Voltage
(b)

4

Figure 9: The absolute resistance of the supply input impedance: (a) resistance varies with
output resistance characteristic of the transistor and (b) an explanation of how current source
operation can appear as nearly a short circuit to low values of supply voltage.

what the amplifier is actually doing.
This is very valuable information
for circuit design.
To understand these four gain
metrics, we need to start from the
two related but different transfer
functions for any amplifier: the voltage transfer function VOUT = fV (VIN)
and the power transfer function
POUT = fP (PIN) . Representative curves
for each of these transfer functions
are provided in Figure 10. The voltage transfer function in Figure 10(a)
exhibits linear operation as long as
the output voltage is less than 60%
of its maximum value. Above that,
there is compressed operation until
clipping occurs when the normalized input exceeds 1.25.
The power transfer function in
Figure 10(b) corresponds to a perfectly

1.4

5

1.2

0

1

-5

Output Power (dB)

Normalized Output Voltage

The traditional definition of gain,
which is the change in output magnitude compared to the corresponding
change of the input signal magnitude,
applies naturally to L-mode operation. But what about for C-mode operation? This definition of gain goes to
zero in C-mode, yet the amplifier output power is much greater than the
input power. There is more involved
in the concept of circuit gain than is
traditionally used.
There are actually four different measures of circuit gain that
all apply to any amplifier. These
gain measures are all valuable and
legitimate. And when the amplifier
operates outside of L-mode, they
all provide different answers. This
means that each of these gain measures tells us different things about

0.8
0.6
0.4
Linear
Compressed

0.2
0
0.0

0.5
1.0
1.5
Input Voltage (Normalized to P1dB)

linearized amplifier, where there is no
compression region between linear
operation and clipping in the voltage
transfer function. Here we observe
the expected linear response up to the
onset of clipping. As the amplifier is
driven harder, the output power continues to increase, even though we
know that the output voltage waveform cannot be increasing. This is
very different from the behavior of
the voltage transfer function!
The reason for this behavior difference is shown in Figure 11. As the
clipped output waveform progresses
from sinusoidal in shape toward
becoming a square wave, its power
is indeed increasing while the waveform distortion is also increasing. The
power transfer function by itself tells
us correctly that the output power is
increasing, yet it tells us nothing about
the actual linearity (and nonlinearities) affecting the output waveform. It
is therefore very dangerous to imply
output waveform nonlinearities from
observing only the power transfer
function of an amplifier. The voltage
transfer function is most appropriate
for linearity evaluations and therefore
also for linearizer design.
To quantify these gain metrics,
we represent the voltage transfer
function as a power series [5]

y ^x h =

-10
-15
-20
-25
-30
-35

2.0

-40
-40

-30
-20
-10
0
10
Input Power (Normalized to Clipping Onset)

Figure 10: Amplifier transfer functions for (a) voltage and (b) fundamental frequency signal power.

W I N T E R 2 0 16

IEEE SOLID-STATE CIRCUITS MAGAZINE

k=0

PSAT

(a)

48

3

/ a k x k = a 0 + a 1 x + D^x h,

(b)

(3)



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

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