Copyright © 2011 by Wayne Stegall
Created October 2, 2011. See Document History at end for
details.
Apples and Oranges
A Simple Proof that ClassA and
ClassB Distortion Specifications Are not Comparable
Introduction
Traditional standards for specifying amplifier distortion require
specification at maximum rated RMS power. By these standards,
it seems odd that higher distortion classa amplifiers can subjectively
sound clearer than lower distortion classb
^{1}
amplifiers of the same
power. Lets do the math and find out what is behind this seeming
discrepancy.
Class A Analysis
Class A distortion is due entirely to transfer curve shape.
Because polynomials can be fitted to any curve, a transfer curve could
be represented by the following polynomial:
(1)

H(v) = k_{0} + k_{1}v
+
k_{2}v^{2}+ k_{3}v^{3} + k_{4}v^{4}
+ ... + k_{n}v^{n} + ... + k_{∞}v^{∞} 
Also consider that for many reasons the second order term could
reasonably presumed to
dominate the characteristic polynomial:
 Euphonic design tends to emphasize the second order term.
 Individual transistor curves contributing to transfer curves are
predominantly second order.^{2}
For simplicity, presume a second order error only for the signal+error
voltage equation:
Divide error by signal to get relation of distortion to voltage:
(4)

Dist(v) =

kv^{2}
v

= kv

Where
Make substitution to show relation of distortion to power
Figure
1:
Class
A
distortion
rises
with
power
until
onset
of
saturation 

Class B Analysis
Class B distortion tends to be at a fixed level without regard to
signal magnitude because crossover distortion dominates that of the
overall transfer curve. (Think of crossover distortion as a fixed
distortion region unchanged by signal magnitude.) Therefore
distortion decreases as power
level is increased.
Approximate signal+error voltage equation with fixed error k:
Divide error by signal to get relation of distortion to voltage:
Given
Make substitution to show relation of distortion to power:
Figure
2:
Class
B
distortion
declines
with
power
until
onset
of
saturation


Deductions
Figure
3:
Comparison
of
distortion
profiles


Distortion profile legend:
 Green: Classb amplifier specified at 0.01%
distortion at 100W_{RMS}.
 Red: Somewhat euphonic classa amplifier specified at
1%
distortion at 100W_{RMS}.
 Blue: A more neutral classa amplifier specified at
0.1%
distortion at 100W_{RMS}.

Since distortion varies with power level, it becomes obvious that
distortion specified at maximum power favors class B amplifiers.
Because speaker efficiencies average about 89dB/W, the distortion of
ordinary listening done at power levels of only a few watts is not
represented by maximum power distortion specifications.
From the graph above, the euphonic amplifier has as low distortion as
the lower distortion classb amplifier at the important 1W level.
The neutral classa amplifier excels the lower distortion classb
amplifier everywhere below 10W.
Other observations are to be made as well.
 Because classa distortion diminishes with level, classa has a
clearer window to the smallest musical details that classb cannot show.
 Because distortion adds apparent brightness, the effect differing
with frequency, increasing distortion with magnitude in classa
amplifiers may create an impression of dynamic range expansion, whereas
the inverse relationship in the classb amplifier may create an
impression of dynamic range compression instead.
 Natural distortion processes, as internal to musical instruments
and even in the nonlinear compressibility or compliance of air, are
the
same in nature as classa distortion. The human brain might be
expected to be more accepting of natural distortion tendencies than
contradictory ones, perhaps perceiving them to be more pleasing.
 Listening habits may chose an amplifier class having the least
distortion at the listener's normal listening level. Thus the
classical listener listening to many soft passages in the context of a
wide dynamic range may lean toward classa while those preferring
highly compressed and perhaps loud music find no fault listening to his
classb amplifier. (This is a much more subjective and less
certain statement than the rest.)
Be careful however using this information to interpret actual
distortion measurements to determine the class of an amplifier of
unknown topology. Because real distortion measurements
include noise and because constant noise would appear to have a
declining profile with magnitude as crossover distortion, classa
plots will show classb characteristics at power levels where the noise
level is higher than the distortion.
In the end, I may only be
entertaining you with ideas that most of you already know.
^{1}I use classb here as optimally
biased and not operating for any range in classa which I deem classab.
^{2}It is well known that FETs
and vacuum tubes have
square law distortion characteristics. Less obvious the BJT.
The exponential in the EbersMoll equation I_{E}
= I_{EO}(e^{40V}  1) is well known for its Maclaurin
series:
e^{x} = 1 + x +

x^{2}
2!

+

x^{3}
3! 
+ 
x^{4}
4! 
+ ... + 
x^{n}
n! 
+ ... 
, where n! is the product of all
the number from 1 to n.

This equation holds the potential for a high order error
term especially as the voltage in the exponent is multiplied by 40/V (=
1/V_{T} ≈ 1/25mV). Fourier
analysis shows progressively greater suppression of higher order
harmonics with increased bias and local feedback until the second
harmonic becomes dominant.
Document History
October 2, 2011 Created.