Class AB Biasing
Ed Grochowski
Written 12212022
Introduction
The class AB audio amplifier uses a pair of output transistors in
pushpull configuration. Each transistor conducts during alternate
halves of the waveform. Near the zero crossing, both transistors
conduct. This article describes how to choose the amount of overlap for
minimal distortion.
Model
The pushpull output stage may be modeled as follows.
The emitter current is an exponential function of baseemitter voltage.
This is given by the EbersMoll equation (ignoring the insignificant
constant term):
Ie = Is * exp (Vbe/Vt)
As the input voltage changes, the current slides up and down the
exponential. The pushpull pair has two such exponentials, each a
mirror image of the other. The bias determines how far down the
exponential the current is allowed to go.
The emitter resistors perform the essential function of making the
current less sensitive to Is and temperature. The voltage drop across
the resistors is given by Ohm's Law:
V = I * R
Finally, Kirchoff's laws stipulate that the voltage around a loop must
sum to zero, and the current into a node must sum to zero.
Parameters
It is easy to write a simulator that solves the equations numerically.
The input is a singlecycle sine wave, and the output is analyzed by
FFT.
I chose Is to match the popular 2SC5200. The load resistor is 8 ohms.
The model corresponds to onehalf of the real amplifier which uses four
output transistors to drive a 4 ohm load.
I simulated two common values of emitter resistors, 0.22 ohm and 0.39
ohm. The former leads to lower distortion while the latter leads to
more stable bias current. Choosing the value of the emitter resistors
requires a separate simulator for thermal stability.
The temperature is 300K.
Results
The simulation results are shown below.
The first conclusion is that the emitterfollower output stage is
already quite linear. Not much negative feedback is needed to reduce
distortion to negligible levels.
The graphs show three regions of operation: underbias, optimal bias, and
overbias.
Underbias
With very small bias currents (<25mA), the output waveform exhibits a
notch around zero volts. Distortion is high. This region must be
avoided.
Optimal Bias
Between 50mA and 100mA, distortion reaches a local minimum, but it is
narrow and hard to realize. In practice, one wants to be on the right
side of the minimum.
Overbias
With bias currents over 150mA, the behavior differs according to
amplitude.
For small amplitudes, increasing the bias current lowers distortion
because the transistors are operating over a smaller part of the
exponential. This is where class A amplifiers operate.
For large amplitudes, the opposite happens: increasing the bias current
increases distortion in class AB because the exponential is
causing larger voltage errors in the emitter resistors. This region too
must be avoided.
Implications
The bias currents for minimal distortion require only a few watts of
idle power consumption. Moreover, the idle power does not add to the
maximum power dissipation because very little time is spent with both
transistors conducting at amplitudes that cause maximum dissipation (64%
of Vcc).
In addition to the exponential relationship between current and voltage,
real transistors exhibit HFE variations with current, and also dynamic
effects. With good design, I believe the latter can hide behind the
exponential as contributors to distortion.
Addendum
Setting Re=0 shows that the local minimum and maximum are caused by the
nonlinear terms in the exponential leading to error voltages in the
emitter resistors. These error voltages may result in helpful
cancellation of distortion products or harmful contribution.
Another interesting comparison is with a pushpull pair of MOSFETs. The
MOSFET is governed by a squarelaw relationship between current and
voltage:
Id = Idss * (Vgs  Vth)^2
I chose Idss and Vth to match the 2SK1058. Note that the scales have
changed.
The MOSFET's distortion is highest at maximum amplitude. Compared to
the bipolar transistor, the MOSFET requires much higher bias current to
reach low levels of distortion.
