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16 April 2005

Amplifier auto bias circuits: Class-A,
Class-AB!
Regardless whether the amplifier is single
ended or push pull, solid-state or vacuum tube, class-A or class-AB—to
achieve the best performance—all power amplifiers require a precisely set
idle current for their output stages. In a single-ended amplifier, too
much or too little idle current will limit the potential power output. In
a class-A push-pull amplifier, too much idle current will needlessly
overheat the output devices and too little will force the amplifier out of
class-A into class-AB operation. In a class-AB or class-B push-pull
amplifier, too much idle current will add distortion and an inconsistent
output impedance due to gm doubling and too little will produce crossover
distortion.

Ideally, in a class-AB push-pull amplifier, the goal is to set just the
right amount of overlap between output devices to attain the transfer
function that is closest to linear. In addition, the problem of aging and
failing tubes arises. The bias voltage that works so handsomely when the
output tubes were new may not work as well a few months later or when one
output tube is replaced. With solid-state devices, the problem of
heat-dependent current variations in the output stage must be addressed.

Transistors are particularly egregious offenders when it comes to
heat-induced current changes. The transistor exhibits a large positive
temperature coefficient: as the device gets hotter, it conducts more; the
more it conducts, the hotter it gets...until it burns out. There are
workarounds, such as emitter resistors and thermal auto-bias adjustment
circuits, but each brings its own set of problems. MOSFETs, on the other
hand, (usually) display a negative temperature coefficient: as the device
gets hotter, it conducts less. Because of the MOSFET’s degenerative
response, as opposed to the transistor’s regenerative response, the MOSFET
survives where a transistor would burn out. (Not all MOSFETs are operated
past their negative temperature coefficient transition point, which means
that they too need a thermal auto-bias adjustment circuit to compensate
for the heat induced bias misadjustments.)

Vacuum tubes live and breathe in heat and do not surfer from the
solid-state problems of a heat-shifted bias point. However, tubes do age.
Over time, the bias voltage required to establish a desired idle current
will vary. In a fixed-bias amplifier, adjustments can be made as needed,
which might be as often as daily or as infrequently as yearly, depending
on the tubes. In a cathode-biased amplifier, the cathode resistor offers a
stabilizing degeneration in idle current variations. If the tube conducts
too much, the cathode voltage increases, which decreases the idle current.
Unfortunately, this technique is not perfect.

If nothing else, the large-valued cathode resistor steals potential
watts from the output and adds extra heat to the amplifier’s chassis. In
addition, the cathode resistor must be bypassed with a large-valued
capacitor, which brings its own imperfections to the mix. Finally,
cathode-biased amplifiers work best when run in class-A, as class-AB
amplifiers suffer from a tube-induced-rectification distortion. When a
class-AB cathode-biased amplifier sees a prolonged burst of signal, the
output tubes' conduction can easily increase fivefold over the nominal
idle current setting. This increase in cathode current will slowly charge
up the bypass capacitor, which will effectively increase the negative bias
voltage, as the grid will become more negative relative to the cathode.
This new bias voltage will slowly collapse over time, but until then the
amplifier will distort greatly as the output tubes might even be
completely cut off after the large signal burst (surely, "no output
signal" must come as close as you can get to "100% distortion").

One workaround that I have used (and never seen used elsewhere) is to
place a zener in parallel with the cathode resistor. The zener’s break
voltage is purposely set higher than the bias voltage, so that when the
amplifier leaves class-A, the zener limits the maximum voltage the
capacitor can charge up to, which prevents under biasing the amplifier
after a large current swing.

The past: Auto-bias circuits

The OpAmp has made what would be otherwise impossibly complex circuits
simple. For example, imagine building a 16-band equalizer without OpAmps.
Of course, OpAmps are not perfect, but as setting a DC bias voltage does
not entail passing the delicate audio signal through the OpAmp; thus,
whatever sonic liabilities the OpAmp may possess should not pass into the
output signal.

(I know that many tightly wound audiophiles claim that DC servo
circuits pollute the sound of otherwise blameless amplifiers, but after 25
years of designing and using DC servo circuits, I have never encountered a
sonic liability. Maybe I have been lucky; or maybe I have just been extra
careful; or maybe some people have designed such poor-performing servos
that they do intrude into the audio signal. In fact, I would love
to see such a circuit and explore its failings.)

Class-A amplifiers are the best candidates for an auto bias circuit, as
the average of the current flow equals the idle current. For example, an
output tube biased in class-A might experience a dynamic current swing of
+200mA down to 0A, with an average value of 100mA, the same value as its
idle current. In this case, the simple DC servo circuit below works
handily.

The small-valued cathode resistor allows us to read the current flowing
through the output tube by measuring the varying voltage that develops
across it via the connection to the 1M resistor. The 1M resistor
terminates into the OpAmp’s inverting input and the 0.1µF capacitor. Any
deviation from the reference voltage at the OpAmp’s non-inverting input
will be met with a correction voltage at the OpAmp’s output. If the tube
conducts too much, the OpAmp’s output will swing negatively; if too
little, positively.

Once again, but in greater detail: effectively, the 1M resistor is
grounded (in AC terms) at its connection to OpAmp, as the OpAmp will do
all it can to keep both its input pins at exactly the same voltage, and
since the non-inverting input is set at DC reference voltage, the
inverting input will steadily mimic the AC-free input. When the cathode
resistor swings up in voltage, the 1M resistor will pull current up out of
its connection with the capacitor, which must see its connection to the
OpAmp’s output swing negatively to counter this current. Thus, the
capacitor becomes charged negatively relative to its connection to the 1M
resistor. But when the cathode resistor swings down in voltage, the 1M
resistor will source current into of its connection with the capacitor,
which must see its connection to the OpAmp’s output swing positively to
counter this inrush current, which will charge the capacitor positively
relative to its connection to the 1M resistor. If the signal is
symmetrical and its frequency is higher than the resistor and capacitor’s
transition frequency, then the capacitor will display no
net change in voltage across its leads, as the two-direction swings
average to zero. Below the resistor-capacitor transition frequency, the
capacitor will not be able to suppress any voltage movement at the OpAmp’s
inverting input and the OpAmp will see the signal at its inverting pin and
it will invert and amplify it, causing the OpAmp’s output to alter its DC
output voltage.

This circuit works beautifully as long as its reference voltage is
steady, as long as the amplifier does not amplify asymmetrical signals,
and as long as the output stage’s current swings are within in the class-A
envelope of operation. A reference voltage should be noise-free and
temperature-independent. Fortunately, cheap, excellent IC voltage
references are readily available. Protracted asymmetrical signals are rare
in most music, although some instruments do produce asymmetrical
waveforms, such as the trumpet and piano. Usually, the input signal
averages to something close zero with most non-electronic music (with
computer-generated music, who knows). The last requirement is the hardest
to meet. Reactive loads and wide dynamic ranges conspire to kick the
output stage out of class-A into class-AB operation.

Once the output stage leaves class-A mode, the DC servo will see a net
DC increase at its inverting input and it will strive to bring the
amplifier back into line with its reference voltage. Given a long enough
period of excessive current swinging, the bias voltage will be thrown far
too negative and the once class-A amplifier might end up operating in
class-C, as the output devices might be completely biased off (of course,
some tubes are so sloppy at their cutoff region that they never cut off).
If a global feedback loop is in place, the feedback will try to save the
day, but distortion will still be quite high; in the absence of feedback,
the amplifier may not amplify input signals below its new DC bias
threshold, producing grotesque distortion as a result.

A cathode-bias alternative is easy to implement. The cathode resistor
is replaced with a capacitor-bypassed constant-current source. The
constant-current source strives to maintain a constant DC current draw and
the bypass capacitor shunts the AC sign to ground. The constant-current
source can be made from another tube or from solid-state devices, the
latter being much cheaper and more reliable. For example, a lowly LM317
makes an excellent constant-current source in this application, as it only
requires one resistor and a bypass capacitor. Unfortunately, the same
problems of asymmetrical signals and output stage’s current swings outside
the class-A envelope of operation limit this circuit’s usefulness. The
same workaround that was suggested for the cathode-biased amplifier can be
used here: a zener in parallel with the cathode resistor, which limits the
bypass capacitor voltage charging after a large current swing.

More to come
So far, we
have seen that no auto-bias circuit is difficult even with class-A
amplifiers. How do we tackle claas-AB amplifiers? The answer will have to
wait until the next blog entry, as I am way over my typing limit.

//JRB

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