Feedback
If some percentage of an amplifier's
output signal is connected to the input, so that the amplifier amplifies
part of its own output signal, we have what is known as feedback.
Feedback comes in two varieties: positive (also called
regenerative), and negative (also called degenerative).
Positive feedback reinforces the direction of an amplifier's output
voltage change, while negative feedback does just the opposite.
A familiar example of feedback happens in
public-address ("PA") systems where someone holds the microphone too
close to a speaker: a high-pitched "whine" or "howl" ensues, because the
audio amplifier system is detecting and amplifying its own noise.
Specifically, this is an example of positive or regenerative
feedback, as any sound detected by the microphone is amplified and
turned into a louder sound by the speaker, which is then detected by the
microphone again, and so on . . . the result being a noise of steadily
increasing volume until the system becomes "saturated" and cannot
produce any more volume.
One might wonder what possible benefit
feedback is to an amplifier circuit, given such an annoying example as
PA system "howl." If we introduce positive, or regenerative, feedback
into an amplifier circuit, it has the tendency of creating and
sustaining oscillations, the frequency of which determined by the values
of components handling the feedback signal from output to input. This is
one way to make an oscillator circuit to produce AC from a DC
power supply. Oscillators are very useful circuits, and so feedback has
a definite, practical application for us.
Negative feedback, on the other hand, has
a "dampening" effect on an amplifier: if the output signal happens to
increase in magnitude, the feedback signal introduces a decreasing
influence into the input of the amplifier, thus opposing the change in
output signal. While positive feedback drives an amplifier circuit
toward a point of instability (oscillations), negative feedback drives
it the opposite direction: toward a point of stability.
An amplifier circuit equipped with some
amount of negative feedback is not only more stable, but it tends to
distort the input waveform to a lesser degree and is generally capable
of amplifying a wider range of frequencies. The tradeoff for these
advantages (there just has to be a disadvantage to negative
feedback, right?) is decreased gain. If a portion of an amplifier's
output signal is "fed back" to the input in such a way as to oppose any
changes in the output, it will require a greater input signal amplitude
to drive the amplifier's output to the same amplitude as before. This
constitutes a decreased gain. However, the advantages of stability,
lower distortion, and greater bandwidth are worth the tradeoff in
reduced gain for many applications.
Let's examine a simple amplifier circuit
and see how we might introduce negative feedback into it:
The amplifier configuration shown here is
a common-emitter, with a resistor bias network formed by R1
and R2. The capacitor couples Vinput to the
amplifier so that the signal source doesn't have a DC voltage imposed on
it by the R1/R2 divider network. Resistor R3
serves the purpose of controlling voltage gain. We could omit if for
maximum voltage gain, but since base resistors like this are common in
common-emitter amplifier circuits, we'll keep it in this schematic.
Like all common-emitter amplifiers, this
one inverts the input signal as it is amplified. In other words,
a positive-going input voltage causes the output voltage to decrease, or
go in the direction of negative, and visa-versa. If we were to examine
the waveforms with oscilloscopes, it would look something like this:
Because the output is an inverted, or
mirror-image, reproduction of the input signal, any connection between
the output (collector) wire and the input (base) wire of the transistor
will result in negative feedback:
The resistances of R1, R2,
R3, and Rfeedback function together as a
signal-mixing network so that the voltage seen at the base of the
transistor (in reference to ground) is a weighted average of the input
voltage and the feedback voltage, resulting in signal of reduced
amplitude going into the transistor. As a result, the amplifier circuit
will have reduced voltage gain, but improved linearity (reduced
distortion) and increased bandwidth.
A resistor connecting collector to base
is not the only way to introduce negative feedback into this amplifier
circuit, though. Another method, although more difficult to understand
at first, involves the placement of a resistor between the transistor's
emitter terminal and circuit ground, like this:
This new feedback resistor drops voltage
proportional to the emitter current through the transistor, and it does
so in such a way as to oppose the input signal's influence on the
base-emitter junction of the transistor. Let's take a closer look at the
emitter-base junction and see what difference this new resistor makes:
With no feedback resistor connecting the
emitter to ground, whatever level of input signal (Vinput)
makes it through the coupling capacitor and R1/R2/R3
resistor network will be impressed directly across the base-emitter
junction as the transistor's input voltage (VB-E). In other
words, with no feedback resistor, VB-E equals Vinput.
Therefore, if Vinput increases by 100 mV, then VB-E
likewise increases by 100 mV: a change in one is the same as a change in
the other, since the two voltages are equal to each other.
Now let's consider the effects of
inserting a resistor (Rfeedback) between the transistor's
emitter lead and ground:
Note how the voltage dropped across Rfeedback
adds with VB-E to equal Vinput. With Rfeedback
in the Vinput -- VB-E loop, VB-E will
no longer be equal to Vinput. We know that Rfeedback
will drop a voltage proportional to emitter current, which is in turn
controlled by the base current, which is in turn controlled by the
voltage dropped across the base-emitter junction of the transistor (VB-E).
Thus, if Vinput were to increase in a positive direction, it
would increase VB-E, causing more base current, causing more
collector (load) current, causing more emitter current, and causing more
feedback voltage to be dropped across Rfeedback. This
increase of voltage drop across the feedback resistor, though,
subtracts from Vinput to reduce the VB-E, so
that the actual voltage increase for VB-E will be less than
the voltage increase of Vinput. No longer will a 100 mV
increase in Vinput result in a full 100 mV increase for VB-E,
because the two voltages are not equal to each other.
Consequently, the input voltage has less
control over the transistor than before, and the voltage gain for the
amplifier is reduced: just what we expected from negative feedback.
In practical common-emitter circuits,
negative feedback isn't just a luxury; it's a necessity for stable
operation. In a perfect world, we could build and operate a
common-emitter transistor amplifier with no negative feedback, and have
the full amplitude of Vinput impressed across the
transistor's base-emitter junction. This would give us a large voltage
gain. Unfortunately, though, the relationship between base-emitter
voltage and base-emitter current changes with temperature, as predicted
by the "diode equation." As the transistor heats up, there will be less
of a forward voltage drop across the base-emitter junction for any given
current. This causes a problem for us, as the R1/R2
voltage divider network is designed to provide the correct quiescent
current through the base of the transistor so that it will operate in
whatever class of operation we desire (in this example, I've shown the
amplifier working in class-A mode). If the transistor's voltage/current
relationship changes with temperature, the amount of DC bias voltage
necessary for the desired class of operation will change. In this case,
a hot transistor will draw more bias current for the same amount of bias
voltage, making it heat up even more, drawing even more bias current.
The result, if unchecked, is called thermal runaway.
Common-collector amplifiers, however, do
not suffer from thermal runaway. Why is this? The answer has everything
to do with negative feedback:
Note that the common-collector amplifier
has its load resistor placed in exactly the same spot as we had the Rfeedback
resistor in the last circuit: between emitter and ground. This means
that the only voltage impressed across the transistor's base-emitter
junction is the difference between Vinput and Voutput,
resulting in a very low voltage gain (usually close to 1 for a
common-collector amplifier). Thermal runaway is impossible for this
amplifier: if base current happens to increase due to transistor
heating, emitter current will likewise increase, dropping more voltage
across the load, which in turn subtracts from Vinput
to reduce the amount of voltage dropped between base and emitter. In
other words, the negative feedback afforded by placement of the load
resistor makes the problem of thermal runaway self-correcting. In
exchange for a greatly reduced voltage gain, we get superb stability and
immunity from thermal runaway.
By adding a "feedback" resistor between
emitter and ground in a common-emitter amplifier, we make the amplifier
behave a little less like an "ideal" common-emitter and a little more
like a common-collector. The feedback resistor value is typically quite
a bit less than the load, minimizing the amount of negative feedback and
keeping the voltage gain fairly high.
Another benefit of negative feedback,
seen clearly in the common-collector circuit, is that it tends to make
the voltage gain of the amplifier less dependent on the characteristics
of the transistor. Note that in a common-collector amplifier, voltage
gain is nearly equal to unity (1), regardless of the transistor's β.
This means, among other things, that we could replace the transistor in
a common-collector amplifier with one having a different β and not see
any significant changes in voltage gain. In a common-emitter circuit,
the voltage gain is highly dependent on β. If we were to replace the
transistor in a common-emitter circuit with another of differing β, the
voltage gain for the amplifier would change significantly. In a
common-emitter amplifier equipped with negative feedback, the voltage
gain will still be dependent upon transistor β to some degree, but not
as much as before, making the circuit more predictable despite
variations in transistor β.
The fact that we have to introduce
negative feedback into a common-emitter amplifier to avoid thermal
runaway is an unsatisfying solution. It would be nice, after all, to
avoid thermal runaway without having to suppress the amplifier's
inherently high voltage gain. A best-of-both-worlds solution to this
dilemma is available to us if we closely examine the nature of the
problem: the voltage gain that we have to minimize in order to avoid
thermal runaway is the DC voltage gain, not the AC voltage
gain. After all, it isn't the AC input signal that fuels thermal
runaway: it's the DC bias voltage required for a certain class of
operation: that quiescent DC signal that we use to "trick" the
transistor (fundamentally a DC device) into amplifying an AC signal. We
can suppress DC voltage gain in a common-emitter amplifier circuit
without suppressing AC voltage gain if we figure out a way to make the
negative feedback function with DC only. That is, if we only feed back
an inverted DC signal from output to input, but not an inverted AC
signal.
The Rfeedback emitter resistor
provides negative feedback by dropping a voltage proportional to load
current. In other words, negative feedback is accomplished by inserting
an impedance into the emitter current path. If we want to feed back DC
but not AC, we need an impedance that is high for DC but low for AC.
What kind of circuit presents a high impedance to DC but a low impedance
to AC? A high-pass filter, of course!
By connecting a capacitor in parallel
with the feedback resistor, we create the very situation we need: a path
from emitter to ground that is easier for AC than it is for DC:
The new capacitor "bypasses" AC from the
transistor's emitter to ground, so that no appreciable AC voltage will
be dropped from emitter to ground to "feed back" to the input and
suppress voltage gain. Direct current, on the other hand, cannot go
through the bypass capacitor, and so must travel through the feedback
resistor, dropping a DC voltage between emitter and ground which lowers
the DC voltage gain and stabilizes the amplifier's DC response,
preventing thermal runaway. Because we want the reactance of this
capacitor (XC) to be as low as possible, Cbypass
should be sized relatively large. Because the polarity across this
capacitor will never change, it is safe to use a polarized
(electrolytic) capacitor for the task.
Another approach to the problem of
negative feedback reducing voltage gain is to use multi-stage amplifiers
rather than single-transistor amplifiers. If the attenuated gain of a
single transistor is insufficient for the task at hand, we can use more
than one transistor to make up for the reduction caused by feedback.
Here is an example circuit showing negative feedback in a three-stage
common-emitter amplifier:
Note how there is but one "path" for
feedback, from the final output to the input through a single resistor,
Rfeedback. Since each stage is a common-emitter amplifier --
and thus inverting in nature -- and there are an odd number of stages
from input to output, the output signal will be inverted with respect to
the input signal, and the feedback will be negative (degenerative).
Relatively large amounts of feedback may be used without sacrificing
voltage gain, because the three amplifier stages provide so much gain to
begin with.
At first, this design philosophy may seem
inelegant and perhaps even counter-productive. Isn't this a rather crude
way to overcome the loss in gain incurred through the use of negative
feedback, to simply recover gain by adding stage after stage? What is
the point of creating a huge voltage gain using three transistor stages
if we're just going to attenuate all that gain anyway with negative
feedback? The point, though perhaps not apparent at first, is increased
predictability and stability from the circuit as a whole. If the three
transistor stages are designed to provide an arbitrarily high voltage
gain (in the tens of thousands, or greater) with no feedback, it will be
found that the addition of negative feedback causes the overall voltage
gain to become less dependent of the individual stage gains, and
approximately equal to the simple ratio Rfeedback/Rin.
The more voltage gain the circuit has (without feedback), the more
closely the voltage gain will approximate Rfeedback/Rin
once feedback is established. In other words, voltage gain in this
circuit is fixed by the values of two resistors, and nothing more.
This advantage has profound impact on
mass-production of electronic circuitry: if amplifiers of predictable
gain may be constructed using transistors of widely varied β values, it
makes the selection and replacement of components very easy and
inexpensive. It also means the amplifier's gain varies little with
changes in temperature. This principle of stable gain control through a
high-gain amplifier "tamed" by negative feedback is elevated almost to
an art form in electronic circuits called operational amplifiers,
or op-amps. You may read much more about these circuits in a
later chapter of this book!
- REVIEW:
- Feedback
is the coupling of an amplifier's output to its input.
- Positive,
or regenerative feedback has the tendency of making an
amplifier circuit unstable, so that it produces oscillations (AC). The
frequency of these oscillations is largely determined by the
components in the feedback network.
- Negative,
or degenerative feedback has the tendency of making an
amplifier circuit more stable, so that its output changes less
for a given input signal than without feedback. This reduces the gain
of the amplifier, but has the advantage of decreasing distortion and
increasing bandwidth (the range of frequencies the amplifier can
handle).
- Negative feedback may be introduced
into a common-emitter circuit by coupling collector to base, or by
inserting a resistor between emitter and ground.
- An emitter-to-ground "feedback"
resistor is usually found in common-emitter circuits as a preventative
measure against thermal runaway.
- Negative feedback also has the
advantage of making amplifier voltage gain more dependent on resistor
values and less dependent on the transistor's characteristics.
- Common-collector amplifiers have a lot
of negative feedback, due to the placement of the load resistor
between emitter and ground. This feedback accounts for the extremely
stable voltage gain of the amplifier, as well as its immunity against
thermal runaway.
- Voltage gain for a common-emitter
circuit may be re-established without sacrificing immunity to thermal
runaway, by connecting a bypass capacitor in parallel with the
emitter "feedback resistor."
- If the voltage gain of an amplifier is
arbitrarily high (tens of thousands, or greater), and negative
feedback is used to reduce the gain to reasonable levels, it will be
found that the gain will approximately equal Rfeedback/Rin.
Changes in transistor β or other internal component values will have
comparatively little effect on voltage gain with feedback in
operation, resulting in an amplifier that is stable and easy to
design.
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