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
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. See “Phase shift oscillator” , Ch 9 for a practical application
of positive feedback.
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 distorts the input waveform less 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 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, starting with Figure below.
Common-emitter amplifier without feedback.
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 it 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 move toward negative,
and vice versa. The oscilloscope waveforms are shown in Figure below.
Common-emitter amplifier, no feedback, with reference waveforms for comparison.
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 in Figure below will result in
Negative feedback, collector feedback, decreases the output signal.
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 (with respect to ground) is a weighted
average of the input voltage and the feedback voltage, resulting in
signal of reduced amplitude going into the transistor. So, the amplifier
circuit in Figure above 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 in Figure below.
Emitter feedback: A different method of introducing negative feedback into a circuit.
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 in Figure below.
With no feedback resistor connecting the emitter to ground in Figure below (a) , 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 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 in Figure below (b).
(a) No feedback vs (b) emitter feedback. A waveform at the
collector is inverted with respect to the base. At (b) the emitter
waveform is in-phase (emitter follower) with base, out of phase with
collector. Therefore, the emitter signal subtracts from the collector
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; its 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. 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, (Figure below) however, do not suffer
from thermal runaway. Why is this? The answer has everything to do
with negative feedback.
Common collector (emitter follower) amplifier.
Note that the common-collector amplifier (Figure above) has its load resistor placed in exactly the same spot as we had the Rfeedback
resistor in the last circuit in Figure above (b): 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 ?. This means, among other
things, that we could replace the transistor in a common-collector
amplifier with one having a different ? and not see any significant
changes in voltage gain. In a common-emitter circuit, the voltage gain
is highly dependent on ?. If we were to replace the transistor in a
common-emitter circuit with another of differing ?, 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 ? to some degree, but not as much as before,
making the circuit more predictable despite variations in transistor ?.
The fact that we have to introduce negative feedback into a
common-emitter amplifier to avoid thermal runaway is an unsatisfying
solution. Iis it possibe 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 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: its 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 only function with DC. That is, if we only feed back
an inverted DC signal from output to input, but not an inverted AC
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 in
Figure below, we create the very situation we need: a path from emitter
to ground that is easier for AC than it is for DC.
High AC voltage gain reestablished by adding Cbypass in parallel with Rfeedback
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. An example circuit
showing negative feedback in a three-stage common-emitter amplifier is
Feedback around an “odd” number of direct coupled stages produce negative feedback.
The feedback path from the final output to the input is through a single resistor, Rfeedback.
Since each stage is a common-emitter amplifier (thus inverting), the
odd number of stages from input to output will invert the output signal;
the feedback will be negative (degenerative). Relatively large amounts
of feedback may be used without sacrificing voltage gain, because the
three amplifier stages provide 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 is an advantage for mass-production of electronic circuitry: if
amplifiers of predictable gain may be constructed using transistors of
widely varied ? values, it eases the selection and replacement of
components. 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 much 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 ? or
other internal component values will have little effect on voltage gain
with feedback in operation, resulting in an amplifier that is stable and
easy to design.
Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt