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Multistage Amplifiers
by Kenneth A. Kuhn
Nov. 11, 2007, rev. July 26, 2009
Introduction
There is a limit to how much gain can be achieved from a single stage amplifier. Single
stage amplifiers also have limits on input and output impedance. Multistage amplifiers
are used to achieve higher gain and to provide better control of input and output
impedances. Two significant advantages that multistage amplifiers have over single
stage amplifiers are flexibility in input and output impedance and much higher gain.
Multistage amplifiers can be divided into two general classes, open-loop and negative
feedback. Open-loop amplifiers are easy to understand and design but are sensitive to
environment and component variations. Negative feedback amplifiers are a bit more
difficult to understand but have the advantage of being much less sensitive to
environment and component variations. This note will focus on the open-loop class. A
good closed-loop amplifier begins with a good open-loop design.
For many amplifier applications it is desirable for the input impedance to be very high.
Thus, it is common for the first amplifier stage to be either a common-collector (a.k.a.
emitter follower) bipolar junction transistor stage or a common-drain (a.k.a. source
follower) or even common-source field effect transistor stage. Sometimes high input
impedance is not important and the first stage may be a common-emitter. Field effect
transistors are normally used only for the input stage and for the specific application of
very high input impedance.
It is also common situation that it is desirable for the output impedance of an amplifier to
be low. A common-collector circuit is typically used. But in some cases there is no need
for very low output impedance and the last stage may be a common-emitter.
For the amplifier stages in-between it is common to employ common-emitter circuits
because those can achieve high voltage gain.
Analysis of multistage amplifiers is performed stage at a time starting with the input stage
and progressing to the output stage. The analysis methods are identical to that of single
stage amplifiers. One point of confusion for students analyzing direct coupled amplifiers
is that the collector resistor for one stage becomes the base resistor for the next stage. In
stages involving common-collector amplifiers some modified approaches, including
some simplifying approximations, are necessary because characteristics of commoncollector stages are dependent on external impedances. The student should not be afraid
of approximations since that is routinely done all the time in the profession. An
advantage of closed loop amplifiers is that approximation errors are greatly reduced.
The design of multistage amplifiers begins at the output and progresses backwards to the
input. Initially the number of stages is not known. The design progresses with additional
stages until the requirements are met. It is common for there to be a lot of iteration in the
design and the number of stages might vary with each iteration.
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Multistage Amplifiers
The following table is a summary of some different multistage amplifiers constructions
and their characteristics.
General Characteristics of Typical Multistage Amplifier Structures
Stage Number
1
2
3
4
CE CE
CE CC
CC CE
CC CC
CE CE CE
CE CE CC
CE CC CE
CE CC CC
CC CE CE
CC CE CC
CC CC CE
CC CC CC
CC CE CE CC
Characteristics
Rin
Rout
Medium
Medium
Medium
Low
High
Medium
Very high
Very low
Medium
Medium
Medium
Low
Medium
Medium
Medium
Very low
High
Medium
High
Low
Very high
Medium
Very high
Very low
High
Low
Descriptor
Low
Medium
High
Very high
Extremely high
Rin or Rout
less than a few hundred Ohms
A few hundred to a few thousand Ohms
a few thousand to a few ten thousand Ohms
many tens of thousands of Ohms
Over one hundred thousand Ohms
Voltage gain
High
Medium
Medium
<1
Extremely high
Very high
Very high
Medium
Very high
Medium
Medium
<1
Very high
Voltage gain
less than 50
50 to 500
500 to 5000
Over 5,000
AC coupled versus DC coupled stages
The simplest method to construct a multistage amplifier is to cascade several single stage
amplifiers with their usual AC coupling. AC coupling blocks DC paths and makes the
bias design or analysis of each stage simple. A typical example is shown in Figure 1.
Figure 1: Multistage amplifier with AC coupling
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Multistage Amplifiers
The use of AC coupling requires a lot of capacitors and resistors that could be eliminated
with innovative design. The key to this is to arrange for the quiescent voltage at the
output of one stage to be the same as the desired quiescent voltage at the input of the next
stage. Then the AC coupling capacitor and associated bias resistors are not needed. The
bias resistors and thus reduce the gain of the amplifier. An amplifier designed without
these can achieve higher gain and with much fewer parts. The following circuit shows
the first example with unneeded parts removed. Note the simplicity.
Figure 2: Multistage amplifier with DC coupling
Direct coupled amplifiers are a challenge for the designer as the bias analysis and design
calculations are more complicated. It is important to design the amplifier such that the
DC gain is low. But, that is what engineers are paid to do. Using as few parts as needed
to accomplish a desired function lowers the costs for the manufacturer.
A good question to ask and explore is, “Is there an upper bounds to the amount of gain an
amplifier can have?” The answer is yes but there is not a specific value. It depends on a
variety of factors. One limiting phenomena is random noise which exists in all
electronics. These small voltages often in the nanovolt to microvolt range will dominate
or even saturate the output of the amplifier if the gain is high enough. Depending on the
desired bandwidth and how much noise can be tolerated in the output the practical limit
of gain may range from less than a thousand to many millions. Typical amplifiers in the
audio frequency range that operate on microphone or phonograph pickups have voltage
gains in the one thousand range as that is what is needed. The total voltage gain from
microphone to a several hundred watt speaker system in an auditorium can be in the
50,000 range. The power gain might be in the 120 dB range.
Amplifiers can be either open-loop (no feedback from output to input) or closed-loop
(some of the amplifier output is fed back to the input). In a basic electronics course there
is barely enough time to even discuss open-loop amplifiers. Virtually one hundred
percent of real-world amplifiers are closed loop utilizing negative feedback to reduce
undesirable characteristics of the amplifier. Closed loop amplifiers can achieve a very
specific and stable gain with varying temperature and transistor characteristics as well as
much lower distortion. Many of the challenging bias problems for multistage amplifiers
are eliminated with negative feedback. The mathematics is more complicated (again, that
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Multistage Amplifiers
is what engineers are paid for) and one must first understand open-loop amplifiers before
delving into closed-loop amplifiers.
NPN and PNP transistors are often used in multistage amplifiers for improved
characteristics over what could be achieve by using only one type. Temperature
sensitivity can be greatly reduced using both types in certain circuits such that the baseemitter voltage drops practically cancel – thus greatly reducing the effect of temperature.
Each individual voltage drop is very temperature sensitive but the net result is the
subtraction of the two. Use of an NPN common-emitter stage followed by a PNP
common-collector stage (or vice-versa) for the output enables near optimum bias
conditions for both.
The following are some examples of multistage open-loop amplifiers.
Figure 3: High voltage gain amplifier
The circuit in Figure 3 is capable of very high gain. The gain can be up to several ten
thousand if RE1B and RE2B are zero. These resistors are often non-zero to reduce the
gain to a desired level.
Figure 4: High input impedance amplifier
The circuit in Figure 4 features an emitter follower input stage for high input impedance
followed by a common-emitter amplifier for high voltage gain. This feature provides a
much higher power gain than can be achieved with a common-emitter amplifier alone.
This circuit features very low temperature sensitivity because the base-emitter voltage
drops of the two transistors practically cancel.
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Multistage Amplifiers
Figure 5: High input impedance, low output impedance, high voltage gain amplifier
The circuit in Figure 5 is about the ultimate in what is practical to do with direct coupled
amplifiers without negative feedback. This circuit features an emitter follower for the
input stage thus providing high input impedance and an emitter follower for the output
stage thus providing low output impedance. The two common-emitter stages in-between
are capable of very high voltage gain as discussed in the circuit for Figure 3.
The following are some examples of multistage closed-loop amplifiers.
Figure 6: Simple inverting amplifier with feedback
The circuit in Figure 6 features simplicity and very high output linear signal swing thanks
to the negative feedback. The output DC voltage is generally set to VCC/2 by the ratio of
the feedback resistor to the base resistor to ground. The inverting gain is set by the ratio
of the feedback resistor to the input resistor.
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Multistage Amplifiers
Figure 7: High gain inverting amplifier with feedback
The circuit in Figure 7 is a very high gain version of the circuit in Figure 6. Operation is
similar except that much higher gains can be achieved. The open loop gain of the
amplifier (not practical to operate in this mode) is in the many hundreds of thousands.
Figure 8: Non-inverting amplifier with feedback
The circuit in Figure 8 is an example of in-phase feedback to boost input impedance
while lowering output impedance. The feedback stabilizes the DC bias and voltage gain.
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