Chapter 2 Small-Signal Amplifiers

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Chapter 2Small-Signal Amplifiers

• Most amplifiers in communication circuits are
  small signal amplifiers. Hence, they can be
  described by linear equations. We will consider
  several amplifiers including BJT, FET,
  operational amplifiers and differential
  amplifiers.

Bipolar Transistor Amplifiers

• The equivalent circuit of the BJT is shown below

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• rb is the resistance between the terminal and
  the actual base junction, r? is the base-emitter
  junction resistance.
• Typically r? gtgt rb. An estimation of r? is
• r0 is the collector to emitter resistance
  typically of the order 15k?, r? is the
  collector-base resistance of the order several
  M?.
• The transconductance gm r? ?
• A simplified version of the small-signal model
  equivalent circuit is given below

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Common-Emitter Amplifier

• here the coupling capacitance is treated as a
  short circuit.
• The output voltage is therefore
• The input impedance, not including Rs, is given
  be
• Since r? depends on applied the input resistance
  will depend on it as well.
• The current gain is

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Common Base Amplifier

• The Circuit diagram and its equivalent circuit
  model for the CB amplifier are shown below
• Since the sum of the currents leaving the emitter
  junction is 0, we have the following expression

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• If r0 is assumed to be large compared with Rs, r?
  and RL, the voltage gain is
• if r? gtgt Rs(1?), the magnitude of the voltage
  gain will be the same as that of the
  common-emitter amplifier
• The input impedance of the common-base amplifier
  is determined using the following circuit

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• The output impedance is determined using the
  following circuit
• The common-base amplifier has a voltage gain but
  its current gain is less than unity. It is used
  as non-inverting amplifiers where low input
  impedance and high output impedance is desired.
• It also has much better high-frequency response
  than CE amplifier and is often used in
  high-frequency circuits.

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Emitter Follower

• The EF has a non-inverting voltage gain of less
  than 1
• However, it can combine with other stages, such
  as the CE stage, to realize a greater combined
  gain than CE stage alone

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• Using the equivalent circuit the voltage gain if
  found to be
• EF configuration has the largest input impedance
  compared to the other configurations

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• The output impedance is
• EF is used when low output impedance is needed.
  Also, although it has a voltage gain lt 1, it has
  large current gain. It is frequently used as a
  power amplifier for low-impedance loads.

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Field-Effect Transistors Amplifiers

• There are two types of FETs -- JFETs and MOSFETs.
• The low-frequency small signal model is as shown
• The transconductance is defined as
• For JFETs
• where gm0 is the transconductance when
  gate-to-source bias voltage is 0, ID is the drain
  current and IDSS is the drain current when the
  gate-to-source voltage is 0.
• For MOSFETs, gm is
• where gmR is the transconductance at some
  specified drain bias current IDR

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Common-Source Amplifier

• The common-source amplifier is similar to the
  common-emitter amplifier
• The common-source amplifier is similar to the
  common-emitter amplifier.
• Normally Rg gtgt R so Vi Vg

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• The source voltage is determined from the
  following equations
• since the current leaving output node and source
  is zero
• The current through Rs The source voltage is
• The voltage gain is
• If rd gtgt Rs and RL we have the following
  relationship
• For gm Rs gtgt 1 we have

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Source-Follower

• The circuit diagram and its equivalent circuit
  model for source follower are shown below
• If Rb gtgt Rs, then

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Common-Gate Amplifier

• The output impedance is
• which is much smaller than the other two FET
  amplifier configurations and is the major
  advantage for this configuration

• The common-gate amplifier is often used in
  high-frequency application and has a much larger
  bandwidth than the common source configuration.

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• Thus
• The input impedance at the source can be found by
  solving for the source current
• and
• since

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Multistage Amplifiers

• The output impedance is determined as
• but I0 is also the current passing through the
  source resistance so
• The common gate amplifier has the highest output
  impedance of the three FET amplifier

• Multistage amplifiers are used for impedance
  matching or to obtain extra gain.
• Power transistors have smaller gain-bandwidth
  product than low-power transistors, hence the
  power amplification stage is often operated near
  unity voltage gain in order to maximize the
  bandwidth
• Voltage amplification is carried out in the
  stages preceding the power amplification stage

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Dual Gate FET

• The FET cascode circuit has many high-frequency
  applications that two FETs are often fabricated
  as a single transistor with 2 gates. The source
  of the one transistor is continuous with the
  drain of the other so the device has 1 source, 1
  drain and 2 gates
• The device offers low-noise and high gain in
  radio-frequency applications
• It is a versatile device which can be used as a
  mixer or automatic gain control amplifier. The
  equivalent circuit is as shown

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• Here gate 2 and the source are grounded
• The load resistance of the first stage is the
  input resistance of the second stage, and the
  second stage is a common-gate amplifier.
  Therefore
• Since
• where gmR is the transconductance at some
  specified drain bias current IDR.
• Since both transistors have the same drain
  current gm1gm2. Thus Vi-VD1 and Vgs2-Vs2-VD1
  

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Push Pull Amplifiers

• Transistors all exhibit a nonlinear
  characteristic that causes distortion of the
  input signal levels. Such distortion can be
  eliminated by push-pull amplifier
• The above example uses 2 center-tapped
  transformers. The input transformer separates
  the input signal into 2 signal 180? out of phase.
  The output transformer is used to sum the output
  currents of the two transistors.
• Hence
• If the input signal is

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• then the output of the 2 transistors are also
  periodic, and they can be expressed in a Fourier
  series
• If the two transistors are identical then I1 and
  I2 are identical except I2 lags I1 by 180 ?.
  Thus
• The output current is
• The even harmonics are eliminated from the
  output. This is important as FET have a
  square-law characteristic that generates a
  relatively large second harmonic.

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Differential Amplifier

• The differential amplifier is an essential
  building block in modern IC amplifiers. The
  circuit is shown below
• The operation of this circuit is based on the
  ability to fabricate matched components on the
  same chip. In the figure IEE is realized using a
  current mirror. We assume that Q1 and Q2 are
  identical transistors and both collector
  resistors fabricated with equal values.
• The KVL expression for the loop containing the
  two emitter-base junctions is

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• The transistors are biased in the forward-active
  mode, the reverse saturation current of the
  collector-base junction is negligible. The
  collector currents IC1 and IC2 are given by
• where we assumed that
• where Vd is the difference between the two input
  voltages. KCL at the emitter node requires
• Similarly The
  transfer
• characteristic for the emitter-coupled pair is
  shown on the following page.
• If Vd 0 then IC1 IC2

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• If we incrementally increase V1 by
  and simultaneously decrease V2 by .
  The differential voltage becomes . For
  lt 4kT as indicated in the transfer
  characteristics above the circuit behaves
  linearly. IC1 increases by and IC2
  decreases by the same amount.

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Common Mode

• Consider both V1 and V2 are increased by
  . The difference voltage remains 0, and IC1
  and Ic2 remain equal. However, both IC1 and Ic2
  exhibit a small increase . Hence the
  current in RE increases by . The
  voltage VE is no longer constant but increase by
  an amount of . This situation
  where equal signal are applied to Q1 and Q2 is
  the called the common mode.
• Usually differential amplifiers are designed such
  that only differential signals are amplified.

Analysis of Differential Amplifiers

• The analysis of differential amplifiers is
  simplified using half-circuit concept. The
  equivalent circuit model for differential and
  common modes are shown

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• Differential mode gain
• Common mode gain is
• The Common Mode Rejection Ration (CMRR) is
  defined as
• From the above we obtain
• If arbitrary signals V1 and V2 are applied to the
  inputs then

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FET Differential Amplifier

• A typical differential amplifier connection is
  shown below