2 Small-Signal Amplifier
of Differential 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.
- The equivalent circuit of the
BJT is shown Fig. 2-1
is the resistance between the terminal and the actual base junction, rp
is the base-emitter junction resistance. Typically rp
An estimation of rp
is the collector to emitter resistance typically of the order 15kW,
rm is the collector-base resistance
of the order several MW
- The transconductance gm
rm = b
- A simplified version of the small-signal
model equivalent circuit is given Fig. 2-2
- Fig. 2-3
- 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 rp depends on applied
the input resistance will depend on it as well.
- The current gain is
Common Base Amplifier
- The Circuit diagram and its equivalent circuit model for the CB amplifier
are shown in Fig. 2-4
- Since the sum of the currents leaving the emitter junction is 0, we have
the following expression
- If r0 is assumed to be large compared with Rs,
rpà and RL,
the voltage gain is
- if rp>> Rs(1+b),
the magnitude of the voltage gain will be the same as that of the common-emitter
- The input impedance of the common-base amplifier is determined using the
- Fig. 2-5
- The output impedance is determined using the following circuit
- Fig. 2-6
- 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.
- 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
- Fig. 2-7 , Fig. 2-8
and Fig. 2-9
- Using the equivalent circuit the voltage gain if found to be
- EF configuration has the largest input impedance compared to the other configurations
- The output impedance is
- EF is used when low output impedance is needed. Also, although it has a
voltage gain < 1, it has large current gain. It is frequently used as a power
amplifier for low-impedance loads.
- There are two types of FETs -- JFETs and MOSFETs.
- The low-frequency small signal model is as shown in Fig.
- 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
- The common-source amplifier is similar to the common-emitter amplifier
- Fig. 2-11
- Normally Rg >> R so Vi
- 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
- The voltage gain is
- If rd >> Rs and RL
we have the following relationship
- For gm Rs >> 1 we have
- The circuit diagram and its equivalent circuit model for source follower
are shown in Fig. 2-12
- If Rb >> Rs,
- 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.
- Fig. 2-13
- Multistage amplifiers are used for impedance matching or to obtain extra
- 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
Dual Gate FET
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
- Fig. 2-15
- The above example uses 2 center-tapped transformers. The input transformer
separates the input signal into 2 signal 180o out of phase. The
output transformer is used to sum the output currents of the two transistors.
- If the input signal is Vi = A cos wt
- 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 180o. 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
- The differential amplifier is an essential building block in modern IC amplifiers.
The circuit is shown Fig. 2-16
- 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
- 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 exp(Vbb/kT) >>
- where Vd is the difference between the two input voltages. KCL at the emitter
- Similarly ,
The transfer characteristic for the emitter-coupled pair is shown in Fig.
- If Vd = 0 then IC1
- If we incrementally increase V1 by Dv/2and
simultaneously decrease V2 by Dv/2.
The differential voltage becomes Dv. For Dv<
4kT as indicated in the transfer characteristics above the circuit behaves
linearly. IC1 increases by DIC
and IC2 decreases by the same amount.
- Consider both V1 and V2
are increased by Dv/2. The difference voltage remains
0, and IC1 and Ic2 remain equal. However,
both IC1 and IC2
exhibit a small increase dIC.
Hence the current in RE increases by 2dIC.
The voltage VE is no longer constant but
increase by an amount of 2dICRB.
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