Differential and Multistage
Amplifiers
ELZ 303 - Elektronik II
Microelectronic Circuits – Fourth Edition
Adel S. Sedra, Kenneth C. Smith, 1998 Oxford University Press
Dr. Mehmet Siraç
Siraç Özerdem
Elektrik Elektronik Müh. Bö
Bölümü
Dicle Üniversitesi
The basic BJT differential-pair configuration.
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1
Different modes of operation of the BJT differential pair
Mode 1
The differential pair with a common-mode input signal vCM
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Different modes of operation of the BJT differential pair
Mode 2
The differential pair with a “large” differential input signal.
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2
Different modes of operation of the BJT differential pair
Mode 3
The differential pair
with a large differential
input signal of polarity
opposite to that in
mode2.
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Different modes of operation of the BJT differential pair
Mode 4
The differential pair
with a small differential
input signal vi. Note that
we have assumed the
bias current source I to
be ideal (i.e., it has an
infinite output
resistance) and thus I
remains constant with
the change in vCM.
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3
Large-Signal Operation of the BJT Differential Pair
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Large-Signal Operation of the BJT Differential Pair
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4
Large-Signal Operation of the BJT Differential Pair
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Small-Signal Operation of the BJT Differential Amplifier
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5
Small-Signal Operation of the BJT Differential Amplifier
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Small-Signal Operation of the BJT Differential Amplifier
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6
An alternative viewpoint
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An alternative viewpoint with emitter resistances
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7
Input Differential Resistance
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15
Differential Voltage Gain
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8
Differential Voltage Gain
If the output is taken differentially,
If the output is taken single-endedly,
For the differential amplifier with emitter resistances,
if the output is taken differentially,
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Equivalence of the Differential Amp. to a Common Emitter Amp.
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9
Equivalence of the Differential Amp. to a Common Emitter Amp.
Input resistance =
The differential half-circuit
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Equivalence of the Differential Amp. to a Common Emitter Amp.
The differential amplifier fed in a single-ended fashion.
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10
Common- Mode Gain (Assume that the circuit is perfectly symmetric)
(a) The differential amplifier fed by a common-mode voltage signal vicm.
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(b) Equivalent “half-circuits”
common-mode
calculations.
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Press, Inc.
Common- Mode Gain (Assume that the circuit is perfectly symmetric)
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Common- Mode Gain (Assume that the circuit is perfectly symmetric)
If the output is taken single endedly, the common mode gain
Since in this case the differential gain is
The common-mode rejection ratio (CMRR)
The common-mode rejection ratio (CMRR) in dB
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Common- Mode Gain (Assume that the circuit is NOT symmetric)
For a mismatch
Rc in the collector resistances
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Common- Mode Gain
The circuit is symmetric
The circuit is NOT symmetric
>
CMRR
<
CMRR
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Input Common-Mode Resistance (Ricm)
(a) Definition of the input common-mode resistance Ricm.
(b) The equivalent
common-mode
half-circuit.
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Input Common-Mode Resistance (Ricm)
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Example
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14
Other nonlinear characteristics of the differential amplifier
The BJT differential pair with both
inputs grounded.
If the two sides of the differential
pair were perfectly matched, then
the current I would split equally
between Q1 and Q2, and Vo would
be zero.
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Other nonlinear characteristics of the differential amplifier
Practical circuits exhibit mismatches
that result in a dc output voltage Vo
even with both inputs grounded.
Vo : The output dc offset voltage
VOS = VO / Ad
Vos : The input offset voltage
Ad : The differential gain
If we apply a voltage –Vos between the input terminals, then the
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output voltage will
be reducedCopyright
to zero.
15
Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in the load resistance Rc1 and Rc2.
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in the load resistance Rc1 and Rc2.
Example
Consider the situation where the collector resistors are
accurate to within ±1%. Then the worst case mismatch will be
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Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in their emitter-base junction areas.
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Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in their emitter-base junction areas.
Example
An area mismatch of 4% gives rise to ( Is/Is)=0.04 and input
offset voltage of 1mV.
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17
Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in
In a perfectly symmetric differential pair
A mismatch in make the two input dc current unequal. The
resulting difference is the input offset current, IOS .
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Other nonlinear characteristics of the differential amplifier
Let the transistors have a mismatch in
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Biasing in BJT integrated Circuits
The diode-connected transistors
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Biasing in BJT integrated Circuits
The Current Mirror
IREF=IO
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Biasing in BJT integrated Circuits
The Current Mirror
IREF=IO
Microelectronic
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Analysis of the current
mirror
taking
Copyright into
2004 by account
Oxford Universitythe
Press,finite
Inc.
of the BJTs.
Biasing in BJT integrated Circuits
A simple current source
IREF=IO
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Biasing in BJT integrated Circuits
Current
steering
circuits
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Biasing in BJT integrated Circuits
Improved current source circuits
1
A current mirror
with base-current
compensation.
IREF=IO
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Biasing in BJT integrated Circuits
Improved current source circuits
2
The Wilson bipolar
current mirror
IREF=IO
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Biasing in BJT integrated Circuits
Improved current source circuits
3
The Widlar
current source
IREF
IO
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22
Biasing in BJT integrated Circuits
Example
Io=10μA (Const.)
R1=?
Assume that
VBE=0.7V at a
current of 1mA.
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Biasing in BJT integrated Circuits
Example
Io=10μA (Const.)
R1=?
R3=?
Assume that
VBE=0.7V at a
current of 1mA.
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Example
A four-stage
bipolar op amp
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Example
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MOS Differential Amplifiers
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MOS Differential Amplifiers
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MOS Differential Amplifiers
Eqn. (1)
At the bias point, vid=0
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MOS Differential Amplifiers
vGS1 - vGS2 = vid = 0
→
vGS1 = vGS2 = VGS
Reform of Eqn. (1)
Eqn. (2)
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MOS Differential Amplifiers
For small-signal approximation
Reform of
Eqn. (2)
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MOS Differential Amplifiers
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MOS Differential Amplifiers
Offset Voltage
(a) The MOS differential pair with both inputs grounded. Owing to
device and resistor mismatches, a finite dc output voltage VO results.
(b) Application of a voltage equal to the input offset voltage VOS to
the terminals with opposite polarity reduces VO to zero.
Microelectronic Circuits - Fifth Edition Sedra/Smith
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MOS Differential Amplifiers
Let the transistors have a mismatch in load resistance
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MOS Differential Amplifiers
Let the transistors have a mismatch in the W/L ratios
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MOS Differential Amplifiers
Let the transistors have a mismatch in the W/L ratios
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MOS Differential Amplifiers
Let the transistors have a mismatch in the Vt
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MOS Differential Amplifiers
Let the transistors have a mismatch in the Vt
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MOS Differential Amplifiers
Current Mirrors
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MOS Differential Amplifiers
Current Mirrors
ID2
ID1
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MOS Differential Amplifiers
Current Mirrors
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MOS Differential Amplifiers
Current Mirrors
The Wilson MOS mirror
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MOS Differential Amplifiers
Current Mirrors
Modified circuit.
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Multistage Amplifiers
Example
a) input resistance ?
b) voltage gain
c) output resistance ?
= 100
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Multistage Amplifiers
Example (cont.)
a)
Equivalent circuit for calculating the gain of the input stage
of the amplifier
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Multistage Amplifiers
Example (cont.)
b)
Equivalent circuit for
calculating the gain of the
input stage of the amplifier
Equivalent circuit for calculating the gain of
the second stage of the amplifier
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Multistage Amplifiers
Example (cont.)
b)
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Equivalent circuit for evaluating
the gain of the third stage in the
amplifier
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Multistage Amplifiers
Example (cont.)
b)
Equivalent circuit of the
output stage
of theCircuits
amplifier
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Multistage Amplifiers
Example (cont.)
c)
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Analysis Using Current Gains
The circuit of the multistage amplifier prepared for smallsignal analysis. Indicated are the signal currents throughout
the amplifier and the input resistances of the four stages.
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