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Chapter 9
Frequency Response
EE 3120 Microelectronics II
Suketu Naik
Operational Amplifier Circuit Components
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1. Ch 7: Current Mirrors and Biasing
2. Ch 9: Frequency Response
3. Ch 8: Active-Loaded Differential Pair
4. Ch 10: Feedback
5. Ch 11: Output Stages
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Op Amp Circuit Components
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Two Stage
Op Amp
(MOSFET)
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PART C:
High Frequency Response
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9.3 High-Frequency Response of the CS and CE Amplifiers
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 What limits high-frequency performance of the
amplifier?
 What is the Amplifier gain, AM?
Figure 9.12: Frequency
response of a directcoupled (dc) amplifier.
Observe that the gain
does not fall off at low
frequencies, and the
midband gain AM extends
down to zero frequency.
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Estimating fH
Using Miller's Approximation
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Miller Effect or Miller Multiplier




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Impedance Z can be replaced with two impedances:
Z1 connected between node 1 and ground
(9.76a) Z1 = Z/(1-K)
Z2 connected between node 2 nd ground where
 (9.76b) Z2 = Z/(1-1/K)
EE 3120 Microelectronics II
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9.3.1. The Common-Source Amplifier
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High-frequency equivalentcircuit model of a CS
amplifier
 It may be simplified
using Thevenin’s
theorem.
 Also, bridging capacitor
(Cgd) may be redefined.
 Cgd gives rise to much
larger capacitance Ceq
 The multiplication effect
that MOSFET
undergoes is known as
the Miller Effect.
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9.5.1 High Frequency Model of CS Amplifier
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9.5.2 Analysis Using Miller’s Theorem
Figure 9.20: The high-frequency equivalent circuit model of the CS amplifier
after the application of Miller’s theorem to replace the bridging capacitor Cgd
by two capacitors: C1 = Cgd(1-K) and C2 = Cgd(1-1/K), where K = V0/Vgs.
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9.3.1. The Common-Source Amplifier
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Ex9.8
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Compare AM and fH with the ones found in example 9.3
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9.5.5. CE Amplifier
Circuit after
Applying Miller's
Theorem?
Figure 9.24: (a) High-frequency equivalent circuit of the common-emitter
amplifier. (b) Equivalent circuit obtained after Thévenin theorem has been
employed to simplify the resistive circuit at the input.
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9.3.2 The Common-Emitter Amplifier
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Ex9.10
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Note the trade-off between gain and bandwidth
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Estimating fH
Using Miller's Theorem
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9.4.1 ωH from the High Frequency Gain Funcion
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 Amp gain is expressed as function of s (=jω)
 The value of AM may be determined by assuming transistor
internal capacitances are open-circuited
 High-frequency transfer function
 Goal: find dominant pole and corresponding frequency
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9.4.2. Determining the 3-dB Frequency fH
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 High-frequency band closest to midband is generally of
greatest concern.
 Designer needs to estimate upper 3dB frequency.
 If one pole (predominantly) dictates the high-frequency
response of an amplifier, this pole is called dominantpole response.
 As rule of thumb, a dominant pole exists if the lowestfrequency pole is at least two octaves (a factor of 4)
away from the nearest pole or zero.
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The High Frequency Gain Funcion
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 No dominant pole? Approximate ωH as follows:
Based on Miller's Theorem
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Example 9.5
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Transfer function
First approximation
Second
approximation
-3 dB frequency
= 9537 rad/s
Exact Value
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Estimating fH
Using Open Circuit Time Constants
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9.4.3 ωH from the open-Circuit Time Constants
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 Find individual time constants by replacing all other caps
as open circuits (C=0)
 Next, sum all the time constants to find ωH
CS
CE
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P9.60, 9.61: CS Amp
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Omit the % contribution. Just calculate fH
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P9.64, 9.65: CE Amp
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Omit the % contribution. Just calculate fH
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The Common-Gate Amplifier
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Figure 9.26 (a) The common-gate amplifier with the transistor internal capacitances shown. A
load capacitance CL is also included. (b) Equivalent circuit for the case in which ro is neglected.
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The Common-Gate Amplifier
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Expl 9.12: CG Amp and Widening of BW
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9.8.2 Active-loaded MOS differential amplifier
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Figure 9.37 (a) Frequency–response analysis of the active-loaded MOS differential
amplifier. (b) The overall transconductance Gm as a function of frequency.
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Summary
 The coupling and bypass capacitors utilized in discrete-circuit
amplifiers cause the amplifier gain to fall off at low
frequencies. The frequencies of the low-frequency poles can
be estimated by considering each of these capacitors
separately and determining the resistance seen by the
capacitor. The highest-frequency pole is that which
determines the lower 3-dB frequency (fL).
 Both MOSFET and the BJT have internal capacitive effects
that can be modeled by augmenting the device hybrid-π
model with capacitances.
 MOSFET: fT = gm/2π(Cgs+Cgd)
 BJT: fT = gm/2π(Cπ+Cμ)
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Summary
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 The internal capacitances of the MOSFET and the BJT cause
the amplifier gain to fall off at high frequencies. An estimate
of the amplifier bandwidth is provided by the frequency fH at
which the gain drops 3dB below its value at midband (AM). A
figure-of-merit for the amplifier is the gain-bandwidth
product (GB = AMfH). Usually, it is possible to trade gain for
increased bandwidth, with GB remaining nearly constant. For
amplifiers with a dominant pole with frequency fH, the gain
falls off at a uniform 6dB/octave rate, reaching 0dB at fT =
GB.
 The high-frequency response of the CS and CE amplifiers
is severly limited by the Miller effect.
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Summary
 The high-frequency response of the differential amplifier can
be obtained by considering the differential and commonmode half-circuits. The CMRR falls off at a relatively low
frequency determined by the output impedance of the bias
current source
 The high-frequency response of the current-mirror-loaded
differential amplifier is complicated by the fact that there are
two signal paths between input and output: a direct path and
one through the current mirror
 Combining two transistors in a way that eliminates or
minimizes the Miller effect can result in much wider
bandwidth
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Summary
 The method of open-circuit time constants provides a simple
and powerful way to obtain a reasonably good estimate of the
upper 3-dB frequency fH. The capacitors that limit the highfrequency response are considered one at a time with Vsig = 0
and all other capacitances are set to zero (open circuited).
The resistance seen by each capacitance is determined, and
the overall time constant (tH) is obtained by summing the
individual time constants. Then fH is found as (1/2π)tH.
 The CG and CB amplifiers do not suffer from the Miller
effect.
 The source and emitter followers do not suffer from
Miller effect.
EE 3120 Microelectronics II
Suketu Naik