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Transcript
Chapter #9: Frequency
Response
from Microelectronic Circuits Text
by Sedra and Smith
Oxford Publishing
The College of New Jersey (TCNJ) – ELC251 Electronics I
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Introduction
 IN THIS CHAPTER YOU WILL LEARN
 How coupling and bypass capacitors cause the gain of discrete
circuit amplifiers to fall off at low frequencies, and how to
obtain an estimate of the frequency fL at which the gain
decreases by 3dB below its value at midband.
 The internal capacitive effects present in the MOSFET and the
BJT and how to model these effects by adding capacitances to
the hybrid-p model of each of the two transistor types.
 The high-frequency limitation on the gain of the CS and CE
amplifiers and how the gain falloff and the upper 3-dB
frequency fH are
mostly determined by the small capacitances
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between
the
drain
and
gate (collector and base).
Based on Textbook:
Microelectronic
Circuits
by Adel S. Sedra
(0195323033)
Introduction
 IN THIS CHAPTER YOU WILL LEARN
 Powerful methods for the analysis of the high-frequency
response of amplifier circuits of varying complexity.
 How the cascode amplifier studied in Chapter 7 can be
designed to obtain wider bandwidth than is possible with CS
and CE amplifiers.
 The high-frequency performance of the source and emitter
followers.
 The high-frequency performance of differential amplifiers.
 Circuit configurations for obtaining wideband amplification.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Introduction
 Previously assumed that gain is constant and
independent of frequency.
 implied that bandwidth was infinite
 this is not true
 Middle-frequency band (midband) is the range of
frequencies over which device gain is constant.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure 9.1: Sketch of the magnitude of the gain of a discrete-circuit BJT or MOS
amplifier
versus
TheI graph delineates the three frequency bands
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(TCNJ) – ELC251 Electronics
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relevant
toS. frequency-response
determination.
Based on Textbook: Microelectronic
Circuits by Adel
Sedra (0195323033)
9.1. Low Frequency
Response of the CommonSource and CommonEmitter Amplifiers
 Figure 9.2(a) shows a discrete-circuit, common-source
amplifier.
 coupling capacitors CC1 and CC2
 bypass capacitor CS
 Objective is to determine the effect of these
capacitances on gain (Vo/Vsig).
 At low frequencies, their reactance (1/jwC) is high and
gain is low.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.1.1. The CS Amplifier
 Determining Vo/Vsig
 figure 9.2(b) illustrates this process
 circuit with dc sources eliminated
 small-signal analysis
 ignore ro
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.1.1. The CS Amplifier


RG

(9.1) transistor gate voltage: Vg  Vsig
R  1 R
sig
 G sC
C1

1
(9.2) break frequency #1: wP 1  w0 
CC 1  RG  Rsig 
s
(9.3) transistor drain current: Id  gmVg
g
s m
CS
gm
(9.4) break frequency #2: wP 2 
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CS
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)






9.1.1. The CS Amplifier
RD RL
(9.5) output voltage: Vo  Io RL  Id
RD  RL s 
s
1
CC 2  RD  RL 
1
(9.6) break frequency #3: wP 3 
CC 2  RD  RL 
 RG
(9.9) midband gain: AM   
R R
sig
 G

 gm  RD ||RL  

 s  s   s 
Vo
(9.7) transfer function:
 AM 



VI
 s  wP 1  s  wP 2  s  wP 3 
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure 9.2: (a) Capacitively coupled common-source amplifier. (b) Analysis of the
CS amplifier
itsElectronics
low-frequency
transfer function. For simplicity, ro is
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neglected.
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure 9.3: Sketch of the low-frequency magnitude response of a CS amplifier for
which
the ofthree
pole
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appear distinct.
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.1.1. The CS Amplifier
 Determining the Pole Frequencies by Inspection
 Reduce VSig to zero.
 Consider each capacitor separately.
 Find the total resistance seen between terminals of
each capacitor.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.1.2. The CE Amplifier
 Figure 9.4. shows common-emitter amplifier.
 coupling capacitors CC1 and CC2
 emitter bypass capacitor CE
 Effect of these capacitors felt at low frequencies.
 Objective is to determine amplifier gain and transfer
function.
 This analysis is somewhat more complicated than CS
case.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure
9.4: of(a)
capacitively
coupled
common-emitter amplifier. (b) The circuit
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prepared
for small-signal analysis.
Based on Textbook: Microelectronic Circuits by
Adel S. Sedra (0195323033)
9.1.2. The CE Amplifier
 RB ||r 
(9.12) midband gain: AM  
gm  RC ||RL 
 RB ||r   Rsig
 

Vo
1

(9.10) voltage gain:
 AM  s /  s 
Vsig
  CC 1  RB || r   Rsig   
1
(9.11) break frequency #1: wP 1 
CC 1  RB || r   Rsig 
(9.14) break frequency #2: wP 2 
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)

C E re

1
RB ||Rsig 

  1 
Figure 9.5: Analysis of the low-frequency response of the CE amplifier of Fig. 9.4:
(a) the effect of CC1 is determined with CE and CC2 assumed to be acting as
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New Jersey (TCNJ)
perfectTheshort
(b)– ELC251
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effectI of CE is determined with CC1 and CC2 assumed
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Based on Textbook: Microelectronic Circuits
Sedra (0195323033)
toby Adel
beS.acting
as perfect short circuits;
Figure 9.5: (continued ) (c) the effect of CC2 is determined with CC1 and CE
assumed to be acting as perfect short circuits; (d) sketch of the low-frequency gain
underThethe
assumptions
CC1, CE,
and CC2 do not interact and that their break
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of New Jersey (TCNJ) – that
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pole)
Based on Textbook: Microelectronic(or
Circuits
by Adel S.frequencies
Sedra (0195323033) are widely separated.
9.1.2. The CE Amplifier
Vo
RB || r
(9.15) low frequency gain:

gm  RC ||RL  
Vsig  RB || r   Rsig
 

1
  s /  s 
 
  CC 2 RC  RL   
1
(9.16) break frequency #3: wP 3 
CC 2 RC  RL 
 s  s   s 
Vo
(9.17) transfer function:
  AM 



Vsig
s

w
s

w
s

w

P 1 
P 2 
P3 
1  1
1
1 
(9.18)
frequency: fL  Electronics I


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
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2  CC 1RC 1 C E RE CC 2RC 2 
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.2. Internal Capacitive
Effects and the HighFrequency Model of the
MOSFET and BJT
 MOSFET has internal capacitance (this is apparent).
 The gate capacitive effect: The gate electrode forms a
parallel plate capacitor with the channel.
 The source-body and drain-body depletion layer
capacitances: These are the capacitances of the
reverse-biased pn-junctions.
 Previously, it was assumed that charges are acquired
instantaneously - resulting in steady-state model.
 This assumption poses problem for frequency
analysis.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
The Gate Capacitive
Effect
1
(9.20) triode region: Cgs  Cgd  WLC ox
2
2

C

WLC ox
 gs
(9.21/22) saturation region: 
3
 Cgd  0

Cgs  Cgd  0
(9.23/24) cutoff region: 
 Cgb  WLC ox
(9.25) overlap capacitance: C ov  WLov C ox
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
The Junction
Capacitances
(9.26) source-body capacitance: C sb 
C sb 0
1
(9.27) drain-body capacitance: Cdb 
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
VSB
V0
Cdb 0
VDB
1
V0
Figure 9.6 (a) High-frequency, equivalent-circuit model for the MOSFET. (b) The
equivalent
circuit
case
in which
the source is connected to the substrate
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra(body).
(0195323033)(continued)
FigureThe9.6:
The
equivalent-circuit
model of (b) with Cdb neglected
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(to(0195323033)
simplify analysis).
Based on Textbook: Microelectronic Circuits by Adel S. Sedra
The MOSFET UnityGain Frequency (fT)
(9.28) output current: Io  gmVgs
(9.29) gate-source voltage: Vgs  Ii / s  C gs  C gd 
Io
gm
(9.30) current-gain: 
Ii s  C gs  C gd 
gm
(9.31) unity-gain frequency: fT 
2  C gs  Cgd 
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.2.2. The BJT
 Like MOSFET, previously it was assumed that transistor
action was instantaneous.
 steady-state model
 neglects frequency-dependence
 Actual transistors exhibit charge-storage.
 An augmented BJT model is required to examine this
dependence.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.2.2. The BJT
 F forward-base
transit time
(9.32) stored electron charge: Qn   F iC
diC
dQn
(9.33) small-signal diffusion capacitance: Cde 
F
dvBE
dvBE
IC
(9.34) small-signal diffusion capacitance: C de   F gm   F
dvBE
(9.35) base-emitter junction capacitance: C je  2C je 0
(9.36) depletion capacitance: C  
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
C 0
 VCB 
1 

V
0c 

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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
The Cutoff Frequency
(9.37) short-circuit collector current: Ic   gm  sC  V
Ib
(9.38) pi -model voltage: V  Ib  r ||C ||C   
1/ r  sC  sC 
1
(9.40) 3-db frequency: w 
 C  C  
(9.41) unity-gain bandwidth: wT   0w
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.3. High-Frequency
Response of the CS and CE
Amplifiers
 Objective is to identify the mechanism that limits high-frequency
performance.
 As well as fine 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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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.3.1. The CommonSource Amplifier
 Figure 9.13(a) shows high-frequency equivalent-circuit
model of a CS amplifier.
 MOSFET is replaced with model of Figure 9.6(c).
 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 it undergoes is known
as the Miller Effect.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure 9.13: Determining the high-frequency response of the CS amplifier: (a)
equivalent
circuit;
(b)
theElectronics
circuit
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(Continued)
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Figure 9.13: (Continued) (c) the equivalent circuit with Cgd replaced at the input
side with
theof New
equivalent
capacitance
Ceq; (d) the frequency response plot, which is
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that
ofby Adel
a low-pass,
single-time-constant circuit.
Based on Textbook: Microelectronic
Circuits
S. Sedra (0195323033)
9.3.2. The CommonEmitter Amplifier
 Figure 9.14(a) shows high-frequency equivalent circuit of
a CE amplifier.
 BJT is replaced.
 This figure applies to both discrete and IC amps.
 This figure may be simplified using Thevenin’s theorem.
 Cin is simply sum of C and Miller capacitance
C(1+gmRL’)
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Figure 9.14: Determining the high-frequency response of the CE amplifier: (a)
equivalent
(b)– ELC251
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circuitI of (a) simplified at both the input side and the
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output
side; (continued)
Based on Textbook: Microelectronic Circuits by Adel S. Sedra
(0195323033)
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.4. Useful Tools for the
Analysis of the HighFrequency Response of
Amplifiers
 The approximate method used in previous sections to
analyze the high-frequency response of amps provides
an “ok” estimate.
 However, it does not apply to more complex circuits.
 This section discusses other tools.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.4.1. The High Frequency
Gain Funcion
 Amp gain is expressed as function of s in equation (9.61).
 A(s) = AMFH(s)
 The value of AM may be determined by assuming
transistor internal capacitances are open circuited.
 This allows derivation of equation (9.62).
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9.4.2. Determining the
3-dB Frequency fH
 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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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.4.4. Miller’s Theorem
 Consider the situation shown in Figure 9.17(a).
 It is part of a larger circuit which is unknown.
 Miller’s Theorem states that 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)
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Figure 9.17: The Miller equivalent circuit.
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9.5.1. The Equivalent
Circuit
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Figure
9.19:
Generalized high-frequency equivalent circuit for the CS amplifier.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
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
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by two
capacitors: C = C (0195323033)
(1-K) and C2 = Cgd(1-1/K), where K = V0/Vgs.
Based on Textbook: Microelectronic Circuits by Adel1S. Sedragd
9.5.3. Analysis Using OpenCircuit Time Constants
Figure 9.21: Application of
the open-circuit timeconstants method to the
CS equivalent
circuit of Fig.
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9.19.
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.5.4. Exact Analysis
Figure 9.22: Analysis of the CS high-frequency equivalent circuit.
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9.5.4. Exact Analysis
Figure 9.23: The CS circuit at s = sZ. The output voltage Vo = 0, enabling us to
determine sZ from a node equation at D.
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Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.5.5. Adapting the
Formulas for the Case of
the CE Amplifier
Figure 9.24: (a) High-frequency equivalent circuit of the common-emitter
amplifier.
(b) Equivalent circuit obtained after Thévenin theorem has been
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employed to simplify the resistive circuit at the input.
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
9.5.6. The Situation
When Rsig is Low
Figure 9.25: (a) High-frequency equivalent circuit of a CS amplifier fed with a
signal
source having a very low (effectively zero) resistance. (b) The circuit with
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VsigS. Sedra
reduced
to zero. (continued)
Based on Textbook: Microelectronic Circuits by Adel
(0195323033)
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-pi model with
capacitances.
 MOSFET: fT = gm/2(Cgs+Cgd)
 The
BJT:
f = gm/2(C
College ofTNew Jersey
(TCNJ) – ELC251
Electronics
+C
) I
http://anthony.deese.googlepages.com
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Summary
 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.
The College of New Jersey (TCNJ) – ELC251 Electronics I
http://anthony.deese.googlepages.com
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
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 high-frequency
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
(H) is obtained by summing the individual time constants. Then fH
is found as 1/2H.
 The CG and CB amplifiers do not suffer from the Miller effect.
 The source and emitter followers do not suffer from Miller effect.
The College of New Jersey (TCNJ) – ELC251 Electronics I
http://anthony.deese.googlepages.com
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)
Summary
 The high-frequency response of the differential amplifier can be
obtained by considering the differential and common-mode halfcircuits. 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 eliminated or minimizes
the Miller effect can result in much wider bandwidth.
The College of New Jersey (TCNJ) – ELC251 Electronics I
http://anthony.deese.googlepages.com
Based on Textbook: Microelectronic Circuits by Adel S. Sedra (0195323033)