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ELEN 3312
Electronics II
Chapter 7
Frequency Response
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
In this chapter, we will:
Discuss the general frequency response
characteristics of amplifiers.
Derive the system transfer functions
Develop the Bode diagrams of the magnitude
and phase of the transfer functions.
Analyze the frequency response of transistor
circuits with capacitors.
Determine the Miller effect and Miller
capacitance.
Determine the high- and low- frequency
response of basic transistor circuit
configurations.
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
1
Amplifier Gain Versus Frequency
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Transfer Functions of
the Complex Frequency
Name of Function
Expression
Voltage Transfer Function
T(s) = Vo(s)/Vi(s)
Current Transfer Function
Io(s)/Ii(s)
Transresistance Function
Vo(s)/Ii(s)
Transconductance Function
Io(s)/Vi(s)
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
2
Series Coupling Capacitor Circuit
sτ
T (s) = K 2 (
)
1 + sτ
τ = ( RS + RP )CS
K2 =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Rp
R p + Rs
Chapter 7
Parallel Load Capacitor Circuit
1
T ( s ) = K1 (
)
1 + sτ
τ = ( RS RP )C P
K1 =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Rp
R p + Rs
Chapter 7
3
Bode Plot of Voltage Transfer Function
Magnitude:
Series Coupling Capacitor Circuit
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Bode Plot of Voltage Transfer Function
Magnitude:
Parallel Load Capacitor Circuit
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
4
Circuit with Series Coupling and
Parallel Load Capacitor
τ S = ( RS + RP )C S
τ P = ( RS RP )C P
fL =
fH =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
1
2πτ S
1
2πτ P
Chapter 7
Bode Plot of Magnitude of Voltage
Transfer Function:
Series Coupling and Parallel Load Capacitor
Example 7.2
Page 484
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
5
Steady-State Output Response
Coupling Capacitor
Prof. Rubén Flores
Donald A. Neamen
Load Capacitor
Microelectronics
McGraw-Hill
Chapter 7
Common Emitter with Coupling
Capacitor
fL =
1
2π ( RSi + Ri )CC
Ri = RB [rπ + (β + 1)RE ]
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
6
Common Source with Output
Coupling Capacitor
fL =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
1
2π ( RD + RC )CC
Chapter 7
Emitter Follower with Output
Coupling Capacitor
fL =
1
2π ( Ro + RL )CC 2
 R' + r
Ro =r o RE  s π
 β +1
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill



Chapter 7
7
Problem-Solving Technique:
Bode Plot of Gain Magnitude
1. Determine whether capacitor is producing a
low-pass or high-pass circuit.
a. Sketch general shape of Bode plot
2. Corner frequency is f = 1/(2πτ) where τ = ReqC
a. Req is resistance seen by capacitor
3. Maximum gain magnitude is midband gain.
a. Coupling and bypass capacitors act as
shorts
b. Load capacitors act as opens
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Common Source with Load Capacitor
fH =
1
2π ( Ro RL )C L
Ro = rd RD
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
8
Coupling and Parallel Load Capacitors
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Small-Signal Equivalent Circuit:
Coupling and Parallel Load Capacitor
fL =
1
2π [ RS + ( R1 R2 Ri )]CC
fH =
Ri = RB [rπ + (β + 1)RE ]
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
1
2π ( RC RL )C L
Chapter 7
9
Emitter Bypass Capacitor
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Bode Plot of Voltage Gain Magnitude:
Emitter Bypass Capacitor
A v ω →0 =
g m rπ RC
RS + rπ + (1 + β ) RE
Av ω →∞ =
fA =
1
2π ⋅τ A
g m rπ RC
RS + rπ
fB =
1
2π ⋅τ B
τ A = RE C E
τB =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
RE C E (RS + rπ )
RS + rπ + RE (β + 1)
Chapter 7
10
Two Coupling Capacitors and a
Emitter Bypass Capacitor
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
PSpice Results for Two Coupling
Capacitors and a Emitter Bypass
Capacitor
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
11
Estimation of the Lower Cutoff
Frequency
Coupling and Bypass Capacitors
Each capacitor affects the overall lower cutoff
frequency.
To determine the exact lower cutoff frequency is
necessary to determine the amplifier’s transfer
function and plot the Bode diagram.
To estimate the lower frequency we have to:
Determine the individual cutoff frequency of each
capacitor and use the following formula
f L ≈ f c (Cc1 ) + f c (Cc 2 ) + f c (C E )
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Estimation of the Lower Cutoff
Frequency
To determine the cutoff frequency of each capacitor
assume that all capacitor behaves as a short circuit
(C=∞) except the one you are analyzing. For
previous example
To determine the cutoff frequency of Cc1, replace
capacitors Cc2 and CE with a short.
To determine the cutoff frequency of Cc2, replace
capacitors Cc1 and CE with a short.
To determine the cutoff frequency of CE, replace
capacitors Cc1 and Cc2 with a short.
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
12
High Frequency Model for BJT
Transistors
rb,rc and rex are very small
rµ is very large (MΩ)
rb,rc,rex and rµ can be
neglected.
Prof. Rubén Flores
Donald A. Neamen
Expanded Hybrid π Equivalent
Circuit
Microelectronics
McGraw-Hill
Chapter 7
High Frequency Parameters
rb, rc and rex are the base, collector and
emitter series resistances and usually are very
small and can be neglected.
rµ is the reverse-biased diffusion resistance
and usually is in order of MΩ and can be
neglected.
Cµ is the reverse-biased diffusion capacitance.
Cπ is the forward-biased junction capacitance.
CS is the junction capacitance of the reversebiased collector-substrate junction, usually can
be neglected.
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
13
Simplified High Frequency Model for
BJT Transistors
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Short-Circuit Current Gain
To understand the frequency effects of the BJT
transistor we have to determine the shortcircuit current gain.
This analysis help us to determine at what
frequency the transistor stops amplifying.
Using the simplified hybrid- π model
neglecting all series, diffusion resistances and
Cs junction capacitance.
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
14
Short-Circuit Current Gain:
Analysis of Frequency Response of BJT
Ai =
h fe (ω ) =
Prof. Rubén Flores
Donald A. Neamen
IC
= h fe (ω )
IB
g m rπ
β0
=
1 + jωrπ (Cπ + Cµ ) 1 + jωrπ (Cπ + Cµ )
Microelectronics
McGraw-Hill
Chapter 7
Bode Plot:
Short-Circuit Current Gain
fβ =
1
2π rπ (Cπ + Cµ )
Prof. Rubén Flores
Donald A. Neamen
fT = β o f β fT = gain-bandwidth product
Microelectronics
McGraw-Hill
Chapter 7
15
Unity-Gain Bandwidth Product (fT)
fT is a function of the DC
collector current.
The cutoff frequency (fT) is
lower at low collector
currents levels.
However the cutoff
frequency also decreases at
high currents levels in the
same way that β decreases
at large currents.
The fT is usually specified on
the transistor data sheets.
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
The Miller Effect
Z in , Miller =
Zf
1 − AV
Z out ,Miller =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Z f AV
Av − 1
Chapter 7
16
Bypassed Common Emitter
Small-Signal Equivalent
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Small-Signal Equivalent Circuit with Miller
Capacitance: Bypassed Common Emitter
CM = Cµ [1 + g m ( RC RL )]
fH =
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
1
2π [rπ RB (CM + Cπ )]
Chapter 7
17
Common-Base Amplifier
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
High-Frequency Equivalent Circuit:
Common Base
f Hπ =
1
f Hµ =
 r

2π  π RE RS Cπ
1 + β

Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
1
2π ( RC RL )C µ
Chapter 7
18
Emitter-Follower Circuit
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
High-Frequency Equivalent Circuit:
Emitter Follower
1
fH ≅
2π [ RS RB (1 + g m RL' )rπ ](C µ +
Prof. Rubén Flores
Donald A. Neamen
Cπ
)
1 + g m RL'
Microelectronics
McGraw-Hill
Chapter 7
19
Equivalent Circuit for n-Channel
Common Source MOSFET
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Unity-Gain Bandwidth
fT =
Prof. Rubén Flores
Donald A. Neamen
gm
2π (C gs + C gd )
Microelectronics
McGraw-Hill
Chapter 7
20
Small-Signal Equivalent Circuit with
Miller Capacitance: MOSFET
C M = C gd [1 + g m RL ]
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
4 Equivalent 2-port Networks
Voltage Amplifier
Current Amplifier
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
21
4 Equivalent 2-port Networks
Transconductance
Amplifier
Transresistance
Amplifier
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
Frequency Response of Multistage
Amplifiers
Prof. Rubén Flores
Donald A. Neamen
Microelectronics
McGraw-Hill
Chapter 7
22