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8/3/2019 Nonlinear Analog Circuits
1/47
Rectifier transfer characteristic and response for sinusoidal input waveform. (a) Half-
wave rectifier. (b) Full-wave rectifier.
8/3/2019 Nonlinear Analog Circuits
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Simple diode half-wave rectifier. (a) Rectifier circuit. (b) Equivalent circuit for Vin > -0.6 V.
(c) Equivalent circuit for Vin < -0.6 V. (d) dc transfer characteristic. (e) Response tosinusoidal input.
8/3/2019 Nonlinear Analog Circuits
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-
! 1exp T
io
S
V
VV
II
io aVV !
out
S
T
iV
IIIn
aVV !
! 1
1
8/3/2019 Nonlinear Analog Circuits
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Active precision half-wave rectifier. (a) Rectifier circuit. (b) dc transfer
characteristic.
8/3/2019 Nonlinear Analog Circuits
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Active precision half-wave rectifier. (c) Input and output waveforms for the
precision half-wave rectifier.
8/3/2019 Nonlinear Analog Circuits
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Improved precision rectifier. (a) Rectifier circuit. (b) Equivalent circuit for
Vin < 0. (c) Equivalent circuit for Vin > 0.
8/3/2019 Nonlinear Analog Circuits
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The Emitter-Coupled Pair as a Simple Multiplier
!
T
id
EE
c
V
V
II
exp1
1
!
T
id
EE
c
VV
II
exp1
2
8/3/2019 Nonlinear Analog Circuits
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!!(
T
id
EEccc
V
VIIII
2
tanh21
1222tanh }T
id
T
id
T
id
V
V
V
V
V
V
!(
T
id
EEc
VVII2
8/3/2019 Nonlinear Analog Circuits
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Emitter-coupled pair.
8/3/2019 Nonlinear Analog Circuits
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The dc transfer characteristic of emitter-coupled pair.
8/3/2019 Nonlinear Analog Circuits
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onBEioEE VVKI $ 2
T
onBEiido
c
V
VVVKI
2
2
!(
8/3/2019 Nonlinear Analog Circuits
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Two-quadrant analog multiplier.
8/3/2019 Nonlinear Analog Circuits
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Gilbert multiplier circuit.
8/3/2019 Nonlinear Analog Circuits
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The dcAnalysis of the Gilbert Multiplier Cell
!
T
c
c
V
VII
1
1
3
exp1
!
T
c
c
VV
II
1
1
4
exp1
8/3/2019 Nonlinear Analog Circuits
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!
T
c
c
VV
II
1
2
5
exp1
!
T
c
c
VV
II
1
2
6
exp1
!
T
EE
c
V
V
II
2
1
exp1
!
T
EE
c
V
V
II
2
2
exp1
8/3/2019 Nonlinear Analog Circuits
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-
-
!
TT
EE
c
V
V
V
V
II
21
3
exp1exp1
-
-
!
TT
EE
c
V
V
V
V
II
12
4
exp1exp1
-
-
!
TT
EE
c
V
V
V
V
II
21
5
exp1exp1
-
-
!
TT
EE
c
V
V
V
V
II
12
6
exp1exp1
8/3/2019 Nonlinear Analog Circuits
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46536453 cccccc
IIIIIII !!(
5463 cccc
IIII !
-
-
!
TT
EE
V
V
V
VI
2tanh
2tanh 21
8/3/2019 Nonlinear Analog Circuits
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The Gilbert Cell as anAnalog Multiplier
3tanh
3
xxx ! .
xx }tanh
}(
TT
EE
VV
VVII
2221 V1, V2,
8/3/2019 Nonlinear Analog Circuits
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Gilbert multiplier with emitter degeneration applied to improve input
voltage range on V2 input.
8/3/2019 Nonlinear Analog Circuits
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1111 VKII o !
1112VKII
o!
8/3/2019 Nonlinear Analog Circuits
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Gilbert multiplier with predistortion circuits.
8/3/2019 Nonlinear Analog Circuits
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Inverse hyperbolic tangent circuit.
8/3/2019 Nonlinear Analog Circuits
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!(
S
o
T
S
o
T
IVKIInV
IVKIInVV 111111
!
111
111
VKI
VKIInV
o
o
T
8/3/2019 Nonlinear Analog Circuits
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!
x
x
Inx
1
1
2
1
tanh
1
!(
1
111tanh2o
T
IVKVV
!(2
22
1
11
oo
EE
I
VK
I
VKII
8/3/2019 Nonlinear Analog Circuits
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1
11
1
1
K
I
VK
Ioo
2
2
2
2
2
K
IV
K
Ioo
8/3/2019 Nonlinear Analog Circuits
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Complete four-quadrant multiplier.
8/3/2019 Nonlinear Analog Circuits
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Input and output waveforms for phase detector with large input signals.
8/3/2019 Nonlinear Analog Circuits
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tVtVmmm
[cos!
4
2sin
,cos1 T
T
[n
n
AtnAtVnc
nnc
!g
!
8/3/2019 Nonlinear Analog Circuits
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Input and output spectra for a balanced modulator.
8/3/2019 Nonlinear Analog Circuits
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Typical input and output waveforms for a phase detector.
8/3/2019 Nonlinear Analog Circuits
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Phase-locked-loop system
Phase-Locked Loop Concepts
8/3/2019 Nonlinear Analog Circuits
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Typical phase detector output during capture transient.
8/3/2019 Nonlinear Analog Circuits
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The Phase-Locked Loop in the Locked Condition
dt
tdt oscosc
J[ !
dtttt
osctoscosc ! ! 00 [JJ
oOoosc VK! [[
8/3/2019 Nonlinear Analog Circuits
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Block diagram of PLL system.
8/3/2019 Nonlinear Analog Circuits
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8/3/2019 Nonlinear Analog Circuits
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(a)
Root locus and frequency response of a first-order, phase-locked loop.
8/3/2019 Nonlinear Analog Circuits
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Response of loop output voltage to step changes in input frequency, example
first-order loop.
(b)
8/3/2019 Nonlinear Analog Circuits
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Integrated-Circuit Phase-Locked Loops
!
T
J21
CEEaverage RIV
-
!
J T
J[[[[
T 0sinsin
1tdttdtVRgV iCmaverage
T
Jcos2iCm
VRg!
8/3/2019 Nonlinear Analog Circuits
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Sinusoid multiplied bya synchronous square wave.
8/3/2019 Nonlinear Analog Circuits
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Voltage-controlled, emitter-coupled multivibrator.
8/3/2019 Nonlinear Analog Circuits
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Equivalent circuit during one half-cycle.
8/3/2019 Nonlinear Analog Circuits
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Waveforms within the emitter-coupled multivibrator.
8/3/2019 Nonlinear Analog Circuits
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8/3/2019 Nonlinear Analog Circuits
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Phase comparator of the 560B phase-locked loop
8/3/2019 Nonlinear Analog Circuits
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Nonlinear Function Synthesis
(a)
(b)
Bipolar nonlinear function circuits. (a) Square root. (b) Square law.
8/3/2019 Nonlinear Analog Circuits
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Folded-cascode OTA
8/3/2019 Nonlinear Analog Circuits
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Fully differential folded-cascode op-amp
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