nonlinear analog circuits

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.


2/47

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.


3/47

-

! 1exp T

io

S

V

VV

II

io aVV !

out

S

T

iV

IIIn

aVV !

! 1

1


4/47

Active precision half-wave rectifier. (a) Rectifier circuit. (b) dc transfer

characteristic.


5/47

Active precision half-wave rectifier. (c) Input and output waveforms for the

precision half-wave rectifier.


6/47

Improved precision rectifier. (a) Rectifier circuit. (b) Equivalent circuit for

Vin < 0. (c) Equivalent circuit for Vin > 0.


7/47

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


8/47

!!(

T

id

EEccc

V

VIIII

2

tanh21

1222tanh }T

id

T

id

T

id

V

V

V

V

V

V

!(

T

id

EEc

VVII2


9/47

Emitter-coupled pair.


10/47

The dc transfer characteristic of emitter-coupled pair.


11/47

onBEioEE VVKI $ 2

T

onBEiido

c

V

VVVKI

2

2

!(


12/47

Two-quadrant analog multiplier.


13/47

Gilbert multiplier circuit.


14/47

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


15/47

!

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


16/47

-

-

!

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


17/47

46536453 cccccc

IIIIIII !!(

5463 cccc

IIII !

-

-

!

TT

EE

V

V

V

VI

2tanh

2tanh 21


18/47

The Gilbert Cell as anAnalog Multiplier

3tanh

3

xxx ! .

xx }tanh

}(

TT

EE

VV

VVII

2221 V1, V2,


19/47

Gilbert multiplier with emitter degeneration applied to improve input

voltage range on V2 input.


20/47

1111 VKII o !

1112VKII

o!


21/47

Gilbert multiplier with predistortion circuits.


22/47

Inverse hyperbolic tangent circuit.


23/47

!(

S

o

T

S

o

T

IVKIInV

IVKIInVV 111111

!

111

111

VKI

VKIInV

o

o

T


24/47

!

x

x

Inx

1

1

2

1

tanh

1

!(

1

111tanh2o

T

IVKVV

!(2

22

1

11

oo

EE

I

VK

I

VKII


25/47

1

11

1

1

K

I

VK

Ioo

2

2

2

2

2

K

IV

K

Ioo


26/47

Complete four-quadrant multiplier.


27/47

Input and output waveforms for phase detector with large input signals.


28/47

tVtVmmm

[cos!

4

2sin

,cos1 T

T

[n

n

AtnAtVnc

nnc

!g

!


29/47

Input and output spectra for a balanced modulator.


30/47

Typical input and output waveforms for a phase detector.


31/47

Phase-locked-loop system

Phase-Locked Loop Concepts


32/47

Typical phase detector output during capture transient.


33/47

The Phase-Locked Loop in the Locked Condition

dt

tdt oscosc

J[ !

dtttt

osctoscosc ! ! 00 [JJ

oOoosc VK! [[


34/47

Block diagram of PLL system.


35/47


36/47

(a)

Root locus and frequency response of a first-order, phase-locked loop.


37/47

Response of loop output voltage to step changes in input frequency, example

first-order loop.

(b)


38/47

Integrated-Circuit Phase-Locked Loops

!

T

J21

CEEaverage RIV

-

!

J T

J[[[[

T 0sinsin

1tdttdtVRgV iCmaverage

T

Jcos2iCm

VRg!


39/47

Sinusoid multiplied bya synchronous square wave.


40/47

Voltage-controlled, emitter-coupled multivibrator.


41/47

Equivalent circuit during one half-cycle.


42/47

Waveforms within the emitter-coupled multivibrator.


43/47


44/47

Phase comparator of the 560B phase-locked loop


45/47

Nonlinear Function Synthesis

(a)

(b)

Bipolar nonlinear function circuits. (a) Square root. (b) Square law.


46/47

Folded-cascode OTA


47/47

Fully differential folded-cascode op-amp

nonlinear analog circuits

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