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Winter 2008 1

Active Circuits

Associate Prof. Dr. Soliman Mahmoud

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Winter 2008 2

Chapter1:

Design of Compensated Finite Gain

op-amp based Amplifiers for High

Frequency Applications.

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

Objectives and outlines:

1. Introduction

Typical frequency response of the operational amplifiers

The effect of finite GB of op-amp on the performance of op-amp

amplifiers.

Definitions: Error Function (S), Magnitude error () andPhase error ()

2. The compensation of Non-Inverting Amplifier

Passive Compensation

Active Compensation

3. The compensation of Inverting Amplifier

Passive Compensation

Active Compensation (Assignment 1)

Design of Compensated Finite Gain op-amp based

Amplifiers for High Frequency Applications.

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

1. Introduction

The non-inverting and inverting finite gain amplifiers arebasic building blocks in the realization of active RC filtersand oscillators.

The finite gain bandwidth product of the op-ampdegrades significantly the phase and magnitude of the

conventional finite gain amplifiers.The purpose of this lecture is to introduce two methodsof compensated non-inverting and inverting finite gainamplifiers using passive or active elements.

The compensated amplifiers have negligible phase andmagnitude errors up to an extended frequency range.

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

Typical frequency response of the operational amplifiers Av(S=j)

).........1)(1)(1(

)(

321

SSS

ASA vov

Assuming the zeros are neglected

Note: 1 is much lower than the

rest of the break-frequencies,

causing 1 to be the dominantinfluence in the frequency

response.

)1(

)(

1

S

ASA

vo

v

SS

GB

S

ASA

tvo

v

1)(For 2 > >> 1,

Where GB is the gain-bandwidth of

the op-amp and t is the unity gain

radian frequency

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

Vin

Vout

K R

R

A

+

-outin

outout VKVA

VVVAV

1

1)(

t

in

out

SKK

A

K

K

V

V

)1(1

1)1(

)1(1

)1(

The effect of finite GB of op-amp on the performance of op-amp amplifiers

For Non-inverting Amplifier

For ideal Amplifier )1( KV

V

Ain

out

Therefore, we define the error function

(s) as follows:

t

SKS

)1(

1

1)(

Lett

K

1

SS 1

1

)(

jj

1

1)(

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

jj

1

1)(From the error function , we can define also:

(a) Phase error : ()

)(tan0)(tan)( 11

1)()( for

(b) Magnitude error : )(

1)(1

1)(

2

1)(21)( 2 for

From (a) and (b), we note that the phase error is more dangerous than

the magnitude error

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Associate Prof. Dr. Soliman MahmoudElectronics and Electrical Engineering Department

Vin

Vout

K R

A

+

-

R)( VVAVout

SK

K

AK

K

V

V

t

in

out

)1(1

1

)1(1

1

The effect of finite GB of op-amp on the performance of op-amp amplifiers

For inverting Amplifier

For ideal Amplifier KV

V

Ain

out

Therefore, we define the error function(s) as follows:

t

SKS

)1(

1

1)(

Lett

K

1

SS

11)(

jj

1

1)(

]1

1

1[0 outin

out VK

VK

K

A

V

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jj

1

1)(From the error function ,

(a) Phase error : ()

)(tan0)(tan)( 11

1)()( for

(b) Magnitude error : )(

1)(1

1)(

2

1)(21)( 2 for

2 f

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2. The compensation of Non-Inverting

Amplifier(a) Passive Compensation (Wilson1976)

VinVout

K R

R

A

+

-

C

)(

VVAVout

)()1(1

)1

(1

)1(2

tt

in

out

KCRS

KS

KKCRS

KV

V

KSCRK

VV

A

V outin

out

)1(

)()1(1

)1

(1

)(2

tt

KCRS

KS

KKCRS

s

; second order error function

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Note: For the error function

2

2

1

1

1)(

bSSa

Sas

]3

)[()()( 2

3

2

3

13

21 baaa

aa

]2[2

)( 222

1

2

baa

The magnitude and phase errors are given as follows:

Therefore the condition for minimum phase error is a1=a2 and in this case

][)( 23 ba

][)( 2 b

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)()1(1

)1

(1

)( 2

tt

KCRSKS

K

KCRS

s

Therefore, the design value of C for minimum phase error , we must force

the coefficient of S in the Numerator and to be the same;

t

K

K

KCR

1

1 tKR

KC

2)1(

Let

1

1

K

KRCK

t

2211)(

SS

Ss

3

)()(

2)()(

Note :The main disadvantages of the passive compensation is that the valueof C is determined in terms of t but t is sensitive to the process and

temperature variation, hence active compensation is uses.

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(b) Active Compensation

VinVout

K1R1

R1

A1

+

-+

-

K2R2

R2

Phase Corrector

Vo1

A2

For op-amp 1: inVV

1

1

1 K

VV o

For op-amp 2:outVV

1

22

2

1

1

1 oout V

KV

K

KV

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VinVout

K1R1

R1

A1

+

-+

-

K2R2

R2

Phase Corrector

Vo1

A2

Calculation of Vo1 :

outo V

A

KV

2

21 )1(

1

1

)1

1

1( 1

22

2

2

1ooutout

o VK

VK

KV

A

V

Calculation of Vout :

])1(

1[1

1

1

1

2

21

1

11

A

K

V

KVV

KV

A

V outinoin

out

21

21

1

1

2

2

1 )1)(1()

1(1

)

1

(1)1(

AA

KK

A

K

A

K

KV

V

in

out

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2

21

21

1

1

2

2

)1)(1()

1(1

)1(1

)(S

KKS

K

SK

s

ttt

t

; second order error function

Therefore, the error function is given by:

For minimum phase error:

2

2

1

1 )1()1(

tt

KK

If A1 and A2 are matched (t1= t2) K1= K2

Let

2

2

1

1 11

tt

KK

221

1)(

SS

Ss

3)()(

2)()(

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3. The compensation of Inverting Amplifier

(a) Passive Compensation (Wilson)

Vin

Vout

K R

A

+

-

R

C

C/K

(1)

A

Vout

By applying KCL at

node (1):

01

)()1

)(( KRA

VV

K

SC

A

VSC

RA

VV outout

outoutin

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)1()

1(1

1

A

KSCR

A

K

SCRK

V

V

in

out

RCK

SK

S

SCRs

tt

)1()

1(1

1)(

2

; second order error function

Therefore;

For minimum phase error: RCK

t

)1(

tR

KC

)1(

Let RCK

t

1

221

1)(

SS

Ss

3)()(

2)()(

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(b) Active Compensation (Assignment 1)

Vin

Vout

K1R

A1+

-

R

+

-

K2R

R

Phase Corrector

A2

Show that:

(a) The closed loop gain is given by:

21

21

1

1

2

2

1 )1)(1()1(1

)1(1

AA

KK

A

K

A

K

KV

V

in

out

(b) Find the necessary condition for phase compensation and determine

the resulting phase and magnitude errors of the compensated amplifier