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B EE 433/University of Washington, Bothell

Lesson 8: Dynamic Op AmpLimitations

EE 433 Electronic Circuit

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Key Terms

open-loop response

closed-loop response

input impedance

output impedance

transient response

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Open-loop Response

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741 Op Amp Circuit Diagram

Input stage

Second stage

Outputstage

Q8

CC

Q6Q5

Q4Q3

Q2

Q1

IA

vN vPv

O

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Simplified Op Amp Block Diagram

Transcondcutancegain of the first stage

Voltage gain of

the second stage

Voltage follower ofthe ouput stage

Net equivalent resistanceand capacitance between

the first and second stages

CC

gm1v

N

vP vOio1

ReqCeq

-a21

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Simplified Op Amp Block Diagram

Low frequency: Ccis open circuit,

For the 741 op amp, gm1= 189 A/V; Req= 1.95 M, and a2=544 V/V, those yields DC open-loop gain = 200,000 V/V.

CC

gm1v

N

vP vOio1

ReqCeq

-a21

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Simplified op amp block diagram

For the 741 op amp, dominant-pole frequency = 5 Hz.

While increasing frequency, the equivalent impedance would decrease,gain starts to roll off at the frequency,fb, when,

This frequency, called dominant-pole frequency,fb,

Huge

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Simplified op amp block diagram

To achieve this high capacitance, large device cross section area isrequired,

In order to avoid high cross section area, an additional capacitor Cc isadded in parallel to amplifier to provide an acceptable capacitance tostart with, and its equivalent value can be realize using Millers Theorem.

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Millers theorem

Known voltage gain Av

This is identical to

1

2

1

11

v

v

zz

A

zz

A

z

Network N

v1 v2i1

i2

iz

z1

Network N

v1 v2

i1

i2

z2

Ceqcan be realized using Millerseffect:

= 16.3 = 544

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Expression for the Open-loop Gain

fbis chosen low enough that other op ampinternal frequency poles and zeros areinsignificant.

Hence, 741 is approximated withdominant pole:

a0Dc open-loop gainfbopen-loop bandwidth

Magnitude:

Phase: a(jf) = -tan-1(f/fb)

fb ft

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ftis unity-gain frequency or transitionfrequency

Magnitude:

Phase: a(jf) = -tan-1(f/fb)

For the 741 op amp, unity-gain

frequency = 1 MHz.

a0>> 1

fb ft

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GBPGain bandwidth product =ft. Every point on -20db?decade line meets GBP=ft.

At high frequency:

with a = 1,

For the 741 op amp, unity-gain frequency = 1 MHz.gm1= IA/4VT, Cc= 30 pF; therefore, pickIA= 19.6 A.

Note:a1/f

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Closed-loop Response

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Open-loop gain:

With feedback circuits, the feedback factor:

Loop gain:

Closed-loop gain:

With a very large loop gain, then Feedback network control

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More accurately,

Error functionDesired response

Loop gain T(jf)solely determines the error function which gives thedeparture from the ideal or desired response.

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Graphically Visualization of Loop Gain

From loop gain, T,

Bode plot of Tis difference between theindividual plots of aand (1/).

Crossover frequency is very important point inassessing closed-loop stability:ffx; a significant departure from ideal fx: crossover frequency

ft

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Non-inverting op amp:

R1 R2vN

vIvO

and

Closed-loop gain

= 1 +2

1

1

1 +1 +

21

= = 1 + 1

1 + 2

= = (

1

1 + 2 )

() =

= 1 +

2

1

1

1 +1 +

21

= 1 +2

1

1

1 +1 +

21

/(1 +

)

= /(1 +

)

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Closed-loop ResponseNon-inverting op amp:

From

1. At low frequency, T >> 1, error is smallandA Aideal

2. AtfB,A = Aideal/(1+j)

3. At high frequency, T

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Example: use 741 op amps to design an audio amp with a

gain of 60 dB. Note: audio amp has fB20 kHz. What is

the individual gain of the opamp used.

First approach: use a single 741 op amp, ft= 1MHz:

Solution

Insufficient BW for audio applications; nextidea: cascade (common in series) two lower gainbut wider bandwidth amplifiers.60 dB

|A|

fB

ftlogf

= = = /

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Example: use 741 op amps to design an audio amp with a

gain of 60 dB. Note: audio amp has fB20 kHz.

Second approach: using two op amps in cascade each with a gain

Solution

Fulfill the requirement

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Solution

So: the -3 dB frequency of the seriescascade is less than the -3 dB frequency ofthe individual amplifiers.

.

a0

60 dB

30 dB

|A|

fBfB1

ft log f

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Inverting Op Amp:

Where:

Therefore,

R1 R2vN

vI

vO

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Inverting Op Amp:

For non-inverting amplifier

For inverting amplifier; shift down

a0

|A0|

fB

ft

log f

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Unity-gain non-inverting amplifier:

Unity-gain inverting amplifier:

Significant BW loss for inverting amplifier

R R

GBP= ftvIvO

vI

vO

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Input and Output Impedance

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Op Amp Input/Output Impedance with Feedback

+_

roand rdare open-loop output/inputimpedancesWe normally make the assumption that ro0; rd .But in reality, ro and rdare not ideal.

With voltage-sampling/voltage-series feedback, closed-loopRiandRoare bothimproved!

Riincreases;Rodecreases

Results:Ri= (1+a)rd;Ro= ro/(1+a)

rd

ro

a(vP

-vN

)

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Input impedance

Use non-inverting op amp as an example:

If vN= 0; thenZi = rd

+_

Case of no feedback

Case of feedback

R1 R2 vN

vIvO

Ziii

vP

ii

rd

ro

a(vP - vN)

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Input Impedance


Also: vo= a(vP- vN)

Substituting into previous result, this yields vN= a(vP- vN).

Rearranging and collecting,

Substituting into iiequation,

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Input impedance


So that

If the op amp has a single pole atfb, then

whereft= a0fb

DC portionFrequency dependence

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Input Impedance


Pole:fb; zero:fb(1+a0)

Frequency increasing, inputimpedance decreasing like acapacitorcapacitive betweenfbandfb(1+a0).

|Zi|

fb

rd

(1+ ao)rd

logf[fb(1+ ao)]

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Input Impedance

At high frequency, capacitor as a short circuit,

RP//Rs= rd; butRP>> rd, so

Zi

RP

RS

C

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Output Impedance


Applying KCL at vO,

and

R1 R2vN

vO

ZO

iO

ix

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Output Impedance


If the op amp has a single pole atfb, then

where

Zero:fb; pole:fb(1+a0)DC portion Frequency dependence

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Output Impedance


Frequency increasing, output

impedance increasing like aninductorinductive betweenfb

andfb(1+a0)

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Output Impedance

At DC, inductor is like a short circuit,

As frequency is increasing, impedance is also increasing as a open circuit,

RP

RS

L

ZO

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Typical Values of Input/Output Impedances

Example: An non-inverting op amp with

(a) Find the elements values in the equivalent circuit of Zi; (b)

the elements values in the equivalent circuit of Zo

R1 R2vN

vOvI

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Typical Values of Input/Output Impedances

Example: An non-inverting op amp with

(b) the elements values in the equivalent circuit of ZoSolution:

So

Therefore:

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Speed Limitations of Op Amps

Time response of a single pole op amp:

How does a response of gain behave to a transient?

Transform the circuit to s domain:

Unit step input:

Where:

Output voltage:

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Time response of a single pole op amp:

How does a response of gain behave to a transient?

Transform it back to time domain,

Transient response

v

t

a0

= =0.35

741 opamp t=159ns and tR=350ns

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Bandwidth Limiting affects small signals and large signals quality

Drop in gain

Effects are independent ofamplitude

Effects do not distort sinewave

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Slew rate (SR) Limiting :

Slew rate is a dv/dtlimitation of the op amp output

Usually, SRrisingSRfaliing

Effects are dependent of amplitude

Effects distort input signalsSquare wave input

Ideal output

Real output

= (1 /)

=

= SR

=1

2=

1

2

Voltage follower is used here:ft=fB*A=fB*1=fB

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Full Power Bandwidth (FPB):

Full power bandwidth is the maximum frequency at which the op amp will yield anundistorted ac output with the largest possible amplitude.

A 741 with vsat= 13 V, SR = 0.5 V/s, has FBP = 6.1 kHz.When applying this op amp, we must make sure SR or fBsmaller thanFBP.

=

=

12

= SR

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