1

Characteristics of an Ideal Op-Amp

• Infinite input impedance

• Zero output impedance

• Zero common-mode gain, or, infinite common-mode rejection

• Infinite open-loop gain A

• Infinite bandwidth.

2

Difference Amplifier• A difference amplifier is one that responds to the difference between the two

signals applied at its input and ideally rejects signals that are common to the two inputs.

21Idv

IcmvIv −=

+-

-+

+-

2Idv

22Idv

IcmvIv +=

2Idv

Icmv

12 IvIvIdv −=

)21(2

1IIIcm vvv +=

cmAdA

IcmvcmAIdvdAov

log20CMRR =

+=

3

More Characteristics of Op-Amp

• Since the ideal op-amp responds only to the difference between the two input signals, the ideal op-amp maintains a zero output signal when the two input signals are equal.

• When the two input signals are unequal, there is what is called a common-mode input signal.

• For the ideal op-amp, the common-mode output signal is zero. This characteristic is referred to as common-mode rejection.

• Another characteristic, because op-amp is biased by both positive and negative power supplies, most op-amps are direct coupled devices (no coupling capacitors are required on the input). Accordingly, the two input voltages can be DC.

• Because the OP is composed of transistors biased in the active region by the DC power supply, the output voltage is limited.

4

Difference Amplifier

R2

R1

R3

R4

vI1

vI2

vo

-

+

5

Figure 8.10

A Single Difference or Differential Amplifier

( )121

2 vvR

Rvout −=

1

2

1

2

R

RdA

IdvR

Routv

=

=

6

Figure 8.14, 8.15

Instrumentation Amplifier Input (a) and output (b) stages of Instrumentation amplifier

+=

−=

1

2

21

21

R

R

R

R

vv

vA Fout

V

7

Design Example: Determine the range required for resistor R1 in the instrumentation amplifier to realize a differential gain adjustable from 5 to

500. Assume RF = 2R, so that the difference amplifier gain is 2.

• Assume R1 is a combination of a fixed resistor R1f and a variable resistor R1v. Assume R1v = 100 kΩ

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+=

+=

=

++=

+=

+=

−=

k 5.752 and k 606.01

1001

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1001

225.1

124922

expressiongain maximum thefrom and 1001

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21

RfR

fR

fR

fR

R

fRR

fR

R

fR

R

R

R

RFR

vvoutv

VA R1f

R1v

8

Figure 8.35

Op-amp Differentiator

dt

tdvCRtv S

SFout

)()( −=

9

Large Signal Operation of Op Amp

• Like other amplifiers, op amps operate linearly over a limited range of output voltages.

• Another limitation of the operation of op amps is that their output current is limited to a specified maximum. For example, the op amp 741 is specified to have a maximum output current of ±20 mA.

• Read Example 2.5.

• Another phenomenon that can cause nonlinear distortion when large output signals are present is that of slew-rate limiting. This means there is a specific maximum rate of change possible at the output of a real op amp. This maximum is known as the slew rate (SR) of the op amp and isdefined as

maxSR

dtodv

=

10

Design Example. Design a difference amplifier with a specified gain and minimum differential input resistance.

Design the circuit such that the differential gain is 30 and theminimum differential input resistance is Ri = 50 kΩ

kΩ 75042 havemust we

,301

2 isgain aldifferenti theSince

k 25 3 1

kΩ 5012

==

=

Ω====

RR

R

R

RR

RiR

11

Design Example: Calculate the common-mode rejection ratio of a differential amplifier. Consider the difference amplifier shown in page 2.

Let R2/R1 = 10 and R4/R3 = 11. Determine CMRR (dB)

dB 6.410.0833

10.0421020logCMRR(dB)

0833.0;042.10

;0833.0042.10

)2

(10)2

(0833.10

22;

21;2

21 ;12

11020833.101)10(2)111

11)(101(

1)1

2(2

3

41

3

4

)1

21(

21

=

=

==+=+=

−−+=

+=−=+=−=

−=−+

+=

−

++=

+=

cmAdAcmvcmAdvdAovcmvdvov

dvcmvdv

cmvvo

dvcmvvdv

cmvIvIvIvcmvIvIvdv

IvIvIvIvov

IvR

RIv

R

RR

R

R

Rov

vovovo

12

Figure 8.20

Op-amp Circuits Employing Complex Impedances

S

F

S

out

S

F

S

out

Z

Zj

V

V

Z

Zj

V

V

+=

−=

1)(

)(

ω

ω

13

Figure 8.21, 8.23

Active Low-Pass Filter

Normalized Response of Active Low-pass Filter

14

Figure 8.24, 8.25

Active High-Pass Filter

Normalized Response of Active High-pass Filter

15

Figure 8.26, 8.27

Active Band-Pass Filter

Normalized Amplitude Response of Active Band-pass Filter

16

Figure 8.30

Op-amp Integrator

∫∞−

−=t

SFS

out dttvCR

tv )(1

)(

17

Figure 8.35

Op-amp Differentiator

dt

tdvCRtv S

SFout

)()( −=