Operational Amplifier Circuits Objectives

1

Operational Amplifier Circuits

Objectives

1. To familiarize with the fundamental OP-Amp circuits.

2. To verify and implement the basic function of OP-Amp circuits.

Overview

In Fig. 1 and Fig. 2, the schematic figures of classical OP-Amp are shown.

The specification of a classical OP Amp is shown as follow:

Parameters Ideal Value Test Value

Input resistance Ri ∞ 2 MΩ

Output resistance Ro 0 75 Ω

Voltage Gain A ∞ > 100 dB

Bandwidth BW ∞ Dominant Pole < 10Hz

CMRR

(Common-Mode Rejection Ration)∞ 90 dB

Temperature Shift 0 < 15 V/oC

Fig. 1 Equivalent Circuit Fig. 2 Equivalent Circuit with input

of an Ideal OP-Amp and output resistance

Experiment

2

2

The A741 is a general-purpose operational amplifier featuring offset-voltage

null capacity. The high common-mode input voltage range and the absence of

latch-up make the amplifier ideal for voltage-follower applications. The device is

short-circuit protected and the internal frequency compensation ensures stability

without external components.

Inverting OP Amp

1、 Close-loop gain of an ideal inverting OP AMP

Fig. A

Because of virtual short (Open-Loop Gain～∞), the circuit will become

following:

0V =

1

22

121

11 ,,

0

R

R

V

VAR

R

VRiV

R

Vi

i

ov

io

i

2、 Closed loop gain of a non-ideal inverting OP AMP (Open-Loop Gain ≠ ∞)

1 21 1 1

2 2 21

( ) (0 )

( ),

( )

o o

i i o i o

o i oo

V A V V A V V A V V A

V V V V A V V Ai i

R R R

V V V AV V i R R

A R

3

2 2

1 1

2 2 2 1

1 1 2 1

( )

1[1 (1 )]

1 (1 )

o oo i o i

oo i

i

V VR RV V V A V

A R R A

VR R R RV V

A R R V R R A

3、 Frequency response

If the open-loop gain of an OP AMP is not finite, the close-loop gain of the

inverting structure OP AMP will be

,)1(1 12

12

ARR

RR

V

V

i

o

Because the OP AMP is a Low-Pass circuit, the gain versus frequency may

be expressed as

00( ) , : Open-Loop Gain

1 b

AA s where A

s

Then

2 1

02 1

2 1

2

0 1 2 1

2 1 20

1

2 1

( )( )

( ) 1 (1 )1

( )( )

1( ) 1 (1 )(1 )

( )( ) , (1 )

( ) 1(1 )

o

i

b

o

i

t

o

i

t

V s R RA s

AV s R RS

V s R RA s

R sV sA R R R

V s R R RA s where A

sV s RR R

That is,

)1(1

)(

12

12

RR

jRR

jA

t

And we could get the f3dB from the math expression shown above

03 2 1 2 1 2 13

33

2 1

3 32 1 2 1

( )( ) 45

( ) 1 1 21(1 )

, : Unit-gain frequency(1 ) (1 )

o dBdB

dBi dB

t

t tdB dB t

V j R R R R R RA j

jV j jR R

ff where f

R R R R

which means that the output phase of voltage will be delay 45 degree from

the input phase of voltage.

4

Non-Inverting OP AMP

1. Close-loop gain an ideal non-inverting OP AMP

Fig. B

Because of virtual short (Open-Loop Gain～∞), the circuit will become

following:

)1(),1(,0

1

2

1

221

11 R

R

V

VA

R

RVRiVV

R

Vi

i

oviio

i

2. Closed loop gain of a non-ideal inverting OP AMP (Open-Loop Gain ≠ ∞)

ARR

RR

ARR

RA

V

V

AVARR

RVAV

RR

RVV

i

o

iooio

)1(1

1

1

)1()(

12

12

21

1

21

1

21

1

3. Frequency response

If the open-loop gain of an OP AMP is finite, the close-loop gain of the

inverting structure OP AMP will be

ARR

RR

V

V

i

o

)1(1

1

12

12

5

Because the OP AMP is a Low-Pass circuit, the gain versus frequency may

be expressed as

00( ) , : Open-Loop Gain

1 b

AA s where A

S

then

2 1

02 1

2 1

2

0 1 2 1

2 1 20

1

2 1

( ) 1( )

( ) 1 (1 )1

( ) 1( )

1( ) 1 (1 )(1 )

( ) 1( ) , (1 )

( ) 1(1 )

o

i

b

o

i

t

o

i

t

V s R RA s

AV s R RS

V s R RA s

R sV sA R R R

V s R R RA s where A

sV s RR R

That is,

)1(1

1)(

12

12

RR

jRR

jA

t

And we could get the f3dB from the math expression shown above

3 2 13

33

2 1

02 1 2 13

3 32 1 2 1

( ) 1( )

( ) 1(1 )

(1 ) (1 )( ) 45

1 1 2

(1 ) (1 )

o dBdB

dBi dB

t

dB

t tdB dB

V j R RA j

jV jR R

R R R RA j

j

ff

R R R R

which means that the output phase of voltage will be delay 45 degree from

the input phase of voltage.

Pre-Lab Work (預報)

Please use PSPICE to simulate the frequency response of the circuit shown

in Fig. A, B, and Fig. 8.

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Instrument Requirement

Instrument Quantity Components Quantity

Oscilloscope 1 Power supplier 1

Function Gen. 1 Multi-meter 1

Component Requirement

Components Quantity Components Quantity

A 741 1 Resistance (100 Ω) 2

Resistance (1 kΩ) 1

Resistance (4.7 kΩ) 1

Instrument confirmation

Before you proceed to any part of the experiment, please remember to do

the Instrument Examinations to the instruments before performing any

experiment. The examining procedures are shown in experiment 1.

Components confirmation

PINOUT － A741 (Operational Amplifier)

※ Note: Supply voltage is regularly being applied by −15V ~ +15V.

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Lab Work

1. DC confirmation of the inverting OP-Amp circuit

Fig. 3 Inverting OP-Amp DC Circuit

Use R1 = 100 Ω, R2 = 1 kΩ in Fig. 3.

Reference value of each pin in Fig. 3:

Pin Reference value (V)

4 15V

7 15V

2, 3, 6 0V

Record the measured value in the table 1:

Pin Measured value (V)

4

7

2, 3, 6

Table 1 Measured value of each pin in Fig. 3

※ Note: If the measured values are far different from those shown in the

reference value table, try to change a chip of A741 and repeat step 1 until

they are correct.

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2. The close-loop gain G of inverting OP-Amp circuit

Fig. 4 Inverting OP-Amp Circuit

(1) Use R1 = 100 Ω, R2 = 1 kΩ in Fig. 4.

(2) Supply voltage source VCC = +15V, and −VCC = −15V to the circuit.

(3) Provide the small signal vi to the breadboard by using function generator to

generate vi = vac × sin(2ft), 2vac = 100mV(p-p), f = 1 kHz.

(4) Make sure that the vi is measured from the breadboard by using the probe

from CH1 in oscilloscope.

(5) Function generator Press the FUNC button Set FREQ =1 kHz, SIN

wave ATTN 40dB.

(6) Keep the previous adjustment of vi constantly, and do not adjust the

amplitude tuner in function generator any further.

(7) Record the voltage gain (R2 = 1 kΩ) AM = V/V by observing the

differentiation of input and output voltage value shown in the curve at YT

mode.

(8) Change the frequency of input voltage signal vi, and record the input and

output voltage shown in oscilloscope to the following table.

R2 = 1 kΩ

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

10 5K

20 10K

50 20K

100 50K

200 100K

500 200K

1K 500K

2K 1M

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(9) Function generator Press the FUNC button Adjust Frequency and

observe the voltage gain AV in oscilloscope until AV = 0.707 × AM.

(10) Record the frequency (R2 = 1 kΩ) f3dB = Hz.

※ Homework #1: Apply the measured data in the above table to the editing

software EXCEL or MATLAB, and illustrate the frequency-response

diagram with marking f3dB and the corresponding voltage.

(11) Change R2 = 4.7 kΩ in Fig. 3-2 and repeat step (7) ~ (9).

(12) Change the frequency of input voltage signal, and record the input and


R2 = 4.7 kΩ

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

10 5K

20 10K

50 20K

100 50K

200 100K

500 200K

1K 500K

2K

(13) Record the voltage gain (R2 = 4.7 kΩ) AM = V/V.

(14) Record the frequency (R2 = 4.7 kΩ) f3dB = Hz.




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3. DC confirmation of the non-inverting OP-Amp circuit

Fig. 5 Non-inverting OP-Amp DC Circuit

Use R1 = 100 Ω, R2 = 1 kΩ in Fig. 5

Reference value of each pin in Fig. 5


4 15V

7 15V

2, 3, 6 0V

Record the measured value in the table 2:


4

7

2, 3, 6

Table 2 Measured value of each pin in Fig. 5

※ Note: If the measured values are far different from those shown in the

reference value table, try to change a chip of A741 and repeat step 3 until

they are correct.

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4. The close-loop gain G of non-inverting OP-Amp circuit

+15V

Vi

VO

R1

R2

–15V

(2)

(3)

(4)

(6)

(7)

CH 1CH 2

Fig. 6 Non-inverting OP-Amp Circuit

(1) Use R1 = 100Ω, R2 = 1 kΩ in Fig. 6


(3) Function generator Press the FUNC button Set FREQ = 1 kHz, SIN

wave ATTN 40dB.

(4) Keep the previous adjustment of vi constantly, that is, vi = vac × sin(2ft),

2vac = 100 mV(p-p), f = 1 kHz, and do not adjust the amplitude tuner in

function generator any further.

(5) Record the voltage gain (R2 = 1 kΩ) AM = V/V by observing the

differentiation of input and output voltage value shown in the curve at YT

mode.



R2 = 1 kΩ

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

10 5K

20 10K

50 20K

100 50K

200 100K

500 200K

1K 500K

2K

12



(8) Record the frequency (R2 = 1 kΩ) f3dB = Hz.

(9) Change R2 = 4.7 kΩ in Fig. 6 and repeat step (7) ~ (9).



R2 = 4.7 kΩ

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(V) AV

10 5K

20 10K

50 20K

100 50K

200 100K

500 200K

1K 500K

2K

(11) Record the voltage gain (R2 = 4.7 kΩ) AM = V/V

(12) Record the frequency (R2 = 4.7 kΩ) f3dB = Hz.




5. DC confirmation of the voltage-follower OP-Amp circuit

Fig. 7 Voltage-follower OP-Amp DC Circuit

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Reference value of each pin in Fig. 7


4 15V

7 15V

2, 3, 6 0V

Record the measured value in the table 3


4

7

2, 3, 6

Table 3. Measured value of each pin in Fig. 5-1

※ Note: If the measured values are far different from those shown in the above

table, try to change a chip of A741 and repeat step 5 until they are correct.

6. The close-loop gain G of voltage follower of OP-Amp circuit

Fig. 8 Voltage follower of OP-Amp Circuit


(2) Keep the previous adjustment of Vi shown in 7−(7) constantly, that is, vi =

vac×sin(2ft), 2vac =100mV(p-p), f = 1 kHz, and do not adjust the amplitude

tuner in function generator any further.

(3) Record the voltage gain AM = V/V by observing the differentiation

of input and output voltage value shown in the curve at YT mode.



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f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(mV) AV

f

(Hz)

Vi(p-p)

(mV)

VO(p-p)

(mV) AV

10 5K

20 10K

50 20K

100 50K

200 100K

500 200K

1K 500K

2K 1M



(6) Record the frequency f3dB = Hz.


software such as EXCEL and MATLAB, and illustrate the

frequency-response diagram with marking f3dB and the corresponding

voltage.

Homework Questions 1. What is the importance of CMRR of the amplifier circuits?

2. According to your measured data, try to calculate the Gain-bandwidth

product (GBP), and compile the calculation in a table.

3. Theoretically, as G = 1 for inverting OP-Amp and voltage follower circuit,

which bandwidth is larger? Why?

4. The applied small signal in the experiment is 100mV(p-p). Is it possible to

apply 1V to the circuit? Why?

5. Try to demonstrate (by word or diagrams) how to measure the phase

different between vi and vo.

6. Homework #1, 2, 3, 4.

Reference 1. A.S. Sedra and K.C. Smith, Microelectronic Circuits, 5th ed., Oxford

University Press publishing, New York, August 2007.

2. A.S. Sedra and K.C. Smith, Laboratory Manual for Microelectronic Circuits,

3rd ed., Oxford University Press publishing, New York, 1997.

Operational Amplifier Circuits Objectives

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