Chapter 1 Operational Amplifiers

Objectives

 Describe basic op-amp characteristics  Discuss op-amp modes and parameters  Explain negative feedback  Analyze inverting, non-inverting, voltage follower, and inverting amp configurations  Describe the impedance characteristics of the three op-amp configurations  Discuss op-amp compensation  Troubleshoot op-amps

1. INTRODUCTION

Operational amplifier (op-amp) is a differential amplifier with characteristics as follows: (1) very high input impedance (Z in ), (2) very low output impedance (Z out ), (3) very high voltage gain (A V ). Figure 1-1: Schematic symbol for an op-amp.

Figure 1-2: Basic op-am The overview of a basic op-amp is as follows:  powered by TWO (2) dc voltages, one positive (+V) and other negative (-V),  has TWO (2) input terminals, an inverting (-) input and a non-inverting (+) input,  has ONE (1) output terminal.

Internal Block Diagram of an Op-Amp

A typical op-amp is made up of three types of amplifier circuits: (1) a differential amplifier input stage, (2) a voltage amplifier gain stage, (3) a push-pull amplifier output stage.

Figure 1-9 (a): Basic internal arrangement of an op-amp.

INPUT STAGE OUTPUT STAGE GAIN STAGE Figure 1-9 (b): Basic internal arrangement of an op-amp.

Op-amp is produced as a circuit of components integrated into one chip. Top View Figure 1-3: Typical packages. Pin 1 is indicated by a notch or dot on dual in-line (DIP) and surface-mount technology (SMT) packages. Inverting Non-Inverting Figure 1-4: 741 chip packaged in an 8-pin DIP.

Differential Amp.

Voltage Amp.

Output Amp.

Figure 1-5: Schematic diagram of a 741 chip.

The differential amplifier determines the

input signal modes

of an op-amp. The modes are:  Single-ended input mode  Double-ended (differential) input mode   Common-mode operation Common-mode rejection

1.1 Single-ended input mode

This mode operates when the input signal is connected to one input and the other is grounded.

Figure 1-6: Single-ended operation.

1.2. Double-ended (differential) input mode

This mode can be operated by using only one signal or by applying two signal at each input.

Figure 1-7: Double-ended (differential) operation.

1.3. Common-mode operation

In common mode, two signal voltages of the same phase, frequency, and amplitude are applied to the two inputs. When equal input signals are applied to both inputs, they tend to cancel, resulting in a zero output voltage.

Figure 1-8: Common-mode operation.

1.4. Common-mode rejection

The measure of an op-amp’s ability to reject unwanted signals (noise) is called the

common-mode rejection ratio (CMRR)

. This parameter causes the unwanted signals do not appear on the output Technically, CMRR is the ratio of the open-loop differential gain, A d , to the common-mode gain, A c .

CMRR



A d A c

(1-1) The CMRR is often expressed in decibels (dB) as

CMRR

(log)



20 log

10  

A d A c

  (1-2)

2. DIFFERENTIAL AMPLIFIER CIRCUIT

The

differential amplifier

a circuit that has two separate inputs and produces two separate outputs where the emitters are connected together. is (I) (NI) It amplifies the difference voltage between the two input (V diff ).

There are three operations can be done in a differential amplifier circuit;

operation

and dc bias, ac

common

mode operation. Figure 1-10: The basic differential amplifier.

2.1 DC Bias

The dc bias is determined by connecting each base voltage to 0 V where we obtain,

V E



V B



V BE

  0 .

7

V

.............................(1-3) The emitter dc bias current is

I E



V E

 ( 

V EE

)

R E

.............................(1-4) Figure 1-11: DC bias of differential amplifier circuit.

If both transistors have

equal values of base-emitter

voltage, V

BE1 = V BE2

(well matched), we obtain

I C

1 

I C

2 

I E

2 (1-5) resulting in a collector voltage of

V C

1 

V C

2 

V CC



I C R C



V CC



I E

2

R C

(1-6)

2.2 AC Operation of Circuit

To operate a differential amplifier in an ac connection, two separate ac voltage sources are connected to both bases. There are two voltage gain can be calculated in ac operation: (a) Single-Ended AC Voltage Gain.

(b) Double-Ended AC Voltage Gain.

Figure 1-12: AC connection of differential amplifier circuit.

To carry out an ac analysis, each transistor is replaced by its ac equivalent.

Figure 1-13: AC equivalent of differential amplifier circuit.

(a) Single-Ended AC Voltage Gain

Single-ended ac voltage gain is calculated by connecting one of voltage sources to one input and the other connected to ground. The single-ended ac voltage gain magnitude at either collector can be expressed as,

A v



V V i

1

o



R C

2

r e

where, (1-6)

r e

 26

mV I E

r e = ac emitter resistance (1-7) Figure 1-14: Connection to calculate a single-ended ac voltage gain.

(b) Double-Ended AC Voltage Gain

By similar analysis, the differential ac voltage gain magnitude is

A d



V V d o

 

R C

2

r i

(1-8) where, β = current gain of a transistor r i = internal resistance of a transistor V d = V i1 -V i2

2.3 Common-Mode Operation of Circuit

To operate a differential amplifier in a common-mode connection, the same ac voltage source is applied to both inputs.

In most ac operation, a differential amplifier provides large amplification, but in this operation it provides small amplification. The voltage gain magnitude is expressed as,

A c



V o V i



r i

 2 (  

R C

 1 )

R E

..................................(1-9) Figure 1-15: Common-mode connection.

3. DIFFERENTIAL AND COMMON-MODE OPERATION 3.1 Differential Input Difference voltage, V d

input signals (V i1 and V applied to an op-amp.

i2 is defined as the difference between two ). It is produced from two separate inputs

V d



V i

1 

V i

2 (1-10)

3.2 Common Input

When both input signals is same, a

common voltage, V c

by the two inputs can be defined as the

average

two signals, caused of the sum of the

V c

 1 2 (

V i

1 

V i

2 ) (1-11)

3.3 Output Voltage

Since any signals applied to an op-amp in general have both in-phase and out-of-phase components, the resulting

output voltage, V o

is

V o



A d V d



A c V c

(1-12) where A d = differential gain of amplifier.

A c = common-mode gain of the amplifier.

The output voltage in terms of the value of CMRR can be expressed as,

V o



A d V d

  1  1

CMRR V V d c

  (1-13)

3.4 Opposite-Polarity Inputs

If opposite-polarity inputs are applied to an op-amp,

V i1 = V s

, the resulting difference voltage is

= -V i2

V d



V i

1 

V i

2 

V s

 ( 

V s

)  2

V s V c

 1 2 (

V i

1 

V i

2 )  1 2 [

V s

 ( 

V s

)]  0

V o



A d V d



A c V c



A d

( 2

V s

)  0  2

A d V s

(1-14) These equations illustrate that the

times twice the input signal output

is the

differential gain

applied to one of the inputs when the inputs are an ideal opposite signal with no common element.

3.5 Same-Polarity Inputs

If same-polarity inputs are applied to an op-amp, V i1 the resulting difference voltage is = V i2 = V s ,

V d



V i

1 

V i

2 

V s



V s

 0

V c

 1 2 (

V i

1 

V i

2 )  1 2 (

V s



V s

) 

V s V o



A d V d



A c V c



A d

( 0 ) 

A c V s



A c V s

(1-15) These equations illustrate that the

output mode gain times

operation occurs.

the input signal V

s

is the

common-

when the inputs are an ideal in-phase signals, which shows that only common mode

3.6 Common-Mode Rejection

The equations (1-14) and (1-15) provide the relationships that can be used to measure A d and A c in op-amp circuits.

1. To measure V c A d : Set V i1 = 0 V and V o = A d = -V i2 = V s = 0.5 V, we obtain V d = 1 V,

Thus, setting the input voltages V value of A d .

i1 = -V i2 = 0.5 V results in an output voltage numerically equal to the

2. To measure A c : Set V i1 V c = 1 V and V o = A c = V i2 = V s = 1 V, we obtain V d = 0 V,

Thus, setting the input voltages V i1 = V i2 = 1 V results in an output voltage numerically equal to the value of A c .

4. OP-AMP BASICS

Ideal op-amp

as follows: has the characteristics (1) infinite input impedance (Z in ), (2) infinite output impedance (Z out ), (3) infinite voltage gain (A V ), (4) infinite bandwidth.

Characteristics of

practical op-amp

are: (1) very high input impedance (Z in ), (2) very low output impedance (Z out ), (3) very high voltage gain (A V ). Figure 1-16: Basic op-am.

Figure 1-17: AC equivalent of op-amp circuit: (a) practical; (b) ideal.

Basic Op-Amp

A basic op-amp has the circuit characteristics as follows:  If a voltage source is connected to the minus (-) input, the resulting output is

opposite in phase

to the input signal.  If a voltage source is applied to the plus (+) input, the output is

in phase

with the input signal.

Figure 1-18

: Basic op-amp.

5. PRACTICAL OP-AMP CIRCUITS

The op-amp have several circuit connections that provide various operating characteristics. The op-amp can be connected as: 1. an inverting amplifier 2. a non-inverting amplifier 3. an unity follower 4. a summing amplifier 5. an integrator 6. a differentiator

5.1 Inverting Amplifier

An op-amp connected as a inverting amplifier has the characteristics as follows:  The input signal is applied to the inverting (-) input through a input resistor R 1 .

 The non-inverting (+) input is grounded.

 The output is obtained by multiplying the input by a constant gain and fed back to the same input through a feedback resistor R f .

V o

 

R f R

1

V

1

Figure 1-19

: Inverting amplifier.

(1-16)

5.2 Non-inverting Amplifier

The characteristics of non inverting amplifier are:  the input signal is applied to the non-inverting (+) input  the output is applied back to the inverting (-) input through the feedback circuit (closed loop) formed by R 1 and R f .

V o

  

1



R f R

1  

V

1 Figure

1-20

: Non-inverting amplifier.

(1-17)

5.3 Unity Follower

An unity follower circuit is characterized as follows:  provides a voltage gain of 1 (which means there is no gain)  all of the output voltage is fed back to the inverting (-) input.

Figure 1-21

: (a) Unity follower; (b) virtual-ground equivalent circuit.

5.4 Summing Amplifier

The summing amplifier is an op-amp circuit that provides an output proportional to the

sum

of its inputs. Each input voltage is multiplied by a constant-gain factor.

Figure 1-22

: (a) Summing amplifier; (b) virtual-ground equivalent circuit.

The output voltage can be expressed as the sum of the equations for each as follows:

V o

   

R f R

1

V

1 

R f R

1

V

2 

R R

3

f V

3   (1-18)

5.5 Integrator

If the feedback component used is a capacitor that forms an

R C

circuit with the input resistor, the resulting connection is known as an

ideal

integrator.

Figure 1-23: An ideal integrator.

The output voltage can be written as:

V o

  1

j



RC V

1 (1-18) This expression can be rewritten in the time domain as:

v o

(

t

)   1

RC



v

1 (

t

)

dt

(1-19) Equation (1-19) shows that the output is the integral of the input, with an inversion and scale multiplier of 1/RC.

If more than one input voltage may be applied to an integrator, the output voltage can be calculated as the sum of the equations for each as follows:

v o

(

t

)     1

R

1

C



v

1 (

t

)

dt



R

2 1

C



v

2 (

t

)

dt

 1

R

3

C



v

3 (

t

)

dt

  ......................................................................................(1-20) Figure 1-24: Summing-integrator circuit.

Practical

integrators often have an

additional resistor

parallel with the feedback capacitor to prevent saturation.

in R f Figure 1-25: A practical integrator.

5.6 Differentiator

If the positions of the integrator feedback capacitor (C) and input resistor (R) are reversed, we have a differentiator. Figure 1-26: Differentiator circuit.

The output voltage can be calculated by using the following formula:

v o

(

t

)  

RC dv

1 (

t

)

dt

(1-21) This equation illustrates that a differentiator provides an output that is proportional to the

rate of change

of its input signal.

Slew Rate

The slew rate of an op-amp is maximum rate at which the output voltage can change in response to a change at either signal input and written as:

SR

 

V o



t

(

V

/ 

s

) (1-22) Since frequency is related to time, the slew rate can be used to determined the maximum signal frequency of the op-amp:

f

max 

SR

2 

K

where, K = the peak output voltage from the op-amp.

(1-23)

The peak output voltage is half the peak-to-peak output voltage value and expressed as:

K

 1 2

V o pp

(1-24) While the peak-to-peak output voltage is found as

V o pp



A d V i

(1-25)