Operational Amplifier: Types, Configurations, and Equations, Slides of Electronics

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Kristin Ackerson, Virginia Tech EE

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Table of Contents

• The Operational Amplifier______________________________slides 3- Kristin Ackerson, Virginia Tech EE
• The Four Amplifier Types______________________________slide
  • Noninverting Configuration____________slides 6- VCVS(Voltage Amplifier) Summary:
  • Inverting Configuration________________slides 10-
• ICIC(Current Amplifier) Summary________________________slide
• VCIS (Transconductance Amplifier) Summary_____________slides 14-
• ICVS (Transresistance Amplifier) Summary_______________slides 16-
• Power Bandwidth_____________________________________slide
• Slew Rate____________________________________________slide
• Slew Rate Output Distortion____________________________ slide
• Noise Gain___________________________________________slide
• Gain-Bandwidth Product_______________________________slide
• Cascaded Amplifiers - Bandwidth________________________slide
• Common Mode Rejection Ratio__________________________slides 25-
• Power Supply Rejection Ratio___________________________slide
• Sources_____________________________________________slide

• i (+)

, i (-)

: Currents into the amplifier on the inverting and noninverting lines

respectively

• vid : The input voltage from inverting to non-inverting inputs
• +V S

, - V S

: DC source voltages, usually +15V and – 15V

• Ri : The input resistance, ideally infinity
• A : The gain of the amplifier. Ideally very high, in the 1x

10 range.

• RO: The output resistance, ideally zero
• v O

: The output voltage; v O

= A OL

v id

where A OL

is the open-loop voltage gain

The Operational Amplifier

Kristin Ackerson, Virginia Tech EE

+V

S

- V

S

v id

Inverting

Noninverting

Output

_

i (-)

i (+)

v O

= A

d

v id

R

O

A

R

i

The Four Amplifier Types

Kristin Ackerson, Virginia Tech EE

Description

Gain

Symbol

Transfer

Function

Voltage Amplifier

or

Voltage Controlled Voltage Source (VCVS)

A

v

v o

/v in

Current Amplifier

or

Current Controlled Current Source (ICIS)

A

i

i o

/i in

Transconductance Amplifier

or

Voltage Controlled Current Source (VCIS)

g m

(siemens)

i o

/v in

Transresistance Amplifier

or

Current Controlled Voltage Source (ICVS)

r m

(ohms)

v o

/i in

Kristin Ackerson, Virginia Tech EE

VCVS (Voltage Amplifier) Summary

Noninverting Configuration Continued

The closed-loop voltage gain is symbolized by A v

and is found to be:

A

v

= v o

= R

F

v in

R

1

The original closed loop gain equation is:

A

v

= A

F

= A

OL

1 + A

OL

Ideally A OL

  , Therefore A v

Note: The actual value of A OL

is given for the specific device and

usually ranges from 50k  500k.

 is the feedback factor and by assuming open-loop gain is infinite:

 = R 1

R

1

+ R

F

AF is the amplifier

gain with

feedback

Kristin Ackerson, Virginia Tech EE

VCVS (Voltage Amplifier) Summary

Noninverting Configuration Continued

Input and Output Resistance

Ideally, the input resistance for this configuration is infinity, but the a

closer prediction of the actual input resistance can be found with the

following formula:

R

inF

= R

in

(1 + A

OL

) Where R in

is given for the

specified device. Usually R in

is

in the M range.

Ideally, the output resistance is zero, but the formula below gives a

more accurate value:

R

oF

= R

o

Where R o

is given for the

A

OL

• 1 specified device. Usually R o

is in

the 10

s of 

s range.

Kristin Ackerson, Virginia Tech EE

VCVS (Voltage Amplifier) Summary

Inverting Configuration

_

R

L

v O

v in

_

R

i^1 1

R

i F F

The same

assumptions used to

find the equations for

the noninverting

configuration are

also used for the

inverting

configuration.

General Equations:

i 1

= v in

/R

1

i F

= i 1

v o

= - i F

R

F

= - v in

R

F

/R

1

Av = RF/R 1  = R 1 /RF

Input and Output Resistance

Ideally, the input resistance for this configuration is equivalent to R 1

However, the actual value of the input resistance is given by the

following formula:

R

in

= R

1

+ R

F

1 + A

OL

Ideally, the output resistance is zero, but the formula below gives a

more accurate value:

R

oF

= R

o

1 + AOL

Note:  = R 1

This is different from the equation used

R

1

+ R

F

on the previous slide, which can be confusing.

Kristin Ackerson, Virginia Tech EE

VCVS (Voltage Amplifier) Summary

Inverting Configuration Continued

ICIS (Current Amplifier) Summary

Kristin Ackerson, Virginia Tech EE

 Not commonly done using operational amplifiers

_

Load

i in

i L

Similar to the voltage

follower shown below:

Both these amplifiers have

unity gain:

A

v

= A

i

_

i

in

= i

L

v

in

= v

o v in

_ +

v O

Voltage Follower

1 Possible

ICIS

Operational

Amplifier

Application

VCIS (Transconductance Amplifier) Summary

Kristin Ackerson, Virginia Tech EE

Voltage to Current Converter

_

Load

i L

R

i^1 1

v in

_

OR

_

Load

i L

R

i^1 1

v in

_

v in

_

General Equations:

i L

= i 1

= v 1

/R

1

v 1

= v in

The transconductance, g m

= i o

/v in

= 1/R

1

Therefore, i L

= i 1

= v in

/R

1

= g m

v in

The maximum load resistance is determined by:

R

L(max)

= v o(max)

/i L

Kristin Ackerson, Virginia Tech EE

VCIS (Transresistance Amplifier) Summary

Current to Voltage Converter

General Equations:

i F

= i in

v o

= - i F

R

F

r m

= v o

/i in

= R

F

_

i F

i in

R

F

v O

VCIS (Transresistance Amplifier) Summary

Current to Voltage Converter

Kristin Ackerson, Virginia Tech EE

• Transresistance Amplifiers are used for low-power

applications to produce an output voltage proportional to

the input current.

• Photodiodes and Phototransistors, which are used in the

production of solar power are commonly modeled as

current sources.

• Current to Voltage Converters can be used to convert these

current sources to more commonly used voltage sources.

Power Bandwidth

Kristin Ackerson, Virginia Tech EE

The maximum frequency at which a sinusoidal output signal can be

produced without causing distortion in the signal.

The power bandwidth, BW p

is determined using the desired

output signal amplitude and the the slew rate ( see next slide )

specifications of the op amp.

BW

p

= SR

2 V

o(max)

SR = 2fV o(max)

where SR is the slew rate

Example:

Given: V o(max)

= 12 V and SR = 500 kV/s

Find: BW p

Solution: BW p

= 500 kV/s = 6.63 kHz

2  * 12 V

Slew Rate

Kristin Ackerson, Virginia Tech EE

A limitation of the maximum possible rate of change of the

output of an operational amplifier.

As seen on the previous slide, This is derived from:

SR = 2fV o(max)

SR = v o

/t max

Slew Rate is independent of the

closed-loop gain of the op amp.

Example:

Given: SR = 500 kV/s and v o

= 12 V (Vo(max) = 12V)

Find: The t and f.

Solution: t = vo / SR = (10 V) / (5x

5 V/s) = 2x

• 5 s

f = SR / 2 V o(max)

= (5x

5 V/s) / ( 2  * 12) = 6,630 Hz

 f is the

frequency in

Hz