Review of op amp circuits

Review of Op-Amp Circuits

Electronic Engineering

© University of Wales Newport 2009 This work is licensed under a Creative Commons Attribution 2.0 License.

The following presentation is a part of the level 5 module -- Electronic Engineering. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.

The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments.

Contents Review of Linear Op-Amp Circuits Inverting AmplifierNon-inverting AmplifierUnity BufferSumming Amplifier Non-Inverting Summing Amplifier Difference Amplifier Integrator Differentiator Uses of Linear Op-Amp Circuits Ideal Op-Amp Linear Circuit Analysis Credits

In addition to the resource below, there are supporting documents which should be used in combination with this resource. Please see:Clayton G, 2000, Operational Amplifiers 4th Ed, Newnes James M, 2004, Higher Electronics, Newnes

Oscillators

Review of Linear Op-Amp Circuits

We will quickly review the analysis & design of linear op-amp circuits that use negative feedback: Inverting amplifier Non-inverting amplifier Unity Buffer Summing amplifiers Difference amplifier Integrator Differentiator

Review of Op-Amp Circuits

INVERTING AMPLIFIER

+

-

Rin

Vin

Rf

VoutVa

IinIf

Ia

We can generate the following equations:

Rin

VaVinIin

Rf

VoutVaIf

IfIaIin

Combining these gives us:

Rf

VoutVaIa

Rin

VaVin

This is true for any amplifier.

But this is an op-amp and therefore we can make certain assumptions…

1. Va = 0. This is because the gain is very large and therefore Va will be very small.

2. Ia = 0. This is because the input impedance is very large and therefore Ia will be very small.

We can therefore rewrite the equation:

Rf

Vout

Rin

Vin or

Rin

Rf

Vin

VoutGain

The minus sign indicates that this is an inverting amplifier.

This set up is called a Virtual Earth Amplifier as the amplifier input terminal (-) is at earth potential as the + input is at earth.

NON-INVERTING AMPLIFIER

+

-R1

Vin

R2

Vout

Vf

IThe current I flows through both resistors as no current flows into the op-amp (assumption 2)

21 RR

VoutI

from which

21

222

RR

RVoutRIVRVf

But Vf = Vin as the difference in input voltages is zero (assumption 1), so

21

2

RR

RVoutVin

or 2

11

2

21

R

R

R

RR

Vin

VoutGain

Design an amplifier that has a variable gain from 15 to 30. (use a 100K variable resistor)

UNITY BUFFER

+

-

Vin

Vout

In the circuit Vout = Vin

– what is the purpose of this circuit?

SUMMING AMPLIFIER (Inverting)

+

-V2

Rf

VoutVa

I2

IfV1I1

V3I3

R1

R2

R3

This is a virtual earth amplifier.

1

11R

VI

2

22

R

VI

3

33R

VI and

Rf

VoutIf

Using Kirchhoff we can say:

321 IIIIf 3

3

2

2

1

1

R

V

R

V

R

V

Rf

Vout

If R1 = R2 = R3 = Rin 321 VVVRin

RfVout

If Rin = Rf 321 VVVVout

Notes:1. If an input is negative it will be subtracted2. Weighting can be applied to inputs by altering the

value of the input resistance – if R1 was half the value of the other input resistors we would have:

3212 VVVVout

SUMMING AMPLIFIER (Non-inverting)

+

-

V2

R1

Vout

V’

V1

V3

R

R

R

R2The output of the amplifier will be:

'2

11 VR

RVout

What does V’ equal?– Use superposition theory

V1R

R R

V’

3

1

2

21'

VRR

RVV

The same is true for the other inputs so we can say:

3213

1

3

3

3

2

3

1' VVV

VVVV if the gain is

set to 3 then:

321 VVVVout What would we get if – V1 resistor = RV2 resistor = 2RV3 resistor = 3R?

SUBTRACTOR (DIFFERENCE) AMPLIFIER

+

-

R1

V2

R2

Vout

R1

V1

R2

I

To determine the output we will use Superposition.

V1 input only V2 = 0

We have a non inverting amplifier with a gain of:

1

21

1

21

R

RR

R

RGain

The voltage appearing on the + input V+ is equal to:

121

2V

RR

RV

The output is therefore input times gain:

11

21

21

2

1

21V

R

RV

RR

R

R

RRVout

V2 input only V1 = 0

The V+ input will be at 0v and the amplifier will act as an inverting amplifier.

1

2

R

RGain

The output will

therefore be:2

1

2V

R

RVout

Combining these gives us the overall output equation:

211

22

1

21

1

2VV

R

RV

R

RV

R

RVout

This circuit will take the difference between two inputs and amplify it by a factor R2/R1.

INTEGRATING AMPLIFIER

We can generate the following equations:

CR

Vout

Vin

I

From what we know of op-amps we can say: V- is at earth potential (virtual earth point)The current through the resistor equals the current through the capacitor.

R

VinIR

The current through a capacitor depends upon the rate of change of voltage across it and the capacitor value.

 Equating gives  

Hence the name integrator.

dt

dVoutC

dt

dVCI C

C

R

Vin

dt

dVoutC

CR

Vin

dt

dVout

dtVinCR

Vout1

DIFFERENTIATING AMPLIFIER

We can generate the following equations:

C

R

Vout

Vin

I

Once again from what we know of op-amps we can say: V- is at earth potential (virtual earth point)The current through the resistor equals the current through the capacitor.R

VoutIR

The current through a capacitor depends upon the rate of change of voltage across it and the capacitor value.

 Equating gives  

Hence the name differentiator.

dt

dVinC

dt

dVCI C

C

R

Vout

dt

dVinC

CR

Vout

dt

dVin

dtdVinCRVout

Uses of Linear Op-Amp Circuits

Amplifiers Signal conditioning

Summing Amp Mixing (e.g. audio applications) Analogue arithmetic

Integrator Analogue computing Active filter design

Difference Amp Noise reduction in audio amplification.

Review of Op-Amp Circuits

Ideal Op-Amp Linear Circuit Analysis

When negative feedback is applied, the use of these assumptions makes design/analysis much easier (although not necessarily simple!).

Of course, they aren’t really true…

VV

II

.

and .

2

001

Review of Op-Amp Circuits

Review of Op-Amp Circuits

This resource was created by the University of Wales Newport and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

© 2009 University of Wales Newport

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