Amplifier Compensation

Amplifier Compensation

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 1 st 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 Variation of Gain and Phase Shift with Frequency Multistage Amplifiers The Control of Gain using Negative Feedback Problems associated with phase shift and NFB. 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


Variation of Gain and Phase Shift with FrequencyIn both the Bipolar Transistor and FET devices the

gain is dependent upon frequency.The relationship between Gain and Frequency in

each case is:

where ALF is the low frequency gainC is the effective input capacitanceR is the effective resistance is the angular frequency = 2 f

RCj

ALFGain

1


This equation can be split up into a gain magnitude and a phase shift:

2222 )(1)(1 RC

RCALFj

RC

ALFGain

this gives 22

222

)(1

1||

RC

CRALFGain

RCTanPhase 1

ExampleIf ALF = 100, R = 10 k and C = 10nF plot the gain

against frequency curve and phase against frequency curve.

Note plot gain in dB. dB gain = 20 log (actual gain)


Frequency Gain dB gain Phase

100 99.80 39.98 -3.60

200 99.22 39.93 -7.16

400 96.98 39.73 -14.11

700 91.54 39.23 -23.74

1000 84.67 38.55 -32.14

2000 62.26 35.88 -51.49

4000 36.97 31.36 -68.30

7000 22.17 26.91 -77.18

10000 15.72 23.93 -80.95

20000 7.93 17.99 -85.44

40000 3.98 11.99 -87.71

70000 2.27 7.13 -88.69

100000 1.59 4.03 -89.08

200000 0.80 -1.99 -89.53

400000 0.40 -8.01 -89.76

700000 0.23 -12.87 -89.86

1000000 0.16 -15.96 -89.90

Bode Plot

-5

0

5

10

15

20

25

30

35

40

100 1000 10000 100000 1000000

Frequency

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Rather than carry out the detailed analysis and calculations each time we wish to plot a response, can we find a simple way of drawing the response which is quick, simple and accurate enough for whatever investigation we are undertaking?

Examine the gain curve.

It is flat at low frequencies and rolls off at a constant rate at high frequencies.

Where do these two straight lines cross?What is the significance of this value?What is the slope of the lineWhat is the value of phase at this point?What is the maximum error?Amplifier Compensation

Asymptotic Approximation for the gain curve.Draw a straight line at the low frequency gain up to the

break frequency fC.

From this point on draw a line at -20dB/dec.

-5

0

5

10

15

20

25

30

35

40

100 1000 10000 100000 1000000

Frequency

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Asymptotic Approximation for the phase curve.This is a little more complex and a little less

accurate.

-5

0

5

10

15

20

25

30

35

40

100 1000 10000 100000 1000000

Frequency

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Draw a straight line at 0 phase shift up to one-tenth the break frequency 0.1 fC.

From 0.1 fC to 10 fC draw a line which rolls off at -45/dec.

Draw a straight line at 90 phase shift above 10 fC.

-5

0

5

10

15

20

25

30

35

40

100 1000 10000 100000 1000000

Frequency

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Multistage Amplifiers.Many amplifiers will consist of more than one

amplification stage. This is so that larger gains can be achieved which permit feedback control of gain. In addition the different amplification stages may possess different characteristics which will allow the overall amplifier to interface to its input and output more effectively.

A1 A2

The overall gain would be A1 x A2 or A1 + A2 if the two gains are expressed in dBs.

We now have two break frequencies fC1 and fC2.

How do we plot this?Gain curve - assume fC1 is at a lower frequency than

fC2.

Draw a straight line at the low frequency gain (A1 and A2) up to the break frequency fC1.

From this point draw a line at -20dB/dec. up to fC2.

From this point on draw a line at -40dB/dec.


Phase curve -Draw a straight line at 0 phase shift up to one-tenth

the break frequency 0.1 fC1.

From 0.1 fC1 to 10 fC1 draw a line which rolls off at -45/dec.

From 0.1 fC2 to 10 fC2 draw a line which rolls off at -45/dec.

If the fC1 and fC2 roll off regions overlap, roll off at -90/dec within this region

Draw a straight line at 180 phase shift above 10 fC2.

If we have more than two stages follow the same reasoning as above.


Example. An amplifier has two stages of amplification. The first stage has a gain of 350 and a break frequency of 15 kHz, the second stage has a gain of 85 and a break frequency of 300 kHz. Construct the gain and phase bode plots over the range 1 kHz to 10 MHz.

Overall gain = 350 x 85 = 29750 = 89.47 dB

Scale – gain 0 to 90 dB- phase 0 to -180°- frequency 1 kHz to 10 MHz


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

1000 10000 100000 1000000 10000000

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

Straight line up to 15 kHz at 89.5 dB

Straight line from this point at -20 dB/dec up to 300 kHz

x

Now from this point the line rolls off at -40 dB/dec

x

Gain CurvefC1 fC2

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

1000 10000 100000 1000000 10000000

-180

-160

-140

-120

-100

-80

-60

-40

-20

0Gain CurvefC1 fC2

Now the phase curve

Effect of fC1 Effect of fC2

Line at 0° up to 1/10 fC1

Now a line at -45°/dec up to 1/10 fC2

x

Now a line at -90°/dec up to 10 fC1

x

Now a line at -45°/dec up to 10 fC2

x

Line at -180° above 10 fC2

Phase Curve

The Control of Gain using Negative FeedbackAs we have seen we can create large amplifier gains by

cascading a number of amplifier stages together. A typical gain may be 250.With two stages this rises to 62 500With three stages this rises to 15 625 000 The problem with doing this is that we have little

control over the final gain value also the value is effected by:

variation in components hfe values changes in the supply voltage changes in temperature ageing etc.


To control the gain we adopt a process of sampling the output then feeding it back to the input then subtracting it from the input.

This process is called Negative Feedback.This can be shown in a block diagram below.

A

B

VoutVin

Vf

Va

We can derive a relationship between Vout and Vin.

AVaVout (i)

BVoutVf (ii)

VfVinVa (iii)

By substituting values for Va and Vf from (i) and (ii) into equation (iii) we get

This is the equation for an amplifier with negative feedback NFB.

If A is large then >> 1 and this gives us a gain of:

i.e. independent of A and controlled solely by B.

BVoutVinA

Vout VinBVout

A

Vout

VinA

ABVout

)1(

AB

A

Vin

VoutGain

1

AB ABAB 1

BAB

AGain

1


Let us get back to our Bode example.If the gain of the amplifier is controlled with NFB,

determine the bandwidth of the amplifier if the gain is:a) 70 dBb) 50 dBc) 30 dB


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

1000 10000 100000 1000000 10000000

-180

-160

-140

-120

-100

-80

-60

-40

-20

0Gain CurvefC1 fC2

Phase Curve

Gain Bandwidtha) 70 dB 150 kHzb) 50 dB 700 kHzc) 30 dB 2.1 MHz

Note that as the gain changes so does the phase shift.

What are the phase shifts at these three gains?


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

1000 10000 100000 1000000 10000000

-180

-160

-140

-120

-100

-80

-60

-40

-20

0Gain CurvefC1 fC2

Phase Curve

Gain Bandwidth Phase Shifta) 70 dB 150 kHz -123°b) 50 dB 700 kHz -152°c) 30 dB 2.1 MHz -174°

What we can say is that as the gain is reduced the Bandwidth increases

Also we can say that as the gain is reduced the phase shift (lag) increases.


Problems associated with phase shift and NFB.Consider the amplifier

below with feedback – no phase shift

A

B

VoutVin

Vf

Va


Consider the amplifier below with feedback – 180° phase shift

A

B

VoutVin

Vf

Va


What can be seen is that as the phase shift increases and approaches 180° the negative feedback becomes positive feedback and the gain increases – this leads to instability.

What is the critical value? 135°

Any value above this is unacceptable.

Where does this occur on our plot?


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

1000 10000 100000 1000000 10000000

-180

-160

-140

-120

-100

-80

-60

-40

-20

0Gain CurvefC1 fC2

Phase Curve

-20dB/dec

-40dB/dec

135° occurs at the point when the gain curve changes from -20dB/dec roll-off to -40dB/dec.

Any gain line hitting the -20dB/dec will produce a stable amplifier.

Any gain line hitting the -40dB/dec will produce an unstable amplifier.

We therefore do not normally have to worry about the phase curve when considering the stability of an amplifier.



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

This work is licensed under a Creative Commons Attribution 2.0 License.

The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence. All reproductions must comply with the terms of that licence.

The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.

The name and logo of University of Wales Newport is a trade mark and all rights in it are reserved. The name and logo should not be reproduced without the express authorisation of the University.