Compensation Methods

Compensation Methods 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
Instructions
Gain Curve
Compensation Methods
Dominant Pole Compensation
Frequency Compensation
Lead Lag Compensation.
Summary
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

For our amplifier we are going to apply negative feedback to reduce the gain to 55dB.
Comment on the amplifiers stability.

Gain Curve f C1 f C2 Phase Curve -40dB/dec

For our amplifier we are going to apply negative feedback to reduce the gain to 55dB.
Comment on the amplifiers stability.
Unstable as it crosses the Gain Curve on the -40dB/dec line.
The amplifier is therefore unsuitable for this application.
Can we do anything about it?

There are three methods which we will examine.
Dominant Pole compensation
Frequency compensation
Lead Lag compensation.

Dominant Pole Compensation
In this method the Manufacturer introduces an artificial break frequency (pole) which causes the gain to drop to 0dB before the first natural one occurs.
f C1 f C2 Unstable Stable New f C Original Curve New Curve gain frequency Desired gain

Try this out on our plot and answer the following questions:
At what frequency does the dominant pole need to be placed?
What is the Bandwidth of the compensated amplifier?

Gain Curve f C1 f C2 Phase Curve x 9.5dB – 5.1kHz 29.5dB – 510Hz 89.5dB – 0.51Hz 15dB – 2.8kHz 35dB – 280Hz 55dB – 28Hz

0.51 Hz 28 Hz Compensation Methods

Notes
This method is stable for all applications.
The user does not need to carry out the compensation exercise.
Bandwidths are limited in size using this method.

Frequency Compensation
This method is similar to the first in that a dominant pole is introduced. This time its position is selected by the user and is positioned so that the gain drops to the desired gain at the point the first natural break frequency occurs.
f C1 f C2 Unstable Stable New f C Original Curve New Curve gain frequency Desired gain Compensation Methods

A table supplied by the amplifier manufacturer allows the user to convert the new pole frequency measured from the plot into a capacitor value which is connected between two pins on the amplifier.

Gain Curve f C1 f C2 Phase Curve x 69.5dB – 3kHz 89.5dB – 300Hz f C1 – 15kHz

300 Hz 15 kHz (f C1 ) Compensation Methods

Notes
The user must compensate each amplifier according to its use.
The Bandwidth, using this method is always at the first break frequency.
Once compensated if the gain is reduced the amplifier will become unstable.

Lead Lag Compensation.
Let us examine the problem we have with our amplifier.
f C1 f C2 Unstable Original Curve gain frequency Desired gain The amplifier would be stable if either f C1 occurred at a lower frequency or f C2 occurred at a higher frequency Compensation Methods

We cannot move the two break frequencies as they are inherent parameters of the amplifier.
BUT
We can make f C1 “look” as though it started at a lower frequency using the circuit below.
Compensation Methods R1 R2 C V IN V OUT

Series combination of R2 and C
Now we can generate an equation for V OUT in terms of V IN

Quantative Analysis At low frequencies ω parts << 1 so the gain = 1 phase will be 0 ° At high frequencies ω parts >> 1 so the gain = R2/(R1 + R2) phase will be 0 ° In between gain must roll off in some way. e.g. R1 = 10k  , R2 = 1k  , C = 10nF Plot over the range 100 Hz to 100 kHz

Frequency Gain Gain dB Phase 100 0.99764 -0.0205249 -1.99651 200 0.990659 -0.0815145 -3.97231 400 0.964149 -0.3171164 -7.78572 700 0.901053 -0.9049962 -12.9442 1000 0.82426 -1.6787185 -17.2528 2000 0.590744 -4.572012 -26.0858 4000 0.350726 -9.1006474 -31.1146 7000 0.221129 -13.107079 -30.3226 10000 0.169115 -15.436358 -27.5696 20000 0.115878 -18.719977 -19.0967 40000 0.097777 -20.195268 -10.903 70000 0.093209 -20.610813 -6.45841 100000 0.092044 -20.720125 -4.5634

Referring to our equation for the network, we will have two break frequencies, one for the top line and one for the bottom.
Break frequency where roll off begins f 1 is given by:
Break frequency where roll off stops f 2 is given by:
Gain after roll-off is given by

x x f 1 f 2 -20dB/dec Compensation Methods

Note
The phase is not a concern as it returns to a low value by the time the gain curve stops reducing.
Let us return to our amplifier.

f C1 f C2 Unstable Original Curve gain frequency Desired gain Introduce a lead lag network which starts before f C1 and stops at f C1 f 1 f 2 Stable f C1 now looks as though it starts at f 1 Compensation Methods

What component values do we need – assume C has a value of 100pF

Firstly f 2 must equal f C1
Secondly what drop in gain is required

Gain Curve f C1 f C2 Phase Curve Required drop in gain = -10dB

Firstly f 2 must equal f C1
Secondly what drop in gain is required
Finally, what is f 1

Gain Curve f C1 f C2 Phase Curve x x f 1 f 2 Bandwidth f C2

What component values do we need – assume C has a value of 100pF
f C2 = 300kHz Compensation Methods 229k  106k  100pF V IN V OUT

Notes
The user must compensate each amplifier according to its use.
The Bandwidth, using this method is always at the second break frequency.
Once compensated if the gain is reduced the amplifier will become unstable.

Summary
No compensation – Unstable
Dominant Pole Compensation – B.W. = 28Hz
Frequency Compensation – B.W. = 15kHz
Lead Lag Compensation - B.W. = 300kHz

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. Compensation Methods

Compensation Methods

by School of Design Engineering Fashion & Technology (DEFT), University of Wales, Newport on Feb 25, 2010

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