Compensation Methods Electronic Engineering. The following presentation is a part of the level 5...
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Transcript of Compensation Methods Electronic Engineering. The following presentation is a part of the level 5...
CompensationMethods
Electronic Engineering
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
Compensation Methods
For our amplifier we are going to apply negative feedback to reduce the gain to 55dB.
Comment on the amplifiers stability.
Compensation Methods
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1000 10000 100000 1000000 10000000
-180
-160
-140
-120
-100
-80
-60
-40
-20
0Gain CurvefC1 fC2
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?
Compensation Methods
Compensation Methods
There are three methods which we will examine.
1. Dominant Pole compensation
2. Frequency compensation
3. Lead Lag compensation.
Compensation Methods
Dominant Pole CompensationIn this method the Manufacturer introduces an
artificial break frequency (pole) which causes the gain to drop to 0dB before the first natural one occurs.
fC1
fC2
Unstable
Stable
New fC 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?
Compensation Methods
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1000 10000 100000 1000000 10000000
-180
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-140
-120
-100
-80
-60
-40
-20
0Gain CurvefC1 fC2
Phase Curve
x 9.5dB – 5.1kHz
29.5dB – 510Hz
89.5dB – 0.51Hz
15dB – 2.8kHz
35dB – 280Hz
55dB – 28Hz
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?
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.
Compensation Methods
Frequency CompensationThis 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.
fC1
fC2
Unstable
Stable
New fC 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.
Compensation Methods
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?
Compensation Methods
0
5
10
15
20
25
30
35
40
45
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55
60
65
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75
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1000 10000 100000 1000000 10000000
-180
-160
-140
-120
-100
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-60
-40
-20
0Gain CurvefC1 fC2
Phase Curve
x
69.5dB – 3kHz
89.5dB – 300Hz
fC1 – 15kHz
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?
300 Hz
15 kHz (fC1)
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.
Compensation Methods
Lead Lag Compensation.Let us examine the problem we have with our amplifier.
fC1
fC2
Unstable
Original Curvegain
frequency
Desired gain
The amplifier would be stable if either fC1 occurred at a lower frequency or fC2 occurred at a higher frequency Compensation Methods
We cannot move the two break frequencies as they are inherent parameters of the amplifier.
BUTWe can make fC1 “look” as though it started at a
lower frequency using the circuit below.
R1 R
2
C
VIN VOUT
Compensation Methods
Series combination of R2 and C
Now we can generate an equation for VOUT in terms of VIN
Cj
CRjRCj
2121
)( 211
21
121
21
121
21
RRCj
CRjV
CRjCRj
CRjV
RCjCRjCjCRj
VV NIININOUT
)( 211
21
RRCj
CRjGain
Compensation Methods
)( 211
21
RRCj
CRjGain
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
222
22
211
2122121
)(
)()(
RRC
RRRCRRCjCRjGain
)( 211
21
RRCj
CRjGain
222222
22
211
1
211
2121
)()(
)(
RRC
CRj
RRC
RRRCGain
222
2222
211
12121
)(
)(
RRC
CRRRRCGain
)( 2121
122
1
RRRC
CRTanPhase
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
Lead Lag Network
-25
-20
-15
-10
-5
0
100 1000 10000 100000
Frequency
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Compensation Methods
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 f1 is given by:
Break frequency where roll off stops f2 is given by:
Gain after roll-off is given by
)( 211
21
RRCj
CRjGain
kHzRRC
451212
1.
)(
kHzCR
91522
1.
dBRR
R83200910
21
2..
Compensation Methods
Lead Lag Network
-25
-20
-15
-10
-5
0
100 1000 10000 100000
Frequency
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0x
x
f1
f2
-20dB/dec
Compensation Methods
NoteThe 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.
Compensation Methods
fC1
fC2
Unstable
Original Curvegain
frequency
Desired gain
Introduce a lead lag network which starts before fC1 and stops at fC1
f1
f2
Stable
fC1 now looks as though it starts at f1
Compensation Methods
Try this out on our plot and answer the following questions:
What component values do we need – assume C has a value of 100pF
What is the Bandwidth of the compensated amplifier?
Compensation Methods
Firstly f2 must equal fC1
Secondly what drop in gain is required
kHzCR
1522
1
k
pFkR 106
100152
12
Compensation Methods
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1000 10000 100000 1000000 10000000
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-40
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0Gain CurvefC1 fC2
Phase Curve
Required drop in gain = -10dB
Firstly f2 must equal fC1
Secondly what drop in gain is required
Finally, what is f1
kHzCR
1522
1
k
pFkR 106
100152
12
21
2316010
RR
RdB
. kR
RR 2292
3160
21
.
kHzkkpFRRC
7542291061002
1
212
1.
)()(
Compensation Methods
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1000 10000 100000 1000000 10000000
-180
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-120
-100
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-60
-40
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0Gain CurvefC1 fC2
Phase Curve
x
xf1
f2
Bandwidth fC2
Try this out on our plot and answer the following questions:
What component values do we need – assume C has a value of 100pF
What is the Bandwidth of the compensated amplifier?
229k 106k
100pF
VIN VOUT
fC2 = 300kHz
Compensation Methods
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.
Compensation Methods
Summary
No compensation – Unstable
Dominant Pole Compensation – B.W. = 28Hz
Frequency Compensation – B.W. = 15kHz
Lead Lag Compensation - B.W. = 300kHz
Compensation Methods