The document discusses feedback instability in electronic systems. It defines instability as negative feedback becoming positive feedback, causing the system to be unstable. The author provides equations to check for stability using a Nyquist plot or mathematically. Design considerations to add stability include decreasing gain, adding poles, and using compensating capacitors. The author then presents an original unstable 4-pole filter design and a modified stable design that decreases the gain and adds a pole.

1. Feedback Instability
By:
Loren Schwappach
Prepared for:
Professor Monica Young
CTU – EE415 – Advanced Electronic Design
September 2010
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2. Overview
• Definition of Stability
• Equations
• Design Considerations
• Unstable Design
• Stable Design
• Questions
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3. Instability:
In a negative feedback system, a portion of the output
signal is subtracted from the input signal to produce an
error signal.
However, this error may change as a function of frequency
causing subtraction to result in addition.
Negative feedback becomes positive feedback resulting in
an unstable system.
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4. How to check for stability:
Use a Nyquist frequency plot or verify
mathematically.
How to add stability:
•Decrease gain
•Add pole
•Use compensating capacitor
4

5. Equations for OPAMP filter design.
1
1 1
= = =
1 1 + 1 +
+
1 + = 1 +
1 + 1 1 + 2
2
2 + 2 +
5

6. The Design:
Requirements: Design a 3 stage filter for an audio signal (voice
components (0 to 4kHz), amplification is preferred but not a
requirement.
Design 1:
Four pole filter, using non-inverting Amps for large gain at cutoff
designed as:
1 1
= → = → = 5Ω → = 1.59
2 × × × 2 × × 20 × 1.59
Design #2:
Drop gain to 1, and add pole to stabilize circuit at 0dB. To find new
pole:
−180° = − tan−1 −135 / + tan−1 −135 / + tan−1 −135 /
6

7. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable):
PSpice Schematic - Audio Filter/Amplifer
Designed by Loren K. Schwappach
Designed for Cutoff of 20kHz
Actual Cutoff = 6kHz Vcc
0
Gain-1 5Vdc
Vin 7 uA741
3 V+ 5 Buffer-1
0 + OS2 R3 7 uA741
6 3 V+ 5 Buffer-2
1mVac R1 OUT + OS2 R4 7 uA741
0Vdc 2 1 5 1.59u 6 3 V+ 5 Buffer-3
0 - 4 OS1 C1 OUT + OS2 R5 7 uA741
1 V- 2 1 5 C2 6 3 V+ 5 Gain-4
- 4 OS1 1.59u OUT + OS2 R6 7 uA741
V- 2 1 5 C3 6 3 V+ 5
R2 - 4 OS1 1.59u OUT + OS2
V- 2 1 5 C4 6
0 - 4 OS1 R7 OUT
0 1.59u
50 V- 2 1
0 - 4 OS1
0 V-
1
0
100
R8
Vee
0
-5Vdc
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8. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable):
8

9. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable): Results
9

10. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable): Results
10

11. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable): Results
11

12. Simple 4 pole LP Filter w/ OPAMP buffer’s (unstable): Results
PSpice Schematic - Audio Filter/Amplifier - Stable
Designed by Loren K. Schwappach
Designed for Cutoff of 20kHz
0Vdc
1mVac Actual cutoff 5.689kHz
Vcc
Vin
7
3 5 0
V+
0
7
+ OS2 R9 5Vdc
Amp-1 6 3 5
V+
7
R1 OUT + OS2 R3
2 1 70 1.59u B-4 6 3 5
V+
0
7
- 4 OS1 C5 OUT + OS2 R4
1 5
uA741 V- 2 1 1.59u B-1 6 3 5
V+
7
R2 - 4 OS1 C1 OUT + OS2 R5
5
uA741 V- 2 1 1.59u B-2 6 3 5
V+
7
- 4 OS1 C2 OUT + OS2 R6
1 0 5
uA741 V- 2 1 1.59u B-3 6 3 5
V+
- 4 OS1 C3 OUT + OS2
0 5
uA741 V- 2 1 1.59u Amp-2 6
- 4 OS1 C4 R7 OUT
0 uA741 V- 2 1
0 - 4 OS1
0 1
uA741 V- R8
Vee
0
0 1
-5Vdc
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13. Simple 4 pole LP Filter w/ OPAMP buffer’s (Stable): Results
13

14. Simple 4 pole LP Filter w/ OPAMP buffer’s (stable): Results
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15. Simple 4 pole LP Filter w/ OPAMP buffer’s (stable): Results
15

16. Conclusions:
• After reducing gain to 1, I was still in an unstable
condition forcing me to add another pole.
•By adding another pole I was finally able to stabilize
the design.
• If I was going to push forward with this design, I
would need to either increase the LP cutoff frequency,
recalculate/change the added pole, and add at least
3dB gain.
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17. Questions:
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