Feedback InstabilityBy:

Loren Schwappach

Prepared for:

Professor Monica Young

CTU – EE415 – Advanced Electronic Design

September 2010

1

Overview

• Definition of Stability

• Equations

• Design Considerations

• Unstable Design

• Stable Design

• Questions

2

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.

3

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

Equations for OPAMP filter design.

𝑉𝑜𝑢𝑡

𝑉𝑖𝑛=

1𝐶𝑠

𝑅 +1𝐶𝑠

=1

1 + 𝑅𝐶𝑠=

1

1 + 𝜏𝑠

1 + 𝐴𝛽 = 1 +𝐾

1 + 𝜏1𝑠 1 + 𝜏2𝑠

𝑠2 + 2𝜁𝜔𝑁𝑠 + 𝜔𝑁2

5

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:

Design #2:Drop gain to 1, and add pole to stabilize circuit at 0dB. To find new pole:

𝑓 =1

2 × 𝜋 × 𝑅 × 𝐶→ 𝑅 =

1

2 × 𝜋 × 20𝑘𝐻𝑧 × 1.59𝑢𝐹→ 𝑅 = 5Ω → 𝐶 = 1.59𝑢𝐹

−180° = − tan−1 𝑓−135/𝑓𝑐𝑢𝑡𝑜𝑓𝑓 + tan−1 𝑓−135/𝑓𝑐𝑢𝑡𝑜𝑓𝑓 + tan−1 𝑓−135/𝑓𝑐𝑢𝑡𝑜𝑓𝑓

6

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

Vin

1mVac

0Vdc

Gain-1

uA741

+3

-2

V+7

V-4

OUT6

OS11

OS25

0

0

Buf f er-1

uA741

+3

-2

V+7

V-4

OUT6

OS11

OS25 Buf f er-2

uA741

+3

-2

V+7

V-4

OUT6

OS11

OS25

R4

5 C21.59u

0

Gain-4

uA741

+3

-2

V+7

V-4

OUT6

OS11

OS25

Buf f er-3

uA741

+3

-2

V+7

V-4

OUT6

OS11

OS25

R5

5 C31.59u

R1

1

0

R6

5 C41.59u

0

R2

50

0

Vee

-5Vdc

R8100

0

Vcc

5Vdc

R7

1

0

PSpice Schematic - Audio Filter/Amplifer

Designed by Loren K. Schwappach

Designed for Cutoff of 20kHz

Actual Cutoff = 6kHz

R3

5C11.59u

0

7

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

8

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

9

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

10

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

11

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

Amp-1

uA741

+3

-2

V+

7

V-4

OUT6

OS11

OS25

R3

5B-1

uA741

+3

-2V

+7

V-4

OUT6

OS11

OS25

C11.59u

R9

70R4

5

B-4

uA741

+3

-2

V+

7

V-4

OUT6

OS11

OS25

C51.59u

B-2

uA741

+3

-2

V+

7

V-4

OUT6

OS11

OS25

C21.59u

0

R5

5B-3

uA741

+3

-2

V+

7

V-4

OUT6

OS11

OS25

C31.59u

R6

5Amp-2

uA741

+3

-2

V+

7

V-4

OUT6

OS11

OS25

C41.59u

R7

1R8

1

0

0

0

0

0

0

0

Vcc

5Vdc

Vee

-5Vdc

0

0Vin

1mVac0Vdc

R2

1

R1

1

PSpice Schematic - Audio Filter/Amplifier - Stable

Designed by Loren K. Schwappach

Designed for Cutoff of 20kHz

Actual cutoff 5.689kHz

12

Simple 4 pole LP Filter w/ OPAMP buffer’s (Stable): Results

13

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

14

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

15

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.

16

Questions:

17