Analog Electronics - Miunapachepersonal.miun.se/~amiyou/AE/Lecture6.pdf · Electronic Devices, 9th edition Thomas L. Floyd Analog Electronics Lecture 6 Muhammad Amir Yousaf Op amp

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Thomas L. Floyd

Analog Electronics

Lecture 6

Muhammad Amir Yousaf

Op amp Stability Analysis and Op-

amp Circuits



Thomas L. Floyd

Lecture:

Stability analysis and compensation of op-amps

Op-amp Circuits



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Op-amp’s gain is so high that even a slightest input signal

would saturate the output.

Negative feedback is used to control the gain.

A classic form of feedback equation



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Feedback equation:

Loop Gain

The term AolB( or AB for simplicity) is called ‘Loop

Gain’

o The system gain is determined by only feedback factor B.

o Feedback factor is implemented by stable passive components

o Thus in ideal conditions the closed loop gain is predictable and stable

because B is predictable and stable.

When loop gain is higher i.e. AB >> 1



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System output heads to infinity as fast as it can

when 1+ AB approaches to zero.

Or |AB| =1 and ∠AB = 180o

If the output were not energy limited the system

would explode the world.

System is called unstable under these conditions




Thomas L. Floyd

Non-inverting amplifier

Feedback equation for Op-amp feedback systems

Rf

Ri

Vf

Vin

+

–

Feedbackcircuit

Vout

Non-inverting amplifier

fR

iR

iR

AAB



Thomas L. Floyd

Inverting amplifier

Feedback equation for Op-amp feedback systems

–

+

Rf

Vout

Ri

Vin

Replace ZF with Rf and ZG with Ri

Loop Gain for both inverting and non inverting amplifier

circuits are identical, hence the stability analysis is identical.

fR

iR

iR

AAB



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Bode plots of loop gain are key to understanding Stability:

Stability is determined by the loop gain,

when AB = -1 = |1| ∠180o

instability or oscillation occurs

Bode plot analysis of Feedback circuits



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Loop gain plots are key to understanding Stability:

Notice that a one pole can only accumulate 90° phase shift, so when a

transfer function passes through 0 dB with a one pole, it cannot

oscillate.

A two-slope system can accumulate 180° phase shift, therefore a

transfer function with a two or greater poles is capable of oscillation.



Thomas L. Floyd

Op-amp transfer function

The transfer function of even the

simplest operational amplifiers will

have at least two poles.

At some critical frequency, the phase

of the amplifier's output = -180°

compared to the phase of its input

signal.

The amplifier will oscillate if it has a gain of one or more at this critical

frequency.

This is because:

(a) the feedback is implemented through the use of an inverting input that adds

an additional -180° to the output phase making the total phase shift -360°

(b) the gain is sufficient to induce oscillation.



Thomas L. Floyd

Phase Margin = ΦM

Phase margin is a measure of the difference in the

actual phase shift and the theoretical 180° at gain

1 or 0dB crossover point.

Phase Margin, Gain Margin

Gain Margin = AM

The gain margin is a measure of the

difference of actual gain (dB) and 0dB at

the 180° phase crossover point.

For Stable operation of system:

ΦM > 45o or AM > 2 (6dB)



Thomas L. Floyd

The phase margin is very small, 20o

So the system is nearly stable

A designer probably doesn’t want a 20°

phase margin because the system

overshoots and rings badly.

Phase Margin, Gain Margin

Increasing the loop gain to (K+C) shifts

the magnitude plot up. If the pole

locations are kept constant, the phase

margin reduces to zero and the circuit will

oscillate.



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Dominant Pole Compensation (Frequency Compensation)

Gain Compensation

Lead Compensation

Compensation Techniques:



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Dominant Pole Compensation is

implemented by modifying the gain and

phase characteristics of the amplifier's open

loop output or of its feedback network, or

both, in such a way as to avoid the

conditions leading to oscillation.

This is usually done by the internal or

external use of resistance-capacitance

networks.


A pole placed at an appropriate low frequency in the open-loop

response reduces the gain of the amplifier to one (0 dB) for a frequency

at or just below the location of the next highest frequency pole.



Thomas L. Floyd

The lowest frequency pole is called the

dominant pole because it dominates the effect

of all of the higher frequency poles.


Dominant-pole compensation can be

implemented for general purpose operational

amplifiers by adding an integrating capacitance.

The result is a phase margin of ≈ 45°, depending on the proximity of still

higher poles.



Thomas L. Floyd

The closed-loop gain of an op-amp circuit is related to the loop gain. So

the gain can be used to stabilize the circuit.

Gain Compensation

Gain compensation works for both

inverting and non-inverting op-amp

circuits because the loop gain

equation contains the closed-loop

gain parameters in both cases.

As long as the application can stand the higher gain, gain

compensation is the best type of compensation to use.

fR

iR

iR

AAB



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Gain Compensation



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Lead Compensation

It consists of putting a zero in the loop transfer function to cancel out

one of the poles.

The best place to locate the zero is on top

of the second pole, since this cancels the

negative phase shift caused by the second

pole.



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Lead Compensation



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Lecture:


Op-amp Circuits



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Comparators

A comparator is a specialized nonlinear op-amp circuit that

compares two input voltages and produces an output state that

indicates which one is greater.

Comparators are designed to be fast and frequently have other

capabilities to optimize the comparison function.



Thomas L. Floyd

Comparator with Hysteresis

Noise contaminated signal may cause an unstable output.

To avoid this, hysteresis can be used.

Hysteresis is incorporated by adding regenerative (positive) feedback, which

creates two switching points:

The upper trigger point (UTP) and the lower trigger point (LTP).

After one trigger point is crossed, it becomes inactive and the other one

becomes active.

Vin 0 t

VUTP

VLTP

+Vout(max)

–Vout(max)



Thomas L. Floyd

Schmitt Trigger

A comparator with hysteresis is also called a Schmitt trigger. The

trigger points are found by applying the voltage-divider rule:

2UTP ( )

1 2

out max

RV V

R R

and 2LTP ( )

1 2

out max

RV V

R R

What are the trigger points for the circuit

if the maximum output is ±13 V?

2UTP ( )

1 2

10 k+13 V

47 k + 10 kout max

RV V

R R

R1

47 k

–

+

R2

10 k

Vout

Vin

= 2.28 V

By symmetry, the lower trigger point = 2.28 V.



Thomas L. Floyd

Output Bounding

Some applications require a limit to the output of the

comparator (such as a digital circuit). The output can be

limited by using one or two Zener diodes in the feedback

circuit.

The circuit shown here is bounded as a positive value equal to

the zener breakdown voltage.

+VZ

Ri

–

+

Vin

0 V0

–0.7 V



Thomas L. Floyd

Comparator Applications

Simultaneous or flash analog-to-digital

converters use 2n-1 comparators to

convert an analog input to a digital

value for processing. Flash ADCs are a

series of comparators, each with a

slightly different reference voltage.

The priority encoder produces an

output equal to the highest value input.

In IC flash converters, the priority

encoder usually includes a latch that

holds the converter data constant for a

period of time after the conversion.

Vin

(analog)

R

R

R

R

R

R

R

R

VREF

Op-ampcomparators

Binary

output

D2

D1

D0

(7)

Priorityencoder

(6)

(5)

(4)

(3)

(2)

(1)

(0)

Enableinput

+

–

+

–

+

–

+

–

+

–

+

–

+

–



Thomas L. Floyd

Comparator Applications

Over temperature sensing circuit:

o R1 is temperature sensing resistor with a negative temperature

coefficient.

o R2 value is set equal to the resistance of R1 at critical temperature

oAt normal conditions R1 > R2 driving op-amp to low

An over

temperature

sensing circuit

At R1=R2, balance bridge

creates high op-amp output,

energizes relay, activates

alarm.



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Summing Amplifier

A summing amplifier has two or more inputs; normally all inputs have

unity gain. The output is proportional to the negative of the algebraic sum

of the inputs.



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Summing Amplifier

VOUT = (VIN1 + VIN2 + VIN3)

= (+5.0 V 3.5 V + 4.2 V)

–

+

VIN1

VIN2

VIN3

VOUT

R

R

1

3

Rf

R2

What is VOUT if the input voltages are +5.0 V, 3.5 V and +4.2 V and all

resistors = 10 k?

= 5.7 V

10 k

Example



Thomas L. Floyd

Averaging Amplifier

An averaging amplifier is basically a summing amplifier with the gain

set to Rf /R = 1/n (n is the number of inputs). The output is the negative

average of the inputs.

VOUT = ⅓(VIN1 + VIN2 + VIN3)

= ⅓(+5.0 V 3.5 V + 4.2 V)

–

+

VIN1

VIN2

VIN3

VOUT

R

R

1

3

Rf

R2

What is VOUT if the input voltages are +5.0 V, 3.5 V and +4.2 V? Assume

R1 = R2 = R3 = 10 k and Rf = 3.3 k?

= 1.9 V

3.3 k



Thomas L. Floyd

Scaling Adder

A scaling adder has two or more inputs with each input having a different

gain.

It is useful when one input has higher weight than the other.

The output represents the negative scaled sum of the inputs.

Assume you need to sum the inputs from three microphones. The first two

microphones require a gain of 2, but the third microphone requires a gain

of 3. What are the values of the

input R’s if Rf = 10 k?

5.0 k –

+

VIN1

VIN2

VIN3

VOUT

R

R

1

3

Rf

R2

10 k

1 2

1

10 k

2

f

v

RR R

A

3

3

10 k

3

f

v

RR

A

3.3 k



Thomas L. Floyd

Scaling Adder: D/A Converter

An application of a scaling adder is the D/A converter circuit shown

here. The resistors are inversely proportional to the binary column

weights. Because of the precision required of resistors, the method is

useful only for small DACs.

–

+

8R

VOUT

R

20

23

Rf

4R

21

2R

22

+V



Thomas L. Floyd

R/2R Ladder DAC

A more widely used method for D/A conversion is the R/2R ladder. The

gain for D3 is 1. Each successive input has a gain that is half of previous

one. The output represents a weighted sum of all of the inputs (similar to

the scaling adder).

–

+Vout

Inputs

D0 D1 D2 D3

Rf = 2 R

R8

R

R6

R

R4

R

R2

2R

R1

2R

R3

2R

R5

2R

R7

2R

An advantage of the

R/2R ladder is that

only two values of

resistors are required

to implement the

circuit.



Thomas L. Floyd

The Integrator

The ideal integrator is an inverting amplifier

that has a capacitor in the feedback path. The

output voltage is proportional to the negative

integral (running sum) of the input voltage.

–

+

Vin

R

Vout

C

Ideal

Integrator

An op-amp integrator simulates mathematical

integration, a summing process that determines

total area under curve.

Ii

IC



Thomas L. Floyd

The Integrator

Capacitor in the ideal integrator’s feedback is

open to dc.

This implies open loop gain with dc offset.

That would lead to saturation.

The practical integrator overcomes these

issues– the simplest method is to add a

relatively large feedback resistor.

Rf should be large enough

–

+

Vin

R

R

Vout

C

f

Practical

Integrator



Thomas L. Floyd

The Integrator

If a constant level is the input, the current is constant. The capacitor

charges from a constant current and produces a ramp. The slope of the

output is given by the equation:

Example

out in

i

V V

t R C

220 k

–

+

Vin

R

R

Vout

C

f

i

10 k

0.1mF

Sketch the output wave:

Vin

2 V

2 V/ms10 k 0.1 μF

out in

i

V V

t R C

+1.0 V

1.0 V

0 V0.5 1.0 1.5 2.0

t (ms)0.0

Vout

+2.0 V

2.0 V

0 V0.5 1.0 1.5 2.0

t (ms)0.0



Thomas L. Floyd

The Differentiator

The ideal differentiator is an inverting amplifier that has a capacitor in

the input path. The output voltage is proportional to the negative rate of

change of the input voltage.

–

+

C

Vout

Vin

R

An op-amp differentiator simulates

mathematical differentiation, a process to

determine instantaneous rate of change of a

function.

Ideal

Differentiator



Thomas L. Floyd

The Differentiator

Example

The output voltage is given by

–

+

C

Vout

Vin

R

R

R

in

c

f

Cout f

VV R C

t

Sketch the output wave: Vin

+1.0 V

1.0 V

0 V0.5 1.0 1.5 2.0

t (ms)0.0

Vout

220

10 k

0.1mF

10 k

C

1 V10 k 0.1 μF 2 V

0.5 ms

out f

VV R C

t

+2.0 V

2.0 V

0 V0.5 1.0 1.5 2.0

t (ms)0.0



Thomas L. Floyd

References

Slides by ‘Pearson Education’ for Electronic Devices

by Floyd

‘Op.amp for every one’ by Ron Mancini

’Stability Analysis for volatge feedback op-amps’,

Application Notes byTexas Instruments (TI)

’Feedback amplifiers analysis tool’ by TI

‘Feedback, Op Amps and Compensation’ Application

Note 9415 by Intersil

Modified by Muhammad Amir Yousaf

Documents

Analog Electronics - Miunapachepersonal.miun.se/~amiyou/AE/Lecture6.pdf · Electronic Devices, 9th edition Thomas L. Floyd Analog Electronics Lecture 6 Muhammad Amir Yousaf Op amp