lecture6

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Transcript lecture6

Electronic Devices, 9th edition

Thomas L. Floyd

Analog Electronics

Lecture 6 Op amp Stability Analysis and Op amp Circuits Muhammad Amir Yousaf

Lecture:



Stability analysis and compensation of op-amps



Op-amp Circuits

Electronic Devices, 9th edition

Stability analysis and compensation of op-amps

 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

Electronic Devices, 9th edition

Loop Gain



Feedback equation:

The term A ol B( or AB for simplicity) is called

‘Loop Gain’

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

Electronic Devices, 9th edition

Stability analysis and compensation of op-amps

System output heads to infinity as fast as it can when

1+ AB

approaches to zero.

Or |

| =1 and ∠

= 180 o If the output were not energy limited the system would explode the world.

System is called unstable under these conditions

Electronic Devices, 9th edition

Feedback equation for Op-amp feedback systems



Non-inverting amplifier

V in

V f

–

R f V out

Feedback circuit

R i

Non-inverting amplifier

Electronic Devices, 9th edition

Thomas L. Floyd



A R i R i



R f

Feedback equation for Op-amp feedback systems



Inverting amplifier

V in R i

– +

R f V out AB



A R i R i



R f

Replace Z F with R f and Z G with R i

Loop Gain for both inverting and non inverting amplifier circuits are identical, hence the stability analysis is identical.

Electronic Devices, 9th edition

Bode plot analysis of Feedback circuits

Bode plots of loop gain are key to understanding Stability:

Stability is determined by the

loop gain

, when

= -1 = |1| ∠ 180 o instability or oscillation occurs

Electronic Devices, 9th edition

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.

Electronic Devices, 9th edition

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.

Electronic Devices, 9th edition

Phase Margin, Gain Margin

Phase Margin = Φ M

Phase margin is a measure of the difference in the actual phase shift and the theoretical 180° at gain 1 or 0dB crossover point.

Gain Margin = A M

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:

Φ M

> 45 o or

A M

> 2 (6dB)

Electronic Devices, 9th edition

Phase Margin, Gain Margin

The phase margin is very small, 20 o So the system is nearly stable A designer probably doesn’t want a 20° phase margin because the system overshoots and rings badly.

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.

Electronic Devices, 9th edition

Compensation Techniques:

 Dominant Pole Compensation (Frequency Compensation)  Gain Compensation  Lead Compensation

Electronic Devices, 9th edition

Dominant Pole Compensation (Frequency Compensation)

 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.

Electronic Devices, 9th edition

Dominant Pole Compensation (Frequency Compensation)

 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.

Electronic Devices, 9th edition

Gain Compensation

 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.



A R i R i



R f

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.

Electronic Devices, 9th edition

Gain Compensation

Electronic Devices, 9th edition

Lead Compensation

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

Electronic Devices, 9th edition

Thomas L. Floyd 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.

Lead Compensation

Electronic Devices, 9th edition

Lecture:



Stability analysis and compensation of op-amps



Op-amp Circuits

Electronic Devices, 9th edition

Comparators

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.

Electronic Devices, 9th edition

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.

UTP

V in

LTP +

V out

(

max

) –

V out

(

max

)

t Electronic Devices, 9th edition

Schmitt Trigger

A comparator with hysteresis is also called a

Schmitt trigger

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

UTP 

2 

2  

)  and

LTP 

2 

2  

)  What are the trigger points for the circuit if the maximum output is ±13 V?

UTP 

2 

2  

)   10 k  47 k + 10 k   +13 V 

V in

– +

V out R

1 47 k  = 2.28 V By symmetry, the lower trigger point =  2.28 V .

Electronic Devices, 9th edition

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.

V in R i

0 V – + +

Z 0 –0.7 V

Electronic Devices, 9th edition

Comparator Applications

Simultaneous or flash analog-to-digital converters use 2

-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.

V in

(analog)

REF

R R R R

Op-amp comparators + – + – + – + –

+ –

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.

R R

+ – + –

Electronic Devices, 9th edition

Thomas L. Floyd (7) (6) (5) (4) (3) (2) (1) (0) Priority encoder

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 o At normal conditions R1 > R2 driving op-amp to low At R1=R2, balance bridge creates high op-amp output, energizes relay, activates alarm.

An over temperature sensing circuit

Electronic Devices, 9th edition

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.

Electronic Devices, 9th edition

Example

Summing Amplifier

What is

OUT if the input voltages are +5.0 V,  3.5 V and +4.2 V and all resistors = 10 k  ?

OUT =  (

IN1 +

IN2 +

IN3 ) =  (+5.0 V  3.5 V + 4.2 V) =  5.7 V

IN1

IN2

IN3

Electronic Devices, 9th edition

Thomas L. Floyd

R f

– 10 k  +

Averaging Amplifier

averaging amplifier

is basically a summing amplifier with the gain set to

R f

= 1/

(

is the number of inputs). The output is the negative average of the inputs.

What is

OUT

1 =

2 =

3 if the input voltages are +5.0 V,  3.5 V and +4.2 V? Assume = 10 k  and

R f

= 3.3 k  ?

R f R

IN1 3.3 k 

OUT =  ⅓(

IN1 +

IN2 +

IN3 )

IN2

3 –

OUT =  ⅓(+5.0 V  3.5 V + 4.2 V)

IN3 + =  1.9 V

Electronic Devices, 9th edition

Scaling Adder

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

’s if

R f

= 10 k  ?

IN1

R f

10 k 

3 

2  

 

A v f

R A v

1  

  10 k  10 k   3  2   3.3 k 5.0 k  

IN2

IN3

3 – +

OUT

Electronic Devices, 9th edition

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. +

2 0 4

2 1 2

2 2

2 3 – +

R f V

OUT

Electronic Devices, 9th edition

R

/2

R

Ladder DAC

A more widely used method for D/A conversion is the

R/2R ladder

. The gain for

3 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). An advantage of the

ladder is that only two values of resistors are required to implement the circuit.

2 2

R D

1 2

R R

Inputs

3 2

R R

R D

5 2

R R

R D

7 2

R R f

= 2

– +

V out Electronic Devices, 9th edition

The Integrator

An op-amp integrator simulates mathematical integration, a summing process that determines total area under curve. 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.

V in

I i

I C

– + Ideal Integrator

V out Electronic Devices, 9th edition

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. R f should be large enough

V in R R f C

– + Practical Integrator

V out Electronic Devices, 9th edition

Example

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: 

V out



 

V in R C i

Sketch the output wave: +2.0 V

V in

0 V  2.0 V 0.0



V out



+1.0 V 0.5

1.0

1.5

2.0

(ms)  

V in R C i

  10 k  2 V  0.1 μF   2 V/ms

V out

0 V 0.0

 1.0 V 0.5

1.0

1.5

2.0

(ms)

V in R i

10 k  +

R f

220 k 

– 0.1

m F

Electronic Devices, 9th edition

Thomas L. Floyd

V out

The Differentiator

R C

An op-amp differentiator simulates mathematical differentiation, a process to determine instantaneous rate of change of a function.

V in

– +

V out

Ideal 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.

Electronic Devices, 9th edition

Example

The Differentiator

The output voltage is given by

V out

 

R C f

+1.0 V Sketch the output wave:

V in

0 V 0.0

 1.0 V

V out



C 

R C f

0.5

1.0

1.5

2.0

(ms) +2.0 V

V out

0 V  2.0 V 0.0

   1 V 0.5 ms  10 k   0.1 μF   2 V 0.5

1.0

1.5

2.0

(ms)

R f V in

10 k 

R in C

– 220  0.1

m F +

R c

10 k 

Electronic Devices, 9th edition

Thomas L. Floyd

V out

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

Electronic Devices, 9th edition

lecture6

Transcript lecture6

Analog Electronics

Lecture 6 Op amp Stability Analysis and Op amp Circuits Muhammad Amir Yousaf

Lecture:

Stability analysis and compensation of op-amps

Op-amp Circuits

Stability analysis and compensation of op-amps

Loop Gain

Feedback equation:

Stability analysis and compensation of op-amps

Feedback equation for Op-amp feedback systems

Non-inverting amplifier

Feedback equation for Op-amp feedback systems

Inverting amplifier

Bode plot analysis of Feedback circuits

Loop gain

plots are key to understanding Stability:

Op-amp transfer function

Phase Margin, Gain Margin

Phase Margin, Gain Margin

Compensation Techniques:

Dominant Pole Compensation (Frequency Compensation)

Dominant Pole Compensation (Frequency Compensation)

Gain Compensation

Gain Compensation

Lead Compensation

Lead Compensation

Lecture:

Stability analysis and compensation of op-amps

Op-amp Circuits

Comparators

Comparator with Hysteresis

Schmitt Trigger

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.

Comparator Applications

Comparator Applications

Summing Amplifier A

Example

Summing Amplifier

Averaging Amplifier

Scaling Adder

Scaling Adder: D/A Converter

R

/2

R

Ladder DAC

The Integrator

The Integrator

Example

The Integrator

The Differentiator

Example

The Differentiator

References

Directory