analog integrated circuits lecture 8: two-stage...

Analog Integrated Circuits

Lecture 8: Two-Stage Opamp Design

Analog Integrated Circuits

Lecture 8: Two-Stage Opamp Design

ELC 601 – Fall 2013

Dr. Ahmed Nader

Dr. Mohamed M. Aboudina

[email protected]

[email protected]

Department of Electronics and Communications Engineering

Faculty of Engineering – Cairo University

Introduction to two-stage opamps

© Mohamed M. Aboudina, 2011

2

Two-Stage Opamp

• 1st stage DC-gain ~ ��

• 2nd stage DC-gain ~ ��

• Total DC-gain ~ �� (Find

Exact !!)

• Do we need a high-swing first stage? NO

• Why don’t we replace it with a high-gain stage and lower swing ?

• Total DC-gain ~ �� (Find Exact !!)

• High Output Swing

Closed-loop opamp stability


3

Introduction

• What happens if βH(s) = -1 ? OSCILLATIONS or INSTABILITY

– Phase = -180 and Magnitude ≥ 1



4

Single vs Multiple Poles

• Remember:

– The slope of the magnitude changes by +20dB/dec at every zero frequency and by -20 dB/dec at every pole frequency.

– The phase begins to change at one-tenth of the pole (zero) frequency, changes by -45 degrees (+45 degrees) at the pole (zero), and approaches a -90-degree (+90-degree) change at 10 times the pole (zero) frequency.



5

Effect of β

• Changing the feedback factor β

does not change the phase plot.

• From a PM point of view: worst

case comes at β = 1.



6

Phase Margin

• If Gain = 1 when phase = 180 � Oscillations,

• Phase Margin (PM) presents how far we are away from the cross over point ≡ phase @ (0 dB gain) + 180



7

Phase Margin – How much is adequate?

• Frequency Compensation:

– Minimize number of poles.

– Keep one dominant pole.

For a step input, x(t)

Telescopic Opamp Stability


8

Example

• What if the PM is not good enough ?

– Add more CL .

Telescopic Opamp Stability


9

Example

• Design for a 450 phase margin.

• Keep increasing CL to move down the dominant pole � increase PM to reach 450 or more.

Original dominant

pole

New dominant

pole

Two-stage opamp stability

© Ahmed Nader, 2013

10

Pole Locations

• 3 poles:

– �� =�

��

– �� =�

��

– �� =��

��

• How to compensate

it?



11

Compensation – Pole Splitting

• �� = ��!" + �$ 1 + &'� ≅ �$&'�

• �� =�

��)*+�

• �� = ?

– At high frequencies, �$ can be considered a short circuit � Output

resistance ≅�

��(prove !! )

• �� =��

��



12

Compensation – Pole Splitting

• �� =�

��)*+�

• �� =��

��



13

Two-stage opamp compensation – Pole Splitting

• �� =�

��)*+�

• �� =��

��

��

��

&-�

./ ≡ unity-gain freq.



14

Two-stage opamp compensation – Pole Splitting

• �� =�

��)*+�

• �� =��

��

• ./ = 012 =��

�)

��

��

&-�

./ ≡ unity-gain freq.

012 = &-� × ��

= &'�&'� ×1

4�/5��$&'�

=��4�/5�

4�/5��

=��

�$



15

Transfer Function Zeros

• 6�/5 =�

�78

9:�

+�

�78

9:�

=�7;(

�

9:�7

�

9:�)

(�78

9:�)(�7

8

9:�)

=�7

8

9>

(�78

9:�)(�7

8

9:�)

• Multipath creates zeros.

1

1 +?

��

1

1 +?

��

1

1 +?

��

1

1 +?

��

@A�

Σ @�/5

-@A�

_

+



16

Transfer Function Zero

• B�$ = B�� + B��/5 ⇒ @D − @�/5 ?�$ = @D�� +'��

��

• ? = ?F@ @�/5 = 0 ⇒ ?F =��

�)(Right or Left half plane zero?)

• IJKLJ M�KN?.O� .PNQRSTN =*U) ��

8

9>

(�78

9:�).(�7

8

9:�)

• Does this zero increase or reduce the PM? – This zero reduces PM and can cause instability

Cc

@D

RoutB�$

= (@D−@�/5)?�$

B�� = @D��



17

Transfer Function Zero - Solution

• @ @�/5 = 0

– B�$ ='W

�>7�

8X)

– B�$ = B�� ⇒

• Options:

– Option 1: Set F = ∞ ⇒ 4F =�

��

– Option 2: Use F to cancel one of the already existing non-dominant poles to improve PM even further.

Cc

@D

Rout

B�� = @D��

Rz

?F =1

��1

��− 4F

?F =1

��1

��− 4F

Two-stage opamp


18

Recap

• Max. Output Swing = 6-- − 6f-ghfi − 6f-jhfi

• &-� = &'�&'�

• 012 = ./ =��

�)(Assuming Dominant first pole)

• �� =��

��

• F =�

�X�

k��>

Two-stage opamp


19

Noise

• The noise of the second stage can be neglected since it is divided by the gain of the 1st stage when refereed to the input

• The noise performance of 2-stage amplifier is similar to a 1-stage amplifier

Two-stage opamp


20

Slew Rate

SR+ = ISS/CC

SR- = ID3/CC

If I1 < ISS


21

Multi-Stage Opamps

• More stages can be cascaded to get more gain.

• Each stage contributes a pole.

• That requires multi-level compensation (for example Miller) to

result in only 1 dominant pole.

• A buffer stage (for example common-gate) can be added at the end

to reduce the output impedance if needed. (Note that if the

Opmap is used in feedback the output impedance will be already

reduced by the loop gain).

• An Opmp will no output buffer stage is referred as OTA.

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