MICROELECTRONICS ELCT 703 (W17) OP-AMP CMOS CIRCUIT DESIGNeee.guc.edu.eg/Courses/Electronics/ELCT703 Microelectronics... · TWO STAGE CMOS OP-AMP The model parameters are derived

MICROELECTRONICS ELCT 703 (W17)

LECTURE 3: OP-AMP CMOS CIRCUIT DESIGN

Dr. Eman Azab

Assistant Professor

Office: C3.315

E-mail:

[email protected]. EMAN AZAB

ELECTRONICS DEPT., FACULTY OF IET

THE GERMAN UNIVERSITY IN CAIRO

1

TWO STAGE CMOS OP-AMP

It consists of two stages:

First stage amplifier is a differentialamplifier: Q1-Q2 with active loadsQ3-Q4 and biasing current sourceQ5- Q8

Second stage amplifier is a CommonSource amplifier Q6 with active loadQ7

DR. EMAN AZAB



2Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.


The two stage CMOS op-amp can be modeled as follows:

Gm1 & Gm2 is the trans-conductance gains of the 1st and 2nd stage respectively

R1 & R2 is the output resistances of the 1st and 2nd stage respectively

C1 & C2 is the parasitic capacitances of the 1st and 2nd stage respectively

Cc is used as a compensation capacitance to control the bandwidth

DR. EMAN AZAB



3Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.


The model parameters are derived at the mid-band (All capacitors areopen circuit)

DR. EMAN AZAB



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𝑉𝑜1 = −𝑔𝑚1,2𝑅1 𝑉1 − 𝑉2

𝑅1 = 𝑟𝑑𝑠2 ∕∕ 𝑟𝑑𝑠4

𝑉𝑜𝑢𝑡 = −𝑔𝑚6𝑅2𝑉𝑜1

𝑅2 = 𝑟𝑑𝑠6 ∕∕ 𝑟𝑑𝑠7

𝐺𝑚1 = 𝑔𝑚1,2

𝐺𝑚2 = 𝑔𝑚6

𝐴𝑉𝑑 = 𝑔𝑚1,2𝑔𝑚6𝑅1𝑅2


Op-amp High frequency gain is given by:

The transfer function is characterized by two poles and one zero

DR. EMAN AZAB



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𝐴𝑉𝑑 𝑠 =𝐺𝑚1𝐺𝑚2𝑅1𝑅2 1 −

𝐶𝑐𝐺𝑚2

𝑠

1 + 𝑠 𝐶𝐶 + 𝐶2 𝑅2 + 𝐶𝐶 + 𝐶1 𝑅1 + 𝐺𝑚𝑅1𝑅2𝐶𝐶 + 𝑠2𝑅1𝑅2 𝐶𝐶𝐶1 + 𝐶𝐶𝐶2 + 𝐶1𝐶2


Op-amp High frequency gain is given by:

CC controls the bandwidth of the op-amp!

DR. EMAN AZAB



6

𝐴𝑉𝑑 𝑠 =𝐴𝑉𝑜 1 −

𝑠𝜔𝑧

1 +𝑠

𝜔𝑝11 +

𝑠𝜔𝑝2

𝐴𝑉𝑜 = 𝐺𝑚1𝐺𝑚2𝑅1𝑅2

𝜔𝑧 =𝐺𝑚2

𝐶𝑐𝜔𝑝1 ≅

1

𝐺𝑚2𝑅1𝑅2𝐶𝑐𝜔𝑝2 ≅

𝐺𝑚2𝐶𝑐𝐶1𝐶2 + 𝐶𝐶 𝐶1 + 𝐶2

≈𝐺𝑚2

𝐶1 + 𝐶2

COMPENSATION THEORY Stability of Closed-loop

Systems

DR. EMAN AZAB



7

CLOSED-LOOP SYSTEMS USING OP-AMPS

Voltage op-amps are used to realize different analog signal processingapplications

Negative feedback concept is used to implement these applications

Example: Inverting amp.

This transfer function is derived under the assumption that the amplifier is ideal (infinitegain and zero input current)

This is a closed loop system formed with op-amp in feed-forward path and resistornetwork (R1 and R2) in the feedback path

DR. EMAN AZAB



8

𝑣𝑂𝑣𝐼

= −𝑅2𝑅1

Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.


Comparing the inverting amplifier with the closed-loop system

DR. EMAN AZAB



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𝑣𝑂𝑣𝐼

= −𝑅2𝑅1

𝐴 =𝑣𝑂𝑣𝐼

=𝑎(𝑠)

1 + 𝑎 𝑠 𝑓

𝑣𝑂𝑣𝐼

≅1

𝑓𝑓𝑜𝑟 𝑎𝑓 ≫ 1

𝑓 = −𝑅1𝑅2 𝐴(𝜔 = 0) =

𝑎(𝜔 = 0)

1 + 𝑎(𝜔 = 0) 𝑓

Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.


Closed-loop system employingnegative feedback must be stablefor proper operation

Thus, the system eqn. roots mustsatisfy the stability condition , Polesare in the left half plane

A critically stable system isrealized when the poles are on thej𝜔 axis

Since the feedback network ispurely passive, the stabilitydepends on the amplifier’sfrequency response “a(s)”

DR. EMAN AZAB



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𝑎𝑓 @𝑢𝑛𝑖𝑡𝑦 𝑔𝑎𝑖𝑛 𝑓𝑟𝑒𝑞.= 1 = 0𝑑𝐵

Phase 𝑎𝑓 @𝑢𝑛𝑖𝑡𝑦 𝑔𝑎𝑖𝑛 𝑓𝑟𝑒𝑞.> 180°


An important frequency is theunity gain freq. 𝝎𝑻The frequency at which the loop gain𝑎 𝑠 = 𝜔𝑇 × 𝑓 = 1 magnitude equalsto one (Zero dB)

Critically stable system condition

Phase margin is an indication forstability

It is calculated as the phase of the loopgain at the unity gain frequency (Criticalstable condition)

DR. EMAN AZAB



11



𝐴 =𝑣𝑂𝑣𝐼

=𝑎(𝑠)

1 + 𝑎 𝑠 𝑓

𝐶𝑟𝑖𝑡𝑐𝑎𝑙𝑙𝑦 𝑠𝑡𝑎𝑏𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 @ 1 + 𝑎 𝑠 = 𝜔𝑇 𝑓 = 0

𝑃ℎ𝑎𝑠𝑒 𝑚𝑎𝑟𝑔𝑖𝑛 = 180° + Phase 𝑎 𝑠 = 𝜔𝑇 𝑓


A standard 60 deg. Phase marginis sufficient to stabilize the loop andreduce the overshoot in the systemtransient response

DR. EMAN AZAB



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𝐴 𝑠 = 𝜔𝑇 =𝑎 𝑠 = 𝜔𝑇

1 + 𝑒−𝑗120°

𝐶𝑟𝑖𝑡𝑐𝑎𝑙𝑙𝑦 𝑠𝑡𝑎𝑏𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 @ 1 + 𝑎 𝑠 = 𝜔𝑇 𝑓 = 0

𝑃ℎ𝑎𝑠𝑒 𝑚𝑎𝑟𝑔𝑖𝑛 = 180° − 120° = 60°

Phase 𝑎 𝑠 = 𝜔𝑇 𝑓 = −120°

𝑎 𝑠 = 𝜔𝑇 × 𝑓 = 1 𝑎 𝑠 = 𝜔𝑇 =1

𝑓

𝐴 𝑠 = 𝜔𝑇 =1

𝑓

COMPENSATION OF CLOSED LOOP AMP.

Assume that a(s) is a three pole amplifier, and f=1

The phase margin is negative for the closed loop

We have to stabilize the loop by adding a dominant pole to the system

DR. EMAN AZAB



13

EX.: COMPENSATION OF OP-AMPS By adding a compensating capacitoracross the second stage, we can controlthe phase margin of the op-amp

Increasing the phase margin stabilizeany closed-loop system realized using theop-amp

We have to select the value of Cc toachieve the desired phase margin

DR. EMAN AZAB



14


𝑠𝜔𝑧

1 +𝑠

𝜔𝑝11 +

𝑠𝜔𝑝2 𝜔𝑧 =

𝐺𝑚2

𝐶𝑐

𝜔𝑝1 ≅1

𝐺𝑚2𝑅1𝑅2𝐶𝑐𝜔𝑝2 ≈

𝐺𝑚2

𝐶1 + 𝐶2

COMPENSATION OF OP-AMPS

The first pole P1 is the dominant pole (verysmall compared to the zero and the secondpole)

P1 introduces 90° phase shift before theunity gain frequency

The phase margin is affected by the secondpole and zero

DR. EMAN AZAB



15


𝑠𝜔𝑧

1 +𝑠

𝜔𝑝11 +

𝑠𝜔𝑝2

≅𝐴𝑉𝑜

1 +𝑠

𝜔𝑝1

≈𝐴𝑉𝑜𝜔𝑝1

𝑠

𝜔𝑧 =𝐺𝑚2

𝐶𝑐𝜔𝑝1 ≅

1

𝐺𝑚2𝑅1𝑅2𝐶𝑐𝜔𝑝2 ≈

𝐺𝑚2

𝐶1 + 𝐶2

𝑢𝑛𝑖𝑡𝑦 𝑔𝑎𝑖𝑛 𝑓𝑟𝑒𝑞.≡ 𝜔𝑇 ≈ 𝐴𝑉𝑜𝜔𝑝1

EXAMPLE

For a two stage voltage Op-amp given in figure, calculate the unity gainfrequency and phase margin?

For stable system the phase margin should be greater than zero

DR. EMAN AZAB



16


𝑠𝜔𝑧

1 +𝑠

𝜔𝑝11 +

𝑠𝜔𝑝2

𝑃ℎ𝑎𝑠𝑒 𝑚𝑎𝑟𝑔𝑖𝑛 = 180° − tan−1𝜔𝑇

𝜔𝑧− tan−1

𝜔𝑇

𝜔𝑝1− tan−1

𝜔𝑇

𝜔𝑝2𝐴𝑉𝑑 𝑗𝜔𝑇 =

𝐴𝑉𝑜 1 +𝜔𝑇𝜔𝑧

2

1 +𝜔𝑇𝜔𝑝1

2

1 +𝜔𝑇𝜔𝑝2

2

= 1


Note: To check the speed of op-amp, the Slew rate iscalculated/measured

Slew rate is the rate of change of the output voltage, when the op-amp is used as a buffer at unit step input

DR. EMAN AZAB



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𝑆𝑅 =𝑑𝑉𝑂𝑑𝑡

𝑉𝑖(𝑡) = 2 𝑉𝑖(𝑠) =2

𝑠

𝐴𝐹𝐵 𝑠 ≈1

1 +𝑠

𝜔𝑝1

𝑉𝑂(𝑠) =2

𝑠×

1

1 +𝑠

𝜔𝑝1

𝑉𝑂(𝑡) = 2 × 1 − 𝑒−𝜔𝑝1𝑡

Figure from Gray/Meyer Copyright © by John Wiley & Sons, Inc.


The higher the 3-dB frequency is the fasterthe output response

However, the high input voltage causes theinput stage to saturate (Q1 off and Q2 on)

Thus all the current of Q5 will flow in CC

DR. EMAN AZAB



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𝑆𝑅 =𝑑𝑉𝑂𝑑𝑡

=𝐼𝐷5𝐶𝑐

𝑉𝑂(𝑡) = 2 × 1 − 𝑒−𝜔𝑝1𝑡

Predicted Response Actual Response

Figure from Gray/Meyer Copyright © by John Wiley & Sons, Inc.

NOTES

We can control the op-amp specs asfollows:

Choosing the transistors’ trans-conductance gaingm controls the gain (Change biasing current ID orAspect ratio W/L)

gm can be used to control poles (consequently itcontrols phase margin, stability and slew rate)

There are different techniquesto change the poles of the op-amp (Check the reference!)

DR. EMAN AZAB



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DESIGN EXAMPLE CMOS Op-amp design

DR. EMAN AZAB



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CMOS DESIGN OF VOLTAGE OP-AMPS

For the two stage op-amp shown inFigure, find the following:

All DC currents as a function of IREF

Expression of the mid-band gain

The maximum and minimum input voltagerange

The maximum and minimum output Voltagerange

Expressions of the poles and zeros

If the zero is 5 times the unity gainfrequency, what is the value of the secondpole to achieve 45° phase margin?

DR. EMAN AZAB



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MICROELECTRONICS ELCT 703 (W17) OP-AMP CMOS CIRCUIT DESIGNeee.guc.edu.eg/Courses/Electronics/ELCT703 Microelectronics... · TWO STAGE CMOS OP-AMP The model parameters are derived