Book Chapter 6: Basic Opamp Design and Compensation · Wide-Swing Current Mirrors Think this...

INF3410 — Fall 2014

Book Chapter 6: Basic Opamp Design andCompensation

contentIntroductionTwo Stage Opamps

CompensationSlew RateSystematic Offset

Advanced Current MirrorsOperational Transconductance Amplifiers

Current Mirror OpampsFolded Cascode Opamp

Fully Differential AmplifiersAdvanced Circuits Essentials Summary

Operational Transconductance AmpsFully Differential OpAmpsAdvanced Current Mirrors

Book Chapter 6: Basic Opamp Design and Compensation 2

ContentIntroductionTwo Stage Opamps







Classic Uses of Opamps

An Operational Amplifier (Opamp) is a high gain voltageamplifier with differential input.Classic applications are:









Two Stage CMOS Opamps

The classic way of getting high gain is a two stagesolution, also providing high output swing (as opposedto e.g. cascode gain stages).

General principle: The compensationcapacitor Ccmp inconjunction withtheoutput resistance of thefirst stage limits thebandwidth, which can behandy to stabilize thecircuit when employed ina feedbackconfiguration.Book Chapter 6: Basic Opamp Design and Compensation 6

Two Stage CMOS Opamp ExampleA simple example:

DC Gain (in afirst, mostlyvalidapproximation):

A = Av1Av2


First Order Approximation of FrequencyResponse

In mid range (only CC

matters) simplified to:

Av1 = −gm1Zout1 (6.5)

≈ −gm1

�

rds2 ‖ rds4 ‖1

sCCAv2

�

(6.5− 6.7)

Av(s) ≈ Av2gm1

sCCAv2=gm1

sCC

ωta <∼

gm1

CC(6.9)

=Ibias

Veff1CC(6.10, strong inv.)

=qIbias

2nkTCC(weak inv.)


Second Order Approximation of FrequencyResponse (1/2)

Second order becomes necessary for analysis close toωta. Without RC:

Av(s) =gm1gm7R1R2

�

1− sCCgm7

�

1+ sa+ s2b(6.15)


Interrupt: Second Order ApproximationDeduction 1

v1(1

R1+ sC1 + sCC) + vingm1 = voutsCC |1

vout(1

R2+ sC2 + sCC) + v1gm7 = v1sCC |2

v1 = vout

1R2

+ sC2 + sCC

sCC − gm7|� 2→ 3



vout

1R2

+ sC2 + sCC

sCC − gm7(

1

R1+ sC1 + sCC) + vingm1 = voutsCC |3→ 1 = 4

vout

sCC −1

R1R2+ s(

C2+CCR1

+C1+CCR2

) + s2(C1 +CC)(C2 +CC)

sCC − gm7

= vingm1 |� 4 = 5

vout

sCC(sCC − gm7)− 1R1R2

− s( C2+CCR1

+C1+CCR2

)− s2(C1 +CC)(C2 +CC)

sCC − gm7

= vingm1 |� 5 = 6



vout− 1R1R2

− s(CCgm7 +C2+CCR1

+C1+CCR2

) + s2�

C2C − (C1 +CC)(C2 +CC)

�

sCC − gm7= vingm1 |� 6 = 7

vout

vin= gm1

sCC − gm7

− 1R1R2

− s(CCgm7 +C2+CCR1

+C1+CCR2

) + s2�

C2C − (C1 +CC)(C2 +CC)

�|� 7 = 8



vout

vin=

R1R2gm1gm7(sCCgm7

− 1)

−1− s(CCgm7R1R2 +R2(C2 +CC) +R1(C1 +CC)) + s2�

R1R2(C2C − (C1 +CC)(C2 +CC))

� |� 7 = 8

z1 = −gm7

CC



z1 = −gm7

CC

with RC

(sCC

gm7− 1) → (

sCC

(1+ sCCRC)gm7− 1)

→ (sCC − gm7 − sgm7CCRC

(1+ sCCRC)gm7)

Nominator:

s(CC − gm7CCRC)− gm7/gm7→ s(CC

1

gm7− RC)− 1


Second Order Approximation of FrequencyResponse (2/2)

|ω1| ≈1

gm7R1R2CC(6.19)

|ω2| ≈gm7

C1 +C2(6.20)

z1 =gm7

CC

The problem with positive zeros is negative phase shift,here dependent on CC: Increasing CC will reduce ωta butalso the frequency at which the phase shift becomes-180o, making a feedback system no more stable.Book Chapter 6: Basic Opamp Design and Compensation 15

Compensation ToolsDominant polecompensation: Moving(only) the dominant pole ofthe open loop gain to alower frequency. (Shiftingωt to a frequency smallerthan the second mostdominant pole)Lead compensation:Introducing a ’right handside’ zero that shifts the-180o phase shift to higherfrequencies.


Lead compensation (1/2)

With RC the zero becomes (without much influencingthe poles!):

z1 =−1

CC

�

1gm7− RC

� (6.43)

RC can now be chosen to eliminate the zero:

RC =1

gm7(6.44)

or to negate the non-dominant pole ω2 (using (6.20)):

RC =1

gm7

�

1+C1 +C2

CC

�

(6.45)Book Chapter 6: Basic Opamp Design and Compensation 17

Lead compensation (2/2)

Or to choose RC even higher to not cancel phase shiftdue to ω2/eq to -180o entirely but to ’delay’ it (create aphase lead), e.g. (dependent on a β in a closed loopapplication):

RC ≈1

1.7βgm1

IN all of the above RC may conveniently beimplemented as transistor Q9 in triode region (this β isthe EKV notation β = μCox

WL ):

RC =1

βVeff9Book Chapter 6: Basic Opamp Design and Compensation 18

Slew Rate Concept

The ’speed’ of an OpAmp output is not only limited bybandwidth but also by the bias current, as the outputcurrent cannot be bigger than the bias current. Thus, abig input step will get the transconductance out of itslinear range and the output current saturates. Thus themaximum output gradient of an OpAmp is called slewrate (SR) in units [V/s].


Slew Rate Illustration

Vstep,max < SRτ̇


Increasing the Slew Rate

The slew rate is dictated by the bias current and thecompensation capacitor:

SR =ID5

CC

However, simply increasing the bias current ordecreasing CC will raise ωta, potentially making thecircuit unstable. Thus, one needs also to increase ω2and/or Veff1 (i.e. reduce (W/L)1) to maintain propercompensation, which the book says are the only waysto design for higher slew rate.


Systematic Offset

Basically the ’zero output’ of stage one has to closelymatch the ’zero input of stage two. (What happensoterwise?) ’Zero input’ of stage two means the currentsin Q6 and Q7 need to be equal. ’Zero output’ from stageone means that Q4 is sinking half the bias current(while Q5 is sourcing the whole bias current). Thus, if forinstance Q5 and Q6 have the same W/L, then Q7 neddsto have twice the W/L of Q4. More generally:

W/L7

W/L4

!= 2

W/L6

W/L5(6.38)









Cascode Current Mirror

The cascode current mirror in chapter3 reduces the output headroom byVout > 2Veff +Vt0 (3.42). The problemis that the sources of the transistorclosest to the output is at Veff +Vt0.There are alternatives that provideequally high output resistance withless loss of headroom/output-swing.


Wide-Swing Current Mirrors

Think this circuit through for thecase where Ibias = Iin. Then thecurrent through all transistors isthe same. For constant current instrong inversion (!) if you scaleW/L by 1/a2, Veff scales with a.

Vs1 = Vg5 − Vgs1 = (Veff (n+ 1) +Vt0)− (Veffn+Vt0) = Veffand thus Vout > (n+ 1)Veff (6.78) for all transistors to besaturated. For instance for n=1 the optimumVout > 2Veff (6.79) is obtained. For Iin < Ibias, theminimum Vout will shrink in absolute terms, but will nolonger be optimal in terms of Veff . For Iin > Ibias theoutput resistance drops dramatically as the transistorsenter the triode region.


Enhanced Output Impedance Current Mirrors(1/2)

Similarly to the cascode currentmirror Vd2 (and thus the currentthrough Q2) is attempted to bekept as constant as possible.While Vg1 is constant and only inthe cascode current mirror, hereit is actively moved tocompensate the influence of Vouton Vd2

So while the a circuit with constant Vg1 would haveRout ≈ gm1rds1rds2 (like a cascode current mirror), thiscircuit has:

Rout ≈ (A+ 1)gm1rds1rds2 (6.82)Book Chapter 6: Basic Opamp Design and Compensation 26

Enhanced Output Impedance Current Mirrors(2/2)

Note:É Vbias needs to be big enough

to keep Q2 in saturation!É Stability of feedback loop

needs to be veryfied!É Parasitic resistance from

drain to bulk may becomethe actual limiting factor!


Enhanced Gain Cascode Gain Stage

The same techniquecan be used toenhance the outputresistance, and thusthe gain of a cascodegain stage. Note: Thecurrent source needsa similarly enhancedoutput resistance!

AV(s) = −gm2

�

Rout ‖ 1sCL

�

(6.83)

Rout(s) = gm1rds1rds2 (1+A(s)) (6.84)Book Chapter 6: Basic Opamp Design and Compensation 28

Enhanced Output Impedance Current MirrorsImplementation

The amplifier is a commonsource gain stage. Note:Again the output swing isquite limited byVout > Veff3 +Vtn+Veff1 (oneway of looking at this is thatthe amp’s Vbias = Veff3 +Vtn)

rout(s) ≈ gm1rds1rds2(gm3rds3

2) (6.93)


Wide Swing AND enhanced impedance


Space and Power Conserving Variant

Quite equivalent withworse currentmatching but lesspower and layoutspace consumption.More modular withsplitting Q2 andpresumably betterstability.









Operational Transconductance Amplifiers

These are operational amplifiers with high outputimpedance, limited in bandwith by the output load (andnot in internal nodes that are low impedance nodes).Thus, mainly suited for capacitive output loads only!


Basic Concept

A simple conceptboosting the outputcurrent resulting ingood bandwidth andgood slew rateassuming CL isdominant.

AV(s) =Kgm1rout1+sroutCL

(6.119)

ωta ≈ Kgm1CL

= 2KID1CLVeff1

(6.121)

SR = KIbCL

(6.124)Book Chapter 6: Basic Opamp Design and Compensation 34

Basic ConceptIgnore Q12 and Q13 foran initial analysis.Think of it as anextension of adifferential pair: thecascodes simplyincrease the outputresistance of thedifferential outputcurrent ⇒ highervoltage gain given thesametransconductance.









Interrupt: Common Mode Rejection Ratio

On the white board...


Basic TransAmp with Diff Output


Small Signal Considerations


Fully Differential Current Mirror Opamp


Dual Single Ended Structure

Actively pulling the output up and down. (Class ABamplifier as opposed to class A). Better symmetricalslew rate. CMFB needed!


Partially Dual Single Ended Structure

Actively pulling theoutput up and down.Also better(symmetrical) slewrate, but maybeworse bandwith (dueto more capacitancein current mirrors).CMFB needed!


Wide Input Fully Differential Cascode OpAmp

A problem with lowsupply voltage isthe minimumrequirement for thecommon modevoltage.Complementaryinput pairs help.


Two Stage Differential OpAmp

Another challenge with low supply voltage is the outputswing. Common source output stages do comparativelywell: just one Veff away from the rails.


Common Mode Feedback Principle

Carefull: A feedback loop that needs to be stable!Book Chapter 6: Basic Opamp Design and Compensation 45

Continuous Common Mode Feedback Variant1



Saturation of thediff-pairs is a problemas the outputs swingmuch wider as theinput ⇒ reduce gain.




Switched Cap Common Mode Feedback









DiffPair

At the core of almost all differential CMOS amplifiers isthe diff-pair. The diff-pair invariably translates adifferential input voltage into a differential outputcurrent around a small signal operating point.(Interestingly this is true for any large signal monotonicfunction of ID(VGS)...) From here on it is best to think incurrents for a while rather than voltages.

g vm +x

vx

g vm -xrdsrds

i+ i-


Differential Current Source

With complementary inputs (v+x = −v−x), vx will beclamped to 0V, simplifying things considerably: twosmall signal current sources with a paralleloutput-resistance (common source gain stages, in fact).The simplification holds even for the large signal modelwhere the output current is limited by [0, IB] and the DCVx± is the average of both inputs. The large signalmodel is a sinking(!) current source for an nFET pair: sopractically you can only connect anything at the topterminal.

g vm +x g vm -xrdsrds

i+ i-


Differential Transconductance Amplifier

Using a current mirror you can turnone of your large signal sinking currentsources into a sourcing current source.Thus, you can connect the two outputcurrents in a single node therebysubtracting them: you get a singleended current output if you connect itto a low (input) impedance node.

g vm +x

g vm -x

rds

rds

i+

i-

iout


Differential Operational TransconductanceAmplifier (1/2)

Or you get a single ended voltageoutput if you connect it to a high(input) impedance node.

g vm +x

g vm -x

rds

rds

voutCL


Differential Operational TransconductanceAmplifier (2/2)

Rearranging the circuit yields avery simple small signal (DC)model. If the output is connectedto a significant capacitive load,this model is even good enoughfor AC.

g (v - v )m +x

rdsrds

vout

-x

CL


Folded Casode OpAmp

The only difference from a smallsignal perspective of the foldedcascode opamp is an increasedoutput resistance. Simply see thecascode gain stage in chapter 3if you want to understand howthis is achieved starting from twoDifferential Current Sources, ormore precisely from twodifferntial common source gainstages.

g (v - v )m +x

g r rds

vout

-x

dsm g r rds dsm CL


Current Mirror OpAmp

And the current mirror opampsimply increases thetransconductance Kg (v - v )m +x

rdsrds

vout

-x

CL


Fully Differential OpAmps

Fully Differential Opamps are in a way simpler, as onecan go back to only considering the diff-pair smallsignal model with complementary inputs. The tricky bitis the large signal point of operation, as one needs toprovide exactly matched current sources of Ib

2 for eachbranch of the diff pair to ensure zero output for zeroinput. Thus, the common mode feedback circuits.

g vm +x g vm -xrdsrds

i+ i-


Cascode Principle

This whole section deals (again) withthe marvels of a cascode transistorthat hugely enhances a commonsource stage output resistance,bringing it closer to a ideal currentsource. It basically adds a seriesresistance of gmrds:

g vm in

rds

vx

g (-v )m

rds

iout

x


Advanced Current Mirrors

The rest of this section in the book introduces variousways to a) deduce an optimal Vbias to maximize theoutput swing and b) to make Vbias dynamic to increasethe output resistance even more. The basic principle ofb) is illustrated in:

Cadence demonstrationslive ...


Date post:	19-Mar-2020
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

Book Chapter 6: Basic Opamp Design and Compensation · Wide-Swing Current Mirrors Think this...

Documents