T09 OTA_sss.pdf - bSpace

EECS 240 

Analog Integrated Circuits 

Topic 9: 

Operational 

Transconductance Amplifier 

Bernhard E. Boser and Ali M. Niknejad 

Department of Electrical Engineering and Computer Sciences 

EECS 240 Topic 9: OTA 

© 2007 B. Boser & A. Niknejad

Logistics 

•HW2 Due today 

•HW3 posted today (due in two weeks) 

•Next week: Tuesday no class (ISSCC) 

•Midterm on March 15 

•Project assigned around March 15 as well (form groups of 2) 



Operational 

Transconductance Amplifiers 

• OTA versus OpAmp, Applications 

• Differential versus Single-Ended Output 

• Characteristics 

– Frequency response, settling time, stability 

– Open-loop gain 

– Noise, dynamic range 

– PSRR, CMRR 

– Common-mode feedback circuit 

• Topologies 

– Single-stage (telescopic, folded cascode, …) 

– Multi-stage, Miller compensation 

– Class A, A/B 



OpAmp versus OTA 

OpAmp 

OTA 

• Voltage source output 

(low impedance) 

• Essential to drive 

resistive loads 

• Essentially OTA + buffer 

• Buffer increases power 

dissipation, noise 

• Current source output 

(high impedance) 

• Cannot drive resistive 

loads 

• Use capacitive (SC) 

feedback 

• Transistors are 

transconductors 



Resistive Feedback 

OpAmp 

• Gain independent of 

feedback network 

• Feedback network 

adds noise 


OTA 

• Resistive feedback 

network lowers loop gain 

• Large feedback resistors? 

– Large area 

– Parasitic poles stability? 

• Solution: capacitive 

feedback 

– Needs initialization 

– Needs clock 

Linear, time-variant circuit 

• kT/C noise 


OpAmp versus OTA Noise 

Opamp and switch noise add 

OTA contributes no excess noise 

(actual designs can increase noise) 



• Phase 1: 

– sample V i onto C s : 

SC Gain Stage 

ϕ1 

– Q s = V i * C s 

– Null charge on C f 

• Phase 2: 

– Amplifier “moves” 

charge from C s to C f : 

– Q f = Q s = V i * C s 

vi 

ϕ2 

ϕ1 

C f 

ϕ1 

ϕ2 

C i 

vx 

1mS 

C f 

C L 

vo 

– V out = Q f / C f 

= V i * C s / C f 

• Implement switches with MOSFETs. Drive with “2-phase nonoverlapping 

clock”. 

• Gain set by capacitor ratio (precise). Output valid only at end 

of phase 2 and during phase 1. 

• Cannot drive resistive load. 



SC Gain Stage 



SC Gain Stage 



F C L,eff = 

FV 

i 2 gmR E 

on + Ī2 n,R E 

| 

| 2 Noise 

s 

2 

1+gmRg E m,1 =2πC L,eff N log (2) C L,eff 

F 

Phase 1: 

ī 2 1 

on = Ī2 nc | 

| 2 +i 2 gmR E 

¯V C 2 s 

= KT 

on + 

1+gmR Ī2 n,R E 

| 

| 2 

E 1+gmR E 

n F 1 Noise factor of driving amplifier 

C s 

¯V C 2 f 

= KT n F 2 

C f 

¯V Noise 

C 2 s 

= KT factor n F 1 of this amplifier 

T n F 2 

+ KT 

C s 

1 

C f 

Phase C L,eff 

2: F n F 2 

¯V C 2 f 

= KT 

C f 

C f 

F = 

C 

¯V on 2 

f + 

=( C s 

C s C+ ) 

f 

Ci 

2 2 ¯V Cs 

+ KT + KT 1 

C f C L,eff F n F 2 

F = 

C f 

C f + C s + C i 



Common-Source Example 

• Openloop gain, A vo , a vo 

• Output range, ΔV o 

• Bandwidth, f u , f 3dB 

• Noise 

gmroN=23 (L=150nm) 

Rout,P=240K 

CL=2pF 

V*N~140mV 

V*P~280mV 

V*cas,P=140mV 



AC Gain and noise 

Av,dc=27.5dB 

Virn=8nV/rt(Hz) 



Noise Summary 

Cadence: Results-> Print -> Noise Summary.... 

Input diff pair (why 

different?) 

PMOS load 

(V*P/V*N=0.5) 



Gain, Output Range 

Note: plot is for 

V out_o = 0V and 

V in_o = 0V (unrealistic). 



Differential Output 

“Fully differential amplifier” 

• Differential versus 

common-mode signals 

• Balun 

• Common-mode feedback 

CMFB 



Differential Output 

“Fully differential amplifier” 

• Differential versus 

common-mode signals 

• Balun 

• Common-mode feedback 

CMFB 



PSRR & CMRR 

• Any terminal is an input 

• Important “undesired” 

inputs: 

– Supply 

– (Input) common-mode 

• Figure-of-merit: 

– Desired gain over 

undesired gain >> 1 

– E.g. PSRR, CMRR 



PSRR Example 



PSRR 

Fully differential circuit has 

excellent PSRR limited 

only by matching 



ī i on = I nc | | +i on + I n,RE | | 

on = Īnc | 1+gmRE | +i on + Īn,R 1+gmRE 1+gmRE E 

| | 

1+gmRE 

Fully differential noise 

vi 

Feedback factor F 

¯V 

¯V C 2 s 

= KT n F 1 

C 2 s 

= KT n1/F 

F 1 

C C s s 

¯V 

¯V C 2 f 

= KT 

C 2 f 

= KT 

C 

- 

Vop 

CLeff 

+ 

f 

¯V on 2 =( C s 

) 2 2 ¯V 

C 

Cs 

+ KT 

C f 

Von 

+ KT 1 

¯V 2 

f C f C L,eff F n F 2 

on =( C s 

) 2 2 ¯V 

C 

Cs 

+ KT + KT 1 

+ - 

f C f C L,eff F n Von 

F 2 

1/F CLeff 

CLeff 

C f 

C f 

F = F = 

C C f + C s + C i 

f + C s + C i 

¯v out 2 =¯v on 2 +¯v op 2 =2 KT n F 


FC Leff 

Vop 

FC Leff 

CLeff 

Signal Swing: 

V on,0−pk = V dd − V lim,up − V lim,dwn 

2 

V out,0−pk = V dd − V lim,up − V lim,dwn 

(5) 



Fully differential noise 

vi 

- + 

+ - 

Vop 

Von 

CLeff 

CLeff 

on 

C 

C s 

f C f C L,eff ¯V 

F 

C 2 C 

f 

= KT 

f 

C f 

F = 

¯V 

C f + C s + C i 

on 2 =( C s 

) 2 2 ¯V 

C 

Cs 

+ KT + KT 1 

f 

¯v out 2 =¯v on 2 C f 

+¯v op 2 C L,eff 

=2 KT F n n F 2 

F 

F = 

FC C f Leff 

C f + C s + C i 


2X Noise Power! 

FC Leff 

V on,0−pk = V dd − V lim,up − V lim,dwn 

2 

V out,0−pk = V dd − V lim,up − V lim,dwn 

SNRdiff=SNR,se+3dB 

Cost:2x cap, area 

4X Signal Power! 



Differential Input 

• Differential input: 

eliminates systematic offset 

• Tail current source: 

provides CMRR 



Differential Pair – CMRR 



Simulation Result 

For all cases: 

g m = 290 µS 

V * = 180 mV 

A vo = 5.5 



CMRR Analysis 

No tail current source Tail / No Body Effect Tail / With Body Effect 

• Ignoring ΔG m , Δr o 

(use superposition) 

• E.g. 

1/0.01 = 100 = 40dB 

• E.g. 

2 x 1mS * 1MΩ / 0.01 

= 200,000 = 106dB 

• E.g. 

10/0.01 = 1000 = 60dB 



CMRR Summary 

No tail current source With tail current source Well tied to source 

• CMRR limited by 

matching 

• Bias current is a 

strong function of 

input common-mode 

• Impractical in most 

situations 

• CMRR improved by … 

• High frequency CMRR 

limited by 

capacitance at 

common-source node 

(C SB ) 

• Eliminates g mb 

matching constraint 

• CMRR limited by I D 

modulation; cascode 

helps 

• C well sets high 

frequency CMRR 

• C well < C SB in some 

deep sub-micron 

processes (with high 

S/D doping)

T09 OTA_sss.pdf - bSpace

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?