SubcircuitsExample

subcircuits

Each consists of one or more transistors.They are not used by themselves.

Subcircuits

• Switches

• Diodes/active resistors

• Current mirrors

• Current sources/current sinks

• Current/voltage references

• Band gap references

MOS switchesIdeal Switch

MOS transistor as a switch

Non-idealities in a switch

Simple approximationOn operation: VG >> VS or VD, VDS small, triode

RONA B

111

)()(

TGSox

DSTGSox

DS

DON VV

L

WCVVV

L

WC

v

iR

Off operation: VGS < VT , cutoff

A B

1

DS

DOff v

iR Very good off-char

Observations:

•RON depends on W, L, VG, VT, VDS, etc

•RON is nonlinear (depending on signal)

Strategies:

•Use large W and small L to reduce RON

•Use large VGS to reduce the effect of signal dependency•Use bootstrapping to increase VGS beyond VDD–VSS

•Use constant VGS

•Use constant VB so as to have fixed VT

Want: RON small and constant

Effects of switch non-idealities• Finite ON Resistance

– Non-zero charging and discharging time– Limit settling– Limits conversion rate

Ideally: instantaneous charging

Actually: takes time

• Signal level dependence of RON

– Different settling behavior at different signal levels

– Introduces nonlinearity– Generate higher order harmonics

Vin: puresine wave

VC1: has harmonicdistortions

• Finite OFF Current– Leakage of a held voltage– Coupling through the switch– Accumulates with time

Clock Feed through

EXAMPLE - Switched Capacitor Integrator (slow clock edge)

Assume:

At t2:

At t3:

Once M2 turns on at t3, all charge on C1 is transferred to C2

Between t3 and t4 additional charge is transferred to C1 from the channel capacitance of M2.

At t4:

Ideal transfer:

Total error:

Charge injection

When switch is turned off suddenly, charges trapped in the channel injected both either D and S side equally.

The amount of trapped charges depends on the slope of VG

=Uslow regime:

Hold value error on CL:

L

In the fast edge regime:

Hold voltage error on CL:

Study the example in the book

Dummy transistor to cancel clock feed through

Complete cancellation is difficult.

Requires a complementary clock.

Use CMOS switches

Advantages -1.) Larger dynamic range.2.) Lower ON resistance.

Disadvantages -1.) Requires complementary clock.2.) Requires more area.

Voltage doubler for gate overdrive

t2t1

Constant VGS Bootstrapping

=0

VDDVG=0

=1

VGS~VDD

When =1:

Cp: total parasitic capacitance connected to top plate of C3.

PMOS version

offon

Concept:

Switched capimplementation

Summary on Switches• To reduce RON

– Use large W and small L– Use CMOS instead of NMOS or PMOS– Use large |VGS|

• To reduce clock feed through– Use cascode– Use dummy transistor

• To reduce charge injection– Use dummy– Use slow clock edge– Use complementary clock on switch and dummy

• To improve linearity– Use large |VGS|– Use vin-independent VGS– Use vin-independent VBS (PMOS switch)

Diodes And Active Resistors

• Simple diode connection

• Voltage divider

• Extending the dynamic range

• Parallel MOSFET resistor– Extending the dynamic range

• Differential resistor– Single MOSFET– Double MOSFET

Diode Connection VDS = VGS Always in saturation

If v > VT, i > 0else i = 0

diode

v

i

VT

Generally, gm ≈ 10 gmbs ≈ 100 gds

If VBS=0,

mdsmout gggr

11

Voltage Division

Equating iD1 to iD2 results in:

VDS1 +VDS2 = VDD - VSS

Can use different W/L ratio to achievedesired voltage division

Use less power than resistive divider

Active vs passive resistors

Ro

Ro

Suppose Vo=(VDD+VSS)/2

gm1=gm2=VEB=10*0.2=2 m

Ro=1/4m = 250 ohm

Io=/2 *(VEB)2=0.2mA

To achieve the same Ro, needtwo 500 ohm resistors.

Io=/(2*500)=2mA, 10 times

=2

=0

Consumes 10 times more power

Current sources / sinks

Current sink

Current sourceI

I

V

V

V

I

Non-ideal current sources / sinks

Two critical figures of meritHow flat the operating portion is

How small the non-operating region is

rout and vmin

For the simple sink on prev slide:

TGS

Dout

VVv

Ir

min

1

Increasing Rout

Cascode Current Sink

Very flat

Too large

Reduction of VMIN

rout ≈ rds1*gm2rds2 is large which is good

But vmin = vT +2VON needs to be reduced

Both just saturating

But the 2 IREFs must be the same. How?

M6 is ¼ the size, it requires 2 times over drive, or 2 times VEB, or 2 time VON

Very flat

VMIN is much smaller

Alternative method

M5 is ¼ the size

Again, the 2 IREFs must be the same.

VON ≈ 0.6V

Larger W/L ratio can significantly reduce VON

Matching Improved by Adding M3

Why is it better now?

Regulated Cascode Current Sink

Near triode, VDS3↓, iout ↓, VGS4 ↓, VD4 or VG5 ↑,Iout ↑.

HW:

As we pointed out, the circuit on the previous page suffers from a large Vmin.

1.Modify the circuit to reduce Vmin without affecting rout.

2.Once you do that, VDS for M1 and M2 are no longer match. Introduce another modification so that the VDSs are matched.

=

Current Mirrors/Current Amplifiers

Simple Current Mirrors

Assuming square law model:

Simplest example

Use of transistor W to control current gains

If Cox and VT matched:

If vDS matched:

Current gain or mirror gain is controlled by geometric ratio, which can be made quite accurate

Sources of Errors • Mismatches in W/L ratios

– Use large W, L– PLI

• Mismatches in Cox

– Large area, common centroid, higher order gradient cancellation

• Mismatches in vDS

– Make vDS the same

• Mismatches in VT

– Large area, cancel gradient, same VBS

effect:

VT mismatch effect:

SensitivityA systematic way of computing errors.

r =

...

,...),(

2

22

21

11

1

21

x

x

y

x

x

f

x

x

y

x

x

f

y

y

xxfy

1

11

22

22

1

1

2

2

1

1

2

2

2

2

1

)()(

1

)1(

1

)1()(2

)(2

)(

1

12

1

12

ox

ox

ox

ox

DS

DS

DS

DS

TGS

TGS

TGS

TGS

LWLW

LWLW

C

C

C

C

v

v

v

v

VV

VV

VV

VV

r

r

Note: common mode errors do not contribute to matching errors, only differential errors do

Therefore, can take:

2/)()()(

2/

2/

1122

12

12

oxoxox

DSDSDS

TTT

CCC

vvv

VVV

ox

ox

DS

DS

TGS

T

LWLW

LWLW

C

C

v

v

VV

V

r

r

)(

12

)(

21

12

21

12

Strategies to reduce errors

• Matching layout– PLI, common centroid, symmetry, gradient,…– Increased area

• Matching operating conditions– VD, VS, VB, current densities, … use cascoding

to fix VDS

• Reduce the sensitivies– Use large VGS-VT

– Make equivalent small, make go small, use cascoding to reduce go

Straightforward layout to achieve mirror ratio of 4:

Matching accuracy not good.

Will have better matchingBut: only approximate common centroid

no plican be more compact

HW: suggest a better layout for ratio of 4.

G G G G G GG G G GS S S S S S

Cascoding

M1 and M2 are the mirror pair that determines io.

VDS1 and VDS2 matched

go is small

Small signal model

Wilson Current Mirror

go is small

VDS1 and VDS2 not matched

Small signal circuit

Computation of rout

Improved Wilson Current Mirror

In the improved Wilson current mirror:

What is rout?

What is Vmin?

The resistance from D2 to GND is 1/gm which is small. Why not connect G2 to a constant bias to increase that impedance?

HW:

SPICE simulation

Regulated Cascode Current Mirror

Same as the regulated cascoded curren sink

VDS2 is very stable with respect to vo, but not insensitive to Ireg change, not necessarily better matching

Implementation of IREG using a simple current mirror

Applications of current mirrors

Common source amplifier: Load for C.S. Amp

Common drain amplifier (source follower)

Differential input single-ended output gain stage