Download Subcircuits

Subcircuits
Example
subcircuits
Each consists of one or more transistors.
They are not used by themselves.
Subcircuits
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•
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Switches
Diodes/active resistors
Current mirrors
Current sources/current sinks
Current/voltage references
Band gap references
MOS switches
Ideal Switch
MOS transistor as a switch
Non-idealities in a switch
Simple approximation
On operation: VG >> VS or VD, VDS small, triode
A
RON
 iD
 
 vDS
RON
B
1
1

 CoxW

 CoxW

  
(VGS  VT  VDS )   
(VGS  VT ) 
 L

 L


1
Off operation: VGS < VT , cutoff
A
ROff
B
 iD
 
 vDS
1

  

Very good off-char
Observations:
•RON depends on W, L, VG, VT, VDS, etc
•RON is nonlinear (depending on signal)
Want: RON small and constant
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
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: pure
sine wave
VC1: has harmonic
distortions
• 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
=U
slow regime:
L
Hold value error on CL:
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
t1
t2
Constant VGS Bootstrapping
f=0
f=1
VDD
VG=0
VGS~VDD
When f=1:
Cp: total parasitic capacitance connected to top
plate of C3.
on
PMOS
version
off
Concept:
Switched cap
implementation
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 > 0
else i = 0
diode
i
VT
v
Generally, gm ≈ 10 gmbs ≈ 100 gds
If VBS=0,
rout
1
1


g m  g ds g m
Voltage Division
Equating iD1 to iD2 results in:
VDS1 +VDS2 = VDD - VSS
Can use different W/L ratio to achieve
desired voltage division
Use less power than resistive divider
Active vs passive resistors
Suppose Vo=(VDD+VSS)/2
=2
gm1=gm2=bVEB=10*0.2=2 m
Ro=1/4m = 250 ohm
Ro
Io=b/2 *(VEB)2=0.2mA
=0
To achieve the same Ro, need
two 500 ohm resistors.
Io=2/(2*500)=2mA,
Ro
10 times
Consumes 10 times more power
Current sources / sinks
V
Current
source
I
I
Current
sink
I
V
V
Non-ideal current sources / sinks
Two critical figures of merit
How flat the operating portion is
How small the non-operating region is
rout and vmin
For the simple sink on prev slide:
rout
1

I D
vmin  VGS  VT
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:
Sensitivity
A systematic way of computing errors.
y  f ( x1 , x2 ,...)
y  f x1  x1  f x2  x2


 
 
 ...
y  x1 y  x1  x2 y  x2
r=
(VGS  VT 2 )
(VGS  VT 1 ) (1  vDS 2 )
r (W2 L1 W1L 2)
 WL
2
2

2 1
r
VGS  VT 2
VGS  VT 1
1  vDS 2
W1L 2
(1  vDS1 ) (  2Cox 2 ) ( 1Cox1 )



1  vDS1
 2Cox2
1Cox1
Note: common mode errors do not contribute to
matching errors, only differential errors do
Therefore, can take:
VT 2  VT 1  VT / 2
vDS 2  vDS1  vDS / 2
(  2Cox 2 )  ( 1Cox1 )  ( Cox ) / 2
r

r
(W2 L1 W1L2 )
W2 L1
W1L2
vDS ( Cox )
VT
2


VGS  VT 1  vDS
Cox
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.
S
G
G S
G
G S
G
G S
G
G S
G
G S
Will have better matching
But: only approximate common centroid
no pli
can be more compact
HW: suggest a better layout for ratio of 4.
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
HW:
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?
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