Lecture 5: DC & Transient Response
Download
Report
Transcript Lecture 5: DC & Transient Response
Lecture 5:
DC &
Transient
Response
Outline
Pass Transistors
DC Response
Logic Levels and Noise Margins
Transient Response
RC Delay Models
Delay Estimation
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
2
Pass Transistors
We have assumed source is grounded
What if source > 0?
VDD
– e.g. pass transistor passing VDD
VDD
Vg = VDD
– If Vs > VDD-Vt, Vgs < Vt
– Hence transistor would turn itself off
nMOS pass transistors pull no higher than VDD-Vtn
– Called a degraded “1”
– Approach degraded value slowly (low Ids)
pMOS pass transistors pull no lower than Vtp
Transmission gates are needed to pass both 0 and 1
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
3
Pass Transistor Ckts
VDD
VDD
VDD
VDD
VDD
VDD
Vs = VDD-Vtn
VDD-Vtn VDD-Vtn
VDD
VDD-Vtn
VDD-Vtn
Vs = |Vtp|
VDD
VDD-2Vtn
VSS
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
4
DC Response
DC Response: Vout vs. Vin for a gate
Ex: Inverter
– When Vin = 0
->
Vout = VDD
– When Vin = VDD
->
Vout = 0
VDD
– In between, Vout depends on
Idsp
transistor size and current
Vin
Vout
– By KCL, must settle such that
Idsn
Idsn = |Idsp|
– We could solve equations
– But graphical solution gives more insight
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
5
Transistor Operation
Current depends on region of transistor behavior
For what Vin and Vout are nMOS and pMOS in
– Cutoff?
– Linear?
– Saturation?
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
6
nMOS Operation
Cutoff
Vgsn < Vtn
Vin < Vtn
Linear
Vgsn > Vtn
Vin > Vtn
Vdsn < Vgsn – Vtn
Vout < Vin - Vtn
Saturated
Vgsn > Vtn
Vin > Vtn
Vdsn > Vgsn – Vtn
Vout > Vin - Vtn
VDD
Vgsn = Vin
Vdsn = Vout
5: DC and Transient Response
Vin
Idsp
Vout
Idsn
CMOS VLSI Design 4th Ed.
7
pMOS Operation
Cutoff
Vgsp > Vtp
Vin > VDD + Vtp
Linear
Vgsp < Vtp
Vin < VDD + Vtp
Vdsp > Vgsp – Vtp
Vout > Vin - Vtp
Saturated
Vgsp < Vtp
Vin < VDD + Vtp
Vdsp < Vgsp – Vtp
Vout < Vin - Vtp
VDD
Vgsp = Vin - VDD
Vdsp = Vout - VDD
5: DC and Transient Response
Vtp < 0
Vin
Idsp
Vout
Idsn
CMOS VLSI Design 4th Ed.
8
I-V Characteristics
Make pMOS is wider than nMOS such that bn = bp
Vgsn5
Idsn
Vgsn4
Vgsn3
Vgsn2
Vgsn1
-Vdsp
Vgsp1
Vgsp2
-VDD
0
VDD
Vdsn
Vgsp3
Vgsp4
-Idsp
Vgsp5
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
9
Current vs. Vout, Vin
Idsn, |Idsp|
Vin0
Vin5
Vin1
Vin4
Vin2
Vin3
Vin3
Vin4
Vin2
Vin1
Vout
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
VDD
10
Load Line Analysis
For a given Vin:
– Plot Idsn, Idsp vs. Vout
– Vout must be where |currents| are equal in
Idsn, |Idsp|
Vin0
Vin5
Vin1
Vin4
Vin2
Vin3
Vin3
Vin4
Vin2
Vin1
Vout
5: DC and Transient Response
VDD
Vin
Idsp
Vout
Idsn
VDD
CMOS VLSI Design 4th Ed.
11
Load Line Analysis
Vin = 0V
0.4V
0.6V
0.8V
.2V
DD DD
DD
|
Idsn
dsn, |Idsp
dsp
Vin0
Vin5
in5
Vin1
Vin4
Vin2
Vin3
Vin3
Vin4
Vin2
Vin1
in0
Vout
out
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
VDD
DD
12
DC Transfer Curve
Transcribe points onto Vin vs. Vout plot
Vin0
Vin5
Vin1
Vin4
Vin2
Vin3
Vin3
Vin4
Vin2
Vin1
Vout
5: DC and Transient Response
VDD
Vin0
Vin1
Vin2
B
A
Vout
C
Vin3
D
0
VDD
Vtn
VDD/2
Vin4
E
VDD+Vtp
Vin5
VDD
Vin
CMOS VLSI Design 4th Ed.
13
Operating Regions
Revisit transistor operating regions
VDD
Vin
Region
nMOS
pMOS
A
Cutoff
Linear
B
Saturation
Linear
C
Saturation
Saturation
D
Linear
Saturation
E
Linear
Cutoff
Vout
VDD
A
B
Vout
C
D
0
Vtn
VDD/2
E
VDD+Vtp
VDD
Vin
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
14
Beta Ratio
If bp / bn 1, switching point will move from VDD/2
Called skewed gate
Other gates: collapse into equivalent inverter
VDD
bp
10
bn
Vout
2
1
0.5
bp
0.1
bn
0
Vin
5: DC and Transient Response
VDD
CMOS VLSI Design 4th Ed.
15
Noise Margins
How much noise can a gate input see before it does
not recognize the input?
Output Characteristics
Logical High
Output Range
VDD
Input Characteristics
Logical High
Input Range
VOH
NMH
VIH
VIL
Indeterminate
Region
NML
Logical Low
Output Range
VOL
Logical Low
Input Range
GND
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
16
Logic Levels
To maximize noise margins, select logic levels at
– unity gain point of DC transfer characteristic
Vout
Unity Gain Points
Slope = -1
VDD
VOH
b p/b n > 1
Vin
VOL
Vout
Vin
0
Vtn
5: DC and Transient Response
VIL VIH VDD- VDD
|Vtp|
CMOS VLSI Design 4th Ed.
17
Transient Response
DC analysis tells us Vout if Vin is constant
Transient analysis tells us Vout(t) if Vin(t) changes
– Requires solving differential equations
Input is usually considered to be a step or ramp
– From 0 to VDD or vice versa
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
18
Inverter Step Response
Ex: find step response of inverter driving load cap
Vin (t ) u (t t0 )VDD
Vin(t)
Vout (t t0 ) VDD
Vout(t)
Cload
dVout (t )
I dsn (t )
dt
Cload
0
2
b
I dsn (t )
V
V
DD
t
2
b VDD Vt Vout (t )
2
5: DC and Transient Response
Idsn(t)
Vin(t)
t t0
Vout VDD Vt
V (t ) V V V
out
out
DD
t
CMOS VLSI Design 4th Ed.
Vout(t)
t0
t
19
Delay Definitions
tpdr: rising propagation delay
– From input to rising output
crossing VDD/2
tpdf: falling propagation delay
– From input to falling output
crossing VDD/2
tpd: average propagation delay
– tpd = (tpdr + tpdf)/2
tr: rise time
– From output crossing 0.2
VDD to 0.8 VDD
tf: fall time
– From output crossing 0.8
VDD to 0.2 VDD
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
20
Delay Definitions
tcdr: rising contamination delay
– From input to rising output crossing VDD/2
tcdf: falling contamination delay
– From input to falling output crossing VDD/2
tcd: average contamination delay
– tpd = (tcdr + tcdf)/2
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
21
Simulated Inverter Delay
Solving differential equations by hand is too hard
SPICE simulator solves the equations numerically
– Uses more accurate I-V models too!
But simulations take time to write, may hide insight
2.0
1.5
1.0
(V)
Vin
tpdf = 66ps
tpdr = 83ps
Vout
0.5
0.0
0.0
200p
400p
600p
800p
1n
t(s)
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
22
Delay Estimation
We would like to be able to easily estimate delay
– Not as accurate as simulation
– But easier to ask “What if?”
The step response usually looks like a 1st order RC
response with a decaying exponential.
Use RC delay models to estimate delay
– C = total capacitance on output node
– Use effective resistance R
– So that tpd = RC
Characterize transistors by finding their effective R
– Depends on average current as gate switches
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
23
Effective Resistance
Shockley models have limited value
– Not accurate enough for modern transistors
– Too complicated for much hand analysis
Simplification: treat transistor as resistor
– Replace Ids(Vds, Vgs) with effective resistance R
• Ids = Vds/R
– R averaged across switching of digital gate
Too inaccurate to predict current at any given time
– But good enough to predict RC delay
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
24
RC Delay Model
Use equivalent circuits for MOS transistors
– Ideal switch + capacitance and ON resistance
– Unit nMOS has resistance R, capacitance C
– Unit pMOS has resistance 2R, capacitance C
Capacitance proportional to width
Resistance inversely proportional to width
d
g
d
k
s
s
kC
R/k
kC
2R/k
g
g
kC
kC
d
k
s
s
5: DC and Transient Response
kC
g
kC
d
CMOS VLSI Design 4th Ed.
25
RC Values
Capacitance
– C = Cg = Cs = Cd = 2 fF/mm of gate width in 0.6 mm
– Gradually decline to 1 fF/mm in 65 nm
Resistance
– R 10 KW•mm in 0.6 mm process
– Improves with shorter channel lengths
– 1.25 KW•mm in 65 nm process
Unit transistors
– May refer to minimum contacted device (4/2 l)
– Or maybe 1 mm wide device
– Doesn’t matter as long as you are consistent
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
26
Inverter Delay Estimate
Estimate the delay of a fanout-of-1 inverter
2C
R
A
2 Y
2
1
1
2C
2C
2C
2C
Y
R
C
R
C
C
C
C
d = 6RC
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
27
Delay Model Comparison
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
28
Example: 3-input NAND
Sketch a 3-input NAND with transistor widths chosen to
achieve effective rise and fall resistances equal to a unit
inverter (R).
2
2
2
3
3
3
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
29
3-input NAND Caps
Annotate the 3-input NAND gate with gate and diffusion
capacitance.
2C
2C
2
2C
5C
2C
2
2C
2
2C
3C
5C
3C
5C
3C
5: DC and Transient Response
2C
2C
2C
3
3
3
CMOS VLSI Design 4th Ed.
9C
3C
3C
3C
3C
30
Elmore Delay
ON transistors look like resistors
Pullup or pulldown network modeled as RC ladder
Elmore delay of RC ladder
t pd
Ri to sourceCi
nodes i
R1C1 R1 R2 C2 ... R1 R2 ... RN C N
R1
R2
R3
C1
C2
5: DC and Transient Response
RN
C3
CMOS VLSI Design 4th Ed.
CN
31
Example: 3-input NAND
Estimate worst-case rising and falling delay of 3-input NAND
driving h identical gates.
2
2
2
Y
3
9C
5hC
n2
3C
3 n1
h copies
3
t pdr 9 5h RC
5: DC and Transient Response
3C
t pdf 3C R3 3C R3 R3 9 5h C R3 R3 R3
12 5h RC
CMOS VLSI Design 4th Ed.
32
Delay Components
Delay has two parts
– Parasitic delay
• 9 or 12 RC
• Independent of load
– Effort delay
• 5h RC
• Proportional to load capacitance
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
33
Contamination Delay
Best-case (contamination) delay can be substantially less than
propagation delay.
Ex: If all three inputs fall simultaneously
2
2
2
Y
3
9C
5hC
n2
3C
3 n1
3
3C
tcdr
5: DC and Transient Response
5
R
9 5h C 3 h RC
3
3
CMOS VLSI Design 4th Ed.
34
Diffusion Capacitance
We assumed contacted diffusion on every s / d.
Good layout minimizes diffusion area
Ex: NAND3 layout shares one diffusion contact
– Reduces output capacitance by 2C
– Merged uncontacted diffusion might help too
2C
2C
Shared
Contacted
Diffusion
Isolated
Contacted
Diffusion
Merged
Uncontacted
Diffusion
2
2
2
3
3
3C 3C 3C
5: DC and Transient Response
CMOS VLSI Design 4th Ed.
3
7C
3C
3C
35
Layout Comparison
Which layout is better?
VDD
A
VDD
B
Y
GND
5: DC and Transient Response
A
B
Y
GND
CMOS VLSI Design 4th Ed.
36