#### Transcript Lecture12 - Brown University

```Design and Implementation of VLSI Systems
(EN1600S08)
Lecture12: Logical Effort (1/2)
Prof. Sherief Reda
Division of Engineering, Brown University
Spring 2008
S. Reda EN1600 SP’08
Impact of transistor sizing
What happens to the delay if we increase the transistor sizes by K?
Is it the case that increasing the size of the transistor always reduces
delay?
S. Reda EN1600 SP’08
Impact of sizing in a path
×K
Cout
Less output resistance; increase output capacitance
→ delay reduces (parasitic delay stays the same)
Larger input capacitance
→ increases delay of previous stage!
What is the final outcome? Should we size? By how much?
S. Reda EN1600 SP’08
Impact of gate sizing
2
2
2
2
3
3
3
2
2
3
5C
3
5C
5C
3
9C
3C
3C
If you decide to increase everything by a factor of k
 12 ps in 180 nm process
40 ps in 0.6 mm process
S. Reda EN1600 SP’08
Expressing delay as a linear model
C is the capacitance of unit width transistor
d = R/k(4h’C+ 6kC)
d = RC(4h’/k + 6)
effort
delay
parasitic
delay
Normalize with respect to 3RC (delay of unloaded inverter)
d = 4/3 * h’/k + 2
logical effort
(affected by
gate type or
geometry)
S. Reda EN1600 SP’08
electric
effort
Summary of linear delay model
• g: logical effort = ratio between input
capacitance of the gate to the input
capacitance of the inverter that would
deliver the same current
• h: electric effort = ratio between load
capacitance and the gate input
capacitance (sometimes called fanout)
• p: parasitic delay
• represents delay of gate driving no load
• set by internal parasitic capacitance
S. Reda EN1600 SP’08
Computing logical effort
S. Reda EN1600 SP’08
Computing parasitic delay
S. Reda EN1600 SP’08
Example: Ring oscillator
• Estimate the frequency of an N-stage ring oscillator
Logical Effort:
Electrical Effort:
Parasitic Delay:
Stage Delay:
Frequency:
S. Reda EN1600 SP’08
g=
h=
p=
d=
fosc =
Example: Ring oscillator
• Estimate the frequency of an N-stage ring oscillator
Logical Effort:
Electrical Effort:
Parasitic Delay:
Stage Delay:
Frequency:
S. Reda EN1600 SP’08
31 stage ring oscillator in
g=1
0.6 mm process has
h=1
frequency of ~ 200 MHz
p=1
d=2
fosc = 1/(2*N*d) = 1/4N
Example: FO4 Inverter
• Estimate the delay of a fanout-of-4 (FO4) inverter
d
Logical Effort:
Electrical Effort:
Parasitic Delay:
Stage Delay:
S. Reda EN1600 SP’08
g=
h=
p=
d=
Example: FO4 Inverter
• Estimate the delay of a fanout-of-4 (FO4) inverter
d
Logical Effort:
Electrical Effort:
Parasitic Delay:
Stage Delay:
S. Reda EN1600 SP’08
g=1
h=4
p=1
d=5