1. Circuit Delay Performance Estimation Most digital designs have multiple signal paths and the slowest one of these paths is called the critical path Timing analyzers can be used to determine this path. The critical path needs to be optimized and this can be done at any of the following levels: –Architectural or micro-architectural level –Logic level –Circuit level and –Layout level.

2. Delay Estimation It is ideal to have the ability to estimate circuit delays without going through extensive simulations. Some definitions of importance in delay estimation: –Rise time is the time the wave-form takes to rise from 10% to 90% of its steady state value –Fall time is the time the wave-form takes to fall from 90% of its steady state value to 10% –The average delay or edge rate is (t r + t f )/2 –Propagation delay is the maximum time from the input crossing the 50% to the output crossing the 50%.

3. RC Delay Model Our model will assume minimum device sizes for delay estimation –A minimum sized nMOS has resistance R –Recall that in general the mobility of electrons is twice that of holes. –We have thus designed pMOS devices to have twice the widths of nMOS devices to attain symmetric rise and fall times. –This fact allows us to estimate the resistance of a pMOS to be 2R.

4. Delay Estimation (RC Models) Transistors with increased widths have reduced resistance i.e. increase a minimum width transistor by k the resistance reduces to R/k. A pMOS device of double width therefore has a resistance value of 2R/2 = R. Parallel and series transistors combine just like resistors in parallel and resistors in series.

5. RC Delay Models Multiple transistors in series and all conducting have a higher resistance. Capacitance to be considered is intrinsic i.e. it is internal to the transistor. We assume that the gate capacitance C g is equivalent to the diffusion capacitance C diff of the source or drain. Contacts increase both resistance and capacitance, thus un-contacted nodes have less capacitance.

6. The Elmore Delay Model Transistors that are conducting must be reviewed as resistors. The Elmore delay estimates the delay of an RC ladder as the sum over each node in the ladder resistance R n-i between that node and the source multiplied by C on the node. V DD V in R3R3 R1R1 R2R2 RNRN C2C2 C3C3 C1C1 CNCN

7. AND Gate Intrinsic Capacitance

8. Two Input NAND Gate