Delay estimation

Draw a CMOS inverter. Analyze the switching characteristics during rise time when Vin change from high to low. 

Derive an expression for the rise time, fall time and propagation delay of a CMOS inverter. 

Important definitions for delay estimation:

Propagation delay time (tpd):

Propagation delay time is defined as maximum time from the input crossing 50% to the output crossing 50%.

Contamination delay time (tcd):

Contamination delay time is defined as minimum time from the input crossing 50% to the output crossing 50%.

Rise time (tr):

Rise time is defined as time for a waveform to rise from 20% to 80% of its steady-state value

Fall time (tf):

Fall time is defined as time for a waveform to fall from 80% to 20% of its steady-state value.

Edge rate is average of rise and fall time, ( trf) = (tr + tf )/2 Delay estimation.

Delay estimation response curve:

• When an input changes, the output will retain its old value for at least the contamination delay and take on its new value in, at most the propagation delay.
• Delays for the output rising is tpdr /tcdr and the output falling is tpdf /tcdf .
• Rise/fall times are also called as slopes or edge rates.
• Propagation and contamination delay times are also called as max-time and min-time respectively.

Delay estimation of CMOS inverter

•  The gate that charges or discharges a node is called the driver. The gates and wires being driven, are called the load. Propagation delay is usually called as delay.
•  Arrival times and propagation delays are defined separately for rising and falling transitions.
• The delay of a gate may be different from different inputs. Earliest arrival times can also be computed based on contamination delays.
• Expression of delay for rising output is tPLH = 0.69 RP.CL

            Where, RP – effective resistance of pMOS transistor

            CL - load capacitance of CMOS inverter.

• Expression of delay for falling output is tPHL = 0.69 RN.CL

            Where, RN – effective resistance of nMOS transistor

• Propagation delay of CMOS inverter is tP = (tPLH + tPHL) / 2