Find C wire

Find C self

C self for complex gates

Find Cin and tao

Find gramma

Find delay

Derivation of the relation of the size of the inverter chain

How to find the N for the interter chain

For complex gate, we need to use logical effort

Definition

So we find the delay of complex gate chain by

Simplify with logical effort and definition of path effort

P is Parasitic Delay which is LE * gramma

Common logical gate LE

How to find LE your self

Flow to optimize the delay of logical chain

One example

Find totoal path effort -> use path effort to find LE for LE x FO for each stage

Find intermidiate C for every stage, and use that to find Wn, which is size of each stage

How to get from cap to size ???? use Cin and Cg_bar and size to find the size

Another example

Branch effort

Pseudo-NMOS Logic

We don't want PMOS in our circuit because PMOS is limiting factor of the mobility

so we have a circuit

More examples

When NMOS is OFF， PMOS pull the outputs to VDD

When NMOS is ON, they fight as PMOS and NMOS become a resistor.

And we need to size NMOS and PMOS to deliver correct $V_{ol}$

Derviation of $V_{oL}$

As you can see, we $W_{p}$ increase $V_{oL}$ increase. We find $W_{p}$ based on the designed .

Some example sizing

For the power useage ??

The benefits of Pseudo-NMOS logic and drawbacks

slow rise time

more static power

Dynamic logic

In static circuit, at every point in time, the outputs is connect to either GND or VDD via a lower resistance path.

• Fan-in of N requires 2N devices

Dynamic circuit rely on the temporary storage of singal value on the capacitracne of high impedancce nodes.

• Requires only N+2 transistorr
• Takes a sequence of pre-charge and conditional evalutaion phase to realize logic functions

Dynamic circuit use two step:

• First precharge the output node to 1
• If pull down is one then output to 0, if pull down is off then output 1

But if pull down is on during precharge, short circuit

Solution

Usually connect this with a clock

Dynamic behavior

Gate Parameters are Time Independent

• Output voltage drops is strongly depended on the the input voltage and the available evaluation time.
• Noise needed to correupt the signal has to be larger if the evalution time is short

Dynamic gates require "monotonically rising" inputs during evaluation.

Dynamic gates produce monotonically falling outputs during evaluation while the inputs of the dynamic logic should be monotonically rising because volrtage drops during high and when it 1 -> 0, the voltage level drops and nevre recover

So it is illegal for one dynamic gate to drive another gate

During the transistion, the voltage of Y leaks

Two solution for this:

1. Place inverter
2. One PDN (Pull down), one PUN (Pull up)

Domino gate

The combination of dynamic/static pair is called domino gate

Logical Effor

Zipper Logic

The second solution is called Zipepr logic

Dynamic Logic Problems

• Charge Sharing
• Charge Leakage
• Feed Through
• Noise Sensitivity
• CAN tools does not support them very well

Charge Sharing

output cap charge shared by other node capacitance

charge CA to Vdd - Vthn

corrupt the output logic

worse case, only charged $C_L$ but during eval, $C_L$ and all other node cap are on.

Charge Leakage

Clock Feed-through

A special case of capacitive coupling between the clock input of the pre-charge transistor and the dynamic output node

Power

Energy Instantaneous power I x V

Energy intergation of Power

Average power E/T

Dynamic powerL when gate switches

• Charging and discharging
• short circuit power during switching

Static power

• subthreshold and junction leakages

Main Dynamic Power

To lower the dynamic power

• Reduce the factor
• smaller capacitance
  • smaller trnasistors
  • shorter wires
• Lower V
• lower f

Activity Factor

Probability that output is “zero” in one cycle and will be “one” in the next cycle

Clock gating

Turn off the clock to registers in unused block

save clock activity

eliminates all switching acivity in the block

Capacitance

• Gate capacitance
  • fewer stages of logic
  • smaller gate size
• Wire capacitance
  • Good floorplanning to keep blockes close to each others
  • Drive long wires with inverter of buffer rather than complex gates

Dynamic Power

Run each block at the lowest possible voltage and frequency that meets performance requirements

Voltage domains

• provide separate supplies to different blocks
• level converter required when corssing from low Vdd to high Vdd domains

Dynamic voltage scaling

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Adject Vdd and frequency according to workload

Larger V -> Faster f -> higher power

PDP and EDP ??

Power-Delay-Product

• PDP is the average energy consumed per switching
• Lower power design could simply be a slower design
• For a given structure the PDP may be made arbitrary low by reducing the supply voltage that comes at the expense of performance

Energy-Delay-Product(EDP)

• EDP is the average energy consumed multiplied by the required computation time
• Takes into account that one can trade increased delay for lower energy/operation (e.g. via supply voltage scaling that increases delay, but decreases energy consumption)

Short-Circuit Power

Small load capacitance -> Output fall time substantially smaller than input rise time

Static Power

Sequential ciruits