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Published byJavier Lease Modified over 5 years ago

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**Topics Electrical properties of static combinational gates:**

transfer characteristics; delay; power. Effects of parasitics on gate. Driving large loads.

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**Logic levels Solid logic 0/1 defined by VSS/VDD.**

Inner bounds of logic values VL/VH are not directly determined by circuit properties, as in some other logic families. VDD logic 1 VH unknown VL logic 0 VSS

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Logic level matching Levels at output of one gate must be sufficient to drive next gate.

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**Transfer characteristics**

Transfer curve shows static input/output relationship—hold input voltage, measure output voltage.

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**Inverter transfer curve**

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Logic thresholds Choose threshold voltages at points where slope of transfer curve = -1. Inverter has a high gain between VIL and VIH points, low gain at outer regions of transfer curve. Note that logic 0 and 1 regions are not equal sized—in this case, high pullup resistance leads to smaller logic 1 range.

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Noise margin Noise margin = voltage difference between output of one gate and input of next. Noise must exceed noise margin to make second gate produce wrong output. In static gates, t= voltages are VDD and VSS, so noise margins are VDD-VIH and VIL-VSS.

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Delay Assume ideal input (step), RC load.

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Delay assumptions Assume that only one transistor is on at a time. This gives two cases: rise time, pullup on; fall time, pullup off. Assume resistor model for transistor. Ignores saturation region and mischaracterizes linear region, but results are acceptable.

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**Current through transistor**

Transistor starts in saturation region, then moves to linear region.

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**Capacitive load CL = S (W/L)i Cl**

Most capacitance comes from the next gate. Load is measured or analyzed by Spice. Cl: load presented by one minimum-size transistor. CL = S (W/L)i Cl

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**Resistive model for transistor**

Average V/I at two voltages: maximum output voltage middle of linear region Voltage is Vds, current is given Id at that drain voltage. Step input means that Vgs = VDD always.

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**Resistive approximation**

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**Ways of measuring gate delay**

Delay: time required for gate’s output to reach 50% of final value. Transition time: time required for gate’s output to reach 10% (logic 0) or 90% (logic 1) of final value.

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**Inverter delay circuit**

Load is resistor + capacitor, driver is resistor.

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**Inverter delay with t model**

t model: gate delay based on RC time constant t. Vout(t) = VDD exp{-t/(Rn+RL)/ CL} tf = 2.2 R CL For pullup time, use pullup resistance.

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**t model inverter delay 0.5 micron process: So Rn = 6.47 kW**

Cl = 0.89 fF CL = 1.78 fF So td = 0.69 x 6.47E3 x 1.78E-15 = 7.8 ps. tf = 2.2 x 6.47E3 x 1.78E-15 = 26.4 ps.

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**Quality of RC approximation**

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**Quality of step input approximation**

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**Power consumption analysis**

Almost all power consumption comes from switching behavior. Static power dissipation comes from leakage currents. Surprising result: power consumption is independent of the sizes of the pullups and pulldowns.

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**Other models Current source model (used in power/delay studies):**

tf = CL (VDD-VSS)/Id = CL (VDD-VSS)/0.5 k’ (W/L) (VDD-VSS -Vt)2 Fitted model: fit curve to measured circuit characteristics.

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Body effect and gates Difference between source and substrate voltages causes body effect. Source for gates in middle of network may not equal substrate: Source above VSS

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**Body effect and gate input ordering**

To minimize body effect, put early arriving signals at transistors closest to power supply: Early arriving signal

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**Power consumption circuit**

Input is square wave.

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Power consumption A single cycle requires one charge and one discharge of capacitor: E = CL(VDD - VSS)2 . Clock frequency f = 1/t. Energy E = CL(VDD - VSS)2. Power = E x f = f CL(VDD - VSS)2.

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**Observations on power consumption**

Resistance of pullup/pulldown drops out of energy calculation. Power consumption depends on operating frequency. Slower-running circuits use less power (but not less energy to perform the same computation).

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**Speed-power product Also known as power-delay product.**

Helps measure quality of a logic family. For static CMOS: SP = P/f = CV2. Static CMOS speed-power product is independent of operating frequency. Voltage scaling depends on this fact.

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**Parasitics and performance**

b c

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Effect of parasitics a: Capacitance on power supply is not bad, can be good in absence of inductance. Resistance slows down static gates, may cause pseudo-nMOS circuits to fail.

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**Effects of parasitics, cont’d**

b: Increasing capacitance/resistance reduces input slope. c: Similar to parasitics at b, but resistance near source is more damaging, since it must charge more capacitance.

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**Driving large loads Sometimes, large loads must be driven:**

off-chip; long wires on-chip. Sizing up the driver transistors only pushes back the problem—driver now presents larger capacitance to earlier stage.

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**Cascaded driver circuit**

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Optimal sizing Use a chain of inverters, each stage has transistors a larger than previous stage. Minimize total delay through driver chain: ttot = n(Cbig/Cg)1/n tmin. Optimal number of stages: nopt = ln(Cbig/Cg). Driver sizes are exponentially tapered with size ratio a.

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