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**CMOS VLSI Design DC Transfer Characteristics and Switch –level RC delay Models**

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**DC Response DC Response: Vout vs. Vin for a gate Ex: Inverter**

When Vin = 0 -> Vout = VDD When Vin = VDD -> Vout = 0 In between, Vout depends on transistor size and current By KCL, must settle such that Idsn = |Idsp| We could solve equations But graphical solution gives more insight

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**Transistor Operation Current depends on region of transistor behavior**

For what Vin and Vout are nMOS and pMOS in Cutoff? Linear? Saturation?

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**nMOS Operation Cutoff Linear Saturated Vgsn < Vgsn > Vdsn <**

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**nMOS Operation Cutoff Linear Saturated Vgsn < Vtn Vgsn > Vtn**

Vdsn < Vgsn – Vtn Vdsn > Vgsn – Vtn

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**nMOS Operation Cutoff Linear Saturated Vgsn < Vtn Vgsn > Vtn**

Vdsn < Vgsn – Vtn Vdsn > Vgsn – Vtn Vgsn = Vin Vdsn = Vout

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**nMOS Operation Cutoff Linear Saturated Vgsn < Vtn Vin < Vtn**

Vdsn < Vgsn – Vtn Vout < Vin - Vtn Vdsn > Vgsn – Vtn Vout > Vin - Vtn Vgsn = Vin Vdsn = Vout

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**pMOS Operation Cutoff Linear Saturated Vgsp > Vgsp < Vdsp >**

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**pMOS Operation Cutoff Linear Saturated Vgsp > Vtp Vgsp < Vtp**

Vdsp > Vgsp – Vtp Vdsp < Vgsp – Vtp

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**pMOS Operation Cutoff Linear Saturated Vgsp > Vtp Vgsp < Vtp**

Vdsp > Vgsp – Vtp Vdsp < Vgsp – Vtp Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0

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**pMOS Operation Cutoff Linear Saturated Vgsp > Vtp**

Vin > VDD + Vtp Vgsp < Vtp Vin < VDD + Vtp Vdsp > Vgsp – Vtp Vout > Vin - Vtp Vdsp < Vgsp – Vtp Vout < Vin - Vtp Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0

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I-V Characteristics Make pMOS is wider than nMOS such that bn = bp

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Current vs. Vout, Vin plot absolute value of pMOS

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**Load Line Analysis For a given Vin: Plot Idsn, Idsp vs. Vout**

Vout must be where |currents| are equal in

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Load Line Analysis Vin = 0

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Load Line Analysis Vin = 0.2VDD

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Load Line Analysis Vin = 0.4VDD

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Load Line Analysis Vin = 0.6VDD

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Load Line Analysis Vin = 0.8VDD

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Load Line Analysis Vin = VDD

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Load Line Summary

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DC Transfer Curve Transcribe points onto Vin vs. Vout plot

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**Operating Regions Revisit transistor operating regions Region nMOS**

pMOS A B C D E

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**Operating Regions Revisit transistor operating regions Region nMOS**

pMOS A Cutoff Linear B Saturation C D E

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**Beta Ratio If bp / bn 1, switching point will move from VDD/2**

If bp / bn < 1, the inverter is LO-skewed If bp / bn > 1, the inverter is HI-skewed

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Noise Margins How much noise can a gate input see before it does not recognize the input? NMH= VOH-VIH NML = VIL - VOL

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Logic Levels To maximize noise margins, select logic levels at

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**Logic Levels To maximize noise margins, select logic levels at**

unity gain point of DC transfer characteristic

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**Pass Transistors We have assumed source is grounded**

What if source > 0? e.g. pass transistor passing VDD

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**Pass Transistors We have assumed source is grounded**

What if source > 0? e.g. pass transistor passing VDD Vg = VDD If Vs > VDD-Vt, Vgs < Vt Hence transistor would turn itself off nMOS pass transistors pull no higher than VDD-Vtn Called a degraded “1” Approach degraded value slowly (low Ids) pMOS pass transistors pull no lower than Vtp

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Pass Transistor Ckts

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Pass Transistor Ckts

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**Tristate Inverter Why (d) is a bad design?**

If EN = 0, Y is supposed to be float, but if A changes, charge at internal node may disturb node Y. more in section 6.3.4)

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**Effective Resistance Shockley models have limited value**

Not accurate enough for modern transistors Too complicated for much hand analysis Simplification: treat transistor as resistor Replace Ids(Vds, Vgs) with effective resistance R Ids = Vds/R R averaged across switching of digital gate Too inaccurate to predict current at any given time But good enough to predict RC delay

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**RC Delay Model Use equivalent circuits for MOS transistors**

Ideal switch + capacitance and ON resistance Unit nMOS has resistance R, capacitance C Unit pMOS has resistance 2R, capacitance C Capacitance proportional to width Resistance inversely proportional to width

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A nMOS transistor of unit size: minimum length and minimum contacted diffusion width, size = 1 means that W = 4 , L = 2 , W/L = 2 A nMOS transistor size = k

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**Unit nMOS has resistance R, capacitance C**

Unit pMOS has resistance 2R, capacitance C

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**RC Values Capacitance C = Cg = Cs = Cd = 2 fF/mm of gate width**

Values similar across many processes Resistance R 6 KW/mm in 0.6um process Improves with shorter channel lengths Unit transistors May refer to minimum contacted device (4/2 l) Or maybe 1 mm wide device Doesn’t matter as long as you are consistent

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**Inverter Delay Estimate**

Estimate the delay of a fanout-of-1 inverter

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**Inverter Delay Estimate**

Estimate the delay of a fanout-of-1 inverter

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**Inverter Delay Estimate**

Estimate the delay of a fanout-of-1 inverter

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**Inverter Delay Estimate**

Estimate the delay of a fanout-of-1 inverter d = 6RC

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