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DC Characteristics of a CMOS Inverter A complementary CMOS inverter consists of a p-type and an n-type device connected in series. The DC transfer characteristics of the inverter are a function of the output voltage (V out ) with respect to the input voltage (V in ). The MOS device first order Shockley equations describing the transistors in cut-off, linear and saturation modes can be used to generate the transfer characteristics of a CMOS inverter. Plotting these equations for both the n- and p-type devices produces voltage- current characteristics shown below.

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IV Curves for nMOS

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PMOS IV Curves

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DC Response DC Response: V out vs. V in for a gate Ex: Inverter –When V in = 0 -> V out = V DD –When V in = V DD -> V out = 0 –In between, V out depends on transistor size and current –By KCL, we that I dsn = |I dsp | –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 V in and V out are nMOS and pMOS in –Cutoff? –Linear? –Saturation?

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nMOS Operation CutoffLinearSaturated V gsn

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nMOS Operation CutoffLinearSaturated V gsn < V tn V gsn > V tn V dsn < V gsn – V tn V gsn > V tn V dsn > V gsn – V tn

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nMOS Operation CutoffLinearSaturated V gsn < V tn V gsn > V tn V dsn < V gsn – V tn V gsn > V tn V dsn > V gsn – V tn V gsn = V in V dsn = V out

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nMOS Operation CutoffLinearSaturated V gsn < V tn V in < V tn V gsn > V tn V in > V tn V dsn < V gsn – V tn V out < V in - V tn V gsn > V tn V in > V tn V dsn > V gsn – V tn V out > V in - V tn V gsn = V in V dsn = V out

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pMOS Operation CutoffLinearSaturated V gsp >V gsp < V dsp > V gsp < V dsp <

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pMOS Operation CutoffLinearSaturated V gsp > V tp V gsp < V tp V dsp > V gsp – V tp V gsp < V tp V dsp < V gsp – V tp

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pMOS Operation CutoffLinearSaturated V gsp > V tp V gsp < V tp V dsp > V gsp – V tp V gsp < V tp V dsp < V gsp – V tp V gsp = V in - V DD V dsp = V out - V DD V tp < 0

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pMOS Operation CutoffLinearSaturated V gsp > V tp V in > V DD + V tp V gsp < V tp V in < V DD + V tp V dsp > V gsp – V tp V out > V in - V tp V gsp < V tp V in < V DD + V tp V dsp < V gsp – V tp V out < V in - V tp V gsp = V in - V DD V dsp = V out - V DD V tp < 0

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I-V Characteristics Make pMOS wider than nMOS such that n = p

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Current vs. V out, V in

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Load Line Analysis For a given V in : –Plot I dsn, I dsp vs. V out –V out must be where |currents| are equal.

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Load Line Analysis V in = 0

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Load Line Analysis V in = 0.2V DD

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Load Line Analysis V in = 0.4V DD

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Load Line Analysis V in = 0.6V DD

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Load Line Analysis V in = 0.8V DD

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Load Line Analysis V in = V DD

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Load Line Summary

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DC Transfer Curve Transcribe points onto V in vs. V out plot

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Operating Regions Revisit transistor operating regions RegionnMOSpMOS A B C D E

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Operating Regions Revisit transistor operating regions RegionnMOSpMOS ACutoffLinear BSaturationLinear CSaturation DLinearSaturation ELinearCutoff

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Beta Ratio If p / n 1, switching point will move from V DD /2 Called skewed gate Other gates: collapse into equivalent inverter

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DC Characteristics of a CMOS Inveter The DC transfer characteristic curve is determined by plotting the common points of V gs intersection after taking the absolute value of the p-device IV curves, reflecting them about the x- axis and superimposing them on the n-device IV curves. We basically solve for V in(n-type) = V in(p-type) and I ds(n-type) =I ds(p-type) The desired switching point must be designed to be 50 % of magnitude of the supply voltage i.e. V DD /2. Analysis of the superimposed n-type and p-type IV curves results in five regions in which the inverter operates. Region A occurs when 0 leqV in leq V t(n-type). –The n-device is in cut-off (I dsn =0 ). –p-device is in linear region, –I dsn = 0 therefore -I dsp = 0 –V dsp = V out – V DD, but V dsp =0 leading to an output of V out = V DD. Region B occurs when the condition V tn leq V in le V DD /2 is met. –Here p-device is in its non-saturated region Vds neq 0. –n-device is in saturation Saturation current Idsn is obtained by setting V gs = V in resulting in the equation:

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CMOS Inverter DC Characteristics

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CMOS Inverter Transfer Characteristics In region B I dsp is governed by voltages V gs and V ds described by: Region C has that both n- and p- devices are in saturation. Saturation currents for the two devices are: Region D is defined by the inequality p-device is in saturation while n- device is in its non-saturation region. Equating the drain currents allows us to solve for Vout. (See supplemental notes for algebraic manipulations).

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CMOS Inverter Static Charateristics In Region E the input condition satisfies: The p-type device is in cut-off: I dsp =0 The n-type device is in linear mode V gsp = V in –V DD and this is a more positive value compared to V tp. V out = 0 nMOS & pMOS Operating points A C B D E V tp V tn VDDVDD 0 V DD /2V DD +V t p VDDVDD Both in sat nMOS in sat pMOS in sat Output Voltage V out =V in -V tp V out =V in -V tn

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