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DC Characteristics of a CMOS InverterA 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 (Vout) with respect to the input
voltage (Vin).
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 ResponseDC Response: Vout vs. Vin for a gateEx: InverterWhen
Vin = 0 -> Vout = VDDWhen Vin = VDD -> Vout = 0In between,
Vout depends ontransistor size and currentBy KCL, we thatIdsn =
|Idsp|We could solve equationsBut graphical solution gives more
insight
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Transistor OperationCurrent depends on region of transistor
behaviorFor what Vin and Vout are nMOS and pMOS
inCutoff?Linear?Saturation?
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nMOS Operation
CutoffLinearSaturatedVgsn
Vdsn
Vdsn >
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nMOS Operation
CutoffLinearSaturatedVgsn < VtnVgsn > Vtn
Vdsn < Vgsn VtnVgsn > Vtn
Vdsn > Vgsn Vtn
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nMOS OperationVgsn = VinVdsn = Vout
CutoffLinearSaturatedVgsn < VtnVgsn > Vtn
Vdsn < Vgsn VtnVgsn > Vtn
Vdsn > Vgsn Vtn
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nMOS OperationVgsn = VinVdsn = Vout
CutoffLinearSaturatedVgsn < VtnVin < VtnVgsn > VtnVin
> VtnVdsn < Vgsn VtnVout < Vin - VtnVgsn > VtnVin >
VtnVdsn > Vgsn VtnVout > Vin - Vtn
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pMOS Operation
CutoffLinearSaturatedVgsp >Vgsp Vgsp Vgsp VtpVgsp <
Vtp
Vdsp < Vgsp Vtp
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pMOS OperationVgsp = Vin - VDDVdsp = Vout - VDDVtp < 0
CutoffLinearSaturatedVgsp > VtpVgsp < Vtp
Vdsp > Vgsp VtpVgsp < Vtp
Vdsp < Vgsp Vtp
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pMOS OperationVgsp = Vin - VDDVdsp = Vout - VDDVtp < 0
CutoffLinearSaturatedVgsp > VtpVin > VDD + VtpVgsp <
VtpVin < VDD + VtpVdsp > Vgsp VtpVout > Vin - VtpVgsp <
VtpVin < VDD + VtpVdsp < Vgsp VtpVout < Vin - Vtp
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I-V CharacteristicsMake pMOS wider than nMOS such that bn =
bp
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Current vs. Vout, Vin
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Load Line AnalysisFor a given Vin:Plot Idsn, Idsp vs. VoutVout
must be where |currents| are equal.
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Load Line AnalysisVin = 0
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Load Line AnalysisVin = 0.2VDD
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Load Line AnalysisVin = 0.4VDD
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Load Line AnalysisVin = 0.6VDD
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Load Line AnalysisVin = 0.8VDD
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Load Line AnalysisVin = VDD
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Load Line Summary
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DC Transfer CurveTranscribe points onto Vin vs. Vout plot
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Operating RegionsRevisit transistor operating regions
RegionnMOSpMOSABCDE
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Operating RegionsRevisit transistor operating regions
RegionnMOSpMOSACutoffLinearBSaturationLinearCSaturationSaturationDLinearSaturationELinearCutoff
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Beta RatioIf bp / bn 1, switching point will move from
VDD/2Called skewed gateOther gates: collapse into equivalent
inverter
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DC Characteristics of a CMOS InveterThe DC transfer
characteristic curve is determined by plotting the common points of
Vgs 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 Vin(n-type) =
Vin(p-type) and Ids(n-type)=Ids(p-type)The desired switching point
must be designed to be 50 % of magnitude of the supply voltage i.e.
VDD/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 leqVin leq Vt(n-type).The n-device is in cut-off
(Idsn =0).p-device is in linear region,Idsn = 0 therefore -Idsp =
0Vdsp = Vout VDD, but Vdsp =0 leading to an output of Vout =
VDD.Region B occurs when the condition Vtn leq Vin le VDD/2 is
met.Here p-device is in its non-saturated region Vds neq 0.n-device
is in saturationSaturation current Idsn is obtained by setting Vgs
= Vin resulting in the equation:
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CMOS Inverter DC Characteristics
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CMOS Inverter Transfer CharacteristicsIn region B Idsp is
governed by voltages Vgs and Vds 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 CharateristicsIn Region E the input
condition satisfies:
The p-type device is in cut-off: Idsp=0The n-type device is in
linear modeVgsp = Vin VDD and this is a more positive value
compared to Vtp.Vout = 0nMOS & pMOS Operating
pointsACBDEVtpVtnVDD0VDD/2VDD+VtpVDDBoth in satnMOS in satpMOS in
satOutput VoltageVout =Vin-VtpVout =Vin-Vtn