DC Characteristics of a CMOS Inverter A complementary

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 (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 voltagecurrent characteristics shown below.

IV Curves for n. MOS

PMOS IV Curves

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, we that Idsn = |Idsp| – We could solve equations – But graphical solution gives more insight

Transistor Operation • • Current depends on region of transistor behavior For what Vin and Vout are n. MOS and p. MOS in – Cutoff? – Linear? – Saturation?

n. MOS Operation Cutoff Vgsn < Linear Vgsn > Saturated Vgsn > Vdsn < Vdsn >

n. MOS Operation Cutoff Vgsn < Vtn Linear Vgsn > Vtn Saturated Vgsn > Vtn Vdsn < Vgsn – Vtn V > V – V dsn gsn tn

n. MOS Operation Cutoff Linear Saturated Vgsn < Vtn Vgsn > Vtn Vdsn < Vgsn – Vtn V > V – V dsn gsn tn Vgsn = Vin Vdsn = Vout

n. MOS Operation Cutoff Vgsn < Vtn Vin < Vtn Vgsn = Vin Vdsn = Vout Linear Vgsn > Vtn Vin > Vtn Vdsn < Vgsn – Vtn Vout < Vin - Vtn Saturated Vgsn > Vtn Vin > Vtn Vdsn > Vgsn – Vtn Vout > Vin - Vtn

p. MOS Operation Cutoff Vgsp > Linear Vgsp < Saturated Vgsp < Vdsp > Vdsp <

p. MOS Operation Cutoff Vgsp > Vtp Linear Vgsp < Vtp Saturated Vgsp < Vtp Vdsp > Vgsp – Vtp Vdsp < Vgsp – Vtp

p. MOS Operation Cutoff Vgsp > Vtp Linear Vgsp < Vtp Saturated Vgsp < Vtp Vdsp > Vgsp – Vtp Vdsp < Vgsp – Vtp Vgsp = Vin - VDD Vdsp = Vout - VDD Vtp < 0

p. MOS Operation Cutoff Vgsp > Vtp Vin > VDD + Vtp Linear Vgsp < Vtp Vin < VDD + Vtp Vdsp > Vgsp – Vtp Vout > Vin - Vtp Vgsp = Vin - VDD Vtp < 0 Vdsp = Vout - VDD Saturated Vgsp < Vtp Vin < VDD + Vtp Vdsp < Vgsp – Vtp Vout < Vin - Vtp

I-V Characteristics • Make p. MOS wider than n. MOS such that bn = bp

Current vs. Vout, Vin

Load Line Analysis • For a given Vin: – Plot Idsn, Idsp vs. Vout – Vout must be where |currents| are equal.

Load Line Analysis • Vin = 0

Load Line Analysis • Vin = 0. 2 VDD

Load Line Analysis • Vin = 0. 4 VDD

Load Line Analysis • Vin = 0. 6 VDD

Load Line Analysis • Vin = 0. 8 VDD

Load Line Analysis • Vin = VDD

Load Line Summary

DC Transfer Curve • Transcribe points onto Vin vs. Vout plot

Operating Regions • Revisit transistor operating regions Region n. MOS A B C D E p. MOS

Operating Regions • Revisit transistor operating regions Region n. MOS p. MOS A Cutoff Linear B Saturation Linear C Saturation D Linear Saturation E Linear Cutoff

Beta Ratio • • • If bp / bn 1, switching point will move from VDD/2 Called skewed gate Other gates: collapse into equivalent inverter

DC Characteristics of a CMOS Inveter • • The 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 xaxis 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 leq. Vin leq Vt(n-type). – – • The n-device is in cut-off (Idsn =0). p-device is in linear region, Idsn = 0 therefore -Idsp = 0 Vdsp = 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 saturation • Saturation current Idsn is obtained by setting Vgs = Vin resulting in the equation:

CMOS Inverter DC Characteristics

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

CMOS Inverter Static Charateristics • In Region E the input condition satisfies: • n. MOS & p. MOS Operating points • • The p-type device is in cut-off: Idsp=0 The n-type device is in linear mode Vgsp = Vin –VDD and this is a more positive value compared to Vtp. Vout = 0 Output Voltage VDD A Vout =Vin-Vtp B Vout =Vin-Vtn C D 0 Vtp Vtn Both in sat n. MOS in sat p. MOS in sat E VDD/2 VDD+Vtp VDD