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Analysis of VTC

Voltage transfer characteristics of cmos inverter with its derivation

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Analysis of VTC

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  1. The Cmos Inverter

  2. CMOS Inverter

  3. Complementary metal–oxide–semiconductor: - is a technology for constructing integrated circuits. - is used in microprocessors, microcontrollers, static RAM. - is also used for several analog circuits such as image sensors (CMOS sensor), data converters, and highly integrated transceivers. - Frank Wanlass patented CMOS in 1967 (US patent 3,356,858).

  4. Why Cmos? Two important characteristics of CMOS devices are: - high noise immunity. - low static power consumption.

  5. CMOS Inverter VTC

  6. VGs,n = VinVDs,n = VoutVGs,p = - (Vdd - Vin) -- (a)VDs,p = - (Vdd - Vout) -- (b)

  7. Regions of Operating Conditions of Cmos Inverter

  8. Calculation of Vth -both pmos and nmos are in saturation Vin = Vout = Vth = Vdd/2 so, both are in saturation and applying KCLId,p=Id,nKn/2(Vgs,n – Vto,h) ^2 = Kp/2 (Vin – Vdd – Vto,p)^2taking root on both side Vin – Vto,n = (Kp/Kn)½ (Vin – Vdd – Vto,p)(Vin – (Kp/Kn)½.Vin) = Vto,h- (1/Kr)½(Vdd + Vto,p)Vin =Vth= (Vto,n – (1/Kr)½ (Vdd + Vto,p) /( 1+ (1/Kr)½)

  9. Calculation for Vil & Vih :- Nmos saturation, Pmos Linearwhen Vin=Vil, slope of VTC curve =-1Applying KCL Id,p = Id,n Nmos current equation in saturation is:-Id,n= Kn/2[Vgs,n – Vto,n]^2 Id,p = Kp/2[2(Vgs,p – Vto,p) Vds,p – Vds,p^2]applyingVgs,n = VinVgs,p = Vin – VddVds,p = Vout – Vdd Vds,n = Vout Kn/2(Vin – Vto,h)^2=Kp/2[2(Vin – Vdd – Vto,p) (Vout-Vdd) – (Vout - Vdd)^2]

  10. diff. w.r.t to Vin Kn(Vin – Vto,h) = Kp[(Vin – Vdd – Vto,p)dvout/dvin + (Vout - Vdd) – (Vout - Vdd)dvout/dvin]put dVout/dVin = -1Kn(Vin – Vto,n) = Kp [-Vin + Vdd + Vto,p + Vout – Vdd + V out - Vdd] Kn(Vin – Vto,n) = Kp (2Vout – Vin + Vto,p - Vdd)put vin = vilKn(Vil – Vto,n) = Kp(2Vout – Vil + Vto,p - Vdd)Vil = (2Vout + Vto,p – Vdd + Kr .Vto,n)/(1+Kr) where Kr = Kn/KpSimilarly, Vih = Vdd + Vto,p + Kr(2Vout + Vto,n) / (1 + Kr).

  11. Calculation for Volwhen Vin>(Vdd+Vto,p)Pmos – cutt offNmos - Linear Id,p = Id,n = 0 Vout = Vol which is almost equal to 0Calculation for Voh when Vin<Vto,nNmos – cutoffPmos – linearby KCLId,p = Id,n = 0Vout = Vdd = Voh(approx)

  12. THANK YOU

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