S. RossEECS 40 Spring 2003 Lecture 27Today we will• Put a twist on our normally linear operational amplifier circuits to make them perform nonlinear computations• Make a linear circuit model for the nonlinear NMOS transistor (Preview of EE 105)Next time we will• Show how we can design a pipelined computer datapath at the transistor level• Use a relay to design an analog circuit that countsLECTURE 27Trying to expose you to various complicated circuits/topics to use the tools you’ve developed and prepare you for final exam…S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27NONLINEAR OPERATIONAL AMPLIFIERSWhen I put a nonlinear device in an operational amplifier circuit, I can compute a nonlinear function.Consider the following circuit using the realistic diode model:+−RVINVOUTS. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27+−RVINVOUTNONLINEAR OPERATIONAL AMPLIFIERSComputes an exponential function of VIN!IDS. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27+−RVINVOUTNONLINEAR OPERATIONAL AMPLIFIERSComputes a natural logarithm function of VIN!IDWhat if I switch the positions of the resistor and the diode (and make sure VIN≥ 0 V)?Changing the position of the elements inverted the function performed!S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27GDSIDSAT+_+_VDDVGSThis circuit acts like a constant current source, as long as the transistor remains in saturation mode.IDSATTRANSISTOR AS CURRENT SOURCELoadLoadBut this hides the fact that IDSATdepends on VGS; it is really a voltage-dependent current source!If VGSis not constant, the model fails. What if VGSchanges? What if there is noise in the circuit?S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27VDSIDVGS= 2 VTHE EFFECT OF A SMALL SIGNALVGS= 2.1 VVGS= 1.9 VIf VGSchanges a little bit, so does ID.S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27THE SMALL-SIGNAL MODELLet’s include the effect of noise in VGS. Suppose we have tried to set VGSto some value VGS,DCwith a fixed voltage source, but some noise ∆VGSgets added in. VGS= VGS,DC+ ∆VGS+VGS-SDG∆IDSAT= g(∆VGS)We get the predicted IDSAT,DCplus a change due to noise, ∆IDSAT.No current flows into or out of the gate because of the opening.IDSAT,DC= f(VGS,DC)S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27THE SMALL-SIGNAL MODELTo be even more accurate, we could add in the effect of λ.When λ is nonzero, IDincreases linearly with VDSin saturation.We can model this with a resistor from drain to source:The resistor will make more current flow from drain to source asVDSincreases.ro+VGS-SDG∆IDSAT= g(∆VGS)IDSAT,DC= f(VGS,DC)S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27THE SMALL-SIGNAL MODELHow do we find the values for the model?IDSAT,DC= ½ W/L µNCOX(VGS,DC–VTH)2This is a constant depending on VGS,DC.This is a first-order Taylor series approximation which works out to∆IDSAT= W/L µNCOX(VGS,DC–VTH)∆VGSWe often refer to W/L µNCOX(VGS,DC–VTH) as gm, so∆IDSAT= gm∆VGS. GSDC,GSGSDSATDSATV)V(VII ∆∂∂≈∆S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27THE SMALL-SIGNAL MODELIncluding the effect of λ via ro, the added current contributed by the resistor isIr0= ½ W/L µNCOX(VGS–VTH)2λVDSTo make things much easier, since the λ effect is small anyway, we neglect the effect of ∆VGSin the resistance, so the current isIr0≈ ½ W/L µNCOX(VGS,DC–VTH)2λVDS= IDSAT,DCλ VDSThis leads tor0= VDS/ Ir0= (λ IDSAT,DC)-1S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27GDSID+VGS_+VDS_+_+_4 V3 V1.5 kΩEXAMPLERevisit the example of Lecture 20, but now the 3 V source can have noise up to ± 0.1 V.Find the range of variation for ID.We figured out that saturation is the correct mode in Lecture 20.The “noiseless” value of IDisVTH(N)= 1 V, W/L µnCOX= 500 µ A/V2, λ = 0 V-1.S. RossEECS 40 Spring 2003 Lecture 27S. RossEECS 40 Spring 2003 Lecture 27GDSID+VGS_+VDS_+_+_4 V3 V1.5 kΩEXAMPLEThe variation in IDdue to noise:So IDcould vary between:Will saturation mode be maintained? S. RossEECS 40 Spring 2003 Lecture
View Full Document
Unlocking...