EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross LECTURE 27 Today 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 counts Trying to expose you to various complicated circuits topics to use the tools you ve developed and prepare you for final exam EECS 40 Spring 2003 Lecture 27 S Ross NONLINEAR OPERATIONAL AMPLIFIERS When 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 VIN R VOUT EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross S Ross EECS 40 Spring 2003 Lecture 27 S Ross NONLINEAR OPERATIONAL AMPLIFIERS VIN R ID VOUT Computes an exponential function of VIN EECS 40 Spring 2003 Lecture 27 NONLINEAR OPERATIONAL AMPLIFIERS What if I switch the positions of the resistor and the diode and make sure VIN 0 V VIN R ID Computes a natural logarithm function of VIN Changing the position of the elements inverted the function performed VOUT EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross TRANSISTOR AS CURRENT SOURCE But this hides the fact that This circuit acts like a IDSAT depends on VGS it is constant current source as really a voltage dependent long as the transistor current source remains in saturation mode Load D VDD If VGS is not constant the model fails What if VGS changes What if there is noise in the circuit IDSAT G VGS IDSAT Load S EECS 40 Spring 2003 Lecture 27 S Ross THE EFFECT OF A SMALL SIGNAL ID If VGS changes a little bit so does ID VGS 2 1 V VGS 2 V VGS 1 9 V VDS EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross THE SMALL SIGNAL MODEL Let s include the effect of noise in VGS Suppose we have tried to set VGS to some value VGS DC with a fixed voltage source but some noise VGS gets added in VGS VGS DC VGS VGS G D IDSAT g VGS IDSAT DC f VGS DC S We get the predicted IDSAT DC plus a change due to noise IDSAT No current flows into or out of the gate because of the opening EECS 40 Spring 2003 Lecture 27 S Ross THE SMALL SIGNAL MODEL To be even more accurate we could add in the effect of When is nonzero ID increases linearly with VDS in saturation We can model this with a resistor from drain to source G VGS IDSAT g VGS IDSAT DC f VGS DC ro D S The resistor will make more current flow from drain to source as VDS increases EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross THE SMALL SIGNAL MODEL How do we find the values for the model IDSAT DC W L N COX VGS DC VTH 2 This is a constant depending on VGS DC IDSAT IDSAT VGS DC VGS VGS This is a first order Taylor series approximation which works out to IDSAT W L N COX VGS DC VTH VGS We often refer to W L N COX VGS DC VTH as gm so IDSAT gm VGS EECS 40 Spring 2003 Lecture 27 S Ross THE SMALL SIGNAL MODEL Including the effect of via ro the added current contributed by the resistor is Ir0 W L N COX VGS VTH 2 VDS To make things much easier since the effect is small anyway we neglect the effect of VGS in the resistance so the current is Ir0 W L N COX VGS DC VTH 2 VDS IDSAT DC VDS This leads to r0 VDS Ir0 IDSAT DC 1 EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EECS 40 Spring 2003 Lecture 27 S Ross EXAMPLE Revisit the example of Lecture 20 but now the 3 V source can have noise up to 0 1 V VTH N 1 V W L nCOX 500 A V2 Find the range of variation for ID 0 V 1 We figured out that saturation is the correct mode in Lecture 20 1 5 k D ID G VDS 4V V G S 3V The noiseless value of ID is S EECS 40 Spring 2003 Lecture 27 S Ross EXAMPLE The variation in ID due to noise 1 5 k D G G S V 3V VDS 4V ID S So ID could vary between Will saturation mode be maintained
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