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# CIRCUIT & ELECTR II ECE 137B

UCSB

GPA 3.91

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This 3 page Class Notes was uploaded by Spencer Ondricka on Thursday October 22, 2015. The Class Notes belongs to ECE 137B at University of California Santa Barbara taught by M. Rodwell in Fall. Since its upload, it has received 76 views. For similar materials see /class/227038/ece-137b-university-of-california-santa-barbara in ELECTRICAL AND COMPUTER ENGINEERING at University of California Santa Barbara.

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Date Created: 10/22/15

VmZ1Z2 X Adz21Z2 Von 39 Z 1Adzzzz Ifthe ampli er gain is reasonably large so that AdZ1 Z1 Z2 gtgt 1 then Z Vout Vin E Z1 Z1 2 which is the desired mode of operation Negative feedback can become positive if there is 1800 phase shift in the ampli er This can and will happen at suf ciently high frequencies because of the ampli ers high frequency rolloff due to transistor capacitances If the feedback is positive and of magnitude greater than 1 then the feedback circuit will oscillate To avoid this the op amp highfrequency response must be tailored so that the gain of the feedback loop decreases gracefully to below unity before the phase shifts add up to more than 180 This is called compensation Above is one opamp circuit Several more are shown in a related handout Most opamps can be broken down into three parts A differential input stage a second voltagegain stage and an output buffer stage The input stage might look like any of the above 3 examples or none of them If we apply symmetry so that relrre2 and the emitterfollower buffers have identical voltage gains Av3Av4 then the overall voltage gains of these three input stage examples are AvRleqrel rst example AvAv3Rleqrel second example and AvAv3RleqRrel third example You get the picture and can generalize to any input stage design you like The factor of 12 has vanished in the gain expressions because of the currentmirror load read the notes In general from the above we can always write the voltage gain of the input stage to be Aim gmvinmeieq where gminput is some number lrel Av3rel and Av3Rrel in the 3 examples above Vdd R91 Rd R g quot Cout RL Cin R92 Problem 1 Use a constantmobility model ofthe NMOS FET 15 nm oxide thickness 250 nm gate length and a 04 V threshold Mobility is 400 cmA2Vs and llambdain nity The gate capacitance C gs is grgngWg TM and we will estimate that ng Cgs 4 Vdd is 30 Volts We will bias device at Vgs05 Volts and Id lmA and V015l V From this you can nd Wg RM 20 k9 The parallel combination of Rg1 and Rgzis 100 kg Cm and CW are both in nite The load resistance is to be twice Rd a Find all resistor values the values of Cgs and ng Also nd the transistor b Using the results derived by nodal analyis nd the lowfrequency gain and the 2 dominant poles of the transfer function and the zero frequency Is it so high in frequency that it can be neglected cNow suppose that the input signal is a 10 mV stepfunction occuring at t0 What will be the output signal voltage waveform compute it as a function of time What is the amplifer s 1090 stepresponse risetime to compute this if one pole is much higher in frequency that the other neglect it in the risetime calculation d Draw a Bode plot on semilog paper of the gainfrequency characteristics Vdd R91 Rd R g Cout RL Cin R92 v Problem 2 Using the same values as in problem 1 now set Cgs and ng to zero and Cm C calculate the lowfrequency gainfrequency characteristics of the amplifier b Now suppose that the input signal is a 1 mV stepfunction occuring at t0 What will be the output signal voltage waveform compute and graph as a function of time 50 pF a compute 0112 dd vss Now let us work with a constantvelocity model 10 nm oxide thickness 45 nm gate length and a 03 V threshold Mobility is 400 cmA2Vs and llambdain nity Problem 3 Vdd 2 Volts V55 2 Volts Bias the transistor at 05 mA drain current and 05 V drain voltage and select a gate width Wg of 2 microns The load resistance is to be 10 times Rd Rgen50 Ohm a Find all resistor values Cgs and ng and transistor ft b Compute the small signal VoutVgen at midband c Using the results derived by nodal analysis nd the rst two poles in

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