University of California College of Engineering Department of Electrical Engineering and Computer Sciences Jan M Rabaey TuTh 2 3 30 Thursday November 9 6 30 8 00pm EECS 105 FALL 06 MIDTERM 2 NAME Last First SID Problem 1 7 Problem 2 8 Problem 3 10 Total 25 Important Notice To get credit for a problem or sub problem it is essential for you to show the steps you took to get to the answer No credit will be given if you just show the answer without any further explanation EECS 105 FALL 06 MIDTERM 2 1 PROBLEM 1 MOS Transistors 7 pts Calculate voltage V1 V2 V3 and V4 and specify the operation region of all the transistors You must clearly show the procedure proof of your answer kn 100uA V2 kp 50u A V2 Vtn 0 5V Vtp 0 5V n p 0 a 4 pt VDD 3V M1 W L 1 2u 0 25u I 100uA V2 V1 M2 W L 2 4u 0 25u M3 W L 3 2u 0 25u V1 V2 b 3 pt VDD 3V I 25uA V3 R1 30M M4 W L 4 1u 0 25u R2 10M V3 EECS 105 FALL 06 MIDTERM 2 2 PROBLEM 2 Amplifiers 8 pts VDD 5V Last week while cleaning the office we stumbled onto a board that contains a mystery amplifier as shown in the picture below One thing we could easily figure out the values of the resistors being Rd 35 K and Rs 20K Rd Vout X1 d g a Using a sweep of the input voltage Vin we plotted the input output relationship of the amplifier as shown below From this plot determine approximately what operation point as expressed by the bias voltage Vin would achieve the highest linear output swing while still giving high gain What is the low frequency gain at this point 2 points Vin Black Box b s AC Vin DC Rs 5 0V V o u t 4 5V 4 0V 3 5V 3 0V 2 5V 2 0V 1 5V 1 0V 0V 0 5V 1 0V 1 5V 2 0V 2 5V 3 0V 3 5V 4 0V 4 5V 5 0V V 2 Vin Vin A Vin EECS 105 FALL 06 MIDTERM 2 3 b Putting the 4 terminal black box device X1 which is at the core of the amplifier on our advanced measurement equipment we managed to extract some interesting curves shown below This surely looks like an MOS transistor hence we will assume it is one albeit with some strange deviations 3 points Id Vgs 2 5V 375uA 350uA 325uA 300uA Vgs 2 25V 275uA 250uA Vgs 2 0V 225uA 200uA 175uA Vgs 1 75V 150uA 125uA 100uA Vgs 1 5V 75uA Vgs 1 25V 50uA Vgs 1V 25uA 0A 0V 0 5V 1 0V 1 5V 2 0V 2 5V 3 0V 3 5V 4 0V 4 5V 5 0V ID M1 Vd Vds Id 100uA 90uA 80uA Vbs 0V 70uA Vbs 25V 60uA Vbs 5V 50uA 40uA 30uA 20uA 10uA 0A 0V 0 5V 1 0V 1 5V 2 0V 2 5V 3 0V 3 5V 4 0V 4 5V 5 0V ID M1 Vd Vds Use these curves to derive the small signal transconductance gm backgate transconductance gmb and output resistance ro of the device at the operational point derived in a You may assume that the input resistance ri is infinite EECS 105 FALL 06 MIDTERM 2 4 gm gmb ro c Given what you obtained from the above draw the small signal model of mystery amplifier Determine its input and output resistance in the operation point 3 points rin rout EECS 105 FALL 06 MIDTERM 2 5 PROBLEM 3 Frequency Response 10 pts A p channel common source amplifier is loaded with a capacitor CL as shown in the figure The main design goal is to achieve a 3 db bandwidth 200 Mrad sec and a low frequency gain amplitude of 25 Assume the transistor is biased to operate in the saturation region and the DC output current is zero Using the following parameters for your calculation pCox 25 A V2 L 2 m p 0 1 L V 1 where L is in m roc Rs 100 CL 50fF For the rest of the question ignore all the internal capacitances of the transistor VDD RS Vs VBIAS Vout ISUP CL a Draw the small signal model of the amplifier 1 point EECS 105 FALL 06 MIDTERM 2 6 b Derive an analytical expression for the transfer function Vout Vs as a function of frequency 2point Vout Vs c Based on the above derive the value of the bias current ISUP so that a 3 db frequency of 200 Mrad sec is obtained 4 point Derive an expression of the 3db point first ISUP EECS 105 FALL 06 MIDTERM 2 7 d Size the transistor width W so that the low frequency gain amplitude requirement of 25 is met 3 points W EECS 105 FALL 06 MIDTERM 2 8
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