University of California at Berkeley College of Engineering Dept of Electrical Engineering and Computer Sciences EE 105 Midterm II Fall 2005 Prof Borivoje Nikoli November 17 2005 Your Name Student ID Number Guidelines Closed book and notes there are some useful formulas in the end of the exam You may use a calculator You can unstaple the pages with formulas but do not unstaple the exam Show all your work and reasoning on the exam in order to receive full or partial credit Time 80 minutes 1 hour 20 minutes Score Problem Points Possible 1 20 2 14 3 18 Total 52 Score 1 1 MOS current source 20 points For the current source shown in Figure 1 dimensions of MOS transistors M1 and M2 are W L 1 2 W L 2 10 VDD 2 5V nCox 100 A V2 VTn 0 5 V n 0 05 V 1 0 a 4 points Find the value of RREF such that IREF 100 A You can ignore channel length modulation in this part VDD RREF IREF IOUT M1 M2 vOUT R1 Figure 1 RREF 2 b 4 points Find the value of R1 that gives IOUT 40 A Assume that M2 is in saturation You can ignore channel length modulation in this calculation R1 c 4 points Find the lowest output voltage vOUT for which the circuit in Figure 1 still acts as a current source You can ignore channel length modulation vOUT min 3 d 6 points Find the small signal output resistance of the current source in Figure 1 Rout 4 e 2 points If body effect parameter 0 would it increase or decrease the value of output resistance from part d Explain your answer Rout increases decreases circle one 5 2 MOS amplifiers 14 pts For the MOS amplifier in Figure 2 W L 1 10 W L 2 20 W L 3 10 IBIAS 50 A VDD 2 5V nCox 100 A V2 pCox 30 A V2 VTn VTp 0 5 V n np 0 05V 1 0 CGS2 2CGS1 2CGS3 100fF CGD2 2CGD1 2CGD3 10fF Input voltage vS has negligible input resistance and contains a DC and an AC component Figure 2 a 2 points Find the bias current of transistor M1 IM1 6 b 4 points Find the small signal voltage gain Av vout vs Av 7 c 4 points Find the maximum and the minimum voltage at the output of this amplifier Vout max d V Vout min V 4 points Find the frequency of the dominant pole of this amplifier rad s 8 3 Amplifier frequency response 18 points An amplifier has all of its poles and zeros in the left hand frequency plane it is a stable minimum phase system and an amplitude frequency response as shown in Figure 3 A j 60 40 20 0 101 102 103 104 105 106 107 20 40 Figure 3 a 6 points Write the transfer function that produces this response b 6 points Draw the phase response that corresponds to this amplitude response 9 c 6 points Write the transfer function that produces the response from Figure 4 Figure 4 10 Some equations Mass action law n p ni 2 T 1 Resistivity n 1 n q n Nd eff Resistance R L L L Rsq Wt t W W Total current e J J drift J diff q n nE qDn Gauss s law Depletion layer Q E dS Q CV 2 s bi 1 1 q Na Nd C j0 qNa x p 0 Cj V V 2 bi 1 D 1 D bi bi X d 0 x p0 x n0 pn depletion layer capacitance pn diffusion current J diff 2 D p Dn qn i N d Wn N aW p Diffusion capacitance C d dn dx E d dx V X d VD X d 0 1 D bi qv D qv D kT e 1 i D I S e kT 1 1 qI D 2 kT 11 Threshold voltage NMOS 1 VTn VFB 2 p 2q s N a 2 p C ox VTn VTn 0 VSB 2 p 2 p p kT Na ln q ni NMOS equations I D 0 VGS VTn v W C ox v GS VTn DS v DS 1 VDS VGS VTn VDS VGS VTn 2 L W C ox v GS VTn 2 1 VDS VGS VTn VDS VGS VTn iD L 2 iD MOS capacitances in saturation Cov LDWCox Cgs 2 3 WLCox Cov MOS signal parameters i W W gm D C ox VGS VTn 1 VDS C ox VGS VTn v GS V V L L GS DS i ro D v DS V V GS DS g mb 1 i D g m v BS Q 2 VBS 2 p Canonic transfer function Bode plots Amplitude Power H G0 j K H j dB 20 log G0 j K H j G0 j K Phase Second order TF LC 1 I DS H j P IV 2 cos I V Re I V 1 j z1 1 j z 2 1 j zn 1 j p 2 1 j p 2 1 j pm 1 j z1 1 j z 2 1 j zn 1 j p 2 1 j p 2 1 j pm 1 j z1 1 j z 2 1 j zn 1 j p 2 1 j p 2 1 j pm N j 20 j 2 j L LC 1 L 1 Z0 1 1 Q 0 R C R CR R 0C R 0 Q 1 Q 2 2 0 1 LC 1 0 12
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