final_sol_04-05-20-10-24

# final_sol_04-05-20-10-24 - UNIVERSITY OF CALIFORNIA College...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences Final Exam EECS 240 B. E. BOSER May 19, 2004 SPRING 2004 Show derivations and mark results with box around them. Erase or cross-out erroneous attempts. Simplify algebraic results as much as possible! Mark your name and SID at the top of the exam and all extra sheets. 1. Derive an analytical expression for the variance of the thermal noise at the output V0 of the circuit below. State your result as a ﬁmction of RL, gml, yl, and kBT. For simplicity, you may ignore the ﬁnite output resistance of the transistor and all capacitors except CL. 2. Derive an expression for the low—ﬁequency diﬁerential—mode input referred thermal noise density “3’ of the circuit below. State your result in terms of the V* of individual transistors (devices with identical index, e. g. Mla and Mlb, have the same V*), Ibias, and kBT. For simplicity you may assume that the output resistance of all devices is inﬁnite. The “noise factor” for all devices is y=1. VDD 2|Liiars1 l V5554 M5a M50 M5b M73 :“_Vbias5 l l: M=2 I VbIaSS V53 chfb V5b Vbiasa M63 E M60 I MGb M=2 l IbiasZ l Zlbias1 |bias1 C V V V Rob cb Voa H 28 xx 2b Fi— Vob Cca Rea Via "l M13 M1b l—Vib V . M3a :I “332 M3b FM— V1a V1b M4a V A M4 M28 :1 blas1 b M= M=2 OTA Core ‘2 e n: h‘; n N 42 (r ‘l I l“ ~c 4. “I \/ \/ ll \$2 fl ’\ + )0 ‘x + U) . Derive an expression for the standard deviation of the relative current mismatch AID/TD of the circuit below. State your result as a function of W, L, Vm, terminal voltages, _A )/(W/L) — and and A1, A2 describing technology mismatches as aim 2 __A, "My ‘ M1 M2 VBiasz VBias1 . l AL’D 0 A (IV/L) 2 A (61,; Lu 4. Calculate the “power—speed-dynamic range ﬁgure~of—merit”, FOMPSD of the circuit below. This metric is deﬁned as P B x DR ’ where P is the power dissipation of the circuit, B the unity-gain bandwidth in [rad/sec], and DR the dynamic range at the output Vo when the switch opens. Consider only thermal noise from M1 and ignore ﬁnite output and switch on—resistance. Formulate your result as a function of V*, IBias, CL, kBT, and the ratio r of the peak-to—peak output voltage range V0,“, to the supply voltage, VDD. 1’ MPSD = V U U s \ ? 2 B a oFl-r‘v‘x =2 QIﬂ'M If Ca V" C; v 1 r? @(L : O‘PI’ K’1: ICE)” 2 L g" 2 “(on/c. ’Vo‘ea fit:— We 29.4 4’ hf“ I/ L r V99 :5 ¢LLI ' (/vM - L " ’1 / 4 Va” ‘4’» I/re m———.__ V; W “H_, / “‘ Vs —.C. e_~’ -" A I Cy “‘2‘” Mg: N E;— + g 21‘” K / C9 3: has" ‘-—--v—-—-" r 1 ill \ és‘hw'fl 27’56/1: Ad'ng “ \ i \\ E’: —(‘S 1, C2... ) \\ CV 277;? C9 - \\‘ — £5; C, CV 5. Sketch the magnitude response and derive expressions for the frequencies and amplitude of all break points for the circuit shown below. Assume that all poles and zeros occur at frequencies that are much smaller than the sampling rate and that the ampliﬁer is ideal. ...
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## This note was uploaded on 08/01/2008 for the course EECS 240 taught by Professor Boser during the Spring '04 term at University of California, Berkeley.

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final_sol_04-05-20-10-24 - UNIVERSITY OF CALIFORNIA College...

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