1 University of California at Berkeley College of Engineering Dept. of Electrical Engineering and Computer Sciences Sample EE 105 Final Examination Spring 2005 Prof. Roger T. Howe May 5, 2005 ________________,_________________ Your Name (Last, First) Guidelines Closed book and notes; three 8.5” x 11” page (both sides) of your own notes is allowed. You may use a calculator. Do not unstaple the exam. Show all your work and reasoning on the exam in order to receive full or partial credit. You have 180 minutes (3 hrs.); use your time wisely. Good luck! Score Problem Points Possible Score 1 30 2 25 3 25 4 20 Total 10021. CMOS two-stage photocurrent amplifier [30 points] V -= - 1.5 VGiven: µnCox = 50 µA/V2, VTn = 1.0 V, λn = 0.05 V-1µpCox = 25 µA/V2, VTp = -1.0 V, λp= 0.05 V-1M1: (W/L)1 = 256/1 (µm/µm) M7: (W/L)7 = 32/1 (µm/µm) M2: (W/L)2 = 256/1 (µm/µm) V+ = 1.5 VIREF = 10 µA M4M1M3 M7 M9 RL M11M3: (W/L)3 = 16 /1 (µm/µm) M4: (W/L)4 = 32 /1 (µm/µm) M5: (W/L)5 = 256/1 (µm/µm)M6: (W/L)6 = 128/1 (µm/µm) M8: (W/L)8 = 32/1 (µm/µm) M9: (W/L)9 = 64/1 (µm/µm) RS = 100 kΩRL = 100 kΩ M5 M8 M10M2 M6Illuminated Photodiode Model: RS isM10: (W/L)9 = 512/1 (µm/µm) M11: (W/L)9 = 64/1 (µm/µm) iout Neglect the backgate effect. (a) [3 pts.] Find the numerical values of the DC drain currents for transistors M1, M10, and M2. You can assume that all transistors are saturated, that the DC output voltage is VOUT = 0 V, and that channel length modulation can be neglected. ID1 = ________ µA -ID10 = ________ µA -ID2 = ________ µA3(b) [3 pts.] Locate the bias point Q, which is the point ID5(VGS5, VDS5), for transistor M5 on the family of curves on the plot below. Select the nearest VGS5 curve from those given on the plot. ID5 [µA] 100 250 300 1 1.5 2 2.5 VDS5 [V]VGS5[V] 200 50 150 0.5 1.20 1.18 VGS5 < 1 V 0 0 1.16 3.0 1.14 1.12 1.10 1.08 (c) [5 pts.] Redraw the circuit with non-ideal (“gray circle”) current supplies and any bias current sources or voltage sources for each amplifier stage. Label with the numerical values of the DC currents ISUP and IBIAS and the DC voltage VDC. There is no need to evaluate the resistances roc. Hint: your circuit should contain two current supplies, one bias current, and one bias voltage.4 (d) [4 pts.] Identify the two-port type for each amplifier stage (e.g., CS, CG, or CD) and fill in the appropriate circuit model (e.g., current buffer, transconductance amp, etc.). You should include the elements (e.g., Rin, Rout, gain element) for each stage in your circuit. There is no need to evaluate any of the parameters for this part. is RS iout First StageSecond Stage RL (e) [3 pts.] Find the numerical value of the input resistance Rin of this amplifier in Ohms. You should make reasonable approximations to simplify the calculations. Rin = ___________Ω5 (f) [5 pts.] Find the numerical value of Ai (the low-frequency short-circuit current gain -- a two-port parameter.) Again, you should make reasonable approximations in order to save time and pencil lead! Ai = ___________ (g) [4 pts.] Find the maximum amplitude MAXOUTi,ˆof the output current iOUT,(t) in µA which avoids clipping. Note that the value of the load resistor is RL = 100 kΩ. =MAXOUTi,ˆ_________ µA6 (h) [3 pts.] Sketch the transfer curve iOUT vs. iS where the output current is in µA and the input current is in nA = 10-9 A. Consider the input source to be “large signal” for this part and neglect RS. Provide your own appropriate scale -- your sketch should be consistent with your answers to parts (f) and (g). If you couldn’t solve these parts, you can assume that the overall short-circuit current gain is 75 and that -1.2 V < vOUT < 0.9 V (not the correct answers, of course). iOUT [µA] iS [nA]72. Frequency Response of a CMOS Photocurrent Amplifier [25 points] Cox = 2 fF/µm2, Cov = 0.1 fF/µm, Ldiff = 2 µm, NMOS: Cdb = 0.5 fF/µm2, PMOS: Cdb = 0.3 fF/µm2 V -= - 1.5 VGiven: µnCox = 50 µA/V2, VTn = 1.0 V, λn = 0.05 V-1µpCox = 25 µA/V2, VTp = -1.0 V, λp= 0.05 V-1M1: (W/L)1 = 256/1 (µm/µm) M7: (W/L)7 = 32/1 (µm/µm) M2: (W/L)2 = 256/1 (µm/µm) IREF = 10 µA M4 M1M3 M7 M9 RL ,CL M11 M3: (W/L)3 = 16 /1 (µm/µm) M4: (W/L)4 = 32 /1 (µm/µm) M5: (W/L)5 = 256/1 (µm/µm) M6: (W/L)6 = 128/1 (µm/µm) M8: (W/L)8 = 32/1 (µm/µm) M9: (W/L)9 = 64/1 (µm/µm) RS = 100 kΩ CS = 100 fF RL = 100 kΩ CL = 100 fF M5 M8 M10M2 M6Illuminated Photodiode Model: CS IsM10: (W/L)9 = 512/1 (µm/µm) V + = 1.5 V RS IoutDevice Capacitance Data: IN OUT X (a) [4 pts.] What is the numerical value of the total capacitance Cin between the input node IN and small-signal ground (in fF)? You can consider any node connected to a DC voltage source through a diode-connected MOSFET to be effectively at small-signal ground. Also, assume VSB1 = 0 V. List all relevant capacitances symbolically (e.g., Cgs1) before calculating their values. Cin = _________fF8(b) [3 pts.] What is the open-circuit time-constant τin associated with Cin (in nanoseconds, 10-9 s)? If you couldn’t solve problem 1(e), you can assume that the input resistance Rin = 2.5 kΩ for this part. τin = _______ns (c) [5 pts.] By using Miller’s theorem and including all relevant capacitors, what is the total capacitance CX between node X and small-signal ground (in fF)? You can consider any node connected to a DC voltage source through a diode-connected MOSFET to be effectively at small-signal ground. List all relevant capacitances symbolically (e.g., Cgd1) before calculating their values. CX = _________fF9 (d) [2 pts.] What is the open-circuit time-constant τX associated with CX (in nanoseconds, 10-9 s)? If you couldn’t solve problem 1(f), you can assume that the short-circuit current gain Ai = 105. τX = _______ns (e) [3 pts.] What is the numerical value of the total capacitance Cout between the output node OUT and small-signal ground (in fF)? You can consider any node connected to a DC voltage source through a diode-connected MOSFET to be effectively at small-signal ground. List all relevant capacitances symbolically (e.g., Cgd6) before calculating their values. Cout = _________fF
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