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 1 30 2 25 3 25 4 20 Total 100 Score 1 1 CMOS two stage photocurrent amplifier 30 points V 1 5 V IREF 10 A M10 M9 M11 M2 iout M1 M8 M3 RL M4 Given M5 M6 M7 V 1 5 V nCox 50 A V2 VTn 1 0 V n 0 05 V 1 Illuminated Photodiode Model pCox 25 A V2 VTp 1 0 V p 0 05 V 1 is RS Neglect the backgate effect M1 W L 1 256 1 m m M2 W L 2 256 1 m m M7 W L 7 32 1 m m M3 W L 3 16 1 m m M8 W L 8 32 1 m m M4 W L 4 32 1 m m M9 W L 9 64 1 m m M5 W L 5 256 1 m m M10 W L 9 512 1 m m M6 W L 6 128 1 m m M11 W L 9 64 1 m m RS 100 k RL 100 k 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 A ID10 A ID2 A 2 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 300 250 1 20 200 1 18 ID5 A 1 16 150 1 14 100 VGS5 V 1 12 1 10 1 08 50 0 0 0 5 1 1 5 2 2 5 3 0 VGS5 1 V VDS5 V 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 3 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 iout is RL RS First Stage Second Stage 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 4 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 i OUT MAX of the output current iOUT t in A which avoids clipping Note that the value of the load resistor is RL 100 k i OUT MAX A 5 h 3 pts Sketch the transfer curve iOUT vs iS where the output current is in A 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 A iS nA 6 2 Frequency Response of a CMOS Photocurrent Amplifier 25 points V 1 5 V IREF 10 A M10 M9 M11 M2 X M1 M8 Iout OUT RL CL IN M4 M3 M5 V 1 5 V Given M6 M7 Illuminated Photodiode Model nCox 50 A V2 VTn 1 0 V n 0 05 V 1 pCox 25 A V2 VTp 1 0 V p 0 05 V 1 CS RS Is M1 W L 1 256 1 m m M2 W L 2 256 1 m m M7 W L 7 32 1 m m M3 W L 3 16 1 m m M8 W L 8 32 1 m m M4 W L 4 32 1 m m M9 W L 9 64 1 m m M5 W L 5 256 1 m m M10 W L 9 512 1 m m RS 100 k CS 100 fF RL 100 k CL 100 fF M6 W L 6 128 1 m m 2 Device Capacitance Data Cox 2 fF m Cov 0 1 fF m Ldiff 2 m NMOS Cdb 0 5 fF m2 PMOS Cdb 0 3 fF m2 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 fF 7 b 3 pts What is the open circuit time constant in 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 k for this part in 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 diodeconnected MOSFET to be effectively at small signal ground List all relevant capacitances symbolically e g Cgd1 before calculating their values CX fF 8 d 2 pts What is the open circuit time constant X 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 X 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 …
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