V DD M 3 M 4 M 5 C C V OUT V 1 2 C L M 6 M 7 V XX. Homework Assignment EE 435 Homework 6 Due Tuesday March 12 Spring 2019

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1 Homework Assignment EE 435 Homework 6 Due Tuesday March 12 Spring 219 In the following problems, if reference to a semiconductor process is needed, assume processes with the following characteristics: CMOS Process ncox=35 A/v 2 pcox=7 A/v 2, VTNO=.5V, VTPO= -.5V, COX=8.5fF/ 2, n p=.1v -1, and V For a bipolar Process -- JS=1-15 A/ 2, β=1 and VAF=15V. Problem 1 A two-stage operational amplifier is shown along with the device sizes in microns. Assume VDD=2V and VXX=.7V and also assume the common-mode input voltage is set so that all transistors are operating in saturation. a) Determine the dc gain of the op amp b) What is the GB of the op amp if CC=4pf and CL=1pf? Neglect all other capacitances in the amplifier c) Determine the power dissipation of the amplifier d) What is the pole Q if used in a noninverting feedback amplifier with β=.25? e) What is the common-mode input range? V DD M 3 M 4 M 5 M M V V 2 C C V OUT C L V XX M 7 V XX M 6 W L Q1 3 1 Q2 3 1 Q3 4 1 Q4 4 1 Q5 7 1 Q Q7 35 1

2 Problem 2 The magnitude and phase plot of an operational amplifier are shown. If another pole can be added on the negative real axis, determine the location of this pole if the feedback amplifier is to have a phase margin of 6 o for β= Gain Plot Gain in db Phase in degrees Phase Plot

3 Problem 3 Assume an open loop forward amplifier (i.e. A(s)) has the magnitude and gain characteristics shown. Determine the phase margin is this amplifier is used in a feedback configuration with β= Magnitude Plot 1 Magnitude in db Phase in degrees Frequency in radians/sec Phase Plot Phase in radians/sec

4 Problem 4 Consider the Bode Plot shown below. a. Determine the Phase Margin if β=1 b. Determine the Gain Margin if β=.2 c. Plot the poles and zeros of the open-loop amplifier d. Determine the Q of the poles of a FB amplifier if β=.5. Assume the gain with A FB is given by AFB 1 A The MATLAB code that generated the Bode plot is

5 Problem 5 The Nyquist plot for an amplifier with a β=.5 is shown below. a) Determine the phase margin of the feedback amplifier b) Determine the dc gain of the open-loop amplifier c) Determine the poles of the open-loop amplifier d) Determine the polse of the feedback amplifier. e) Determine the Q of the poles of the feedback amplifier The MATLAB code used to generate this Nyquist plot is: Problem 6 Assume an operational amplifier has a dc gain of 8dB and poles on the real axis at -1 rad/sec and at -1 4 rad/sec. Plot the locus of the closed loop poles as β changes from to 1. Assume the feedback gain is characterized by the standard feedback equation A FB s OL s AOL. 1 A s

6 Problem rad/sec. Repeat Problem 6 if everything is the same except there is a double pole at Problem 8 Consider an amplifier with poles at -1 rad/sec, -1, rad/second and -25, rad/sec and a dc gain of 1,. a) Give the Nyquist plot for β=.5 if there is a RHP zero at 2, rad/sec b) Determine the phase margin for the same conditions as part a) c) Repeat part a) if the zero is moved to the LHP at -2, rad/sec d) Repeat part b) for the conditions of part c)_

7 TRANSISTOR PARAMETERS W/L N-CHANNEL P-CHANNEL UNITS MINIMUM 3./.6 Vth volts SHORT 2./.6 Idss ua/um Vth volts Vpt volts WIDE 2./.6 Ids < 2.5 < 2.5 pa/um LARGE 5/5 Vth volts Vjbkd volts Ijlk <5. <5. pa Gamma.5.58 V.5 K' (Uo*Cox/2) ua/v 2 Low-field Mobility cm 2 /V*s COMMENTS: XL_AMI_C5F FOX TRANSISTORS GATE N+ACTIVE P+ACTIVE UNITS Vth Poly >15. <-15. volts PROCESS PARAMETERS N+ACTV P+ACTV POLY PLY2_HR POLY2 MTL1 MTL2 UNITS Sheet Resistance ohms/sq Contact Resistance ohms Gate Oxide Thickness 144 angstrom PROCESS PARAMETERS MTL3 N\PLY N_WELL UNITS Sheet Resistance ohms/sq Contact Resistance.78 ohms COMMENTS: N\POLY is N-well under polysilicon. CAPACITANCE PARAMETERS N+ACTV P+ACTV POLY POLY2 M1 M2 M3 N_WELL UNITS Area (substrate) af/um 2 Area (N+active) af/um 2 Area (P+active) 238 af/um 2 Area (poly) af/um 2 Area (poly2) 53 af/um 2 Area (metal1) af/um 2 Area (metal2) 32 af/um 2 Fringe (substrate) af/um Fringe (poly) af/um Fringe (metal1) af/um Fringe (metal2) 48 af/um Overlap (N+active) 26 af/um Overlap (P+active) 278 af/um