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EE 435 Homework 1 Spring 2016 Due Wed Jan 20 Problem 1 Identify one operational amplifier that has been published in one of the following in the past 5 years: IEEE Journal of Solid State Circuits IEEE Trans. On Cirucits and Systems (Part 1 or Part 2) IEEE International Symposium on Circuits and Systems Give the circuit schematic, citation information, and briefly summarize the useful properties that the author claims for this circuit. Problem 2 Identify one operational amplifier that has been patented in the past 5 years. Give the circuit schematic, patent number, and briefly summarize the useful properties that the author claims for this circuit. Problem 3 Consider the following operational amplifier. The goal is to obtain an expression for the small-signal output voltage in terms of the input variables VIN+ and VIN-. a) b) c) d) Write a complete set of small-signal equations that can be solved to obtain VOUT. Assume the small-signal parameter go is present in all MOS devices. Solve these equations by hand for VOUT but, if you do not have a solution at the end of ½ hour, stop, and comment on your progress and the amount of effort that you believe would be required to finish the solution. Obtain a parametric (symbolic) solution for the transfer function VOUT/VIN from this set of equations with MATLAB. This solution will be the ratio of two polynomials in s. Each coefficient will be comprised of the sum of a number of product terms. How many total product terms appear in this solution? In this part, Vin=Vin+-VinSimplify the solution obtained with MATLAB under the assumption that all gm terms are small compared to go terms VDD M3 M4 VOUT VIN M1 M2 VIN CL VB2 M9 Page 1 of 5 Problem 4 Assume the amplifier can be modeled by an input-output relationship VIN VOUT -A VOUT AVIN VXQ VYQ a) Derive an expression that shows how the closed-loop output relates to the closedloop input in the feedback amplifier shown below. Assume the input VIN is comprised of a quiescent component (VinQ) and a small signal component (Vinss) and is given by the expression VIN VinQ Vinss R2 VIN R1 V1 VOUT A b) Show that if A is large, this expression reduces to VOUT R2 R Vinss VXQ 2 VXQ VinQ R1 R1 Page 2 of 5 Problem 5 Assume the amplifier shown below is designed in a 0.5µ CMOS process. and that VDD=5V , VSS=-1.5V, and IDQ=4mA. a) Analytically determine the W and L needed to establish a quiescent output voltage of 1V VDD IDQ VOUT VIN VSS b) c) d) Verify the transfer characteristics by Spice simulation. Analytically determine the dc voltage gain at the Q-point established in a) Using SPICE, obtain a plot of the small signal voltage gain versus the quiescent output voltage. Problem 6 Assume the amplifier in Problem 5 is used as a single-input, single-output operational amplifier. With this op amp, analytically determine the small signal voltage gain and the quiescent output voltage for the circuit shown below if R2=20M and R1=5M. Assume that the dc offset of VIN is 1V. Verify the gain of this amplifier with SPICE simulation. R2 VIN R1 V1 VOUT A Page 3 of 5 Problem 7 A transresistance amplifier with a gain RT is shown. Derive an expression for the voltage gain of the amplifier as a function of the transresistance gain RT and determine what that reduces to if RT is very large. R2 R1 VIN VOUT RT Problem 8 (Extra Credit) It was stated in class that all even-ordered distortion terms introduced by the amplifier vanish in symmetric fully differential amplifiers. Prove this fact. (Hint: assume that if an ideal differential sinusoidal signal is applied at the input, one of the single-input outputs is given by the expression VOUT 1 t A1 sin(1t 1 ) Ak sin k1t k k 2 where ω1 is the frequency of the sinusoidal input and the parameters A2,A3, … and θ2,θ3, … characterize the distortion introduced by the amplifier.) Problem 9 (Extra Credit) A model of an operational amplifier used in a basic feedback amplifier configuration with an inverting gain is shown below. a) Derive the voltage gain of the feedback amplifier that includes the nonideal effects of the input impedance RIN and the output impedance RO of the op amp. b) Show that RIN and RO do not affect the feedback gain if the open loop votage gain AV is large. R2 R0 R1 VIN V1 RIN Op Amp Page 4 of 5 AVV1 VOUT RL Problem 10 (Extra Credit) The “dead network” of a circuit is obtained by setting all small-signal inputs to 0. That is, by replacing all ac voltage sources with short circuits and all ac current sources with open circuits. The β of a feedback amplifier is a characteristic of the “dead network”. Consider the basic inverting and noninverting feedback amplifiers shown below. These are widely used as small-signal voltage amplifiers. R2 R1 V1 VOUT AV VIN R2 R1 VIN V1 VOUT AV a) Show that they both have the same “dead network” b) The β of the two amplifiers shown is R . Show that the gain of the 1 R1 R2 noninverting feedback amplifier can be expressed by the standard feedback equation V AV A VF OUT = VIN 1+A Vβ c) Take the limit at AV goes to ∞ for the gain derived in part b) and compare with that derived in EE 230 for the gain of the noninverting feedback amplifier. d) Derive the gain of the inverting feedback amplifier in terms of AV and β and comment on why it does not look like the standard feedback equation. Page 5 of 5