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final1996

# final1996 - NAME_EE214 Final Examination Fall 1996 This...

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NAME:____________________________________EE214 Final Examination: Fall 1996 Page 1 of 11 This handout contains excerpts from EE214 final exams administered in 1996 and 1997. The final exam this year may or may not resemble these problems. This collection is pro- vided simply for review. No published solutions are available. However, you should feel free to contact the teach- ing staff if you get stuck while trying to solve any of these problems. It is important to keep in mind that EE214’s course content varies somewhat from year to year. For example, “root locus” techniques were not covered this year, so you should not feel worried about the question(s) that ask about this topic.

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NAME:____________________________________EE214 Final Examination: Fall 1996 Page 2 of 11 PROBLEM 3 : This problem concerns the output impedance of practical operational amplifiers. Suppose we add to an otherwise completely ideal operational amplifier some small (but nonzero) series output resistance, r out , to model more closely real op-amps. a) If we use this op-amp/r out combination in a standard inverting amplifier configuration, what is an exact expression for the loop transmission? Call the feedback resistor R f , and the input resistor R i . Assume for now that the op-amp itself simply has a scalar gain G. Watch your signs; we’re going to be very fussy about them. Ans: LT = ___________________________________________ b) Derive an expression for the output resistance of the inverting amplifier; assumptions as above. For this and all subsequent sub-parts to this problem , you may assume explicitly that r out is negligibly small compared with the feedback resistor. Ans: R out = ___________________________________ c) Now consider a more realistic functional form for the op-amp gain. We have seen that Miller compensation is widely used in general-purpose op-amps to force single-pole behavior over a wide frequency range to make them easy to use. Assume that Miller com- pensation results in a transfer function for our op-amp that is well-approximated by: Using this equation, derive an expression for the output impedance of the inverting ampli- fier. Express your answer explicitly as the product of two terms, where the first is the DC value of the output resistance. All polynomials in s should be written with a con- stant term of one. Ans: Z out ( s ) = ______________________________________________________ d) Derive an expression for the crossover frequency. Ans: ϖ c = __________________________________________ G s ( 29 G o τ s 1 + =
NAME:____________________________________EE214 Final Examination: Fall 1996 Page 3 of 11 e) Simplify your answer to c) with the assumption that we are only interested in system behavior for frequencies well below the loop crossover frequency. In that case, the output impedance may be expressed simply as the sum of a resistive and inductive term. Derive the relevant expressions.

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