hmwk 7 sol - EECS 314 Fall 2006 HW 07 Problem 1 Student's...

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EECS 314 Fall 2006 HW 07 Problem 1 Student's name ___________________________ (Last name, first name, IN INK) The big picture Transformers can help match the source and load impedances and thus achieve the maximal power transfer from the given source to the given load. Read the lecture notes and section 7.3 in Rizzoni’s text for discussion and examples. Problem Consider an audio amplifier as the voltage source V T = (80 V) cos( ω t) with the equivalent impedance (equivalent resistance) Z T = R T = 60 Ω , and the speaker as a load with Z LOAD = 8 Ω . Hints: A. In each part of the problem, use the formulas for the average AC power. Notice that, although you do NOT need phasors (there is no phase shift between the voltage and the current in this circuit), the voltage is sinusoidal (not DC) thus you have to use the formulas for AC voltage and average power (not for DC voltage and DC power). B. In each part 2, 3 of the problem, reduce the original circuit (top diagram) to its equivalent (bottom diagram) and determine the apparent load impedance. C. In Part 2, you know the apparent load impedance: it must equal the complex conjugate of the source impedance: since the source impedance is pure resistance, the load impedance is also pure resistance (the phase shift between the voltage and current is zero). D. In Part 3, a very good replacement ensures power transfer (relative to the maximal) of 90% and above, a good replacement ensures 80% and above, and an acceptable replacement ensures 70% and above. Part 1 Consider the circuit with the given source and the given load, connected directly, without any transformer. Calculate the average power P 1 in watts transferred to the load. The problem is continued on the next page © 2006 Alexander Ganago Page 1 of 2
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EECS 314 Fall 2006 HW 07 Problem 1 Student's name ___________________________ (Last name, first name, IN INK) Part 2 Consider the circuit with the same source and the same load, connected through a transformer, which is specially chosen to achieve maximal power transfer. The transformer has n 1 = 1000 turns in its primary coil. Calculate the number of turns n 2 in the secondary coil and the average power P MAX in watts transferred to the load. Calculate the ratio of powers P 1 / P MAX Part 3 Assume that you found a transformer that has 300 turns in one coil and 600 turns in the other coil, and decided to use it in this circuit for impedance matching. Which coil would you use as the primary? What average power P 3 in watts is transferred to the load in a circuit with this transformer? Calculate the ratio of powers P 3 / P MAX Write a brief conclusion on whether this transformer is a good replacement for the perfect transformer discussed in Part 2 (see Hint D above). Write your results below.
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hmwk 7 sol - EECS 314 Fall 2006 HW 07 Problem 1 Student's...

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