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hw1_sol - EE 101 Professor Abbas El Gamal Handout 3 Jan 22...

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EE 101 Handout # 3 Professor Abbas El Gamal Jan. 22, 2002 Homework #1 Solutions 1. (a) Let v denote the output voltage of the CD player. The voltage limit is | v | ≤ 5. The current into the receiver is v/R , so the current limit is | v/R | ≤ 0 . 01, or equivalently, | v | ≤ 0 . 01 R . Therefore for 0 . 01 R < 5, i.e. , R < 500Ω, the current limit is more stringent than the voltage limit. For R 500Ω, the voltage limit is more stringent. (b) When R = 10kΩ (a typical value), the CD player output is limited to ± 5V by the voltage limit; the current limit is irrelevant. The maximum power in this case occurs for v = 5V (or v = - 5V); it is p max = 5 2 / 10kΩ = 2 . 5mW. For R = 400Ω, on the other hand, the CD player output would be limited to ± 4V by the current limit. Another way of looking at this is to sketch the given limits on a v i plot. This forms a box in the plane. Note that the set of points inside the box represents all the possible voltage-current combinations the amplifier can handle. This sketch looks like: i v 10mA - 10mA 5V - 5V R 500Ω R = 500Ω R 500Ω Connecting a resistor across the terminals of the amplifier can be represented by sketching v = iR on the same plot. This equation gives a straight line whose 1
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slope is 1 /R . Thus a line along the vertical axis corresponds to infinite slope or zero resistance, and a line along the horizontal axis corresponds to zero slope or infinite resistance. In other words, these two examples are a short circuit and an
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