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I guess I'll reply to myself. It appears that my problem is that when I turn off the radio, my radio goes from driving the speaker lines, to floating, rather then driving them to ground. When they float, some times, but not always, the lines end up at around 2-3V or higher. When this happens the Monsoon doesn't fully turn off. Causing a dead battery.
So my solution, which is under test now and has had good results so far, is to put a 1K ohm resistor between gnd and the left front - line. Here's the reasoning for using a 1K resistor. My radio claims 50W output for 4 speakers each with 4 ohms, or say 12.5 watts per speaker. I'll assume that's RMS not peak, even thought the real power is probably closer to 8-9 watts RMS. With P = V X I and I = V / R plus a little algebra we get P = V^2 / R or (P X R)^.5 = V = (12.5 X 4)^.5 = 7.07V. Resistors typically come in 1/8 watt or 1/4 watt so I'll choose look to drive it to ground with an 1/8th watt resistor. So we do V^2 / R = P --> R = V^2 / P = (7.07^2) / .125 = 39 ohms. But lets say it can do up to 12V we get (12 X 12) / .125 = 1152 or about 1K. So I chose 1K because you don't have to worry about the power rating of the resistor.
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