Electronics, Power & 1 + 1 = 4

Apr 06, 2009 4 Replies
M

Obviously I've made an elementary mistake.



Consider a sine wave with amplitude 1 from a signal generator and assume that it takes 1 unit of power to make.



Consider it together with a second identical sine wave of the same phase. So total power to make is 1 + 1.



Add the two sine waves together. The result has amplitude 2. Power is proportional to amplitude squared so the total amount of power it carries is 4.



So how is it that I can put 1 + 1 units of power in and get 4 units of power out?



Or of the two had opposite phases how can 1 + 1 = 0?


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A

Let's say we have a power combining network with two 50-ohm inputs and one

50-ohm output. You connect sources to the inputs, which each supply sinusoidal voltages of unit amplitude. If the network is 100% efficient, the output amplitude will be sqrt(2). The only way to get an output of 2 volts would be if the output port was matched to 100-ohms instead of 50-ohms.

If the two sources were connected in series with opposing phase then no net voltage is developed, no current flows and no power is drawn from either source.

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O

I will assume that you measure all voltages over the same impedance.

To "add" both waves you will have to use a passive combiner, which will give you sqrt(2) output amplitude. No passive device will give you 2 volt amplitude since that would violate the passiveness assumption

You may have a look at

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Pere

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M

It works of your stack the two resistors you have in top of each other to double the load resistance. :) 2V across 2 ohms is 2 watts.

If they are out of phase, this simple analysis doesn't apply.

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C

you seem to be mixing up between current and voltage power is proportional to square of current but directly proportional to voltage and voltages are usually used to describe waveforms not current

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