# How to Calculate the Power of a Signal

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A signal is an electromagnetic field that delivers or transfers data or energy from one point to the next. The simplest signal is direct current, or "DC". When turned on, a DC signal stays at the same voltage while it's on. When off, it's at zero. Digital signals are discrete DC signals of 1s and 0s with a 1 represented by 5 volts and 0 represented by 0 volts. More complex signals are time-varying signals where the voltage, once on, changes as time increases.

### Things You'll Need

• Oscilloscope
• Ohmmeter
• Calculator
• Determine the output resistance or,"R, of the circuit that generates the signal. You can get this from a schematic of the circuit. Or, you can measure it by placing an ohmmeter across the output terminals of the circuit.

• Identify your signal. If you have a DC signal, your signal would be the DC voltage, when the DC power supply is turned on. If you have a time-varying signal, your signal is a mathematical representation of the time varying waveform. For example, assume you have a time varying signal, S (t), that changes according to a sine wave. In this case, your mathematical representation will be S (t) = Vsin (t). Here's an example of how it works:

If you assume V = 5-volts:

at t = 0, S (t) = 5 sin (0) = 0, because sin (0) is 0

at t = 1, S (t) = 5 sin (1) = 5 (0.84) = 4.2 v

at t = 2, S (t) = 5 sin (2) = 5 (0.9) = 4.5 v

at t = 3, S (t) = 5 sin (3) = 5 (0.14) = 0.7 v

at t = 4, S (t) = 5 sin (4) = 5 (-0.75) = -3.75 v

at t = 5, S (t) = 5 sin (5) = 5 (-0.95) = -4.5v

at t = 6, S (t) = 5 sin (6) = 5 (-0.28) = -1.4v

at t = 7, S (t) = 5 sin (7) = 5 (0.65) = 3.25v

As you can see, the voltage starts at 0, ramps up to 4.5 and then oscillates between positive 4.5 and -4.5 as time increases. If you plotted this on a graph, it will look like a sine wave. If you do not know your signal representation off hand, you can connect an oscilloscope across the output terminals of the circuit. You can then use the oscilloscope output to mathematically model the waveform.

• Calculate power using the formula: P = S^2/R, where P is the power, S is your signal and R is the resistance. You take your signal, square it and divide it by the resistance to get the power of the signal. If you have a DC signal, then just square your voltage and divide by resistance. If you have time varying signal, square the mathematical representation of your signal and divide the results by the resistance.

## References

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