## Examples of Signal Strength Related to Power

**The Answer to Antenna Puzzle #2 was based on the idea that signal strength is related to power by squares.**

If you remember the power formula from ohm’s law, you know that:

**power = voltage squared / resistance**

and signal strength is most often measured in voltage per unit length (for example micro-volts per meter.)

To show this relationship, here are a few photos of signal strength measured on the 10M band at four different power levels. This was done by connecting an oscilloscope to a nearby monitor antenna, then snapping a photo of the screen.

Each image is twice the power of the previous image.

**For 10 watts** we see 0.39 volts (peak-to-peak):

**For 20 watts** we see 0.542 volts. Notice that we don’t see twice the 0.39 volts, what we see is the square root of two times the square of 0.39. So, thats:

`0.39 squared = 0.152
0.152 x 2 = 0.304
square root of 0.304 = 0.551 (roughly)`

**For 40 watts** we see about 0.846 volts. (Notice that it’s not precisely what we expected. That’s because I don’t have precise control over the radio’s power output. It’s just approximate.)

**For 80 watts** we see 1.192 volts:

So, when you go from 10 watts to 80 watts you** don’t see your signal strength increase by a factor of 8, you only see it increase by about 3! ** (Kind of seems like a rip-off, doesn’t it?)

*That’s worth keeping in mind if you ever need to measure the signal strength of your antenna or figure out strange antenna puzzles posted to miscellaneous ham radio sites on the web.*