Answer #2: Power vs. Signal Strength
Antenna Puzzle #2 asked why 3 db of gain is obvious for two identical dipoles for reception (3 db): But… it’s not so obvious for transmission!
This is a wonderful question because it shows how power and field strength differ, even though they are directly related.
An insight into the answer comes if you ask the question: if you double the power to your dipole, how much does the field strength increase? The answer is that power is related to E-field strength squared. If your power is 100 watts, and you double it to 200 watts, your field strength does not double. That’s because the square root of 100 is 10, and the square root of 200 is 14.14. So, doubling your power only increased your field strength by about 40%.
With that in mind, you can now analyze the dipoles above for transmission. Here’s a diagram that shows the proportional values (not actual values):
So, here’s what’s happening:
- 100W is divided in half, so 50W for each dipole.
- 50W radiates as a field that is proportional to the square root of 50, thus 7.07.
- At the receive antenna, the two fields combine, 7.07 + 7.07 = 14.14.
- The power received is the square of the field strength: 14.14 squared = 200.
So, you must add the field strength of each dipole, not power. (And of course, the above is written to show the proportions, not actual values. The actual received power is substantially less due to distance and antenna pattern.)
You can now see that the power gain of the system is double (3 db, just like before), even though the power was been split between the two dipoles! Another way to write this is:
pwr-recv = (sqrt(pwr-xmit / 2) * 2) ^ 2
If you enter that into your favorite calculator, slide-rule, or programming language, you’ll see that the pwr-recv result is always double the pwr-xmit input.
So, the principle of antenna reciprocity is safe and sound. The gain is the same for both receive and transmit.
For greater detail see: Signal Strength Relationship to Radiated Power.