RF Power Transmission

If EIRP is some measurement unit which takes frequency into account, then it is necessary to know what it is. What is EIRP?

EIRP stands for Effective Isotropically Radiated Power and takes into account the characteristics of the antenna used (i.e. gain, directivity). In the case in question the EIRP will be the same if the antenna is the same and the antenna frequency bandwidth accommodates the TX spectrum in both 20MHz and 40MHz cases.

I'm not an RF engineer, and I'm fairly ignorant in the field, and you won't see any explicit Maxwell's equations describing what happens when a bandwidth is doubled. The efficiency of a half-wave dipole antenna, for example, is certainly a function of radiator lengths, and the farther the signal is from the center frequency of the dipole, the lower the radiated power.

You forgot he said "the antenna frequency bandwidth accommodates the TX spectrum in both 20MHz and 40MHz cases." In this case it has nothing to do with "radiator lengths"! Any ham radio operator can see that!

WARNING: The last comment was attempted humor to parody the "Any caveman can see that..." commercials and was not intended to slam Ham Radio Operators. I are one!

Also, don't confuse center frequency (in GHz or THz?) with bandwidth. He is obviously working in the microwave region if his bandwidths are in MHz. In the HF/VHF spectrum, MHz would be the unit of center frequency, with bandwidth usually expressed in KHz (or very small MHz).

Since we're woefully ignorant of the details of his antenna and carrier frequency, the best we can do is joke about it. :-) Regards, Pre-Caveman

Assuming a perfect sine wave carrier with zero modulation (continuous wave), the total transmitted power should be the same, assuming also that the transmitter has a fixed voltage and current (same load, right?). However, the peak power will be lower for the greater range. Therefore to a receiver with fixed threshold sensitivity and selectivity, it will appear as a weaker signal.

This holds only if the full power of the transmitter were available to the antenna, and not if the 20 MHz wide transmission was simply a 40 MHz wide transmission with its tails clipped off by filters.

Think of it as a probability distribution, the area under a "bell" curve. The total area must be the same in both cases, but the standard deviation (the spread) of the 40 MHz wave will be twice that of the 20 MHz wave, so the peak must be less. I would have to check a Math or Stat book to know how much less.

Now, some statistician please tell me what the lower peak (mean) power level would be in the center of the 40 MHz wide distribution! Is it half? That would be too easy!

Strictly by the equation: EIRP= Carrier Power (avail at antenna input) * Transmission Gain. Within the Transmission Gain, the EIRP is proportional to the square of the carrier frequency. If all other parameters are equal (including time, Watt =Joule/sec), then the EIRP will be four times the EIRP for the f=40MHZ (which is two times the previous frequency). In other words, Fnew= 2*Fold, so EIRP is proportional to the square of (Fcarrier)or the square of (2*Fold)which is equal to 4Fold which correlates to 4 x the previous EIRP.