# Relationship between the carrier frequency and the propagation distance? [duplicate]

For electromagnetic waves, Is there a relationship between the carrier frequency and the propagation distance?

When transmission distance increases the signal tends to lose power, so carrier signal is added along with the message signal ( to strengthen the original message signal). Is that true?

## marked as duplicate by Stanley Pawlukiewicz, MBaz, A_A, lennon310, AlexTPApr 11 '18 at 12:17

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## 2 Answers

Even in vacuum, there exists an attenuation that is inversely proportional to the frequency squared of the signal. It is called the free-space loss.

The ratio of received power vs. transmitted power (for polarization-matched antennas aligned for maximum directional radiation and reception) reduces to:

$$P_r / P_t = (c/(4\pi ~d ~f))^2 ~G_{0t}~G_{0r} ~~~~~~~~~~~~~[1]$$

where $c$ is the speed of light in vacuum ($\approx3\times10^8 ~$m/s), $d$ is the separation between antennas (in meters), $f$ is the central frequency (in Hz) of the signal, and $G_{0t}$, $G_{0r}$ are the antenna gains under the conditions stated above.

As can be seen from Eq. [1], for a specific power ratio (attenuation), there is a fixed relation between the frequency and the propagation distance.

Equation [1] is a particular case of the well known Friis transmission equation. The term $(c/(4\pi ~d ~f))^2$ is called the free-space loss factor, and it takes into account the losses due to the spherical spreading of the energy by the antenna.

See, for example, the following reference for further details:

C. A. Balanis, "Antenna Theory. Analysis and design", 2nd edition, 1997. (Section 2.17, Chapter 2)

The inverse relationship between distance and frequency is not due to the propagation phenomenon itself, but due to the physical dimensions of the receiver antenna (which does depend on frequency, in something called the effective area of the antenna). In practice we always have an antenna matched to the desired frequency, and thus we have a propagation distance limited by this restriction.

Regarding the second part of your question, normally a carrier signal is added (for example, in AM modulation) for simpler detection circuits. Besides, the carrier signal is used sometimes to perform synchronization at the receiver. I have not seen before the use of a carrier to "strengthen" the message signal.

Actually, instead of using an extra power to transmit a carrier, it can be used to increase the power of the message signal, and thus let the message travel a longer distance with the same attenuation.

• No. In free space the wave equation does not predict attenuation as as function of frequency. Friis describes the effects of a finite aperture, not attenuation. – Stanley Pawlukiewicz Apr 10 '18 at 20:55
• Well, actually you are right. The inverse relationship between distance and frequency is not due to the propagation phenomenon itself, but due to the physical dimensions of the receiver antenna (which does depend on frequency). However, in practice we always have an antenna matched to the desired frequency, and thus we have a propagation distance limited by this restriction. That is what I meant before. I just edited my answer to point it out. – Luis M Gato Apr 11 '18 at 13:32
• I'm aware of the convention. In SONAR the frequency term would be part of the antenna gain. The term "propagation loss" isn't universal even inside the DSP community. – Stanley Pawlukiewicz Apr 11 '18 at 15:41

Normally the higher the carrier frequency the more it will be absorbed by the environment (for instance air, water) and the smaller the propagation distance. I think this happens because the smaller the wavelength the more it becomes of the size of small particles in the environment which tend to block it.

When transmission distance increases the signal tend to attenuate, so carrier signal is added along with the message signal ( to strengthen the original message signal). Is that true?

I'm not sure what you are asking here. If you want to avoid attenuation a possible choice is to increase the transmission power. The transmission of carrier signal along with message has to do with modulation. For instance AM uses this.

• I mean that signal modulation (convert message from baseband to bandpass) increase the propagation distance – user24907 Apr 10 '18 at 19:55
• @user24907 that doesn't make any sense. – Marcus Müller Apr 11 '18 at 5:40