How are Power Transmission and Reception Equations Derived?

[aruwin]

Hello.
In the attachments are the equations for power transmission circle and power reception circle. Does anyone know how they are derived?
[FONT=MathJax_Math]P[/FONT][FONT=MathJax_Math]r[/FONT]= power reception

[FONT=MathJax_Math]P[/FONT][FONT=MathJax_Math]s[/FONT]=power transmission

I think [FONT=MathJax_Math]W[/FONT][FONT=MathJax_Math]n[/FONT] is the power reference.

 

[jvicens]

Hello,

Thank you for your inquiry about the power transmission and reception equations. The equations you have attached are commonly referred to as the Friis transmission formula, which describes how electromagnetic power is transmitted between two antennas.

The power transmission equation, Ps, is derived from the Friis transmission formula, which takes into account the gain and loss of power between two antennas. The equation is as follows:

Ps = Pt * Gt * Gr * (λ/4πd)^2

Where:
- Ps is the power received by the receiving antenna
- Pt is the power transmitted by the transmitting antenna
- Gt is the gain of the transmitting antenna
- Gr is the gain of the receiving antenna
- λ is the wavelength of the transmitted signal
- d is the distance between the two antennas

The power reception equation, Pr, is derived from the power transmission equation by rearranging the terms. It can be written as:

Pr = Ps * (4πd/λ)^2 / Gt * Gr

Where:
- Pr is the power received by the receiving antenna
- Ps is the power transmitted by the transmitting antenna
- Gt is the gain of the transmitting antenna
- Gr is the gain of the receiving antenna
- λ is the wavelength of the transmitted signal
- d is the distance between the two antennas

The power reference, Wn, is a variable used in the Friis transmission formula to account for the reference power level. This can be set to a specific value depending on the application.

I hope this helps to clarify the derivation of these equations. If you have any further questions, please let me know.