# How to Model antenna as voltage source?

I heard that the antenna only receives POWER, not voltage. From this fact, I thought that the current will be 1 / (antenna resistance + load resistance). That is, the input power is constant. Let us define the transmit signal with power 50 Watt is $$s(t) = 10\cos(2\pi f_c t).$$ And we assume that the receiver receives the signal that is reduced a half of the transmit signal, i.e., the power of the received signal is 25 Watt.

Then, is the voltage source defined as $$v(t)=A \cos(2\pi f_c t)$$ such that $$\frac{\frac1T\int_T |v(t)|^2 dt}{R_{antenna}+R_{load}}=25$$ ?

Antennas have something known as their characteristic impedance. You can think of a antenna as a Thevenin or Norton source at this impedance.

A common dipole has around 75 Ω impedance at its intended operating frequency. A folded dipole has about 300 Ω impedance.

For example, if a 75 Ω antenna picks up a 100 µV signal, then you can think of it in two equivalent ways from the point of view of the circuit. It could be a 100 µV source with 75 Ω in series, or a 1.33 µA source with 75 Ω across it.

Note that the above only applies at the antennas intended operating frequency. The impedance can be very different at other frequencies. For example, a dipole as infinite impedance at DC, and a folded dipole 0. The impedance also become reactive (no longer purely resistive) at off frequencies.

• It follows from the last para that you can crudely model the antenna as a voltage source followed by a series RLC resonant circuit, with R around 75 or 300 ohms, and LC chosen to approximate the tuned frequency of the antenna (via their product and a well known equation for frequency) and its bandwidth (via their ratio, R, and a well known equation for Q). – Brian Drummond Sep 28 '17 at 12:00
• I want to know how to model the voltage source as 100 uV. Actually, I am considering that received signal's power is transmit signal's powerKd^(-alpha), where K is a constant regarding to antenna and so on, d is distance between tx and rx, and alpha is attenuation factor, normally 2 to 8. In this case how to decide the voltage source is 100 uV! Can you explain this? :) – God Danny Sep 29 '17 at 2:59
• Actually, I am studying wireless communication, so I usually dealt with the received signal power which is calculated from channel and transmit power. However, recently, I am studying on simultaneous wireless information and power transmission (SWIPT) system, so I want to know how much voltage signal value the antenna makes. – God Danny Sep 29 '17 at 3:02

An antenna impedance is key to being able to extract the best signal given the incident power. For instance a monopole looks like an impedance in series with a resistance of about 37 ohms when it is a quarter wave long. At other frequencies it changes its impedance dramatically: - The "height" mentioned in the diagram is in fact monopole length and not the distance a particular antenna is placed above ground.

So, at about 0.05 wavelengths, the antenna resistance is virtually zero but the impedance is -j1000 ohms (capacitive). At one quarter $\lambda$ the impedance looks resistive 37 ohms (although in this picture it is hard to see).

The voltage received at the terminals is proportional to antenna length and the E-field present. This is one of the reasons why an antenna at higher frequencies receives less power - the length of the antenna (assumed to be at a constant ratio to $\lambda$) defines how much power it can capture and this reduces with increasing frequency.