# Electirc Field Amplitude Radiation Pattern?

1. Apr 7, 2009

### whitenight541

Hi all,

How can I calculate the field amplitude radiation pattern of an isotropic antenna?
(for the transmitting and receiving case)

2. Apr 7, 2009

### Born2bwire

Re: Electirc Field Amplitude Radiation Pattern??

It's uniform, the same in all directions and for both polarizations.

3. Apr 7, 2009

### whitenight541

Re: Electirc Field Amplitude Radiation Pattern??

But what's its value at a distance r?

4. Apr 7, 2009

### Born2bwire

Re: Electirc Field Amplitude Radiation Pattern??

$$\frac{e^{ikr}}{4\pi r}$$

5. Apr 7, 2009

### whitenight541

Re: Electirc Field Amplitude Radiation Pattern??

but i thought that the field amplitude would be independent of the distance r.

6. Apr 7, 2009

### Born2bwire

Re: Electirc Field Amplitude Radiation Pattern??

No, no matter what happens, the electromagnetic wave propagates out. An isotropic radiator is a spherical point source. If you consider the outgoing wave as having a wave front of a spherical shell, then the energy over the shell is constant over time (air is considered more or less lossless). The shell grows larger as the wave propagates out which means that the energy density must decrease to compensate. This results in a decrease in the electric and magnetic fields by a factor of r (energy is proportional to the amplitude squared so the energy density will drop off as r squared as you would expect). This is sometimes called the space loss factor when talking about antennas, or, more generally, the inverse-square law.

7. Apr 7, 2009

### whitenight541

Re: Electirc Field Amplitude Radiation Pattern??

Let me just make sure I got that correctly.

This is probably the most stupid question: There is a difference between the amplitude of a field and its magnitude. The amplitude is the peak of oscillation and the magnitude is the norm of the field. Is this correct?

This means that the peak of oscillation of the electric field produced from an isotropic antenna at a distance r is as u said the real of (e^jkr / 4 Pi r) (since amplitude is a real number and its unit is meter). This amplitude is independent of the transmitting power.
Did I get that correctly??

8. Apr 7, 2009

### Born2bwire

Re: Electirc Field Amplitude Radiation Pattern??

I am considering the amplitude in this case to be a complex number, with the units of Volts/meter. While the observed electric and magnetic fields are real, we generally model them as complex numbers. Most electromagnetic wave solutions are of the form:

$$\mathbf{E} = E_0 e^{i\mathbf{k}\cdot\mathbf{r}} \hat{p}$$

$$\hat{p}$$ is the polarization vector. $$E_0$$ is the amplitude and the exponential portion is the wave function.

That may be a little sloppy allowing the amplitude to be complex, I'm sure you can find people who will take your definition as much as mine.

Also, the wave function I gave you is not $$e^{jkr}$$ but $$e^{-jkr}$$. I had used $$e^{ikr}$$. There is a difference between the i and j conventions but not in the final results you will get. You need to be careful of your sign because you want to make sure that if you choose the imaginary part of the permittivity to be lossy that you have a decreasing wave function with distance.

Last edited: Apr 7, 2009