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Isotropic Radiation Equation

  1. Mar 13, 2007 #1

    I'm trying to plot a radio wave propagation plot of an isotropic antenna. I've found a collection of equations that I've tried to use, but the results that I'm getting, aren't exactly what I expect (not a circle or sphere, since the power is equally distributed).

    Here is the equation that I'm currently using.
    ReceivedPower(RxP) = TransmitPower(TxP) - FreeSpaceLoss(FSL)

    Receive gain is equal to the transmit gain, which is equal to 1 or 0dB.

    FSL = -27.55 dB + 20*log[frequency(MHz)] + 20*log[distance(m)]
    TxP = InputPower / 4*Pie*Radius^2
    TxP = EIRP, Effective Isotropic Radiated Power

    So the only variable that I have would be the distance & radius, which I believe to be the same. All the images of an isotropic antenna power distribution demonstrate a spherical (or in a 2d space, a circle with an intensity radiating outwards). Instead I have a spike in the middle of high power, which drastically goes to zero as the distance grows.

    My question is whether or not I'm using the correct equations. If so, is this the sort of output that I should be seeing? Lastly, EIRP generates a unit [W/m2], can is this a valid unit to be using to be measuring dB, or is there a conversion that I should be using?
  2. jcsd
  3. Mar 13, 2007 #2
    Typically, you see:

    Pr (dBW) = EIRP (dBW) + Gr (dB) - FSL (dB)

    where Gr is the antenna gain of your receive antenna, FSL is as you calculated in the equation, and EIRP is the effective isotropic radiated power and is given by

    EIRP (dBW) = Pt (dBW) + Gt (dB),

    where Pt is the transmitter power, and Gt is the gain of your transmit antenna.

    The only parameter that will depend on distance is FSL. When you plot the data, you will need to be careful about letting distance go to zero, as the equations blow up --- they are intended to be used in the "far field" of your transmitting and receiving antennas.
  4. Mar 14, 2007 #3
    [W/m^2] is correct since any "radar/antenna" equation will give you result in this units. Because Radiated power is measured in watts per square meter.

    Basic antenna equation states that:
    Multiply or add-up everything the has to do with gain and divide by everything that has to do with loss, including distance.
  5. Mar 14, 2007 #4
    Hi guys,

    Thanks for the responses. It seems like I'm doing everything that you explained. I didn't add the gain to the equations, because I assumed that there was no gain or loss on both the transmitter or the receiver. Also I was reading on the TxP equation, and the Radius does vary, so it should increase/decrease respectively with the Distance variable. (TxP describes the power at a given distance from the transmitter source).

    I've done a bit more work on this and here is what I think I'm getting confused with. I'm trying to graph my plot in both a 2D and 3D space. For a 3D space, I thought I was supposed to see a sphere (http://www.hp.com/rnd/images/pdf_html/antennas_figure6.jpg) [Broken], but when I graph my plot, it's more like rotating a 1/R^2 equation around the z-axis (looks something like a pitched tent). If I'm understanding this properly, the sphere demonstrates the isotropic propagation pattern (equally distributed in all directions), where my graph represents the power distribution of the isotropic signal (which is distributed in all directions, but the amplitude decreases as the distance grows). So in the end, I believe my graphs and equations are right. Please feel free to correct me here, if anyone disagrees. Thanks again for the help.
    Last edited by a moderator: May 2, 2017
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