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Convert normalized radiation E-field patern to Power in dBs?

 
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dekk0009
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Joined: 17 Jun 2010
Posts: 2

PostPosted: Thu Jun 17, 2010 6:10 pm    Post subject: Convert normalized radiation E-field patern to Power in dBs? Reply with quote

Approximately half way down the following link:
http://www.antenna-theory.com/antennas/travelling/helix.php

the author presents normalized radiation pattern for the E-field components.

How does one convert this E-field pattern/equation to transmit power in dBs? For example if one entered in the parameters for an antenna with a maximum forward gain of 10 dB how does one convert this graph to display it?

I believe that I can convert it to power density via:
P(dBW) = 10*LOG(E^2/Z) (dBW/m^2), base 10, Z = 377 ohms

though I do not know how to go any further.

Thank you,
C
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bigSteve
Antenna Wizard


Joined: 14 Mar 2009
Posts: 265

PostPosted: Fri Jun 18, 2010 4:21 am    Post subject: Reply with quote

The normalized power pattern (linear units) is:

P_lin = sqrt( E_theta^2 + E_phi^2 )

The power is then

P_dB = 10*log10( P_lin ) [W/m^2]

If you would like the total transmit power, this is:

P_trans = integral[0,2pi] integral(0,pi) [ P_lin r^2 sin(theta) ] dtheta dphi

[where r is the radius of the sphere you are integrating over]

or, P_trans_dB = 10*log10( P_trans )

Remember though, to find the actual transmit power in real life you cannot use the normalized radiation pattern, as you need to know the amplitude of the E-field (not normalized). Hope this helps
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dekk0009
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Joined: 17 Jun 2010
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PostPosted: Fri Jun 18, 2010 5:30 am    Post subject: Reply with quote

bigSteve,

I apologize for my ignorance on the subject though I have the following follow up questions?

1. What part of the E-field equation are the Etheta and Epsi components?

Etheta = sin(pi/2N)*cos(theta)
Epsi = (sin((N*omega)/2)/(sin(omega/2))

or

Etheta = sin(pi/2N)
Epsi = cos(theta)*(sin((N*omega)/2)/(sin(omega/2))

or are they something else?

2. All I really want is to generate the gain pattern in dB of the antenna. From there I should be able to find the power at a certain distance from the antenna.
For example, if the max gain (G) of the antenna is say 10 dB in the forward direction then I'd expect to read 10 dBs at 0 degrees from the antenna gain pattern. To find the power (dBW) level at distance D (meters) from the antenna for an input I (dBW) would use the following:

P(dBW) = I + G + 10*LOG((4pi*D/lambda)^2)

I believe that this is in line with the Friis Transmission Formula:
http://www.antenna-theory.com/basics/friis.php

minus the receive antenna.


3. How do I use the radiation pattern E-field equation from:
http://www.antenna-theory.com/antennas/travelling/helix.php

to get a 360 degree representation of G in #2?

4. The far field begins at 2*lambda from the the transmit antenna though does one start measuring from the back plain or from the very tip (N*S) of a helix antenna? I've heard that it starts at the very tip.

Thank you,
C
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bigSteve
Antenna Wizard


Joined: 14 Mar 2009
Posts: 265

PostPosted: Tue Jun 22, 2010 4:28 am    Post subject: Reply with quote

To answer question 1:

Etheta = Ephi (they have equal magnitude, but are out of phase by 90 degrees). This is required for circular polarization.

To answer question 2:

The gain of the antenna is the antenna efficiency (e) times the directivity (D). From the Etheta/Ephi equations, you can calculate the directivity D. For helixes, you can assume the in-band efficiency is pretty high, say 0.8-0.9 is reasonable.

However, to use the Friis Transmission equation, you need to know the transmit power, Pt. Then you can calculate the receive power at some distance away.

To answer question 3:

It depends which 360 degree cut of the spherical radiation pattern you want. Typically, the horizontal plane is defined by theta=90 degrees, then phi is the variable from 0 to 360 degrees. Alternatively, you could look at a vertical cut, where phi=0 degrees, and theta goes from 0 to 180 or 360 degrees.

To answer question 4:

The far field is determined from meeting the far field conditions:
http://www.antenna-theory.com/basics/fieldRegions.php

There's no strict rule on where to measure from. Basically, all the equations should be satisfied relative to any point on the antenna - that is, be conservative and take the worst case scenario.
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