------------------------ From: "Beard, Susan" <[email protected]> Subject: equation for standard gain horns Date: Thu, 7 Jan 1999 16:30:34 -0500 To: "'[email protected]'" <[email protected]>
> Can someone point me to the equation for calculating the gain of a standard > gain horn antenna based on the physical measurements of the aperture? > > Thanks, > Susan Beard > > --------- Susan:: The general formula used for long horn antennas (like you usually use for emission or immunity testing) is: G = 10 * A * B / (l)^^2 where G = Numeric antenna gain referenced to an isotropic radiator A = Horn aperture height in meters B = Horn aperture width in meters l = Wavelength in meters Now, lets see how this works for a typical antenna. A custom pyramidal horn which I built two years ago, for use between 12 GHz and 20 GHz, has an aperture of 12.6cm by 15.2cm, and has a length of 32.5cm from the waveguide feed to the aperture. (BTW, a line drawn across the shorter aperture dimension is parallel to the electric field.) Let's calculate the gain at 15 GHz. A = 0.126 m B = 0.152 m l = 300 / F(MHz) = 300 / 15,000 = 0.02 m G = 10 * 0.126 * 0.152 / (0.02)^^2 = 0.19152 / 0.0004 = 478.8 Converting to dBi G = 10 LOG (G numeric) = 26.8 dBi You didn't ask, but the Receiving Antenna Factor is: AF = 20 LOG (F MHz) - G (dBi) - 29.79 dB = 83.52 - 26.8 - 29.79 = 26.9 dB Now, when I took the antenna to my antenna calibration range, and did an antenna gain measurement per ARP-958 at a 1 meter separation distance, I found that my real gain was 156 (numeric) or 21.93 dBi, giving me an Antenna Factor of 31.8 dB. Hmmm, a calculated gain of 26.8 dBi, but a measured gain of 21.9 dBi. Why the difference? First, the calculated is for an optimum gain horn; my horn was a bit more square at the aperture than a perfect horn (but I needed a wide operating range, so I compromised). Second, everything you build has little wiggles and imperfect angles. Every imperfection is a little bit less gain. And lastly, I did my gain at a 1 meter distance, since I would be using it at that distance. A purer "free space" with much greater separation distance would have been a "cleaner" measurement. The lesson is that you can model and predict all day long, but the antenna range gain is the last word. If you want to explore further, try: 1. EMC For Product Designers by Tim Williams. 2. EMI Methodology by Ed Bronaugh (White Series, Vol 6). 3. Reference Data For Radio Engineers by ITT. 4. Antennas by John Kraus. Regards, Ed -------------------------- Ed Price [email protected] Electromagnetic Compatibility Lab Cubic Defense Systems San Diego, CA. USA 619-505-2780 List-Post: [email protected] Date: 01/08/1999 Time: 08:51:42 -------------------------- --------- This message is coming from the emc-pstc discussion list. To cancel your subscription, send mail to [email protected] with the single line: "unsubscribe emc-pstc" (without the quotes). For help, send mail to [email protected], [email protected], [email protected], or [email protected] (the list administrators).
