What is the theoretical performance of a 2m 1/4 wave ground plane antenna when used at 70cm?

If I have a 2-meter 1/4 wave ground plane antenna with 1/4 wave radials bent down at approximately 45 degrees, what kind of performance in terms of SWR and gain pattern can I expect when using it on the 70cm band, relative to its performance on the 2 meter band?

Let's assume that this antenna you describe, when operated at 145 MHz, has an SWR of 1:1, and behaves like an ideal antenna. At 145 MHz, the 1/4 wave vertical, plus the image antenna formed by the ground plane, make it effectively like a 1/2 wave dipole. It will have a free-space radiation pattern like this, for an antenna oriented vertically along the Z-axis:

At three times this frequency (435 MHz), the antenna will be resonant again. That means its impedance is unchanged, so if you had a 1:1 SWR at 145 MHz, you will have a 1:1 SWR again at 435 MHz.

However, the radiation pattern is different, because now it's not a 1/2 wavelength dipole, but a 1 1/2 wavelength dipole. The radiation pattern looks like this:

In the latter case, at 435 MHz, the maximum gain is the same as it was at 145 MHz. However, the lobes are narrower, and higher elevation. There's a secondary lobe around the horizon, but it's even narrower, and about 4 dB below the main lobes.

These images are from antenna-theory.com, which has a good deal more to say on the issue. Everything there about dipoles is also relevant to verticals, which are just dipoles where half of the dipole is formed by an image antenna through the ground plane.

• Don't the sloping radials make a difference since they're not in a plane? Feb 25 '14 at 20:55
• @KevinReidAG6YO Nope. There will be some minor distortion of the pattern since there aren't infinitely many radials, but otherwise all the sloping does is raise the impedance, from the 35 ohms of a vertical over a perfect ground, to the 50 ohms that we probably want to match the transmission line. Feb 25 '14 at 20:58
• Okay. That's a flaw in the "ground plane is like a mirror" analogy, then (a conical mirror would not have the same reflection as a flat one), which I haven't seen mentioned before. Feb 25 '14 at 21:00
• @KevinReidAG6YO If you calculate the reflection for a plane tangential to one part of the ground "cone", you get an angled image antenna. If you do this for all planes tangential to the cone, you get infinitely many angled image antennas. If you superimpose all of those image antennas, it's equal to one image antenna reflected straight down, with some impedance transformation. Feb 25 '14 at 21:07
• @KevinReidAG6YO I'm having trouble finding a good reference, but consider this: if you continue sloping the radials down, eventually they converge into a line and you have a dipole antenna. For a real antenna, with a finite number and length of radials, this will change the pattern somewhat, but not a lot, and the general conclusion is the same: when the vertical is more than 1/4 wave long, you start getting high-elevation lobes. Feb 25 '14 at 21:29