How does an antenna’s shape impact its performance?

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I’ve never understood why antennas are shaped the way they are. The one on my roof looks totally different than the one on my car looks different than the one in my phone.

But I know the shape matters a lot and meaningfully impacts performance. But how does that work?

In: Engineering
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The ideal antenna for one particular wavelength and beam direction is relatively easy to figure out…it’s a stick of the right length and right orientation relative to the beam. The challenge is usually that nobody wants infinite sticks, you often don’t have room for a stick of the right length, and you don’t know what direction the wave is coming from.

If you know that it’s all going to come at you mostly in a flat plane, but you don’t know what direction, a pole is fine. See: basically every car antenna of the 1900s or all early cell phones. If you can steer the antenna to point at the source that’s also fine (see: all those dishes on satellites and ships and news vans…not the dish itself, that’s just a “radio mirror”, but you can steer the actual antenna.

After that, it’s all compromises that make the antenna worse at actually picking things up but potentially better at fitting into where you want it. If you can make it bigger enough to overcome the performance degradation enough to come out ahead on shape, you’re OK. This is how you can embed antennas in the window glass of your car now, or in the flat panel of your computer, or the edge or back of your phone.

The ideal antenna length scales with wavelength…as we’ve gone to higher and higher frequencies (smaller wavelengths) antennas also got way smaller.