Why is it that the bandwidth of a patch antenna decreases with it's size?

I typically use a larger (25 mm) patch antenna in GPS/GLONASS receiver circuits. As you probably know, L1 bands for GPS and GLONASS are separated by roughly 25 MHz.

For applications where I want to be able to view both satellite systems, I'll typically have the antenna tuned for about 1590 MHz which is roughly in between the two L1 center frequencies.

This becomes more tricky with smaller sized antennas. From conversations with my antenna supplier, they recommend I stick with the broadband, linear antenna (chip antenna) vs. a smaller, circularly polarized patch (rectangular micro-strip) antenna because the Bandwidth drops off greatly as you go smaller in size.

But why?

I would like to explain this to my boss in layman's terms but be able to back it up with some antenna theory or some formula which describes the relationship between gain, size, and bandwidth.

• Chu-Harrington Limit might be the concept you are alluding to en.wikipedia.org/wiki/Chu%E2%80%93Harrington_limit Mar 30, 2016 at 21:36
• Layman version: Just think of it as field (V) and flux (I) from EM. You have to induce mutual resonance and the more power you can get to the antenna, the less loss you have. As the area goes down, you have a less ideal resonator so the information you get is more noisy, and thereby the bandwidth goes down. note: smaller antennas have a larger amp stage to try to get around this issue as the cost of power. Mar 31, 2016 at 11:27
• @bdegnan thanks. that makes sense. let me try to wrap my head around it a little more. Mar 31, 2016 at 14:01
• @Samee87 With a bit of handwaving, something more tangible: another way to think of it is a piano. The register gives the same force when you hit a key, but the time of resonance of an "A" across octaves is different. The movement of the string is the effective bandwidth, and you can see the larger strings move more. The reason that I give a piano analogy is because the size of the tag is related to factional wavelengths, which is the same as octaves in a way. This is also why a grand piano sounds great and a spinet piano sounds like a cat in a box. Small antennas are spinets. :/ Mar 31, 2016 at 15:09
• @MichaelChoi may I suggest you post your comment as an answer? Feb 16, 2018 at 19:16

First of all L1 band ranges from 1563 MHz to 1587 MHz (Bandwidth = 24 MHz). 1590 MHz is falling in E1 which is GALILEO band.

In Layman's term: wavelength decreases with increase in frequency.

In antenna theory, "for efficient radiation of electromagnetic energy the radiating antenna should be of the order of one-tenth or more the wavelength of signal radiated", which can be formulated as:

Size = λ/10, where λ is the wavelength

So as the frequency increases, wavelength decrease and thus the size of antenna. Let's do the calculation for your case: (f=1590 MHz)

λ = c/f = 2.998*10^8 / 1590 * 10^6 = 0.18855 m = 18.855 cm ~ 19 cm

Size = λ/10 = 19/10 = 1.9 cm (which is quite small compared to standard 25 cm GPS patch antenna)

Further, in order to understand total relation between size, gain and bandwidth- theories calculations are mostly different from practical experience. This link provides good insight into the matter. Of course it is Chu–Harrington limit as suggested in primary comment.

• He is asking about bandwidth, not operating frequency Mar 31, 2016 at 8:11
• The edit "Of course it is Chu–Harrington limit as suggested in primary comment." is the only relevant part. Feb 16, 2018 at 19:15