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.
Best Answer
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.