I would like to design an UHF antenna where size limitation (30mm*30mm) will be followed . I was thinking to use high dielectric material so i can minimize the size of spiral antenna. I have tried to increase dielectric constant but it shows there were no change of center frequency in respect of di electric constant.
Take a look at these two
https://people.eecs.berkeley.edu/~culler/AIIT/papers/radio/antenna%20wp_dimension_limits.pdf
https://arxiv.org/ftp/arxiv/papers/1612/1612.07317.pdf
and read the Wheeler reference in the second one.
Your antenna is so small that it needs to be highly resonant to function. This can be achieved by making the antenna very meandering or spiral, or by using a tuning circuit. In either case it will be narrow band or inefficient or both. The pattern is the pattern of an infinitesimal dipole, so the gain will be just over 1 x efficiency. It is hard to test these because the feed circuit (or some nearby object) often radiates more than the antenna.
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