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You can increase the substrate thickness... But from a point further there's a chance to excite surface waves and deteriorate the radiation efficiency...
Try to run some parametric simulations till you get the 13% bandwidth (assuming that its feasible with respect to the center freq), having in mind not to spoil the radiation characteristics...
Try to use a stacked structure , one fix above another , you have feed a lower one only. This way will increase assembling complexity but have a lot of merrits,
I have an antenna with 40% bandwidth using air substrate. The shape of the antenna is an E-shape and the air thickness is 14mm. The total dimension of the patch is 105mm by 45mm
If ull interested i can give u the paper.
I am designing my self an antenna with 13% without air sub, if someone has a papers that can be useful to me i ll be very happy
regards
the range freq of the antenna badsedd is 1.9 GHz to 2.6 GHz
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