As you mentioned in your question about to define the design frequency. So, I would like to tell you that requirement of frequency is first step to design any antennas, second step depends on your requirements and applications, I mean where are going to use such antennas and the supporting device to that antennas (whether transmitter or receiver) inhale how much frequency. Design frequency depends on us and our requirements.
I am sending a document, go through it and clear your concepts.
The short answer would be size and shape. The size of the antenna gnerally defines the central frequency, whereas the shape helps to conform the bandwidth. The chapter that the first answer provided will help you out with that more specifically.
Thanks to Smrity for your valuable suggestions and sending the attachment. There is any mathematical equation through which we can calculate the design frequency of UWB antennas and validate with the simulation results.
The bandwidth can be the range of frequencies on either side of the center frequency where the antenna’s characteristics, such as input impedance, radiation pattern, beam-width, polarization and gain, are close to those values which have been obtained at the center frequency. The bandwidth of a broadband antenna can be defined as the ratio of the upper to lower frequencies of acceptable operation. Bandwidth can be expressed in two ways, as a ratio and as a percentage. Bandwidth as a ratio is usually used for very wide bandwidth applications. Bandwidth for moderately wide-band antennae is usually expressed as a percentage relative to the center frequency fact:
Thanks to all for your valuable suggestions and ideas for the design frequency. But still question arise is that how to calculate the design frequency through the antenna size i.e., L X W. I was designed the antenna from 2.43 to 13.30 GHz with two notches in WiMAX (i.e. 3.4-3.69 GHz) and WLAN (5.15-5.8 GHz) bands. In that case, how to calculate design frequency? or what is the design frequency in that case?
design and development of broadband antenna is given in Antennas by Ballnis as well as broadband antenna by Dr. Girish Kumar and Dr. K. P. Ray Sir book. As par my understanding you have to finalize first frequency of operation as per application point of view. Then by transmission line model calculate dimension of patch antenna.