I have designed a microstrip patch antenna to resonate at 3.5GHz. It also resonates at around 6GhZ and 10GHz. Can you suggest me of how the higher frequencies can be suppressed to get an effective single band antenna?
you can try this using EBG structures such as U slots or truncation of ground planes.
By choosing proper dimensions with the help of appropriate literature, it can be easily suppress the higher resonant frequencies. this is because U slots are used to introduce stop bands in the frequency response.
You could use a different antenna geometry that doesn't resonate at higher frequencies, or alternatively as Raymond has also suggested, place an FSS or low-pass filter in front of the antenna. For the latter you could add a dielectric spacer on top of your antenna with the filter, or suspend the filter above with support posts at the far edges of your antenna.
Is your antenna really square? if so that might be part of the problem. Normally microstrip antennas are rectangular.
The inset width should be the same as the width of the microstrip feed line. But I think the main problem may be the inset length. Increasing inset length is a method for creating a dual frequency inset fed microstrip antenna. I have attached a document that contains an empirical formula for calculating inset length.
What type of laminate are you using? At 3.5 GHz. you should be using a good RF laminate like Rogers 4003.
I would strongly recommend that you not use FR 4. With FR 4 as frequency increases both its dissipation factor (Df) and dielectric constant (Dk) increase. This causes significantly higher insertion loss. Impedance also changes. RF laminates typically have Dk tolerance of +/- 2%; FR 4 is +/- 10%. RF laminates have a thickness tolerance of +/- 75; FR 4 is +/- 15%.
I suggest Rogers 4003. It has good RF performance at a reasonable price.