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how compare resonant frequency of a dielectric monopole antenna with metal one?

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ghasem_008

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Hi.
I want to compare resonant frequency of a dielectric monopole antenna with a metal one.
In a metal antenna,we know that :
resonant frequency = c0/λ0
where co and λ0 are propagation velocity and wavelength in free space,respectively.
But in a dielectric antenna we have to use from :
resonant frequency = v/λ
where v and λ are propagation velocity and wavelength in the dielectric medium,respectively.
Also,In a metal Antenna:
increasing the diameter of the conductor will decrease the velocity of the waves in the element, increasing the electrical length and decreasing resonant frequency.
But in my simulation,for a dielectric antenna,increasing the diameter of the element leads to:
" β/k0 --> 1 " ,So : " v --> c0 " , So : " resonant frequency(dielectric antenna ) --> Increase".
where β is phase coefficient in the dielectric medium.
why in this case,resonant frequency increases???
 

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