when i change the total size of this slot bow tie antenna-without changing the slot size-the radiation pattern is changed and i dont have any broadside pattern in my results.
Changing the size alters the frequency response/bandwidth of the antenna and thus also modifies the radiation pattern at each frequency. Think of what happens to the currents at the ends of the elements. At one size at a given frequency, they must go around the corner at the ends of the element, while at a larger size, they keep going straight where they changed direction before, and eventually make the corner at the new end point. The actual operating bandwidth will depend on how well the antenna can convert those currents to radiated energy, such that negligible current ever sees the end of the element.
Dear Dr Azita, although this is not my active area of research but as far as my understanding based on antenna theory and transmission line is concerned, as we go on increasing the size of antenna, the amount of radiated power/energy will vary differently at different points and hence patterns will definitely be changed or affected.
I must congratulate you for taking a fundamental question in this forum.
The farfield pattern of any radiator is related to the Fourier transform of the current density shape on it. By changing the size of your structure the current configuration is not the same, therefore the farfield pattern may change accordingly.
For your specific case, I understood from your post that the bow tie element is kept the same while the overall substrate size is enlarged, that implied that no broadside radiation was seen anymore. That sounds weird - such an abrupt change strikes me as a possible simulation error. Intuitively as the substrate gets bigger and bigger it reaches a point where no difference is made into the farfield, the edges are too far away from the element. Cant see a reason why it develops a current mode where the radiation turns from endfire to broadside.
Antennas radiate based on the current distribution on the element. For example a dipole antenna the current distribution on the antenna changes depending on its length which results in different radiation patterns. However, in you case, changing the size of the substrate should not change the pattern unless its too small. You substrate in the picture seems too big though, which is not a problem but that big a substrate is not needed.
When the length of a bow-tie is about one wavelength there will be currents in opposite directions in different parts of the antenna that will result in zero radiation in the broadside direction. Just because the vswr is good doesn't mean it still radiates like a dipole - as it gets longer it may radiate as a quadrupole. The usual used bandwidth for dipole radiation and vswr may be about 33%, so the top useable frequency is about 140% of the bottom useable frequency.
There are two effects due to change of size (1) The size of media surrounding the radiating element is loaded on an element for impedance (Resistive and reactive both gets changed). (2) Current distribution gets changed when media size changes.
This affects Effective radiation strength and pattern