voltage across terminals

hi,
I am designing a planner micro strip yagi uda antenna. I wanted to know the formula or method to calculate open circuit voltage across the feed terminals when antenna is used as receiver. I know that for dipole we can calculate this by using effective length of the antenna at particular frequency. but is this formula valid for yagi uda. yagi uda has higher gain so it captures more power so the voltage induced should be higher as compared to dipole if both are designed for same impedance.

Expectable gain values (received power compared either to a dipole or an omnidirectional antenna) of yagi antennas can be found in antenna literature.