Passport Expiry impact on H1B lottery and approval

Hi,

My passport expires in another 8 months and I’m planning for applying for a new passport in tatkal to register before March 9th. Will the new passport numbers impact my H1B lottery process in both regular and Masters quota?.

My concern is getting shorter I-94 validity if H1b gets approved with an old passport number(F1 Visa stamped on this).

Thanks,
Vivek