Impedance and admittance functions of simple bicone and bowtie dipole antennas are modelled using rational functions of low order. Results are presented in terms of the poles and residues of the function, which are studied as functions of the flare angle. Excellent agreement can be obtained between electromagnetic models and the analytic function to low order. Addition of a ground plane is found to produce the expected doubling of the poles at non zero frequencies. For a specimen bowtie, the Q-factor of the first admittance and first impedance pole is rather higher in the flared form than in the thin form. This appears to counter the increase in DC capacitance to give little change in bandwidth.