The surfaces of the Planar Spiral Antennas and Conical Spiral Antennas are analyzed with planar triangle. The surface currents of the antennas are solved by using the Method of Moment (MoM) based on the RWG basis function. The input impedance, directivity, gain, radiated power and radiation field of the antenna can be found. The results indicate that, in very wide frequency band, the value of the input impedance equals to the theoretical value of Self-Compensated antennas (in agreement with Babinet-booker' principle), which is,188.5 ohm , the half of the wave impedance of free space, while the directivity, gain and radiated power are stable within the frequency band. When the antenna is driven by the signal of derivative Gaussian pulse, the radiating electric field waveform is obtained by the Fourier transform. When the spiral antenna is used as the pulse radiation antenna, the waveform of the radiation electric field shows the characteristics of the Gaussian quadratic differential.