Generating analogue FM pulses using a 1 bit digital technique

A method of generating sinusoidal frequency-modulated pulses using a 1 bit digital technique is developed. The method utilises the information in the zero crossings of the signal, rather than sampling and voltage quantisation, to reconstruct the signal. An intuitive view of the spectrum of a frequency-modulated square wave (FMSW) is derived, and confirmed by mathematical analysis. The spectrum consists of a series of harmonics of the form associated with the modulation law used. The bandwidth and TB product of the harmonics increase in direct proportion to the order of the harmonic. The effect of the time quantisation of the zero crossings necessary to generate a FMSW using digital logic is analysed. The relationship between the time quantisation, signal bandwidth and clock frequency is discussed. The generation of nonlinear FM pulses is illustrated using a truncated Gaussian 15 dB spectrum, and the effect of the time quantisation on the compressed pulse sidelobe levels is computed. The effect of Doppler shift on the sidelobe levels is also illustrated. Hardware for generating FMSWs is described, and the effect of the logic risetime on the spectrum is analysed. The concept of the FMSW is verified using a simple TTL circuit to generate a LFM pulse.