In this paper the fundamental formulas of variable frequency electric circuit theory are first developed. These are then applied to a study of the transmission, reception and detection of frequency modulated waves. A comparison with amplitude modulation is made and quantitative formulas are developed for comparing the noise-to-signal power ratio in the two modes of modulation.

Variable frequency electric circuit theory with application to the theory of frequency-modulation

Theory and experimental data are given which show the improvements in signal-noise ratio effected by frequency modulation over amplitude modulation. It is shown that above a certain carrier-noise ratio in the frequency modulation receiver which is called the "improvement threshold," the frequency modulation signal-noise ratio is greater than the amplitude modulation signal-noise ratio by a factor equal to the product of a constant and the deviation ratio (the deviation ratio is equal to the ratio between the maximum frequency deviation and the audio modulation band width). The constant depends upon the type of noise, being slightly greater for impulse than for fluctuation noise. In frequency modulation systems with high deviation ratios, a higher carrier level is required to reach the improvement threshold than is required in systems with low deviation ratios; this carrier level is higher for impulse than for fluctuation noise. At carrier-noise ratios below the improvement threshold, the peak signal-noise ratio characteristics of the frequency modulation receiver are approximately the same as those of the amplitude modulation receiver, but the energy content of the frequency modulation noise is reduced. An effect which is called "frequency limiting" is pointed out in which the peak value of the noise is limited to a value not greater than the peak value of the signal. With impulse noise this phenomenon effects a noise suppression in a manner similar to that in the recent circuits for reducing impulse noise which is stronger than the carrier in amplitude modulation reception.

Frequency Modulation Noise Characteristics

A radar system (44) for a vehicle (42) includes a transmit unit (56) and a receive unit (58). The transmit unit (56) includes a single beam antenna (72) for output of a radar signal (74) into a target zone (46). The receive unit (58) includes a single beam antenna (76) for receiving a direct receive signal (78) and an indirect receive signal (80). The receive signals (78, 80) are reflections of the radar signal (74) from an object (34, 36) in the target zone (46). The indirect receive signal (80) is reflected off the object (34, 36) toward a reflective panel (54) of the vehicle (42), and the indirect receive signal (80) is reflected off the reflective panel (54) for receipt at the receive antenna (76). The receive signals (78, 80) are summed to produce a detection signal (81) indicating presence of the object (34, 36) in the target zone (46).

Automotive radar system and method for using same

When a frequency-modulated wave is received by more than one path, so that two or more of the voltages which are induced in the antenna have nearly the same amplitude, considerable distortion can result. Large objects, such as hills or high buildings, can reflect and absorb the waves and thus cause interference. Two interfering waves will be in phase part of the time and out of phase part of the time during modulation. This causes amplitude modulation on the resultant carrier, and a sharp irregularity in the instantaneous frequency, corresponding to each hole in the carrier caused by the interference. The distortion can often be greatly reduced by detuning the re ceiver or discriminator until the hole in the carrier coincides with the zero-balance point of the discriminator. Directional antennas are helpful when the signals from the desired station are not coming from the same direction. Formulas are derived for the modulated envelope and for the distortion. A Fourier-series analysis of the distorted audio output makes it possible to calculate the effects of de-emphasis networks and other audio selectivity.

Frequency-Modulation Distortion Caused by Multipath Transmission

This paper describes a VHF omnirange, the operation of which is based upon an application of the Doppler effect. Progress in the development of a Doppler VOR is outlined. The Doppler VOR has a measured 7-to-1 improvement with respect to siting effects when compared to the conventional four-loop VHF omnirange. The wave transmitted by the Doppler VOR is horizontally polarized. The unique interchange in the functions of the 30-cps amplitude modulation and the 30-cps frequency modulation of a 9.96-kc subcarrier is described. The Doppler VOR is shown to be compatible with present VHF omnirange receiving equipment. The results reported in this paper were obtained by experimentation and mathematical analysis.

The CAA Doppler Omnirange

Early work on frequency modulation is described wherein the propagation characteristics of frequency modulation were determined for frequencies between 9000 and 18,000 kilocycles. Oscilloscopic wave form and aural program observations, taken on a circuit between California and New York, showed that frequency modulation is much more distorted by the effects of multipath transmission than is amplitude modulation. The distortion is greatest at the lower modulation frequencies and higher depths of modulation where the side frequencies are most numerous. Oscilloscopic observations of the Lissajou figures formed by placing the outputs of receivers connected to spaced antennas on opposite oscilloscope plates showed that the diversity characteristics of frequency modulation are similar to those of amplitude modulation. That is, the detected outputs of the receivers tend to remain in phase for the lower modulation frequencies and become more phase random as the modulation frequency is increased. However, this tendency is almost obliterated on the lower modulation frequencies of frequency modulation by the presence of unequal harmonic distortion in the two receiver outputs. Theory is given analyzing the distortion encountered in a two-path transmission medium under various path amplitude and phase relation conditions. The theory explains phenomena observed in the tests and points out the extreme distortion that can be encountered.

M.G. Crosby

Papers

Frequency Modulation Propagation Characteristics