Henning F. Harmuth

Correction of Maxwell's Equations for Signals II

In the first of two companion papers it was shown that the addition of a magnetic current density to Maxwells equations is a sufficient condition to obtain solutions in lossy propagation media for waves that are not infinitely extended periodic waves. The solutions obtained represented transients that may be used to represent signals having a beginning and an end. This second paper shows that the addition of a magnetic current density is also a necessary condition for the existence of transient solutions in lossy media. The modification of Maxwells equations is thus necessary and sufficient for the study of the propagation of signals in lossy media.

Antennas for Nonsinusoidal Waves. I. Radiators

During the last years numerous applications of nonsinusoidal electromagnetic waves have been discussed in this TRANSACTIONS. The next step is the implementation of these applications. It is generally accepted that the antennas pose the greatest diMculty. In a series of papers on radiators, sensors, and arrays, we will investigate antennas, both theoretically and experimentally. Sufficient information is provided to permit anybody who is equiped for work with pulses of about I-ns duration to build simple radiators and sensors.

Frequency-Sharing and Spread-Spectrum Transmission with Large Relative Bandwidth

Radio transmission has been based traditionally on the concept of a small relative frequency bandwidth, which permits the use of circuits and structures that resonate with sinusoidal functions. This approach created no problems until high-resolution radar advanced to pulse durations in the order of 1 ns, and spread-spectrum transmission to frequency bands in the order of 100 MHz. The use of a small relative frequency bandwidth requires in these cases operation at frequencies above 10 GHz. Absorption by rain and fog as well as the high noise temperature, make these high frequencies less desirable. Furthermore, the lower frequency bands cannot be used, even though they are there and their absolute bandwidth is perfectly sufficient; only the unnecessary requirement of a small relative bandwidth prevents their use. Concepts and equipment that allow operation with a large relative bandwidth make it possible to operate radar with a resolution up to 0.1 ns in the most desirable range from a few hundred megahertz to about 10 GHz; spread-spectrum transmission can operate without regard to the relative frequency bandwidth. This paper explains primarily the motivation for the development of equipment handling large relative bandwidths, since the equipment itself has already been discussed in the literature and is available on an advanced experimental level.

Propagation of Electromagnetic Signals

Electric field strength due to electric step excitation electric exponential ramp function excitation magnetic step and ramp function excitation sinusoidal pulse excitation. Appendix.

Antennas for Nonsinusoidal Waves: II-Sensors

The use of the basic large-current radiator¿discussed in a previous paper¿and the Hertzian electric dipole as sensor is investigated. If the sensor works into a large resistive load, typically implemented by an emitter follower, its output voltage varies like the electric field strength, while a capacitive load produces an output voltage proportionate to the integral of the field strength. The maximum energy is transferred to a load impedance that is equal to the radiation resistance of the antenna. This is the same result as in the case of sinusoidal waves, but the radiation resistance for nonsinusoidal waves differs from that for sinusoidal waves. An effective aperture can be defined, which is again analogous, but not equal, to the same concept used for sinusoidal waves.

Selective Reception of Periodic Electromagnetic Waves with General Time Variation

Several transmitters and receivers for periodic nonsinusoidal electromagnetic waves have been built during the last few years. Various applications of such waves, primarily in radar, have been recognized. The first practical equipment, an into-the-ground radar for construction surveying, has become commercially available. The efficient radiation of nonsinusoidal periodic waves has been discussed in the literature, but very little has been published on their selective reception. This paper describes the principle of selective receivers for periodic waves with general time variation, in analogy to the design of the usual receivers for waves with sinusoidal time variation.

Fundamental Limits for Radio Signals with Large Bandwidth

Radio services have traditionally used narrow frequency bands individually assigned. More recently, the concept of sharing very wide frequency bands by several users has been advanced, and this opens the door for the use of much larger bandwidths than in the past. This paper investigates the limits imposed by nature on the bandwidth of line-of-sight radio services operating in the earths atmosphere. Furthermore, it investigates the limits for time resolution of radio signals, as well as the related limit of the angular resolution of a line array of sensors that receive signals with large bandwidth, and compares it with the classical resolution angle that holds for sinusoidal signals with vanishing bandwidth. Finally, an example is given where the concept of a practically finite bandwidth of a signal reaches its limit, and a more rigorous specification of the signal is required.

Synthetic-Aperture Radar Based on Nonsinusoidal Functions: IX -Array Beam Forming

For sinusoidal waves with bandwidth zero, one obtains the classical formula ϵ = κNL = kc//spl conint/L for the resolution angle of a sensor array, where L is the length of the array, λ the wavelength, /spl conint/the frequency, and c the phase velocity of the wave, while κis a constant whose value is usually chosen to be 1. Waves with the time variation of a rectangular pulse of duration ▵T yield the resolution angle ϵ = 2Kc/▵/spl conint/ P/P /sub N/, where P/P/sub N/ is the signal-to-noise ratio and ▵/spl conint/ = 1/2▵T the nominal bandwidth of the pulse; the same result holds for coded pulse sequences, such as Barker codes or complementary codes, if the main lobe of their auto-correlation function has the shape of a triangle with rise time ▵T. Hence, the resolution angle e can be reduced by increasing the signal power, as well as by increasing the array length L or the bandwidth ▵f. For sinusoidal waves, an increase of the signal power brings no reduction of the resolution angle. The trade between signal power and frequency bandwidth is of interest whenever the attenuation increases rapidly with frequency, e.g., in high-resolution all-weather radar or in underwater acoustic beam forming.

Antennas for Nonsinusoidal Waves: Part: III-Arrays

In the previous two papers, we discussed the Hertzian electric dipole and the large-current radiator, used either as radiators or sensors. Several radiators or sensors can be combined into an array. In the case of sinusoidal waves, such an array would yield more power and a directional pattern of the power called the antenna power pattern. For nonsinusoidal waves, one obtains additional patterns. In the particular case of a time variation of the electric and magnetic field strengths equal to that of a rectangular pulse, one obtains an antenna slope pattern caused by the change of the time variation of the field strengths as functions of azimuth and elevation angles. This change is often called a distortion, but in reality it provides us with additional information for the angular resolution. Sinusoidal waves cannot provide this information due to their lack of a bandwidth. This paper investigates both the regular sensor array using the sum of all sensor outputs, and the monopulse array that uses the difference between the sums of the sensor outputs of the right and the left halves of the array. Radiator and sensor arrays for nonsinusoidal waves have been built at least since 1975, but the circuits required for the utilization of the slope patterns are still at the frontier of our technology for pulse durations in the order of 1 to 0.1 ns, which are primarily of interest.

Sequency Filters Based on Walsh Functions

The theory of filters based on sine and cosine functions leads to frequency filters. They can be implemented almost ideally by coils and capacitors. The arrival of integrated circuits imposes new requirements that are hard to meet by frequency filters: coils are undesirable, and no tuning and no temperature compensation should be required. It is reasonable to look for a theory of filters based on other functions that are more suitable to the demands of integrated circuits, rather than to try to adapt frequency filters to the new technological requirements. Sequency filters based on Walsh functions can be implemented by integrated circuits about as ideally as frequency filters by coils and capacitors.