Reactive Impedance Research Articles

The Physical Interpretation of the Expression for an Outgoing Wave in Cylindrical Coordinates

The sound field generated by a vibrating cylinder of infinite length, whose dynamic configuration is periodic in φ and z, is expressed in terms of acoustic impedance ratios. It is noted that symmetrical modes of vibration are suppressed at certain frequencies because the corresponding reactive impedance is infinite, and that all z dependent modes become nonradiating below certain “cut-off” frequencies, the corresponding impedance being purely reactive. Graphs are presented for the impedance ratios corresponding to certain modes. For modes independent of z, the sound field is in the form of concentric cylindrical waves. For z dependent modes, as the plane wave wavelength increases from zero to a certain critical cut-off value, the sound field changes from a set of concentric cylindrical waves to two sets of conical waves of decreasing vertex angle; at and beyond the cut-off point, the conical waves have degenerated into a set of plane standing waves normal to the z axis. Simultaneously, the sound field has ceased being periodic in the radial direction, and the phase velocity in that direction has become infinite. Practical applications of these phenomena are suggested.

The Physical Interpretation of the Expression for an Outgoing Wave in Cylindrical Coordinates

The sound field generated by a vibrating cylinder of infinite length, whose dynamic configuration is periodic in φ and z, is expressed in terms of acoustic impedance ratios. It is noted that symmetrical modes of vibration are suppressed at certain frequencies because the corresponding reactive impedance is infinite, and that all z-dependent modes become nonradiating below certain “cut-off” frequencies, the corresponding impedance being purely reactive. Graphs are presented for the impedance ratios corresponding to certain modes. For modes independent of z, the sound field is in the form of concentric cylindrical waves. For z-dependent modes, as the plane wave wavelength increases from zero to a certain critical “cut-off” value, the sound field successively assumes the form of a set of concentric cylindrical waves and of two sets of conical waves of decreasing vertex angle; at and beyond the “cut-off” point, the conical waves have degenerated into a set of plane standing waves normal to the z axis. Simultaneously the sound field has ceased being periodic in the radial direction, the phase velocity having become infinite. Practical applications of these phenomena are suggested.

A Precise Sweep-Frequency Method of Vector Impedance Measurement

The impedance of a two-terminal network is defined completely by the insertion loss and phase shift it produces when inserted between known sending and receiving impedances. Recent advances in precise wide-band phase and transmission measuring circuits have permitted practical use of this principle. Reactive and resistive impedance components are read directly from a simple graphical chart in which frequency is not a parameter. The basic principle described promises attractive possibilities in many cases of impedance measurements where present methods are inadequate.

Wave Propagation in a Slipping Stream of Electrons: Small Amplitude Theory

A theoretical study is presented of the TM-waves that can travel along a slipping stream of electrons. A slipping stream is defined as one in which the electrons move in parallel paths with velocity which varies with distance transverse to the motion. It is found that amplifying waves can travel along a slipping stream for all frequencies. It is also found that the slipping-stream tube has the remarkable property of combining the characteristics of a two-beam tube and a travelling-wave tube This is due to the occurrence in the stream under suitable conditions of resonance layers, which act as highly reactive impedance sheets and can guide TM-waves of slow phase velocity in the same way as the spiral or corugated surface in a travelling-wave tube. The slipping-stream tube behaves differently according to the fractional velocity range of the electrons. If the velocity varies linearly from V-a to Va across the stream and α = (Va - V-a)/(Va + V-a) ω1. However, if α > 0.42 it behaves primarily like a travelling-wave tube and the rate of gain is about 0.53ω0/V-a decibels per unit length at all frequencies above the plasma resonance frequency. This rate of gain is low compared with the gain possible with a travelling-wave tube in which the electron velocity is V-a but it is achieved without the need for any external slow-wave waveguide. Wave propagation along a slipping stream inside a waveguide, which in the absence of the electrons can guide a TM-wave of slow phase velocity, is also discussed. It is shown that this slipping stream travelling-wave tube has very much the same characteristics as a travelling-wave tube with a uniform electron beam Maximum gain occurs when the phase velocity v0 of the wave in the empty guide is about equal to the velocity of the electrons nearest to the reactive impedance sheet of the guide - in the example considered this is the fastest electron velocity Va A parametric set of curves is given relating the complex propagation constant to the frequency for different ratios v0/Va.

Automatic Tuning, Simplified Circuits, and Design Practice

The principles underlying automatic frequency control of the oscillator in superheterodyne receivers have been outlined in previous papers given before the Institute of Radio Engineers. This paper deals with simplification and improvements in operation of frequency control circuits and their application to automatic (electronic) tuning control. A new type of "discriminator" which differentiates between mis-tuned signals on the high-frequency side of resonance and those on the low-frequency side is described and its operation demonstrated by means of a visual frequency indicator. The operation of the discriminator is such that it may be used to supply audio-frequency components corresponding to the amplitude modulations of the received carrier wave and automatic volume control potentials as well as the control voltage for the frequency control circuits. This multifunction is described and illustrated. Alternative circuit connections to improve the compromise between discriminator sensitivity, audio fidelity, and selectivity are explained and illustrated. The use of vacuum tubes in such manner that they act as reactive components and the manner in which their apparent reactive impedance may be controlled by varying the tube parameters is demonstrated. The action of a complete receiver embodying automatic (electronic) tuning control in overcoming mis-tuning and oscillator frequency drift will be demonstrated.