The Helix as a Backward-Wave Circuit Structure

The impedance Em2/2βm2P of the backward wave on helical structures is considered from the point of view of the design of backward‐wave oscillators. Curves of impedance versus ka (circumference to free‐space wavelength ratio) for single and bifilar helices are presented. Both the case of thin tape and that of round wire are treated. The impedance curves are calculated on the basis of an approximation to the actual distribution of rf current over the surface of the conductors; the use of this approximation is justified by comparison with an exact solution at specific values of ka. A proof is presented which demonstrates that the backward‐wave impedances of two tape helices are identical if the gap width of one is equal to the tape width of the other. Expressions are derived for effects of dielectric supports upon the velocity and impedance of the backward wave.