AN INVESTIGATION OF THE RESONANT PROPERTIES OF SHORT EXPONENTIALLY AND LINEARLY TAPERED LINES
Cyclotron problems are emphasized. The exponentially and linearly tapered lines are chosen for study with emphasis on the linear line since it can be fabricated practically. The object of the investigation is two-fold: first, to develop the theory of the linear line and to extend the theory of the resonant properties of the exponential line with emphasis on the power and tuning properties of both liness second, to provide unified results comparing the resonant properties of the exponential, linear, and uniform lines. The classical approach employing the method of ordinary transmission line theory is used to develop analytical expressions for both of the tapered lines. For simplicity, emphasis is placed upon lossless lines. The resulting voltage and current expressions for the exponential line are in terms of exponential and circular functions. For the linear line, the expressions for voltage and current are in terms of Bessel functions of the first and second kinds of orders zero and one. Experimental data are presented to verify the mathematical results. Various illustrations of current, voltage, power, and input impedance properties are presented for the two tapered lines. Composite curves are provided to show a concise comparison of the similarities and differences among the exponential, linear, and uniform lines. In addition, the tuning properties of the tapered lines are discussed. It is shown that quarter-wave linear (and exponential) lines can be designed which will operate at a given frequency and which will be either longer, or shorter, than a uniform line operating at the same frequency. It is shown that quarter-wave linear (or exponential) lines, whose nominal characteristic impedance decreases from the shorted end toward the open end, require less power to obtain a given voltage at the open end than the comparable uniform line (where both lines are operating at the same frequency and have the same nomimal characteristic impedance at the open end). With respect to tuning, it is shown that linear (and exponential) lines add considerable design flexibility, and can be use. di advantageously, in the solution of wide-range tuning problems in which the line is the variable parameter. The theory of the linear line is illustrated by two examples, one of which was the cyclotron problem that motivated this research. (auth)
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- DOE Contract Number:
- W-7405-ENG-26
- NSA Number:
- NSA-12-009861
- OSTI ID:
- 4327101
- Report Number(s):
- ORNL-2260
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-58
- Country of Publication:
- United States
- Language:
- English
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