A Stable Tunable Microwave Source

This paper describes a prototype model of a phase-stabilized backward wave oscillator (BWO). The BWO is locked to a harmonic of a crystal oscillator by employing an automatic phase control loop. Tuning is accomplished by pulling the crystal oscillator and switching different crystals into the oscillator circuit. Power spectrum plots are taken in open-and closed-loop conditions, and methods of analyzing these plots are described. With the proper loop bandwidth, the BWO will assume the frequency stability of the reference oscillator. The phase-locked BWO is analyzed by a conventional feedback control technique. Each element in the loop is assigned a transfer function. From this the open-loop transfer function is determined. It is then shown that the improvement in short-term frequency stability is directly proportional to the open-loop transfer function and, hence, the open-loop gain. Utilizing plots of the absolute magnitude and phase angle of the open-loop gain vs. frequency, conclusions are drawn as to the maximum amount of gain which is possible while still maintaining system stability. Possible implementation of a series equalizer is considered in conjunction with this. Comments are also made on the relationship of the closed-loop bandwidth to the system lock-in range and system response to incremental changes in frequency.