Phase and Amplitude Modulation in High-Efficiency Varactor Frequency Multipliers - General Scattering Properties

Abstract

The presence of phase and amplitude modulation in the signals of a varactor frequency multiplier is analyzed, and some general multiplier properties are derived. The following summarizes one of the most important results of this paper. Consider a frequency multiplier which has the following characteristics: (i) a varactor which has a square-law characteristic, (ii) the order of multiplication is N = 2n = 2, 4, etc., (iii) the minimum number of idlers, and (iv) it is lossless and tuned. It is shown that for this multiplier there is no conversion between small-index, low-frequency amplitude and phase modulation. Therefore, since narrow-band noise from external sources will be present at the input and output of the multiplier, the noise components corresponding to phase modulation of the carriers can be treated independently of the noise components corresponding to amplitude modulation. Consider now the input and output noise sidebands corresponding to phase modulation (PM). It is shown that the multiplier behaves with respect to these sidebands as an amplifier with the following properties: (i) a forward voltage transmission equal to N, (ii) unity reverse transmission, (iii) an output reflection of 1, −1, 3, respectively, for N = 2, 4, 8, and (iv) no input reflections. As a consequence of these properties the multiplier is “potentially” unstable with respect to PM. The utility of the multiplier properties derived in this paper will be illustrated by the discussion in a companion paper in this issue which shows how, in practical cases, instability arises and how it can be avoided.