A MATRIX representation which is particularly useful for the linear analysis of circuits with time-varying parameters will be given and will be applied to the case of a variable capacitance transmission line. The line will first be treated on the assumption that only a signal and a pump frequency (2?signal = ?pump) are important, and the conditions which should be satisfied by the respective propagation constants if gain is to be obtained will be presented. If the line is assumed capable of propagating combination frequencies at a velocity close to that of the pump and signal, then the results may be drastically modified. In particular, we will consider the effect of the combination frequency ?signal+?pump. Also treated will be the case where all combination frequencies are allowed to propagate along a dispersionless line.