Intermodulation Distortion and Efficiency Analysis of Multicarrier Repeaters

Under suitable conditions a common RF repeater may be used to amplify a number of modulated carriers. The basic limitations are efficiency and intermodulation distortion introduced within the frequency band of any modulated carrier wave by the other modulated carrier waves. Any repeater contains a high-power tube for which the output-input characteristic has nonlinearities that introduce a certain amount of intermodulation distortion. Over the useful range of input levels one usually finds that high efficiency and large distortion occur at high levels and low efficiency and low distortion at low levels. The range of acceptable distortion is determined by the intended application and in turn determines an efficiency range. This paper will obtain relationships between distortion or efficiency and input power for a third-degree nonlinearity. Although similar problems have frequently been treated previously in the literature, it is felt that the present approach offers a fresh point of view. The following assumptions will be made in the present analysis. It is assumed that the repeater has a bandwidth which accommodates the combined bandwidths of the modulated carriers but is small compared to any frequency within it. For this case the only intermodulation components in the output are of odd order. It is also assumed that the unmodulated carriers are equally spaced within the repeater pass band and have equal levels. Such a spacing should yield pessimistic distortion predictions since it is well known that they can be improved by resorting to suitable unequal spacing. For equal carrier spacing and a large number of channels it turns out that intermodulation distortion is essentially independent of carrier spacing and the exact size of the narrow repeater bandwidth. Another assumption is that the frequency transfer characteristic of the repeater is flat in amplitude and linear in phase over its pass band. The following basic procedure in the distortion and efficiency analysis of a repeater is set up for any kind of power tube in the repeater. The repeater output-input characteristic is assumed to be known in terms of power levels at any frequency within the repeater pass band. This power characteristic is then converted into an equivalent voltage characteristic in terms of output and input peak voltages and finally into an equivalent "instantaneous" voltage characteristic which is used for multicarrier inputs. The input modulated carriers, which may be PCM-FM, for example, are replaced by two extreme cases. In one case they are replaced by unmodulated single-sideband tones of the same total power as the modulated carriers. In the second case they are replaced by flat Gaussian noise of the same total power. Distortion results for the actual case of modulated carriers should be between the corresponding results for the two extreme cases. It is apparent that the present approach does not depend on a particular type of carrier modulation. The above type of analysis is made with either "envelope" or "instantaneous" voltage characteristics which can be approximated by odd-order cubic expressions and can be extended to cover higher odd-order approximations. Intermodulation distortion and efficiency predictions are then made in terms of the coefficients of the approximating cubic. The analysis is later applied to a klystron power amplifier. The results are plotted in the form of signal to intermodulation power and efficiency curves vs a "bunching parameter" X and against each other. These results show that, for the case of a multicarrier input, an output signal-to-distortion ratio of around 25 db corresponds to a practical efficiency of around 6 per cent.