Tangential sensitivity of a detector video system with r.f. preamplification

The paper describes a theoretical analysis of the tangential sensitivity of a crystal-video system preceded by an r.f. amplifier. The detector is allowed to have either a square-law or linear characteristic, and the treatment covers arbitrary values of the ratio n = B1/B2, where B1 and B2 are, respectively, the bandwidths of the r.f. and video amplifiers. For the square-law detector, explicit algebraic expressions are derived from which the tangential sensitivity can be calculated for arbitrary values of n. For the more difficult case of the linear detector, the equation defining the tangential sensitivity is stated and solved numerically for the case in which the gain of the r.f. preamplifier is sufficiently large to make the noise arising from both the crystal (regarded as a Johnson source) and the video amplifier negligible in comparison with that from the r.f. preamplifier. This is a valid approximation for many systems. In addition, an approximate explicit solution, which takes into account the crystal and video noise, is given, and this differs from the exact solution by not more than 0.25dB for n ¿ 2. The results given in the paper also apply to a superheterodyne receiver having a linear or square-law second detector and i.f. and video bandwidths of B1 and B2, respectively.