The Output Signal-to-Noise Ratio of a Power-Law Device
Nelson M. Blachman · Journal of Applied Physics · 1953
An nth law device is fed by a sinusoidal signal and narrow band random noise whose spectrum lies close to the signal frequency. Its output spectrum is different from zero only in the vicinity of harmonics of this frequency. The ratio R′ of output signal power to output noise power in the vicinity of the mth harmonic is computed in terms of the input signal-to-noise power ratio R. In general, R′(R) involves a couple of hypergeometric functions, but for small R we have R′≅Γ2[(m+n)/2+1]Rm/(m!)2Γ(n+1) for m≠0, R′≅Γ2(12n+1)/[Γ(n+1)−Γ2(12n+1)] for m=0. For large R we have R′≅2R/(m2+n2).