It is mathematically proven that a detector tube which has a broken straight line for its plate current‐grid voltage static characteristic will detect the standard radio signal without distortion, regardless of signal strength. The plate detection performance of a tube having a given curve for its static characteristic can be calculated from the extended power series which represents the characteristic. The power series analysis of the curve is obtained from a Fourier series analysis by a method which saves labor and is more accurate than the method of simultaneous equations. Thus, by using twelve or fifteen terms of the power series instead of only the first two or three, and by setting up special formulae, detection performance can be calculated for any signal strength and any modulation. The method is applicable to the tube alone, to a circuit containing the tube and external resistances, and may be applied to any similar non‐linear receiving system.