Residual attenuation equalisation of broadband systems by generalised transversal networks

Abstract

SynopsisResidual attenuation equalisation of broadband coaxial-cable systems has been achieved elsewhere by a set of harmonic cosine characteristics based on an almost linear frequency scale. This method is, however, not efficient for systems which exhibit high distortion near the bandedges. A simple analysis of measured characteristics yields the requirements for suitably transforming, or 'warping', the frequency scale. Generalisations of the transversal-equaliser principle offer the realisation of cosine characteristics with frequency scales which match particular problems. The investigation on which the paper is based was concerned with the coaxial-cable network of the British Post Office, and led to novel designs, of which the 'twin cosine equaliser' has been accepted for service use. This device enables residual distortion of up to 6dB to be reduced to rather less than 1 dB, with a minimum of auxiliary instrumentation. List of symbolsa, b, c = coefficients m, r, s, u,v = indexes v = integer n = order oil = Irfi = lower frequency limit of system a> h = 277-//, = upper frequency limit of system a>1 ~~ J 7 ''} > = limits of approximation interval o; 2 = 277/ 2 J co 0 , 00 r = reference frequenciesx(f) = transformation ('warping') of frequency scale y = normalised frequency F(x) = function to be approximated S n = trigonometric sum of nth order S n = truncated Fourier series of nth order M(d) = modulus of convergence d = limit to modulus of increment of variable /difference or differential quotient Islope of polygon side = constant in Jackson's theorem = quantisation step q = upper limit to equalisation error, dB A + jB = propagation coefficient A o = In k = flat loss of variable equaliser R = resistance W = characteristic impedance K = impedance ratio N = number of components E, U = signal amplitudes T = time constant G(co) = transfer function (output/input ratio) m = shape parameter (j) af (f) b = pair of quadrature phase-shift functions