Chebyshev design of broadband reflectionless quarter-wave transformer
[n,a,b] = chebtr(na,nb,A,DF)
refractive indices of left and right media
dB attenuation of reflectionless band (relative to unmatched case)
fractional bandwidth about center frequency f0, DF = Df/f0
designed refractive indices = [na,n(1),n(2),...,n(M),nb]
order-M denominator and numerator polynomials of reflection response
chebtr(na,nb,A,DF) is used for Chebyshev design of broadband reflectionless quarter-wave transformer. implements the Collin/Riblet design of broadband quarter-wave transmission line transformers; stopband specs are in terms of the reflection response. the design method determines the transmission and reflection polynomials A(z), B(z) from the given specs and implements the backward layer recursions with the help of BKWREC to get the reflection coefficients [r(1),...,r(M+1)], and finally constructs the refractive indices using R2N. the left and right bandedges are at F1 = 1 - DF/2, F2 = 1 + DF/2, the phase thickness of layers is = delta = (pi/2)*(f/f0) = (pi/2)*(la0/la), at f=f0, la=la0, the layers are quarter-wave, the reflection response is Gamma(z) = B(z)/A(z), z=exp(2*j*delta) = exp(j*pi*f/f0). the refractive indices satisfy: n(i)*n(M+1-i) = na*nb, i=1,2,...,M. for transmission lines, replace n = [na,n(1),n(2),...,n(M),nb] by the characteristic admittances Y = [Ya,Y(1),Y(2),...,Y(M),Yb], that is, Y = chebtr(Ya,Yb,A,DF), with Ya=line and Yb=load (Ya,Yb must be real)
add sample pgm
This function uses the functions bkwrec and poly2.