Short-step Butterworth impedance transformers
Based on a relationship among the order n (= 2m) of the impedance transformer, the impedance transformation ratio r and the 3-dB frequencies omega(a) and omega(b), a 2m-order Butterworth semi-lumped-element impedance transformer is designed by using a coaxial structure, consisting of a cascade of line sections having various line impedances z(i) with the same effective length l. The performance of the resulting transformer is comparable to that of a smaller size quarter-wavelength transformer.
impedance transformation butterworth response short-step transformers network synthesis