Low-pass impedance transformation networks

Explicit formulas for the element values of a low-pass impedance transformation network having Butterworth or Chebyshev responses are given. For the second and the fourth-order networks, element values and transformation frequency band are directly determined by the impedance ratios. Since the expressions of the complex conjugate poles of the reflection coefficient of the network are rather concise, formulas for the higher order networks are obtained, thereby reducing the design of these networks to simple arithmetic and avoiding the use of design tables given by Matthaei (1964) and Cristal (1965)