Synthesis of ladder networks to give Butterworth or Chebyshev response in the pass band

Abstract
Simple formulae are derived for the design of low-pass ladder networks to give Butterworth or Chebyshev response in the pass band. These hold for any distribution of load between input and output circuits. Useful expressions are given for the input impedance and reflection coefficient. For networks with more than three branches there are multiple solutions which can be separated by information obtained from the reflection coefficient.