Explicit formulas for element values of the lowpass, highpass and bandpass ladders with Butterworth or Chebyshev response

The paper presents explicit formulas for the element values of an LC-ladder in terms of the coefficients of its impedance function known to be realizable as a resistively terminated lossless lowpass, highpass or bandpass LC-ladder. The formulas for the lowpass LC-ladders are an improvement over Bader's formulas in that they are much the simplest with increased computational accuracy and complexity by avoiding the computation of the n th-order determinants. The extension of these formulas to the LC-ladders with other terminations are also discussed. The paper also demonstrates the application of these formulas to the design of a broadband matching equalizer having the Butterworth response, using an illustrative example.>