Designing LC Ladder Filters with Lossy Elements

Abstract

Many publications and many books have been written on LC Ladder filters, however, most of the material in circulation only deals with ideal (lossless) LC ladder filters. It is assumed that in the lossless design, all of the reactance values are ideal ones. However, since reactance elements are actually lossy, the purpose of this thesis is to show how to design LC ladder filters with lossy components, and achieve optimal responses. Three different methods are presented to correct the lossy ladder filter. The first method uses the Sum Squared Error (SSE) to minimize the difference between the poles of the ideal filer and the lossy filter. The second method uses the SSE to minimize the difference between the coefficients of the ideal filer’s transfer function and the lossy filter’s transfer function. The final method uses the SSE to minimize the difference between magnitude plot of the ideal filter and lossy filter. The first and second methods both use the Nelder-Mead algorithm for the optimization scheme, and the third method uses the Levenberg–Marquardt algorithm. The first two methods work well but only for low-pass filters. In the case of more complex designs, the number of roots and the filters order in the ideal filter and lossy filter do not match, so this method cannot be used. In conclusion, the third method where the frequency magnitude plots of the ideal and lossy filter are being matched, provide the best solution. As a result, this method allows one to design a ladder filter with lossy components, while achieving ideal-like results.