First-Order Estimation and Precorrection of Parasitic Loss Effects in Ladder Filters

A method of estimation and approximate precompensation for the effects of element losses in resistance-terminated LC circuits is presented. Some new theorems are utilized for the special case of ladder networks. The process is valid for a nonuniform distribution of losses; there is, however, a limit to the amount of loss that can be compensated for. The procedure is based on a simple expression giving the firstorder increment of the complex transfer function in terms of quantities normally available from the lossless design. A formula is derived for the lossy response of the network; this has a form which brings out the individual effects of the different parasitic elements in producing distortion, and shows the effects of Q-tolerances of each lossy element. The predistorted transmission function is also given explicitly. The method'is not restricted to treating the effects of dissipation. It is also applicable to other parasitic phenomena (stray capacitances, element tolerances, etc.). The formulas become especially simple and useful for ladder networks. In the case of equal loss factors in elements of the same kind, they present an alternative to Darlington's design equations. Examples are given to illustrate the relative simplicity and accuracy of the method for practical network synthesis.