# Calculation of mismatched ladder filters

Dear Colleagues,
When an electric circuit was mismatched itself, or under the load, or in the signal source impedance, such circuits are known to be
incalculable exactly. We have developed the original, powerful, highly-effective, comprehensive method for such circuits calculation, much more effective than the two-port method being unable to study the wave processes in mismatched ladder filters (as we have it proved). Our method is based on our original Dynamical Electromechanical Analogy DEMA combined with more general methodology to obtain exact analytical solutions for elastic vibration systems. This method offers to calculate ladder filters having any number of sections, transmission lines having any length and heterogeneities inside the line, under the load of any type and with any type of the source interior impedance. By this method we obtain the 3D amplitude and phase-frequency characteristics of any parameter of a line (input impedance, output characteristics, transmission coefficients etc.), where as the third dimension we can give any other variable parameter of the system. Our method perfectly works also for lines composed of both distributed and lumped parameters. Especially are interesting the lines whose each element is in its turn a resonance subsystem. Our method successfully solves the problems of such kind too. Our basic calculation technology has been acknowledged in EU as showing unique results and published as the Technology of the week, "Understanding vibration":
You can find more information of this methodology in our basic paper on this subject,
"The features of oscillation pattern in mismatched finite electric ladder filters"
published in our journal "SELF Transactions", volume 2 (2002), issue 1
The proposed method is basic for the advanced exact calculation of any complex electric circuits, in that number:
1.    Calculation of branched high-frequency feeder systems 2.    Calculation of branched networks and transmission lines 3.    Calculation of wide-range distributed and lumped delay lines 4.    Dynamical mechanical processes simulation with the help of analogy with electric ladder filters
The complex of problems solvable by this method proves its power and opens the prospects. We have checked this method experimentally. As you can make sure comparing the calculation curves in Fig. 6,
and experimental curves in Fig. 10,