Classic filter design methods synthesize filters around known resistive Terminations. However, actual Terminations are frequently complex rather than resistive. Filter Solutions and FilterQuick use RMS error reduction methods to synthesize filters around such complex terminations.
The source and load terminations of lumped LC and transmission line filters may be defined with the use of impedance tables wherein the real and imaginary portions of impedance are defined as a function of frequency, as shown below. Note that impedance may be entered in either Polar, Cartesian or Parallel format. Reactance may be entered directly, in Ohms, or through the equivalent capacitance or inductance.
Termination Impedance Definition
The impedance tables contain two compensation options, "Element Tune" and "Impedance Compensate".
This option tunes all the reactive elements to minimize the RMS error. The default status is "Checked".
This option attempts to improve the synthesis accuracy by adding reactive elements to the complex termination, to make it more resistive. . Sometimes this technique has the effect of improving the filter performance, but frequently it degrades the performance. It is very important for the user to carefully examine the effect of this option on the desired filter prior to accepting the results. The default status of this option is "Unchecked".
Norton, Pi->T, and T->PI
A simple right mouse click on any Pi, T or L combinations of like elements permits the user to perform a Norton transformation, sometimes referred to as a Capacitor Transformer, since most operations are performed on capacitors. A Pi may be converted to a T, and a T may be converted to a Pi. Pi, T and L combinations frequently appear in band pass filters, making this feature a strong tool for custom band pass filter design. Tools exist to add, delete, or change element values with no effect on the shape of the frequency response.
Combinations of elements that are candidates for a Norton transformation by the use of a right mouse click
The theory behind Norton transformations is well known and shown below.
Norton Transformation Equivalent Circuits
Equal Inductor Bandpass Filters
All-Pole and Zigzag filters may be synthesized with only one inductor value. For odd order Zigzags, the single inductor value is selectable by the user within a specified range. The operation changes the value of the source resistance for even order All-poles, but it may be reset by requiring two inductor values instead of one. Equal inductor All-pole filters have the additional advantage, that all the nodes may contain a grounded capacitor, making it easy to absorb any parasitic node capacitance.
Classic All-Pole Band Pass Filter