For this section, we assume that networks are linear and time invariant. Time invariant signifies that the network is constant with time. Linear signifies the output is a linear function of the input. Doubling the input driving function doubles the resultant output. The network may be uniquely defined by a set of linear equations relating port voltages and currents.

As we have seen, designing L-C lowpass filters from the lowpass prototype involves only scaling of the resistance and cutoff frequency of the prototype by simple multiplication and division. The transfer characteristics of the prototype are exactly retained and no special realization difficulties are introduced. The design of other structures, such as highpass, bandpass and bandstop filters, require transformation in addition to the scaling. These transformations naturally modify the attributes of the prototype and may introduce severe realization difficulties, especially for bandpass and bandstop structures. The 'ideal' transformation does not exist, and it becomes necessary to consider alternative transformations and how they relate to specific filter requirements and applications. This chapter considers a number of network transformations and equivalences.

More than easing computational burdens, the digital computer has revolutionized the way we design filters. Any modern treatment of filter design must address strategies which have become practical including real-time tuning, statistical analysis, sensitivity analysis, design centering and optimization. It is now feasible to optimize for desired and customized characteristics while simultaneously considering component losses, parasitics and discontinuities. Many filter synthesis theories which we use today were developed in an age when computing tools were far less sophisticated. Wonderfully elegant mathematical solutions were found for a variety of filter problems, but idealized assumptions were required to make the process manageable. Today, these idealized symbolic theories form a starting point which is followed by brute force numeric techniques.

The introduction of a fractional bandwidth parameter for bandpass filters significantly impacts performance and realizability. Over the years, a number of unique distributed bandpass structures have been developed which provide the best possible performance for certain characteristics at the expense of others. There is no one best solution for all applications. The designer who attempts to apply a favorite structure to all problems will not have the success of those who learn to match filter structures and required specifications. Therefore, this chapter is a study of a range of distributed bandpass structures and the advantages and disadvantages of each. We close with a powerful technique for taming the tricky process of tuning bandpass filters of all types.

When the rejection of a signal is required, it is natural to think in terms of a notch. Just as a true bandpass filter offers improved selectivity over a single resonator, the bandstop filter offers improved rejection over a simple notch or even a cascade of notches. However, the general realization difficulties of distributed structures are worsened by particular difficulties associated with the bandstop structure.

This appendix defines equation variables (symbols) used throughout the book. These variables are listed in this appendix in alphabetical order. This appendix also briefly describes =SuperStar= circuit file model codes and variables written by the =M/FILTER= program to define physical dimensions of distributed filter structures. Model codes are organized by process and by function. Circuit file dimensional variables are listed in alphabetical order.