So far the filters we have made have had only two elements: a capacitor and a resistor or inductor. We can improve the response of our filters by adding more elements. This allows us to make the pass band flatter and the roll-off steeper. Multielement filters behave somewhat like transmission lines, and we need to have the right input and output resistance to avoid problems with reflections. Analyzing these filters by hand is quite difficult, but the calculations are easy on a computer. For this we will use a computer program called Puff, which is included with this book. Instructions for running the program are given in Appendix C.

Ladder Filters

We will consider ladder networks with alternating series and shunt elements like the discrete transmission line we studied in Problem 11. If the series elements are inductors and the shunt elements are capacitors, then the circuit acts as a low-pass filter (Figure 5.1a, b). At low frequencies, the impedance of the inductors and the admittance of the capacitors are small, and the input signal passes through to the output with little loss. In contrast, at high frequencies the inductors begin to act as voltage dividers and the capacitors as current dividers. This reduces the power transmitted to the load. We can also make high-pass filters with series capacitors and shunt inductors (Figure 5.1c, d).

Many different filters have been developed, giving a wide choice of amplitude, phase, pass-band, and stop-band characteristics.