Ladder filter
Through the years, engineers have devised many techniques for realizing
various types of transfer functions with passive elements only. We consider
some of these techniques, particularly techniques that reduce the problem
of realizing a transfer function to that of realizing a DP function. These
techniques are simple, and yet they have been proven to be very useful and
are applicable to a very large class of practical problems.
In this section, we consider the basic circuit structures. Which is
ladder circuits and the basic properties and realization methods of both RC and LC
ladder circuits. We show that RC {LC} ladder circuits can realize only those
transfer functions with simple poles and with all poles and zeros on the
negative real {the imaginary} axis of the .?-plane. Although the realization procedures
are more involved than the previous two circuit structures, it should be pointed out that common to all passive synthesis techniques—by using passive elements only—a transfer function can be realized up to a constant multiple only.
In ladder networks, there are two sources of transmission zeros; they are the complex frequencies where
1. The impedance function of a series branch is infinite, and
2. The impedance function of a shunt branch is zero.
In the first case, a series branch becomes an open circuit. Hence, no signal will pass through toward the output. In the second case, a shunt branch becomes a short circuit. Thus, all current will flow through that short circuit shunt branch, leaving no current flowing toward the output. In both cases, no current will arrive at the output end. Hence, the (steady-state) output will be zero if the input is at the transmission zero frequencies.