LC filters. (inductive capacitive filters)

THE PRIMARY APPLICATION FOR RESonant inductive capacitive (LC) filters these days are in high-frequency circuits. These filters, like resistive capacitive (RC) filters can easily be designed to perform low-pass, high-pass, bandpass, or notch filtering, but they have the additional benefit of offering at least 12 dB per octave or rolloff, compared to the 6 dB per octave of RC filters, which means sharper cutoff characteristics at all operating frequencies.

The series- and the parallel-resonant LC filters are the two "watershed" LC designs from which all others are derived. Figure 1-[a shows a circuit for a series-resonant filter, and Fig. 1-b shows its simplified equivalent circuit. The R represents the resistance of the coil.

Series-resonant filter

The fundamental response of the series filter is that capacitive reactance C decreases with increased frequency, while inductive reactance decreases. The inverse relationship also holds. The filter's input impedance is equal to the difference between these two reactances, plus the value of resistor R.

At some specific frequency, the reactances of C and L could be 10 kilohms and 1 kilohm, respectively. Therefore the filter's input impedance (ignoring the value of R) will be 9 kilohms at that frequency. Many other similar examples can be given.

The key point to be made here is that at resonant frequency, [f.sub.c], the reactances of C and L will be equal (but 90 [degrees] out of phase), and the filter input impedance will equal the value of R, as indicated by the dotted line at the bottom of the impedance vs. frequency characteristic curve Fig. 2-a. For example, if this occurs when the reactances of C and L are both 1000 ohms, and R equals 10 ohms, the input impedance would be 10 ohms, and the entire signal voltage would be generated across R.

The signal currents through …