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# Introduction to Filters

Author: J.B. Hoag

Various combinations of coils and condensers are used:

1. To separate currents of different frequencies from each other.

2. As a coupling unit between two circuits whose impedances are not equal to each other.

3. To shift the phase between voltage and current.

4. To alter the magnitude of voltage or current.

Figure 7 C shows some of the filters with which we are already familiar, together with their curves of output current at different input frequencies, their basic equations, and their names. See also Figs. 5 A and 5 B.

 Fig. 7C. Crude filters. Low-pass types use series inductance (top figure). High-pass use series capacitance. Band-pass use series LC circuits. Band-elimination use parallel LC circuits (bottom figure)

More complicated combinations will serve better in separating neighboring frequencies and in more completely suppressing others. In other words, there are filters which have a sharper cutoff.

Of the host of possible LC combinations, a few simplified forms have been developed under the following assumptions and simplifications :

1. The resistances of all parts of the filter circuits are to be kept as low as possible. We shall assume that the resistances are zero. Such filters are called " ideal " or non-dissipative.

2. There shall be no batteries or other sources of electromotive force, nor vacuum tubes with their attendant amplification, in the filter. Such filters are said to be passive.

3. The inductances of all coils which contain iron cores shall be assumed to be the same for any of the currents which flow through them. Filters constructed with such inductances are said to be linear.

4. There shall be no magnetic coupling of the lines of force from any of the coils to any other coils in the circuits.

5. The output or load circuit shall consist of pure resistance (no coils or condensers), whose value shall be the same as that of the generator or input circuit.

It is possible to describe the characteristic of filters in terms of the output current as in Fig. 7 C, or in terms of the ratio of output to input currents, or the ratio of the output voltage across the load to the input voltage, or the ratio of the power output to the power input, or, as is more common and as we shall now do, in terms of the attenuation of the filter. The attenuation is expressed in decibels and is proportional to the logarithm of the ratio of the output to the input currents or voltages or powers. It is a measure of the losses which take place in the filter at the different frequencies.

 Fig. 7 D. An L-section, low-pass filter. The lower frequencies in the range " A " pass through, while those of higher value are more or less attenuated or lost in the filter

Last Update: 2010-11-21