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Types and Transfer Functions of Filters

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In the circuit shown in the diagram, all resistances are equal, and all inductors are equal.

For building each filter, only 3 terminals are used; nothing is connected to other terminals.

For one of the connections the cutoff frequency wc is given in rad/sec. Calculate wc for other connections; determine the type of each filter.

In the last (blank) row of the table, list the connections for building the High Pass filter with the highest cutoff frequency wc possible in this circuit; calculate this wcH.

Please see the attachment for mentioned diagram and table.

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This solution discusses the types and transfer functions of filters.

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Input signal Common ground Cutoff frequency (rad/sec) Type of filter
3 4 2400 High-pass
3 5 1200 High-pass
3 6 800 High-pass
1 6 2400 High-pass
2 5 2400 High-pass
4 3 2400 Low-pass
5 1 3600 Low-pass
1 4 7200 High-pass

For any filter with a resistor in series with an inductor is going to have a cutoff frequency equal to R/L. This doesn't change regardless whether the filter is a high-pass or low-pass. The cutoff frequency is proportional to the value of the resistor and inversely proportional to the value of the inductor. For the filter in the first row, wC is 2400 rad/s = (R/L).

To see the type of filter (high-pass or low-pass), just ...

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