# Simple Coil & Capacitor Bandpass (Band-Pass) Filters

*Author: R.J.Edwards G4FGQ © 6th
January 2003 *

The majority of L & C filters consist of one or more cascaded basic
L-C sections used in applications where a small loss in the
pass-band is of no consequence and frequencies of 'infinite'
attenuation in the stop-band are not required. E.g., simple,
switchable, bandpass filters at the input of radio receivers or at
the output of radio transmitters where power-handling components may
be needed.

This program assists with design of such simple
filters without the operating inconvenience encountered when using
programs intended for designing more complicated filters. The two
possible basic filter sections, T & Pi, are computed. Note: T and Pi
sections should not be cascaded with each other.

Input data are the pair of filter cut-off
frequencies, terminating resistances, and the variable frequency at
which overall filter insertion loss between its terminations is
computed. For simplicity, internal filter loss is neglected.
Internal loss depends on coil Q. It results in an increase in
attenuation in the pass-band and a decrease in attenuation in the
stop-bands. To approximate the computed filter response coil Q must
exceed the computed minimum Q value although a useful band-pass
response can be obtained at lower values.

Values of L uH and C pF components are output. A
tolerance of +/- 5 or 10 percent will be adequate in many cases
where the bandwidth/mean-frequency ratio exceeds 0.25 When the ratio
is less than 0.25, bandwidth may be widened to ensure low
attenuation over the whole required pass-band. Or variable preset L
and C components can be used. Insertion loss at band-edges is always
3.01 dB.

When coil Q is low and approaches 1/ratio,
greater loss must be accepted in the pass-band and filter design
must be changed to the case of two over-coupled tuned circuits as
for a double-tuned IF transformer.

Insertion loss is defined as that when the filter
is inserted between generator and a termination both of the same
resistance as specified by the input data.

In the case of a Pi network, to obtain more
feasible L and C component values, the filter section can be based
on a high value of terminating resistance and input and output
connections can be tapped down the input/output coils. By the same
means the filter can be designed to operate between different
impedances.

The impedance transforming ratio is proportional
to the square of tapping-turns turns ratio on the end coils of the
Pi-section.

*NOTE: For frequencies out-of-program-range,
multiply/divide L & C by the frequency ratio.*

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