LC band pass filter
- the design considerations and formulae (formulas) for an LC
(inductor capacitor) band pass filter
Band pass filters using LC components, i.e. inductors and
capacitors are used in a number of radio frequency applications. These filters
enable a band of frequencies to be passed through the filter, while those in the
stop band of the band pass filter are rejected.
These filters are typically used where a small band of
frequencies need to be passed through the filter and all others rejected by the
filter.
Like the high pass filters and the low pass filters, there
are two topologies that are used for these filters, namely the Pi and the T
configurations. Rather than having a single element in each leg of the filter as
in the case of the low pass and high pass filters, the band pass filter has a
resonant circuit in each leg. These resonant circuits are either series or
parallel tuned LC circuits.
LC Pi and T section band pass filters
The equations below provide the values for the capacitors and
resistors for a constant-k filter. As the filter is a band pass filter there are
two cut off frequencies. One at the low edge of the pass band and the toher at
the top edge of the pass band.
L1 = Zo / (pi (f2 - f1)) Henries
L2 = Zo (f2 - f1) / (4 pi f2 f1)
Henries
C1 = (f2 - f1) / (4 pi f2 f1 Zo)
Farads
C2 = 1 / (pi Zo (f2 - f1)) Farads
Zo = characteristic impedance in ohms
C1 and C2 = Capacitance in Farads
L1 and L2 = Inductance in Henries
f1 and f2 = Cut off frequencies in Hertz
Further details
The choice of components for any filter such as a low pass
filter or a high pass filter can be crucial to its performance. In the case of a
band pass filter it is even more important as the circuit comprises six
components rather than just three. As a result of this, close tolerance
components should be used to ensure that the required performance is obtained.
It is also necessary to check on the temperature stability to ensure that the
filter components do not vary significantly with temperature, thereby altering
the performance.
Care must be taken with the layout of the filter, especially
when the filter is used for high frequencies. Capacitive and inductive coupling
are the main elements that cause the filter performance to be degraded.
Accordingly the input and output of the filter should be kept apart. Short leads
and tracks should be used, Components from adjacent filter sections should be
spaced apart. Screens used where required, and good quality connectors and
coaxial cable used at the input and output if applicable.
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