# LC band pass filter circuit

### - overview and information about the basics of the design of an RF LC bandpass or band pass filter circuit including the design considerations and formulae (formulas) and construction tips.

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 RF filter including a bandpass 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 RF filter components do not vary significantly with temperature, thereby altering the performance.

Care must be taken with the layout of the RF filter, especially when the RF 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.

By Ian Poole

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