LC low pass filter circuit

- the design considerations and formulae (formulas) for an LC (inductor capacitor) low pass filter

Low pass filters are used in a wide number of applications. Particularly in radio frequency applications, low pass filters are made in their LC form using inductors and capacitors. Typically they may be used to filter out unwanted signals that may be present in a band above the wanted pass band. In this way, this form of filter only accepts signals below the cut-off frequency.

Low pass filters using LC components, i.e. inductors and capacitors are arranged in ether a pi or T network. For the pi section filter, each section has one series component and either side a component to ground. The T network low pass filter has one component to ground and either side there is a series in line component. In the case of a low pass filter the series component or components are inductors whereas the components to ground are capacitors.

LC Pi and T section low pass filters

LC Pi and T section low pass filters

There is a variety of different filter variants that can be used dependent upon the requirements in terms of in band ripple, rate at which final roll off is achieved, etc. The type used here is the constant-k and this produces some manageable equations:

L     =     Zo / (pi x Fc) Henries


C     =     1 / (Zo x pi x Fc) Farads


Fc     =    1 / (pi x square root ( L x C) Hz


Zo = characteristic impedance in ohms
C = Capacitance in Farads
L = Inductance in Henries
Fc = Cutoff frequency in Hertz

Further details

In order to provide a greater slope or roll off, it is possible to cascade several low pass filter sections. When this is done the filter elements from adjacent sections may be combined. For example if two T section filters are cascaded and each T section has a 1 uH inductor in each leg of the T, these may be combined in the adjoining sections and a 2 uH inductor used.

The choice of components for any filter, and in this case for a low pass filter is important. 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. This should be undertaken not just for the pass band frequencies, but more importantly for the frequencies in the stop band that may be well in excess of the cut off frequency of the low pass filter. 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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