# LC high pass filter circuit

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

High pass filters are used in a wide number of applications and particularly in radio frequency applications. For the radio frequency filter applications, the high pass filters are made from inductors and capacitors rather than using other techniques such as active filters using operational amplifiers where applications are normally in the audio range.

High pass filters using LC components, i.e. inductors and capacitors are arranged in ether a pi or T network. As suggested by its name, the pi network has one series component, and either side of it there is a component to ground. Similarly the T network high pass filter has one component to ground and either side there is a series in line component. In the case of a high pass filter the series component or components are capacitors whereas the components to ground are inductors. In this way these filters pass the high frequency signals, and reject the low frequency signals. These filters may be used in applications where there are unwanted signals in a band of frequencies below the cut-off frequency and it is necessary to pass the wanted signals in a band above the cut-off frequency of the filter.

**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 / (4 x pi x Fc) Henries**

**C = 1 / (4 x Zo x pi x Fc) Farads**

**Fc = 1 / (4 x pi x square root ( L x C) Hz**

Where

Zo = characteristic impedance in ohms

C = Capacitance in Farads

L = Inductance in Henries

Fc = Cut off frequency in Hertz

## Further details

In order to provide a greater slope or roll off in the high pass filter, it is possible to cascade several 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 high 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, 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.

* By Ian Poole*

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