# Simple LC High Pass Filter Circuit Design & Calculations

### Design considerations, circuit and formulas for a basic 3 pole LC high pass filter for RF applications.

High pass filters, and in particular LC high pass filters are used in many RF applications where they block the lower frequencies and allow through higher frequency signals.

Although not as widely used as low pass filters, high pass LC filters are used in many areas of RF design to remove unwanted signals and allow though the wanted ones.

Typically LC filters are used for the higher radio frequencies where active filters are not so manageable, and inductors more appropriate. Low frequency designs tend not to use inductors as active designs are more common, and inductors can become large and expensive.

## High pass filter topologies

High pass filters using LC components, i.e. inductors and capacitors or even resistors and capacitors can be arranged in ether a pi or T network. As suggested by its name, the basic π network element has one series capacitor, and either side of it there is an inductor connected to ground. Further network elements can be cascaded if a faster roll off rate is required.

Similarly the T network high pass filter has one inductor to ground and either side there is a series in line capacitor. As with the π section network, further elements can be cascaded for improved roll off performance.

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.

## High pass LC filter design

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:

The π section can be calculated from the equations below and using the multipliers shown in the diagram, i.e. 2L and C.

The T section high pass filter can be designed using the equations below to calculate L and C, but note the diagram shows that this must be scaled as 2C and L are required for this design configuration.

The values for C and L using in the two LC high pass filter design configurations can be calculated from the equations below.

Where
Z0 = characteristic impedance in ohms