Electronic Design

# Quick And Practical Design Of A High-Pass Third-Order Bessel Filter

In the design of a proximity switch using PIN diodes as the receiving element, the signal is first amplified and then must be filtered from any noise before proceeding to the several signal-conditioning stages of the proximity switch. Typically, to reject any noise resulting from 50-Hz supplies, neon lamp frequencies, 100 Hz harmonics, and any other anticipated sources of noise, a unity-gain third-order Bessel filter is a good choice for giving a flat response without damping at the corner frequency (this doesn’t happen with Butterworth or Chebyshev filters).

The filter shown provides a zero response at dc and a flat response from corner frequency fcp, up to fu (Fig. 1). The fu frequency is where Avc gain crosses unity (Fig. 2).

The filter is a high-pass type only for the region between fcp and fu. In practice, fu varies with temperature and the filter will be subjected to more error drift near fu.

The following procedure, which uses equally sized capacitors, enables the selection and calculation of the wider range of resistors that are available as opposed to capacitors:

1. Estimate which frequencies are to be rejected and determine the corner frequency fcp.
2. Select an op amp with a range of frequencies in which the open-loop gain Avlo ≥ 100. This value must be maintained from dc up to the unitygain frequency fu, in order to keep the actual frequency response with 0.1 dB of the theoretical response.
3. Select a value for the three equally sized capacitors C1 = C2 = C3.
4. From the chosen corner frequency, calculate the capacitors initial value C’.
5. For equally sized capacitors, calculate the scaling factor K.
6. Calculate the three final resistor values according to: R1 = KR1’; R2 = KR2’; R3 = KR3’, where R1’ = 0.7027; R2’ = 1.012; and R3’ = 3.940 are the initial resistor values for a high-pass Bessel filter.

The following is an example set up for a PIN diode signal as the input to the filter:

1. The value of the required corner frequency is: fcp = 800 Hz.
2. An HA-4625 op amp, with Avlo = 200, from dc up to 70 MHz is selected.
3. For the three equally sized capacitors, 2.7-nF, 1% film is selected.
4. From the above fcp, the initial value of capacitors, C’ is calculated:
5. The scaling factor K is then calculated:
6. The final resistor values are calculated, according to the high-pass Bessel filter initial values: R1’, R2’, R3:
R1 = KR1’ = 52k
R2 = KR2’ = 75k
R3 = KR3’ = 287k