Radar Basics

Bandpass filter

A bandpass filter (BPF) is a circuit that passes frequencies within a certain range. The frequency ranges below and above the passband are blocked or significantly attenuated. It is at least a second-order filter because a single frequency-dependent component cannot cause two different cut-off frequencies. Passive band-pass filters can be created by connecting a low-pass filter (in the picture consisting of R₁ and C₂) to a high-pass filter (in the picture consisting of C₁ and R₂).

The bandwidth of a bandpass filter is defined as the frequency range between two specified cut-off values that are 3 dB below the maximum value. For a bandpass filter to function as such, the lower cut-off frequency f_low must be below the upper cut-off frequency f_high, which must be taken into account when calculating (R₁, C₂) and (C₁, R₂).

Bandpass filter center frequency

For the bandpass filter, the two cut-off frequencies that are set at the −3 dB limits are primarily decisive. However, a center frequency can also be calculated, which results from the geometric mean of the two cut-off frequencies. At the center frequency, there is no phase shift between the input and output. Below this frequency, capacitive properties dominate, leading to an increasing phase shift approaching +90°. Conversely, above the center frequency, inductive properties prevail, resulting in an increasing phase shift approaching -90°.

(1)

• f_r = center frequency or resonance frequency
• f_low = lower cut-off frequency
• f_high = higher cut-off frequency

In a passive bandpass filter implemented with wide-band resonant circuits, the center frequency is referred to as the resonant frequency.