...under perpetual construction.

Design of a minimum loss bandpass filter for the LF band, with a center frequency of 137.7 kHz and a 26.3 kHz bandwidth at an attenuation of 60 dB. The filter has 3 resonators, with a Q of 350.

The `bpfilt` input screen will be:

Enter Center Frequency [Hz] : 137.7e03 Enter Bandwidth [Hz] : 26300 Enter Stopband Attenuation [dB]: 60 Enter Number of Resonators : 3 Enter Resonators Unloaded Q : 350 Enter Inductance L [H] : 1.031e-03 Enter Source Impedance [ohm] : 50 Enter Load Impedance [ohm] : 50

Here is a graph with the close-in frequency response of four different filters:

- capacitively coupled with parallel capacitor matching (Aplac file)
- inductively coupled with parallel capacitor matching (Aplac file)
- capacitively coupled with series capacitor matching (Aplac file)
- inductively coupled with series capacitor matching (Aplac file)

All the four types have (of course) the same passband, and start to deviate slowly going into the stopband; at -60 dB the bandwidth is about 26 kHz, as requested. The center band loss is about 2.4 dB.

Here is a graph with the frequency response over a larger band.

On the low side the capacitively coupled filters roll of at -60 dB/decade (like a third-order high-pass filter) while the inductively coupled filters roll of at -140 dB/decade (like a seventh-order high-pass filter).

On the high side the capacitively coupled filter with parallel capacitor matching (#1 in the graps) rolls of at -20 dB/decade (like a first-order low-pass filter), the inductively coupled filter with parallel capacitor matching (#2 in the graps) rolls of at -100 dB/decade (like a fifth-order low-pass filter), the capacitively coupled filter with series capacitor matching (#3 in the graps) rolls of at -20 dB/decade (like a first-order low-pass filter), but only after about 10 MHz (off-screen), where there is a spurios resonance, while the inductively coupled with series capacitor matching (#4 in the graps)filters rolls of at -100 dB/decade (fifth-order) but only after about 10 MHz (off-screen), where there is a spurios resonance.

Another design example compares the minimum loss, equiripple and maximally flat filter types