We have previously introduced what network filters are. Here we will mainly introduce what are the parameters, order and duality of network filters.
Main parameters
1. Passband gain: the voltage gain within the filter passband.
2. Characteristic angular frequency and characteristic frequency: It is only related to the parameters of the resistor and capacitor components used for filtering. Bandpass filters typically refer to the center angular frequency or center frequency of the bandpass filter. This is the frequency of the maximum (minimum) point of voltage gain in the passband.
3. Cutoff frequency is the point where the voltage gain decreases.
4. Passband (stopband) width: It is the difference between the two values of the bandpass (bandstop) filter.
5.To calculate the equivalent quality factor, divide the voltage gain of the filter circuit by the passband gain. This calculation applies to both low-pass and high-pass filters. For bandpass or bandstop filters, the quality factor is the center frequency divided by the bandwidth.

Order
The highest number of "S" in the bottom determines the "order" of the active filter equation. The higher the order, the sharper the change in the filter's strength at different frequencies, getting closer to the ideal.
In general, the transition band of a first-order filter decays at a rate of 20dB per decade. A second-order filter decays at a rate of 40dB per decade. You can compose a high-order filter from a series of low-order filters.
Dual relationship
The dual relationship between low-pass and high-pass filters
(1) Dual relationship of amplitude-frequency characteristics
When the passband gain A0, cutoff frequency or f0 of the low-pass filter and the high-pass filter are equal. The amplitude-frequency characteristic curves of the two are symmetrical relative to the vertical line f=f0.
(2) Dual relationship of transfer function
To get the high-pass filter transfer function, replace S with 1/S in the low-pass filter transfer function. This simple substitution will give you the desired result.
(3) Duality relationship in circuit structure
To convert a low-pass filter into a high-pass filter, switch the capacitor with the resistor.
The above is an introduction to the main parameters, order and duality relationship of network filters.