# Characteristic Index Of Filter

The characteristic frequency

1) The band cutoff frequency fp=wp/(2p) is the frequency of the boundary point between the pass band and the transition zone, and the signal gain at that point drops to the lower limit of an artificial setting;
2) The band cutoff frequency fr=wr/(2p) is the frequency of the boundary point between the band and the transition zone, and the signal decay of the point drops to the lower limit of a man;
3) Transition frequency fc=wc/(2p) is the frequency of signal power attenuation to 1/2 (about 3dB), in many cases, FC is often used as a pass or band cutoff frequency;
4) The natural frequency f0=w0/(2p) is that when the circuit has no loss, the resonant frequency of the filter, complex circuits often have multiple natural frequencies.

Gain and decay

The gain of the filter within the band is not constant.
1) for the low-pass filter through the band gain KP generally refers to the gain when the w=0; high-pass refers to the gain at the w→∞; with general rules refers to the gain at the center frequency;
2) for the band Resistance filter, the drag consumption of the belt should be given, and the decay consumption is defined as the inverse of the gain;
3) The band gain change volume KP refers to the maximum variation of the gain of each point in the band, and if KP is in db, it refers to the amount of variation of the gain DB value.

Damping coefficient and quality factor

The damping coefficient is the function of characterizing the diagonal frequency of the filter as the w0 signal, and it is an index to represent the energy decay in the filter. The inverse of damping coefficient is called the quality factor, which is an important index of the frequency selection characteristics of * Valence band pass and band resistance Filter, q= w0/W.
The W in the formula is the 3dB bandwidth of the band-pass or band-resistance filter, the W0 is the center frequency, and in many cases the center frequency is equal to the natural frequency.

Sensitivity The filter circuit is composed of many components.

The sensitivity of a performance indicator y of a filter to the X variation of a component parameter is recorded as SXY, defined as: sxy= (dy/y)/(dx/x).
The sensitivity is not a concept with the sensitivity of the measuring instrument or circuit system, and the smaller the sensitivity, the stronger the fault tolerance of the circuit and the higher the stability.

Post time: Mar-30-2021
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