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# 3 db in filter circuit

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#### lekshmiajitha

##### Newbie level 3
why 3 dB is preffered in filter circuit?

In electronics, cutoff frequency is the frequency either above or below which the power output of a circuit, such as a line, amplifier, or electronic filter has fallen to a given proportion of the power in the passband. Most frequently this proportion is one half the passband power, also referred to as the 3dB point since a fall of 3dB corresponds approximately to half power. As a voltage ratio this is a fall to √1/2 ≈ 0.707 of the passband voltage.

Magnitude transfer function of a bandpass filter with lower 3dB cutoff frequency f1 and upper 3dB cutoff frequency f2

Also point in which the attenuation is -3dB is for frequency 1/(T*2*pi) in amplitude/frequency characteristic for passive RC (in series) filter ( first order system), where T is a time constant of transfer function in the form G(s)=1/(T*s+1) and T=R*C. Approximately after that frequency 1/(T*2*pi) the roll off is -20dB/decade. In this example the -3dB is in relation to frequency 1/(T*2*pi) and it is in relation to natural behaviour of 1. order system when the input is sinus((1/T)*t) the output will be 0.7079*sinus((1/T)*t-45*(pi/180)) because -45° is phase,....if i don't mistake

Magnitude transfer function of a bandpass filter with lower 3dB cutoff frequency f1 and upper 3dB cutoff frequency f2

Where does this "funny" (let`s better say: misleading) diagram comes from?
It is not a classical bandpass because - as indicated by the -3db line - the vertical axis seems to be scaled in dB, however, in this case the function must approach minus infinity for very low and very high frequencies (drop of -n*20 dB/dec) . If this axis is linear the cut-off must be indicated by 0.707*Amax.

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