First-order RC low-pass filter [derivation of principle in detail]

 

 

 

 

Note the cutoff frequencyf_B=\frac1{2\pi RC}

 Because there is an extra f in the complex impedance in the previous derivation

The function here is:

H(f) = \frac{1}{1+\mathrm{j}(f/f_{B})}

Among them: f is the frequency of the input signal, and f_B is the cut-off frequency of the filter.

The phase angle φ of this function, (the arc cosine value of its argument):

arctan(\frac{Im(H(f))}{Re(H(f))})

Bring the function into have:

Re(H(f)) =  \frac{1}{1+(f/f_B)^2}

Im(H(f)) =  -\frac{f/f_B}{1+(f/f_B)^2}

The phase angle φ is:

φ = arctan(\frac{-f/f_B}{1})=-arctan(f/f_B)

 

 

 

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Origin blog.csdn.net/u010087338/article/details/132303594