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Hi, I have been asked to estimate the half-power cutoff frequency of a first order filter that gave this response to a step input.

The problem I am having is I have only ever been given examples with the response in frequency , with db/frequency, here it is volts/sec which has completely stumped me. How can I convert this to a frequency response to allow me to determine the cutoff frequency?


1 Answer 1


At about 63% of the full peak value, the time = RC (if it were an RC filter): -

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This is because: -

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And when Tau = t the answer is 0.6321

Half-power frequency: -

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That to me looks like it's happening at about 0.8 micro seconds and so,

F = 1000000/(2xPix0.8) = 199 kHz

  • \$\begingroup\$ So the formula is 1/2piRC? and when you say 0.8 micro seconds is that taken from the time the step input occurs, as nothing happens at 0.8, so it is 1.8 micro seconds minus 1 micro second = 0.8 micro seconds? Thanks for your help \$\endgroup\$
    – Jdoe
    Jun 3, 2017 at 13:53
  • \$\begingroup\$ Correct, nothing happens in the first interval so it is ignored until the step change occurs. \$\endgroup\$
    – Andy aka
    Jun 3, 2017 at 14:34

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