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Where does the formula BW = 0.35 / t10%-90% come from?

Question :

Where does the formula BW = 0.35 / t10%-90% come from?

Answer :

A scope can be modeled as a single pole RC circuit. From this assumption we can derive the bandwidth and risetime relationship.

  1. Risetime is the time measured from Vout,90% - Vout,10%. The response for an RC network is Vout = Vin (1 – e-t/t) where t= RC.

From the above equation we find t90% = 2.3tand t10% = 0.105t .

The t10%-90% = 2.3t -0.105t» 2.2t .

  1. Bandwidth is defined as the frequency at which the signal is attenuated –3dB.   For the RC model this occurs at BW = 1/ (2px t ).
  2. Combining the equations for t10%-90%and BW we have:

BW = 2.2 / (2px t10%-90%)

       =  0.35 / t10%-90%

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FAQ ID 53721

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