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

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

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 V_out,90% - V_out,10%. The response for an RC network is V_out = V_in (1 – e^-t/t) where t= RC.

From the above equation we find t_90% = 2.3tand t_10% = 0.105t .

The t_10%-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 t_10%-90%and BW we have:

BW = 2.2 / (2px t_10%-90%)

       =  0.35 / t_10%-90%