# Re: [SI-LIST] : RE: Split Plane

From: Doug McKean ([email protected])
Date: Thu May 25 2000 - 16:49:10 PDT

Woops ...

Didn't mean to start anything.

The following derivation uses the -3dB point
or critical frequency for a passive circuit.

- Doug McKean

--------------------------------------------------

Assume V(0) = 0 and V(infinity) = Vmax

Look at only V = 10%Vmax and V = 90%Vmax

Since, V = Vmax*[1 - exp(-t/tau)]

(tau being whatever time constant you wish)

----------
V at 10% ...

V(0.1) = 0.1*Vmax = Vmax - Vmax*exp(-t/tau)

Vmax*exp(-t/tau) = Vmax - 0.1*Vmax
= 0.9*Vmax

exp(-t/tau) = 0.9
ln[exp(-t/tau)] = ln[0.9]
(-t/tau) = -.1
t(10%) = 0.1*tau

----------
V at 90% ...

V(0.9) = 0.9*Vmax = Vmax - Vmax*exp(-t/tau)

Vmax*exp(-t/tau) = Vmax - 0.9*Vmax
= 0.1*Vmax

exp(-t/tau) = 0.1
ln[exp(-t/tau)] = ln[0.1]
(-t/tau) = -2.3
t(90%) = 2.3*tau

----------
Trise = t(90%) - t(10%)
= 2.3*tau - 0.1*tau
= 2.2*tau

Since, f = 1/(2*pi*tau)

makes tau = 1/(2*pi*f)

Trise = 2.2*tau
= 2.2/(2*pi*f)
= 0.35014/f

f = 0.35014/Trise

----------

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