An example would be spectacular!!!! The thing that confused me was that when you use 'w' this term obviously includes the freq, which is exactly what im trying to calculate and not knowing what T(s) is it makes it very difficult to rearrange the equation as I don't know what it is im actually multiply/dividing together.
One thing, the real and imag parts, w= 2*pi*f, either that is all imag or all real yes? there is no 1 + j(2*pi*f) or 2*pi*f + j1
So to start we'll let
C1C2C3 = x
2C3(C1+C2) = y
(C2+3C3) = z
T(s) = 1/(s^3*x + s^2*y + s*z +1)
then,
T(s) = 1/(jw^3*x + jw^2*y + jw*z +1)
where next?
I think im following you,
so real part = -w^2*B+1 = -(2*pi*f)^2 * B + 1
imag part = -j*w^3*A+j*w*C : Not sure how to simplifier this any further
Right, ok I'll try and do that,
so, AmplDenom=sqrt(real^2+imag^2)
First i'll sq real
(-w^2*B +1) * (-w^2*B +1) = w^4*B^2 - w^2*B - w^2*B +1 = w^4*B^2 - 2w^2*B +1
sq imag
(-w^3*A + wC) * (-w^3*A + wC) = w^6*A^2 - w^4*AC - w^4*AC + (wc)^2 = w^6*a^2 - 2w^4*AC + w^2*C^2
so
Ampl=1/sqrt((w^4*B^2 - 2w^2*B +1)+(w^6*a^2 - 2w^4*AC + w^2*C^2))
That looks quite a mouthful, but I guess I know what all the values are apart from the f in 2pif
Im not too sure what you mean when you set w=0, surely that would mean everything on the bottom would cancel out apart from the 1. Im not convinced i've understood you.
one quick question, there is no mention of the resistor values in this equation, but when I simulate the circuit and change the resistor values it does have an effect on the 3dB point, do i need another equation for this?
one quick question, there is no mention of the resistor values in this equation, but when I simulate the circuit and change the resistor values it does have an effect on the 3dB point, do i need another equation for this?
ok i've added in the values that I know and w^2=W and I get this horrible looking thing
5.483698704x10^-51 W^3 + 4.5467928x10^-33 W^2 + 3.8217x10^-16 W + 1
can I just stick the values into these equally horrible looking formulae?
Cubic function - Wikipedia, the free encyclopedia
x=(sqrt(27*D^2+(4*B^3-18*B*C)*D+4*C^3-B^2*C^2)/(6*sqrt(3))-(27*D-9*B*C+2*B^3)/54)^(1/3)+(B^2-3*C)/(9*(sqrt(27*D^2+(4*B^3-18*B*C)*D+4*C^3-B^2*C^2)/(6*sqrt(3))-(27*D-9*B*C+2*B^3)/54)^(1/3))-B/3
my dreams of a simple solution to all this are quickly evaporating. Before I go any further, will I need this other equation instead of the one i've been doing?
Oh yeah, thanks for all the help, it is very much appreciated.
Just found something very curious, my 'a' value = 5.483698704x10^-51, turns out that when you square this the answer is 0, seems like anything to x10^-51 squared = 0
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