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Re: Current Limiting and Impedence
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- Subject: Re: Current Limiting and Impedence
- From: "Tesla list" <tesla@xxxxxxxxxx>
- Date: Tue, 26 Apr 2005 17:10:09 -0600
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Original poster: "Gerald Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
Original poster: "Mark Dunn" <mdunn@xxxxxxxxxxxx>
So to conclude, the way I understand it and re-stated to be sure:
Z <> Z1 + Z2 + ...
Z^2 <> Z1^2 + Z2^2 + ...
Not sure what you are meaning by <> but doing the Z^2 = Z1^2 + Z2^2 would
not be the correct thing to do. You can do the Z^2 = R^2 + X^2 for any one
vector if you like to make the magnitude visible, but there is also a phase
angle that goes with this magnitude that sometimes you dont care
about. The pythagorean theorem only works if the two components are at
right angles to each other (like resistive and reactive components), so you
cant use it to combine arbitrary impedances together to find the resulting
magnitude. When you are adding complex numbers, its best to keep the
numbers in vector form to combine (adding up all the real components and
then adding up all the imaginary components) and then determine the
magnitude as the last step. If you are multiplying (or dividing) complex
numbers, conversion to magnitude/phase representation can be easier as the
magnitudes mulitply (or divide) and the angles add (or subtract).
BTW, when you have a complex number of this form:
You can multiply both the numerator and denominator by is its complex
conjugate (a-jb) to put it into the form of c+jd. Example:
1/(a+jb) * (a-jb)/(a-jb) = a/(aa + bb) - jb/(aa + bb) Note that
j=sqrt(-1) and jj = -1
Instead we must break down the Z's into R, and X
Z1^2 = R1^2 + X1^2
Z2^2 = R2^2 + X2^2
And must assign the correct sign for X in case both inductive and
capacitive reactance is present.
Z^2 = (R1 + R2 + ...)^2 + (X1 + X2 + ...)^2
YES, this is correct
I'm not sure this solves my problem, because in my case the R's were
near zero and the X's were inductive. I will go back and recalculate.
Makes sense because all examples I find in books compute impedence for
the entire circuit and never for an individual components and this is
Finally, the only time Z = Z1 + Z2 +... is when the Z's are vectors and
then this expression represents vector addition.
If you have a reference explaining the complex number system, you might
find this helpful. It has many applications (working with complex
impedances is just one application).