need help again lrc parallel magnitude impedance

[e21959]

Hi . I'd like to see the calculations that lead to the termination impedance formula in 1st picture >> ((a) is the right one answer). i saw another formula to calculate impedance (2nd image from left) and both are right, i ve tried to insert some value for r,C,L and the result is correct in both obviously, but i m interest in 1st one calculation, since i cant figure out how the final formula is obtained.Tvm in advance

 

[Ratch]

Hi . I'd like to see the calculations that lead to the termination impedance formula in 1st picture >> ((a) is the right one answer). i saw another formula to calculate impedance (2nd image from left) and both are right, i ve tried to insert some value for r,C,L and the result is correct in both obviously, but i m interest in 1st one calculation, since i cant figure out how the final formula is obtained.Tvm in advance

Just a matter of simple algebra.



Ratch

 

[e21959]

Tvm Ratch.
I figured out how to move from the first to the second term
doing a common denominator
, but not from the second to the third , may you kindly show me the steps that you did ? did you multiply above and bottom for denominator?

 

[Ratch]

Tvm Ratch.
I figured out how to move from the first to the second term
doing a common denominator
, but not from the second to the third , may you kindly show me the steps that you did ? did you multiply above and bottom for denominator?

To find the absolute value of a complex number, find the positive square root of the sum of the real part squared, plus the imaginary part squared, of the numerator and denominator separately. Don't include the "j" term when you square the numbers. The third term above is the absolute value of the second term. Look up how to find the absolute value of complex numbers.

Ratch

 

[e21959]

Tvm Ratch. i think i got it .say z = complex number, = a +ib
| Z | = sqrt (a^2 +b^2), then in the above expression >>
RXC - RXL = a > a^2 = (RXC -RXL)^2
XCXL = b > b^2 = (XCXL)^2
SQRT (RXC-RXL)^2 + (XCXL)^2 = denominator
RXCXL = b = numerator >> b^2 = (RXCXL)^2>>SQRT = RXCXL. is it right ? Tvm

 

[LvW]

The third term above is the absolute value of the second term.
Ratch

However, Ratch, the question is if you can equalize both sides : complex expression=absolute value ?
For my opinion: complex expression=magnitude*exp(j*phase).

 

[e21959]

Ratch You have not told me if my reasoning is correct .yes or no? ^_^ Best Regards

 

[Ratch]

However, Ratch, the question is if you can equalize both sides : complex expression=absolute value ?
For my opinion: complex expression=magnitude*exp(j*phase).

You are right. The magnitude of a complex expression is not the same as the complex expression itself. The magnitude of a complex expression does not contain any "j" components, only a real number. I should have emphasized that better and not used equal (=) signs to equate the third term to the second term.

Ratch

 

[Ratch]

Ratch You have not told me if my reasoning is correct .yes or no? ^_^ Best Regards

If you are referring to your post #5, then yes, that is basically correct. I would use ----> instead of > or >> to mean "results in". The absolute value of a complex number is well defined. Do some exercises to bond your understanding of absolute value.

Ratch

 

[e21959]

I just wanted to see if I understood exactly , thanks Ratch