Calculating Impedances in Polar Coordinates: Tips and Tricks

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Discussion Overview

The discussion revolves around the process of adding three impedances given in polar form, exploring whether conversion to rectangular coordinates is necessary or if calculators can facilitate the process directly. Participants share their understanding of relevant formulas and methods for combining impedances in both series and parallel configurations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions whether it is necessary to convert polar impedances to rectangular form for addition, seeking quicker methods using a calculator.
  • Another participant suggests that if the impedances are multiplied, the product can be found by multiplying their magnitudes and adding their phase angles.
  • A different participant proposes using the formula for combining impedances in series and parallel, indicating a method for handling two impedances in parallel before adding a third in series.
  • One contributor emphasizes the importance of understanding the multiplication of polar coordinates, suggesting that it involves multiplying magnitudes and adding angles, while also noting the historical context of learning these methods.
  • A participant expresses uncertainty about their calculator's capabilities but is hopeful that it can convert between polar and rectangular forms to assist in their calculations.

Areas of Agreement / Disagreement

Participants express varying levels of confidence in their understanding of the methods for adding impedances in polar form, with some advocating for direct methods using calculators and others emphasizing the importance of manual calculations for accuracy. No consensus is reached on the best approach.

Contextual Notes

Some participants mention potential confusion regarding the use of terminology (e.g., "x-axis" and "y") when discussing polar and rectangular forms, indicating a need for clarity in definitions. There is also an acknowledgment of the historical evolution of tools used for these calculations.

Who May Find This Useful

This discussion may be useful for students and practitioners in electrical engineering or related fields who are learning to work with complex impedances and are seeking methods for combining them effectively.

barry-
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Hello all i have a question about adding 3 impedances given in polar form, must i convert them to x..y.. first or is there a quicker way on a calculator and if so can anyone give advice i have the equation Zo=√Z(oc)Z(sc) but finding it hard to understand many thanks.
 
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barry- said:
i have a question about adding 3 impedances given in polar form, must i convert them to x..y.. first or is there a quicker way on a calculator and if so can anyone give advice i have the equation Zo=√Z(oc)Z(sc)
Are you sure you didn't mean multiplying two impedances? In that case, if Zoc and Zsc are two complex impedances in polar form, their product is a new complex number with magnitude |Zoc|× |Zsc| and phase angel φoc + φsc.

barry- said:
[...]finding it hard to understand many thanks.
It's easier to understand many thanks if you use punctuation.
 
well its 3 impedance in series and parallel so if i use the formula z =z1z2/z1 + z2 and am i right that in polar form you multiply the x-axis and add the y (i.e the value given as the angle)? that will sort the 2 impedances out in parallel then the remaining impedance will be in series with that and i can just add them, Thank you
 
Congratulations on improved punctuation !

Yes - you can add in rectangular,

and you can multiply in polar as you described. I'd have said " Multiply the magnitudes and add the angles" , though. To say X and Y implies rectangular.

I learned this in slide rule days so it's ingrained.
I really suggest you work about ten examples on paper so it'll become habit for you.

I was through college before pocket calculators appeared. When the HP35 came out ~1972 with its one button polar-rectangular conversion the EE world was flabbergasted.

So there's probably an easy way to do it with a modern calculator. But you should become fluent in the method so you can spot errors coming from missed keystrokes.

My two cents !

old jim
 
:) thanks english is not a strong point of mine, thank you for the help, I am sure my calculator can add them but I am not sure how, so as long as it can convert between polar and rectangular and then do what i need to do il be happy, thank you.
 

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