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• (January 12, 2023, 01:18:11 AM)

[Novice]

There was a whole summer in between my Circuits I class and my current Circuits II class that made me forget how to do some simple frequency to frequency, time to frequency, and frequency to time conversions.

Ex.
V = 120√50° --converts to->  V = x + jy (where j is basically i or √-1)

Z = 50 + j50 --converts back to-> x√y°

(Edit: These are actually frequency to frequency, I believe)

The textbook is different and assumes we already know how to do such transformations. Prematurely, I sold my old book and can't find my old notes. I've been introweb searching this but can't find any practical formulas that will work for these cases above. The only one I remember is the following time to frequency transformation:

V = 120sin(4t + 50) --converts to-> 120√50°

I'm still looking for my notes but thought I'd put the homework forum to good use at the same time. Leave it to me to understand all the concepts but be unable to do my homework because I can't convert numbers.

[12AX7]

I understand you need to be able to DO the conversions; not just use the calculator - but it looks like there might be the info you need on this site:

  http://www.sengpielaudio.com/calculator-period.htm

[12AX7]

btw -
  I havent investigated the site; so I dont know for sure if it'll help you.

[Novice]

Well I must say that you caused me to refine my search from just frequency to time conversions, etc to circuit analysis frequency conversions. Most of the sites (like the above) deal with just the actual frequency converted to period.

I was able to find the following:
http://zebu.uoregon.edu/~rayfrey/431/notes3.pdf

It refreshed my memory on the first example:

V = 120√50° = 120(cos(50°) + jsin(50°)) = 77.13 + j91.9

However, I'm still at a loss as to how to go back (50 + j50 --> x√y°).

[Novice]

Got it. Just needed to use my google resources better.

V = 5 + j3

Θ = arctan(3/5)
|V| = √(5^2 + 3^2)

|V|√Θ = 5.83√30.96°

working backwards . .

5.83(cos(30.96) + jsin(30.96)) = 5 + j3

Thanks 12!

[12AX7]

   9.19j + 31.77= ((50)jsin + (50)cos)120 = 50v120 = V

  hehe.. I have no idea, man. I never got past Algebra I in school; and from then on I've just learned what I needed in specific applications. There's a little bit of it being an electrician, and a little more in recording; but not anything like what you're studying. I'll keep my eyes open, tho.

  See if there's something here:
 
http://www.physicsforums.com/

   They are pretty good with help.


  **edit - I see you found it!

[Novice]

I admit a longer example would have probably shed more light on exactly what I needed. I was actually at physicsforums but again their solutions were more general cases. Probably contained what I needed but would have involved a lot of derivation. Thanks again!

[12AX7]

  Heh. A longer example would've just caused me to skip over it faster.

   I read formulas like I read music. I don't. I can look at a note or a symbol and tell you what it means, and how it is used, etc., but looking at a whole page (or a whole formula), it may as well be in Greek. (haha. math. In Greek.)

[TeraHammer]

You make me wonder where frequency enters your problem. On here you are only talking about the maths on (complex) voltages and impedances .

[Novice]

Right. I refer to my previous statement:

I admit a longer example would have probably shed more light on exactly what I needed.

The frequency enters into it when you do something like L (impedance in time domain) to jwL (frequency domain due to w = frequency). At that point, the problem I was having was when adding R to the impedance (Z = R + jwL), I wanted it in the |Z|√Θ form.

Not really a time to freq conversion per se. Misleading, I know.

[TeraHammer]

Hmm can you explain what you mean by time and frequency domain?

Because you can just put j*omega in front of L and 'make it in the frequency domain'. The faster a current oscillates (the higher the frequency, the lower the oscillation time), the higher the impendance of a coil due to self induction.

[Novice]

The way I understand it is |Z| is dependent on frequency. Basically, it is easier for us circuit analyzers to work with the frequency response of a circuit as opposed to the time response.

If we analyzed the circuit in the 'time domain' (z = R + L) as opposed to 'frequency domain' (Z = R + L or |Z|√Θ), we'd have to use differential equations instead of just good 'ol algebra.

Essentially the difference being either using v(t) or v(w).

eh?