Impedance, Reactance, and the J operator

[belwar]

Hey all,

Does any have a good link or care to explain how and what the J operator is in an impedance calculation? I'm having a hard time understanding what the j operator is an how it relates to the reactance. I understand what reactance is, but don't understand the J.

The only description if found is that it is the positive square root of -1.. But why is it there. The book I am reading says " the J operator provides engineers with a mathematical model that perfectly explains the behavior of complex impedances" but it doesn't explain how

Bel

[Joe Gwinn]

How to become Orthogonal to Real

The J operator in electrical engineering is identical to the I of complex variables in mathematics. (In EE, "I" was already used for current, so they used the next available symbol.)

Complex number - Wikipedia, the free encyclopedia

If you plot a complex number in the real-by-imaginary plane (an Argand diagram), each successive multiplication of that complex number by I (J in EE) rotates the complex number by another 90 degrees.

[Koreth]

Edit: Joe explained it better than I could. Never mind.

[shane1b4u]

well...

if I remember right... in everymans terms... its a number that describes the time difference of the current cycle vs voltage cycle, and can be capacitive or reactive.

[Old Tele man]

if I remember right... in everymans terms... its a number that describes the time difference of the current cycle vs voltage cycle, and can be capacitive or reactive.

...phase difference between the voltage and currents in a circuit...or time difference?

...in a purely resistive circuit, the voltage and current are "in-phase," that is they both reach peak and pass through Zero at same time.

...in an inductive circuit, the voltage is "ahead" of the current (ELI), the current is "lagging" and the voltage has "+" phase angle.

...in a capacitive circuit, the current is "ahead" of the voltage (ICE), the current is "leading" and the voltage has "-" phase angle.

[sampattemore]

yes like joe said in EE J=i=sqrt(-1) in your application you can consider J as a phasor where j = j^5 = j^9 = j^13...etc = i =sqrt(-1) = phasor of magnitude =1 and angle = 90degrees = pi/2 also j^2 = j^6 = j^10....etc =-1 = phasor with magnitude 1 angle 180degrees or pi. also j^3 =j^7 = j^11...etc = -j = phasor with magnitude = 1 and angle =270degrees or 3pi/4 and finaly j^4 = j^8 =j^12 ....etc = 1 = phasor with magnitude 1 and angle =0 so this means that essentially j=1/_90 also the "a" opperator is similar but a=1/_ 120 you will encounter both of these extensively if/when you start considering negative sequence or zero sequence power. i hope this has helped and not confused you.

Also know that an ideal resistor of one ohm has impedance = 1/_0 = j^0 or j^4 if you wish, as a purely reistive circuit will leave current in phase with voltage
An ideal capacitor with impedance 1ohm will have impedacne 1/_270 = -j or j^3 if you wish as a purely capacitive circuit will cause current to lag voltage by 90degrees
finaly an Ideal inductor of 1 ohm will have impedance 1/_90 = j = j^5 etc as its current will lead voltage by 90degrees.

examples
a 270ohm capacitor has impedance = -j270 ohm
a 20 ohm inductor has impedance = j20 ohm
a 50 ohm resistor has impedance =50 ohm
and if all three were in series you would just add the three phasors witch gives z= 50 + j20 -j270 = 50-250j ohms which has magnitude =sqrt(50^2 + 250^2) =255 and and angle of tan^-1 (-250/20) = 85.4 degrees.

So those three components in series provides r=50 x=-250 z=50-j250 = 255/_85.4.

I hope this helps. I actually signed up to this forum just to help you out but after writing all of this i saw that you post tis 3 years ago. Ohwell I am sure somone will find it helpful

[David Schwab]

...phase difference between the voltage and currents in a circuit...or time difference?

...in a purely resistive circuit, the voltage and current are "in-phase," that is they both reach peak and pass through Zero at same time.

...in an inductive circuit, the voltage is "ahead" of the current (ELI), the current is "lagging" and the voltage has "+" phase angle.

...in a capacitive circuit, the current is "ahead" of the voltage (ICE), the current is "leading" and the voltage has "-" phase angle.

Phase is a time domain affect.

[Mike Sulzer]

Phase is a time domain affect.

It certainly is, when you are comparing the relationship between two sine waves of the same frequency. But the Fourier transform is a complex quantity and there is both an amplitude and phase at each frequency. That is, when you represent a signal as a sum of sinusoids, you can think in terms of sines and cosines (rectangular projection), or amplitude and phase (polar representation).