Purpose of Complex term in Engineering field

[abusid1170]

Dear Friends,
The parameters that we measure in the engineering world are all real.So where does this complex term ( 'j' ) comes from ?
this question may be absurd.But this one always hunts my mind.I dont get any kind of answer.
Can u people help me?

 

[johnjoe]

Don't mix the word 'real' in terms of mathe and the real world . You use for example complex numbers to express mathematically a real world phenomena.

 

[mrinalmani]

The concept of imaginary term is only to simply mathematical calculations. It does not have any physical interpolation. Consider for example solving an AC circuit by using second order integro-differential equations for every loop. This will have all calculations in the real domain. Instead of performing such tedious calculations, the concept of complex number is used to establish the concept of "impedance and reactance". After the calculations have been performed the answer can be converted to the real form (ie. the polar form)

 

[LvW]

The concept of imaginary term is only to simply mathematical calculations. It does not have any physical interpolation. Consider for example solving an AC circuit by using second order integro-differential equations for every loop. This will have all calculations in the real domain.

No physical interpretation?
Take, for example, a simple RLC series connection.
When you compute the step response you have to solve a second-order diff. eqation - and (in case of under-damping) you arrive at a squareroot with a negative radicand (below the SQRT).
Hence, the solution is complex and leads to a damped sinusoidal wave.

 

[mrinalmani]

But unfortunately that complex term under the roots has still no physical relation, unless it is converted in the real domain (using Euler's identity) to get the picture of a sine wave.

 

[LvW]

But unfortunately that complex term under the roots has still no physical relation, unless it is converted in the real domain (using Euler's identity) to get the picture of a sine wave.

Yes - that is correct. Nevertheless, before we realize how the result may look like we see that analyzing a physical asssembly of three real components (R,L,C) leads to a complex solution.
And - for my opinion, this was the main content of the question.

 

[abusid1170]

I know everything is to ease the calculation.But we ended up with the complex term.
Consider the signal processing field.We analyse everything in terms of complex exponentials.Infact eigen function of LTI system is itself the complex exponential.
but why?

 

[johnjoe]

You are not forced to use complex numbers BUT:
Counterquestion: Without complex numbers, how you want to solve for example sqrt(-1)?
It's a mathematical tool, like the current of a capacitor is given as i(t)=C(dv/dt), the current is a derivation of voltage over time. But nobody ask about the use of the derivation.

 

[albbg]

This:

https://ijopaasat.in/yahoo_site_admin/assets/docs/Antonov_Paper-1.18191424.pdf

seems very interesting, even if I didn't fully read it yet.

johnjoe: I think the physical meaning of the derivation is well known, this is why nobody ask about the use of it.

 

[johnjoe]

johnjoe: I think the physical meaning of the derivation is well known, this is why nobody ask about the use of it.

Yes, ok, maybe not the best example.

 

[D.A.(Tony)Stewart]

In complex geometry applied to Electronics and Electrical Power, there is a direct meaning to Real and Imaginary.

Imaginary (j part) is synonymous to reactive or stored energy. It can be phase Shifted to become real energy by using what is termed Power Factor Correction, but reactive energy or VARs or resonant voltage (j term) cannot be used to dissipate heat, or transfer energy. Only the real component (i term) can do that.

When resonant currents pass they are only stored energy oscillation back and forth with no "real Power or Energy" . However if they pass thru long resistiive cables then Reactive Power can incur real lossesfrom that Real component of impedance.

Power is the product term of ( at least) two vectors , one for Voltage (t) and current (t) ( & more for harmonics) and only the real component of complex power is "real" power. The imaginary part is just reactive or stored power. , which for LC circuits is just oscillating +/- reactive current or voltage or power. It is not accumulated stored power.

Now this can cause "real" problems in inductors if they saturate but only because their impedance is no longer linear and changes with time to have a "real" component during peaks in addition to a lower reactance. This change in imaginary+real impedance is viewed as hysteresis in the BH loop.

Imagine that !