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Author Topic: Impedance and reactance  (Read 1047 times)
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Hi,

I've looked on the WWW. with Google for a "newbie" tutorial or explanation of the above terms, but haven't been able to to grasp it easily - loads of maths and equations  smiley-roll-sweat

I kinda get that it's like resistance but applied to AC, and that extends to digital circuits with ON / OFF states and clocks, crystals etc..

I find the fluid analogy of resistance in DC circuits useful for understanding resistance - anything similar for the Impedance and reactance?

cheers

PS My education is in Biology. Been using Arduino for about a year now.
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Craig Turner, blog: http://gampageek.blogspot.co.uk/ It helps with my learning if I write things down, esp. for others to follow (constructive comments welcomed to improve)

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Alas these concepts really require an understanding of complex number plane - impedance is resistance generalized to complex values, reactance is an impedance that is purely imaginary.  You'll need to find out about imaginary and complex numbers I think - although the short answer is that impedance is like resistance for AC (and encodes phase information).  Try looking up 'phasor' on wikipedia?

Pure reactances have a phase difference (between current and voltage) of + or - 90 degrees - corresponds to the imaginary line on complex plane.  Resistance has 0 degree phase difference, negative resistance has 180 degree phase difference - corresponding to real line on complex plane.  General impedance can have any phase angle and magnitude - any point on the complex plane.
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LOL!!

If math is not your strong point, you can use a reactance chart like this one to approximate the impedance.
http://www.vibrationworld.com/AppNotes/RLCGraph.htm

The inductance is the lines slanted one way, the capacitance is the lines slanted the other, and the frequency is on the bottom (vertical lines). Where they all meet is the impedance in ohms along the left side (horizontal lines).

Does that relieve that headache a bit?

edit: My bad. I was so busy laughing, I gave you incorrect info. The impedance is where the capacitance and inductance lines cross. Where the frequency line crosses is the resonant frequency. At least that is what I remember.
« Last Edit: September 10, 2012, 10:53:44 am by SurferTim » Logged

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Hi,

I've looked on the WWW. with Google for a "newbie" tutorial or explanation of the above terms, but haven't been able to to grasp it easily - loads of maths and equations  smiley-roll-sweat

I kinda get that it's like resistance but applied to AC, and that extends to digital circuits with ON / OFF states and clocks, crystals etc..

I find the fluid analogy of resistance in DC circuits useful for understanding resistance - anything similar for the Impedance and reactance?

cheers

PS My education is in Biology. Been using Arduino for about a year now.

 If an AC circuit has only purely DC resistance components in it (including wire and or trace resistance) then the circuit Impedance is equivalent to the DC resistance and simple ohms law calculations applies in the circuit. However if the circuit has reactance components in the circuit either inductive or capacitance components, or both, then the circuit reactance must be calculated separably and then the resistance component is added to that for a total circuit impedance. The frequency of the AC voltage source is also a variable in the calculation as both capacitance reactance and inductive reactance vary by frequency. For any combination of capacitance and inductive in a AC circuit there will be a specific frequency where the capacitance and inductive reactance will be equal but 180 degrees out of phase, so they will cancel each other out for a reactance of zero, and then only the circuit pure resistance will determine the circuit's total impedance at that specific frequency, which is called the resonance frequency of the circuit.

I'm sure that is clear as mud, but it is all explained in basic AC circuit theory, step by step, and is not all the difficult to learn if you follow a good lesson plan, many are out there.

Lefty  
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I've got an analogy for the inductor.  Think of your standard hoses, (pressure = volts, flow = current), connected to a box with a water wheel, or turbine in it.  As you apply the water the wheel spins faster and faster.  If you stop the water input, it keeps spinning and trying to keep the water flowing, slowing down as the flow continues.  You could even push a point and say as it starts the chambers of the wheel fill up, so the flow when you first start flow is delayed down, and as it spins down the flow carries on.  A bigger box, with a bigger wheel, takes more effort to spin up or down.

A capacitor might be a bit like a bladder or balloon, as you apply the pressure it inflates, and as it gets bigger more water is stored in it, and it gets harder to put more water in. As you start putting water in, the flow is easy and fast, as it inflates the flow going in slows down.  If you stop putting water in, it will push out water under pressure, then as it gets emptied the pressure and flow coming out decreases.  A small bladder cannot store very much water or much energy.

I've got to say, you are better off looking at the circuit theory.
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To toss another 2-cents in here .... and boil down the maths:

- the basic formula is V = I * R for simple resistors, and V = I * Z for impedances
  [circuits with inductors and capacitors].

- with resistors, voltage and current are always in phase with each other.

- with inductors and capacitors, voltage and current are out of phase with
  each other, so it takes more complicated maths [involving both magnitude
  and phase] to solve the equations [as the other tutorials indicated].
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If you want something that's as intuitive as the hydraulic analogy is for DC, you're out of luck.  We try to come up with those, but we always wind up saying, "consider this weird, Rube Goldberg gizmo that nobody's ever seen before ..."

But, here's something you can try at home.  Take a big heavy melon, slather it in bacon grease, and push it back and forth across the counter top.  If you reverse direction rapidly, you'll see that the melon never goes very fast, and it doesn't move very far.  If you reverse direction more slowly, and use the same force to move the melon, you'll see that it moves faster and goes farther.

This works best if you live alone, or the other people in your house are away for a few days.  It works absolutely best at somebody else's house.

Anyway, the mass of the melon is analogous to inductance.  The force you use to push it around is analogous to voltage, and its velocity is analogous to current.  In fact, the equations that we'd use to describe the current through an inductor, in terms of the applied voltage, are exactly the same as those we'd use to describe the velocity of the greasy melon, in terms of the applied force.  The ratio of the average force to the melon's average velocity is analogous to reactance, the ratio of an inductor's average current to its average current.  Reactance is measured in ohms, just like resistance.  It varies with frequency - directly for inductors, and inversely for capacitors.  And, of course, "average" here means root-mean-squared, or something like it.

It seems that it would be fun to play with notions of capacitance, too, but capacitance doesn't have a familiar analog like mass.  It models as a "spring constant" - a number that describes how stiff a spring is.  Without bacon grease, where's the sport?

If you really want to understand reactive components and their action in a circuit, you probably have your work cut out for you.  As others have noted, reactive components are modeled as imaginary numbers - something like resistances multiplied by the square root of -1.  My guess is that they don't teach much of that in the biology department.  Those calculations are weird, and it's a lot of material to wade through to develop a usable set of tools.  It doesn't take a geek or genius to master those calculations, but you do have to be motivated to do it.

If you want more detail, check the Wikipedia articles on "reactance" and "hydraulic analogy."  The latter article does a fairly good job of explaining why analogies break down in describing these phenomena.  
« Last Edit: September 10, 2012, 11:00:33 pm by tmd3 » Logged

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Quote
reactive components are modeled as imaginary numbers
Reactive components are analyzed via differential equations.  The imaginary/complex number (and/or phasors) is a mathematical simplification for the case of sinusoidal signals (ie all interesting signals) because cos(wt+p) = Real(ei*(wt+p)), and exponential functions have lovely properties when it comes to doing calculus on them.  And i has lovely properties in power series. (i2 = -1,   i3 = -i,  i4 = 1,  i5 = i, etc.)  So by using complex numbers, the actual math gets much easier.

But in the end, reactance is just like resistance, except that there's a frequency dependence, and a change of phase in the result.
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Quote
I've got to say, you are better off looking at the circuit theory.

Actually, I know of one university program that used to teach Circuit Theory 101
[don't know if they still do it] in terms of all three types of components, electrical,
mechanical, and fluid, as they all have similar 1st-order defining equations.

resistor, capacitor, inductor    are similar to
dashpot, mass, spring,           are similar to
pipe, reservoir, [something]

[shoot, it's 3AM!].
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Did you ever wonder what you were doing up? and why? at 3:00 AM? I frequently do, wake up at 3 - 4 - 5 AM and load up a sketch to fix it or just because something was nagging at me about it.

Doc
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LOL, actually last night was the first time I've been up past midnight since I
can remember. I was polishing up the final code on a project, and just wasn't
too loopy [till I tried to make a thread reply, and remember what the fluid
analogy of an inductor is - still cannot remember!].

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