Tutorial: Electrical impedance made easy - Part 1

hey everyone I thought I'd talk a little bit today about electrical impedance this is a topic that confuses a lot of people probably because it's taught sort of backwards in my opinion where a lot of people you know spend all their time on the heavy-duty math involved and then kind of end with a practical circuit but I like to go the other way and start with a practical circuit and then as we move along uncover the topics as they become relevant so let me show you what I have set up today our task for today is to build a circuit that can power just a standard cheapo plain led directly from the AC mains while using as few components as possible and to do it in a relatively energy efficient manner so to start we may come up with a circuit that looks something like this where the LEDs are set up back-to-back so that as the AC power switches direction one of the LEDs will light up so one will be on for both halves of the cycle but obviously we can't connect the LED right up to to house current because the voltage is so high that there would be way too much current flowing so if you just took an LED don't do this by the way and just put it right into the outlet it would probably explode in a violent pop because the amount of current would be measured in you know hundreds or thousands of amps or something so we can do to keep that from happening is to put a big fat resistor between the LEDs and the the loop formed by the power source so how do we figure out what resistor value we can do that by measuring the LED I measured this cheapo green LED and it just came out to be about 18 milliamps at two volts and I got that number just by connecting it to my power supply and just getting a really quick you know rough reading okay so if we know that the voltage across the line is a hundred twenty volts on average for one cycle the current will flow out through the line through the diode through the resistor and back and this whole thing reverses obviously when the AC goes into the other phase so we'll just look at this one phase so we've got 120 volts here 118 volts here because we know the diode is going to drop two volts at the proper current and then the resistor has to drop a hundred eighteen volts at the proper current so then we just use Ohm's law voltage over current 118 volts over 18 million member to always enter the units in standard units so amps not milliamps and we end up with 6.6 kilo ohms okay easy enough now what I'm gonna do is just change that up just a little bit and this will become clear later on what I'm gonna do is put 1k here and five point six K here and that may seem a little strange right now but this will make sense later on the LEDs don't really care whether the resistor is on the left side or the right side so splitting the resistance stuff like that doesn't really change anything with the circuit so here it is you can just see the the small resistor the two LEDs and this is a big resistor using a big resistor is necessary because this is going to dissipate some pretty serious power I should also point out that unless you're familiar with the hazards involved with you know AC line current you probably would not want to try this one home this is more of a demonstration so I'm gonna plug this in the LEDs come on and hopefully you can see yeah its drawing about 2.2 watts according to this meter so 2.2 watts for those two measly resistor or two measly LEDs it's not very good at all if you were an electrical engineer and you came up with this the Energy Star people would not be very happy with you at all so I'm gonna unplug it and just after this just after there's five five or 10 seconds of running this this resistor is you know not burning hot but pretty good good and warm and if this were left running for 10 minutes or something that resistor might be too hot to even hold it said well it's a 5 watt resistor it would get pretty warm so we got to come up with another design and that design is this so what I've done is replace the resistor this was the first design here I want to say basically just replace r2 with a capacitor so you might be thinking well what's that going to do they actually serve a very similar purpose in the circuit they both serve to limit the current so let's I built the capacitor circuit that's over here basically the same thing with just a capacitor in place of that fat resistor let's plug this one in the LEDs are about as bright as they were the first time but notice the power meter it's only drawing 0.4 watts instead of 2.2 so our change the change from a resistor to a capacitor has actually made our circuit quite a bit more efficient so let's take a look at why I'm gonna unplug this and also discharge the capacitor it had a little tiny pop I don't know if you heard that or not but you wouldn't want to if you did build this circuit keep in mind that when you unplug from the wall here that capacitor is gonna store a charge and you know just short it out like this like I say you should probably be familiar with with 120 volt safety if you're going to attempt this one so let's take a look at that schematic again okay so I said that the capacitor and the resistor in the in the first circuit are serving similar purposes they're both restricting the amount of current that can flow through this circuit and this the units that we use to describe a restriction of current are ohms so these both actually have a value that we can state in ohms but why are capacitors not rated in ohms like if you go to the electronics catalog and look down the list of capacitors nothing is in there is gonna say anything about owns so how do we do it we use this formula right here one over two pi times the frequency in Hertz times the capacitance in farad's so this capacitor is 0.47 micro farad's and the frequency is 60 Hertz because we I'm in the United States and all the line power is 60 Hertz here so 1 over 2 pi times 60 times 0.47 times 10 to the negative 6 and if you calculate this all out you get 5.6 kilo ohms just like in the first circuit they're almost exactly equivalent and so this this value here X is called reactance and reactance is basically a resistance to alternating current flow so they're both you know in ohms this is the same own value as the resistor the difference is that the reactance depends on the frequency so the reason they don't print capacitors with own values in a catalog is because they don't know what kind of circuit you're gonna put it in so if we were using this in Europe where the power is 50 Hertz the own value would be slightly different because the frequency is different so what's impedance impedance is the combination of reactance and resistance unfortunately we can't just add them together impedance which is represented by Z is equal to the square root of the resistance squared plus the reactance squared and you geometry guys out there will see that this is how to calculate the length of a hypotenuse knowing the leg lengths of a triangle so we'll get into this later but just for now I just wanted to show you where impedance comes from impedance is just the combination of the pure DC resistance and the AC resistance known as reactants so the impedance of a resistor Z equals the square root of R squared plus Z because the resistor doesn't have any reactance a resistor has the same resistance at all frequencies if it's perfect a capacitor has no resistance if it's perfect and it has reactance so the impedance of a pure resistor is just the resistance and the impedance of a capacitor is just the reactance and we had the formula here for the reactance of the capacitor is just 1 over 2 pi the frequency times the capacitance so I'm just going to show you that you can if we let's say we wanted to know the entire amount of RP dance for our whole circuit here what's what's the impedance for this whole thing we're gonna make a really nasty assumption here we're going to assume that the LED is actually behaves like a resistance which of course it doesn't but in this case it's not going to make much difference because it's such a small part of the circuit so here's the Z total for our hole we're going to approximate the resistor with a 110 ohm resistor so we've got 1k plus 110 squared plus 5,600 squared and take the square root of that so the entire impedance for the whole circuit is 5.7 kilo ohms so basically impedance is just a resistance that depends on frequency that's really all it is and so with a capacitor at higher frequencies it will have a lower impedance and a higher impedance at lower frequencies so I think what would happen if you took a capacitor and just put it across a power supply once the capacitor charges up no current flows because that capacitor is infinite resistance at DC currents let me just draw this out here for a capacitor this is reactance and this is frequency when the frequency is low it's you know zero basically the reactance is infinite at the high frequencies the reactance becomes a very low value and this has a a one over F relationship because of the formula we had 1 over 2 pi FC so you can see that for any capacitor at 0 it's the Imperius and resulting impedance is infinite and at infinitely high frequencies the reactance is zero so for infinitely high frequencies the capacitor is like a short sometimes the water analogy is helpful so think of electrical current like water flowing through a pipe in the case of a resistor in our circuit here the electricity flows through here and is restricted the flow is restricted by these resistors but in the case of the capacitor the you know water or electricity flows into here in the capacitor acts like a bucket so the water flows into the bucket and it fills up the bucket and once the bucket is full nothing nothing continues to flow the circuit basically stops but in an AC circuit the voltage flips and in our case 60 times a second so when the voltage flips polarity the bucket dumps its contents back through the circuit and makes these LEDs light up so you might be wondering how does our circuit become more energy efficient it has the same impedance we said that we show that these circuits are almost equivalent we had five point six K for this resistor 5 point 6 K for this capacitor this is the same this is the same how come the power meter only read 2 point 2 watts for this case and only point 4 watts for this case we're going to talk about that next time in the exciting conclusion to our series on impedance here where we're going to talk about power factor volt amps and watts if you've ever wondered about those things I'm going to talk about those next you can actually use these these cool little power meters to measure power factor volt amps and such ok I hope that was helpful stay tuned and subscribe for future electric electrical tutorial and feel free to post comments about what you'd what topics you'd like to see okay see you next time bye PostScript so you might be wondering why I left this resistor in with the capacitor circuit I said that we could you know size a capacitor such that it would replace almost any impedance that we want in this circuit so why did I bother leaving this resistor in it's actually more of a practical matter I mean if in a perfect world we definitely could build this circuit without any resistance and make it purely capacitive use just a capacitor to limit the current but here's the problem in in AC current you know we have a cycle that looks like this and at some point we have to build our circuit and then plug it into the wall so if we happen and and this is just running constantly so if we happened to plug in our circuit right at this point in time everything would be great the circuit would see a wave that was nice and and and you know starting at zero and flowing up and down normally but what happens if we decided to plug in our circuit here that wouldn't be so good so then you know if zero is here our circuit would see something like this voltage would be zero and then suddenly we put the plug into the outlet and suddenly we get a nice sharp transition right up like this and then a nice smooth sine wave now this sharp edge right here is not sixty Hertz it's actually composed of a bunch of frequencies many of which are higher than sixty Hertz so our capacitor has a much lower impedance during this very sharp spike this very sharp voltage transition and that would cause too much current to flow through the circuit and it would cause the LED to die so I tried it you know obviously I wanted to find out what would happen myself so I built the circuit you know just like you see here without the resistor and plugged it in and after about ten cycles of me plugging and unplugging it the LED was just about toasted it would still light but kind of dimly it wasn't doing very well so during this really short time this is probably only gonna last about a millisecond there will be much higher current flowing through the LED so this limits the so called inrush current and it's purely a practical matter just because you know you can't plug in your circuit at the zero cross point every time you have to anticipate this sudden surge

Channel: Applied Science

Views: 639,195

Rating: 4.9382977 out of 5

Keywords: impedance, what, tutorial, howto, reactance, electrical, ac, circuit, power, factor, amphour, watt, introduction

Id: xyMH8wKK-Ag

Length: 16min 8sec (968 seconds)

Published: Wed Jun 08 2011