Tutorial: Electrical impedance made easy - Part 2--- make money online

hey everyone been here this is part 2 of

the video series on impedance but first

I wanted to show you what I've been

working on this week these work benches

even though I've been in this shop for

about a year I haven't had a a good

selection of workspaces so I spent some

time building these benches and I'm

actually really excited about this

because I've got 20 or 30 feet of linear

space now which makes working a whole

lot easier okay let's head over to the

electronics area and I'll show you what

I've got set up today at the end of the

last video we had were comparing these

two circuits here this one built with a

resistor and this one built with a

capacitor and I left off by saying well

how asking the question how is it

possible that the capacitor circuit only

draws 0.4 watts using this you know

kilowatt power meter and yet the

resistor circuit draws 2.2 watts but in

both cases the LEDs are about the same

brightness so it seems like we're kind

of getting something for nothing here

and you know the answer is that the

capacitor if built perfectly actually is

not able to dissipate power so when

current flows through a resistor it

heats up because the resistor is

restricting the current flow through

there but that's actually not what's

happening with a capacitor in a

capacitor you know there's just two

plates and once those plates becomes

charged up and there's an electric field

between them

no more currents going to flow so if the

capacitor is built with zero resistance

parts and the dielectric is perfect

there's actually no way that a capacitor

can dissipate power so you might be

thinking well I said that their

impedances for these circuits are about

the same I chose the capacitor value and

the resistor value such that when we did

the math the circuits are almost

equivalent well I only gave you half the

truth there it's true that the magnitude

of the impedances of these circuits is

about the same but there's another

component to impedance an angle and that

indicates whether the circuit is

resistive

or capacitive and and we're going to get

into inductors later but right now let's

just concentrate on capacitors so to

help you see what's going on in here

let's hook this up to an oscilloscope

what I've done here is modified our test

set up just a little bit this is an

isolation transformer so that I can

connect our circuit directly to my

oscilloscope and I won't fry the scope

or myself the trouble with connecting

things directly to the wall is that that

the voltage that comes out of the wall

is referenced to earth ground so if I

touched one side of the watt this isn't

plugged in right now by the way if I

touched one side of the line and that

happened to be the hot side of the AC

you know current coming out of the wall

and I was referenced to earth ground

because I'm standing on a concrete floor

here I could get a nasty shock and also

when measuring stuff with an

oscilloscope one side of the measuring

system has to be connected to the case

of the oscilloscope to the metal box

that the you know the scope is built in

and if you pick the wrong lead of you

can have a you know you can cause a

breaker to trip so using an isolation

capacity entrace former allows us to

connect in one side of the line directly

to the oscilloscope ground so let me

connect up this circuit here let's look

at the resistor first okay so the scope

is on and the way it's set up is that

channel 1 which is this probe here is

connected across the line so basically

one side is one side of the transformer

and the other side is the other side so

it's just going to measure the voltage

and this is a 10x scope probe so it's

going to divide the voltage here by 10

channel 2 is connected on the other side

of this 1k resistor and what this is

going to do is allow us to measure the

current that's flowing through this

circuit here so and I don't have to

connect this because I've already got a

ground reference right here it would be

the same thing as just connecting this

here so we're measuring the voltage

across this resistor which will tell us

the current and we're measuring the

voltage across the circuit which tells

us the voltage

since this is a 1k resistor if we

measure a voltage of 1 volt across here

that means that 1 milliamp of current is

flowing because this is a thousand ohms

okay I'm going to plug it in hands out

and let's take a look at the scope okay

so this is showing us the voltage and

current going through the circuit and

we're not going to worry too much about

units or making a careful measurement

here what you should be noticing is that

the waveforms are in sync with each

other so this upper one here is the

voltage and this lower one is the

current like I say don't worry about

units or something we're not going to

make a careful measurement here the

thing to notice is just that they're

they're absolutely in phase okay now I'm

going to connect up the capacitor

circuit so I'm gonna unplug it here so

now we have something completely

different the voltage waveform looks the

same addley see that has to be the same

because we're just measuring the voltage

across the circuit so that's that's

basically the same but the current

waveform is very different the current

waveform is in front of the voltage so

this is known as a leading current form

or a current waveform so as the voltage

is coming up the current is also rising

at a faster rate and this makes sense

think about what happens when you

connect a capacitor to voltage a lot of

current flows initially when that

capacitor is charging up and so this is

known as a leading current waveform so

earlier I said that I was only giving

you half the story with impedance not

only is there a a magnitude associated

with impedance but there's also an angle

and the angle indicates the offset

between the current and voltage

waveforms and also tells you whether the

current is behind or ahead of the

voltage waveform so let's draw this out

a little bit it helps to graph it in a

purely resistive circuit we can draw

this with just an arrow on the x-axis

which indicate

a purely resistive circuit and the angle

here at zero degrees in a circuit that

has capacitance we can draw the arrow

coming down at an angle here and the

more capacitance our circuit has

relative to the amount of resistance in

our circuit the more that arrow is going

to point down into the vertical axis so

what these axes actually represent are

real numbers and imaginary numbers now

I'm definitely not going to get into the

heavy-duty math here because I honestly

don't think it helps your understanding

of how to use this in practical circuits

but if you're interested in that you

know let me know maybe I'll make a video

or you can read about it on your own the

reason that you know why not why not

just call this X&Y; what's the deal with

it why choose imaginary numbers the

answer is that it just makes the math

come out easier so when you get into

phaser analysis and all kinds of other

things when you multiply an imaginary

number by another imaginary number you

end up with a negative number and that's

important for the math but anyway it's

it's you can just think of this as

resistance on this axis and reactance on

this axis so when you have a capacitor

and when you have a lot of capacitance

that that arrow is going to be turning

down into the into the vertical axis

more and if you have more resistance

it's going to be closer to the x-axis

what happens if you're over in these two

quadrants what if you're negative on the

real axis that's very unusual that's

negative resistance and you know

typically it doesn't exist but in

certain weird cases it can exist that's

if you're interested in that lookup

negative resistance that's a whole other

topic there for 99 point something nine

percent of stuff in the world you'll

just be in these two quadrants with real

resistance and reactance so let me show

you how this this chart relates to our

calculation of total impedance for our

circuit here so I said if we wanted to

calculate the total impedance for this

circuit we could use this equation here

and we're going to make the nasty

assumption that our LEDs behave like a

resistor which I know

not good but it's a small part of the

circuit and it won't make much of a

difference and I said that you know you

geometry guys would realize that this is

how to calculate the hypotenuse of a

triangle which is exactly what's going

on here so on the real axis we have

resistance and in our case it's 1,000

plus 110 110 is what we're going to

estimate those LEDs to be and a thousand

is the actual resistance from from our

little resistor here that's the 1k

resistor so on the real axis we can you

know say that this length here is

represented by a thousand plus 110 and

this this part which is the imaginary

part is represented by the reactance of

our capacitor which we determined to be

5 point 6 K from the from our earlier

equation 1 over 2 pi FC but currently

here we are the equation for reactance

so we can put that one here 5,600 and

then you can see that the total you know

the sum of these not sorry not the sum

the combination of these is the length

of the hypotenuse here which gives us

the total impedance so let me show you

how this impedance chart relates to

power factor in volt amps and watts and

all that stuff it's actually a very

similar looking chart instead of real

numbers and imaginary numbers

we've got watts which is real power and

volt amps which is reactive power on the

y-axis here so let's let's look at a

couple examples let's say you plugged

just a hundred watt light bulb into your

outlet at home there the light bulb

essentially is purely resistive it has

no reactance to it it's just a plain

resistor pretty much so we would plot

that on this graph by just going

straight across on the real power axis

watts and we plot out 100 watts no

problem just one one line on the graph

but if we plugged in our circuit like

this which has a reactance to it because

of that capacitor we have to plot this

angle here just like we did on this

graph so we come in like this and our

vector here has magnitude in both axes

it has watts and volt amps the Watts the

real power is a measure of how much

power is actually being dissipated in

our circuit full tamps just measure how

much electrical energy is being pushed

back and forth between the power company

and your device so if you take your a

capacitor and just plug a capacitor

straight into the wall every time the 60

Hertz cycle changes the capacitor dumps

its energy back into the power lines so

what's happening is there's a transfer

of power from the power company the

generator wherever it is to the power

substation into that capacitor the

capacitor doesn't lose any energy

because there's nothing in there that

can dissipate if it's perfect and then

the power just goes back to the power

company on the next cycle so in theory

nothing is lost and you could think of

it as you know imaginary power because

it's actually not being consumed it's

just being pushed back and forth so in a

perfect world that would be great no

problem just pushing power back and

forth is is free it doesn't you know

we're not losing anything but in the

real world you know wires have

resistance to them and so the power

company would be very unhappy if all

loads were had high imaginary power draw

because they would be losing power and

all of that pushing back and forth so

the power company would prefer power to

be delivered in watts only and so this

is where power factor comes in so the

hypotenuse is known as a parent power

and the vertical axis or the vertical

component of it is known as reactive

power and the power factor

is the ratio of real power P divided by

the apparent power so having a high

power factor just means that this angle

is very slight and that most of the load

is resistive having a low power factor

means that this angle is large and it

could be you know in the negative in the

lower quadrant here or it could be up

here too so all this time I haven't

really been talking about inductors I've

been concentrating on capacitors but

inductors we perform a similar function

they limit alternating current flow but

sort of in like a the opposite way so

capacitors are down here in the lower

quadrant and the current as we saw in

the oscilloscope leads the voltage

inductors are basically exactly the

opposite the current lags the voltage

but you can treat them in the circuit

almost the same way I mean you can use

them to limit current we could have

built our little circuit here with

instead of a capacitor here we could

have put an inductor there

okay so I've connected up the circuit

I've taken that isolation transformer

back out so we're powering the circuit

directly from the the watt meter here

and it's drawing the 0.3 or 0.4 Watts

that we saw last time if I switch this

into power factor the power factor is

only 0.15 about according to this so

let's see if that agrees with our

calculation okay so here we go so we

knew that power factor was the real

power divided by the apparent power so

what we can say since the voltage is

constant in a circuit what we can do is

just compare the the real and reactive

components of the impedance so what we

can say is our estimated power factor

should be something like 1110 which is

the real component divided by the

apparent oh sorry but yeah the apparent

the total power here including the

reactive parts which we calculated over

here to be 5 points

m'kay so 5700 so that comes out to be

point one nine so you know pretty close

we measured 0.15 calculated point one

nine we're definitely in the right

ballpark here let's take a look at the

resistive circuit now so we're measuring

power factor again and as you can see

the reading is fluctuating a bit in

theory this should be one I said with a

purely resistive circuit the power

factor should be one and the current and

the voltage will be in phase together

now the reason that this is probably not

showing one on the meter is because this

resistor that we're using this five

point six k resistor is probably a wire

wound resistor and that wire winding in

there causes it to have inductance and

thus reactance and then every time you

have reactance of some sort the power

factor is not going to be one so

unfortunately I don't have a LCR meter

where I can actually measure the

inductance of that part but that would

be interesting to find out it looks like

our reading is you know about 0.9 on

average another problem that we're

having is that this circuit draws so

little current that this meter is really

straining to to come up with a reading

and the way it gets this reading is

basically by doing what we did with the

scope it measures the voltage and

current waveforms and figures out how

much of a difference in phase there is

and whether the current is leading or

lagging so it doesn't it doesn't tell us

you know whether it's leading or lagging

it just gives us the the angle basically

and we have to know from our circuit

whether it's capacitive or inductive

from a consumer standpoint you actually

don't really care about power factor all

that much because your your watt meter

on the side of your house that measures

how much electricity you have to pay for

only measures watts so it would be a

little bit strange for a power company

to charge you for imaginary power right

because that power is just going back

and forth between the power company

and your house you're not actually using

that power it's actually the power

company themselves that care about

getting the power factors high because

as I said you you lose power in the

power lines so that's actually a loss on

the power company's side not on the

consumers side it won't show up on your

bill so if a residence is you know

there's really not much going on I mean

basically the power company encourages

electronics manufacturers to build

things with high power factor but

there's not you know they don't come out

to your house and measure your power

factor however they do do that for large

industrial places if you set up a

factory I think the power company

routinely comes out to measure the

factory's overall power factor and if

it's too low the power company will

insist that you install devices to

increase the power factor and in a in a

factory setting almost all the loads are

like big electric motors which are

inductors and the way that you can

increase the power factor of a motor is

to put a capacitor across it so as I was

saying if if a capacitor is below the

horizontal axis and an inductor is above

what we can do is actually add a

capacitor and inductor to make this to

bring this arrow back down to level

which which would make the power factor

high or as close to one as possible so

the most common type of thing you'll see

for power factor correction is a

capacitor strapped on to the side of a

motor and that's very often just to

counteract the inductance of the motor

windings and increase the overall power

factor all right well I hope that was

helpful I think this pretty much does it

on impedance no actually I take that

back

I think I'll do another one on pins and

talk about coaxial cables and impedance

matching and that sort of thing let me

know if you guys have any specific

questions or anything and I'll try to

address in there all right see you later

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