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Thevenin's Theorem
finding the output attributes on the circuit
output voltage and resistance. To make
modular units easier to match up to each other this tutorial will make use
all voltage dividers throughout.
We have a black box
and we may not know what's inside
this module but we can still determine the voltage across
it's the ports 'A' and 'B'
and we can work at its output resistance
we do that like so. First of all we'll measure the
voltage across the ports AB
with a volt meter
next we'll short port 'A' to ground.
so we'll bring bring that to ground and
take it through an ammeter here like so
and record the current. So here we've connected
the 'A' and right back to 'B' with the Ammeter in the middle to record current.
Then finally with the
voltage found with the voltmeter
and the current with the Ammeter we can find the resistance
simply by using Ohm's Law
which will be the voltage we measured divided by the short-circuit current
so then we've got for this module the output resistance
and we've got the output voltage. Commonly the output voltage
is named Vth named after thevenin
and this output resistance can be called
Rth. But we
generally only use those names when we are doing the circuit analysis
with the actual
calculation completed it's not strictly
necessary to use Rth and Vth because what we've done here is what's called a
brute force method
of actually using the instruments on a black box to actually get the output
voltage
and the output resistance so finally once we've got the
output resistance and the output voltage Done,
we can now redraw our module here
in this equivalent diagram form we can emulate it as this circuit here so
the circuit is the Vth voltage measured and includes the
the Rth output resistance.
We can now calculate for any load resistance we put onto this module
we can calculate now that we've done this in a
brute force method of measurement, we can now
just easy user a voltage divider
to calculate many different
load resistance's. But for most modules
we will see in electronics, we will know the circuit analysis beforehand
anyway
so in that case there's a more elegant method
then using this brute force method. But I wanted to show you this
because the logic here is is more or less the same as the way you'd
calculate it
and in the lab I'll do one of these and actually do the brute force method to
show how that works to show that that's
relevant. So just look at the
the analysis method doing this so
in this case a.m. you would
the I've chosen a a
a circuit here which is a
two resistors in series using a voltage source
the race not chosen that he's buys a very very
common liau it's a very common circuit and issues
in lots of different scenarios so is a very useful want to actually
shosh evidence there so festival
at as in the brute force method we can measure the voltage
this summer gonna do it we gonna calculated given
we know what we know that that the components in this circuit
so to find the the output voltage which he will call that that the number I'll
teach
we all we have to do is find the voltage drop to cross
the baby could replace the poor AP across
the resistor are too so what we want to do here now is find
the voltage here was called that involve hitch and that is
jest adult is divided as you can see so it's the proportion
alt the voltage that's dropped across all too
the against the whole of the resistance here so that's basically
are too divided by the total resistance
times the voltage source so that that gives us the
the tether and bolted so we have that now so in step 2
what we wanna do is to find a short circuit current now
what we do here is we is we take a ok
a a sure a to ground
which is what we did in the brute force method but we're gonna calculated
here in this way so if we show a to ground here
obviously we got the r1 here to calculate so here we can find a short
circuit con
is simply the voltage source delighted boy r1
so now we've got a short circuit current now to find the third and resistance
all we need to do is devoid the output voltage by the
a the short-circuit current and that will give us the
output resistance or the third and resistance so that's what we do
we year we gonna take the one
in this case it's one over a just the the short-circuit current
which is them the same as saying
I'm sure or voltage over current year so I just
rain how artists so that you can see the equipment is so
1 I've I S is simply RI over the S
so I've written that here so that's then of course
the the number I'll teach is the
voltage divider calculation we did so we place that their
and you can see here that the two voltage sources cancel
and we left for the Illini solution we left with the fact that
for for this series resistors where you dropped a
the voltage across the bomb resistor you're left with very nice
a.m. result basically at
the r1 arts of you cancelled the voltage issue left with
r1 r2 divided by the total resistance
which is the same as a calculating in a power no resistance equation here
so with that in mind finding
the tether is this is no different from shaming that the voltage sources 0
and treating r1 r2 in parallel looking into the poor so have you get a circuit
such as this which you of them will then you just remember that you just
calculating the year
the power resistance in fact there's a there's a rule for all
for thought for calculating a.m.
the than resistance and that's always to
to sure the voltage sources and open any current sources
last anything really after need to remember about to
than issues sure in other words she said the s2 nor
you shorty and you open any current sources
and then you can work out the than resistance for any circuit
a.m. so in this particular case it's the parallel resistance r1 r2
refused drop to your voltage across our two
so in steps pesci what you do she capped like that though the number I'll teach
as we did then you find a short circuit current and then with the short-circuit
current
you were able to find the there than in resistance
and once you've got those once you've got the sedan a resistance
and you got the third in voltage then you can simply read jewel
this circuit as this I finally we can retool circuit as a feather them
equivalent circuit save Gotham bowl teach
the third in resistance the eye and the ports and any
load research on a place there set for any load resistance we now just have a
simple
voltage divider to calculate so that's basically hey cam plated
okay he just an example so here we've got a circuit
and where the question we came in is calculate
the voltage across the load resistor RL and the current through it
when our alley costs $30 K 10k and 5k
so an because this what we could do
is first step is scanned the beyond the
the ports it convert this this area here in 2008 criven
before we actually need work out the three versions for the RL
be much easier this way so first that tennis to get this circuit
converse to its than equipment like so so we can remove
the load resistor then we gonna find the Fedayeen
voltage which is a
the proportion here so it's twenty over 30 time 60 we got twenty other so it I'm
60
to the penalties for vote very easy so we got this
voltage drop across a a a third than the
the third and resistance is the parallel resistors looking in
night knowing that so we're looking in his 10 in Powell 20
so that comes out to be a six-point 67 killer times
so now we can redraw this and into the equipment in circuit
which is here so we got a full vote so we found across here
and than resistances 6.67 killer times
to now all three load resistor bulges and cons can now be found as follows:
so we start with the 30 so that's a that's our thirty where free per
ours RL 30 here a game we got a very simple voltage dividers here so it's the
RL divided by rth at RL
as a lack gives us at times the voltage
so we got we we've got here
for the for the voltage across the load will be SARL over rth it RL times
for votes who is thirty over 6.7 at at thirty times for acoustic point 27 votes
and for the the current that runs through it well obviously that's Chester
TTH and this total resistance is
a r th at RL so that's just Vth divided by the total resistance
so that gives us the short-circuit current which is .1
Miley amps said we found both the current
and the voltage for 30k and
the same for are 10 which exact same process how one gets a little guy
to just simply I L equals using the same values a gang
comes 2.23 million PCE and for 10 it comes to
a.m. 2.3 99 told she could see
we have an apt to go through any analysis now all we've done issues
these results these these two equations say now we could use many
Lotus you want so we done the 5k one as well which issues these two questions
again
and we've got point 30 formally amps
and 1.71 boats so
point this is a few hours to to do this the
by actually the old you know if you didn't use it and bolted after
captured a powerful resistance here and then find
the current through it and then find the the current through this once again the
voltage drop across this one
so it would take much longer and this is quite simple circuit I mean if you had
more components things going on here
and it would initially take a while to get your initial
that involved teach and than resistance but once she got them
for monks follow dubious quickest issues in this equation
so that's why than the room is really useful the other reason it's really
useful
is the fact that a is great for matching up modulus a futile one module you'll
know for example
if you've got your module and you've worked out better than resistance
and if there than in voltage then you've just got to two attributes that module
which allows you to mash up to other modules
so you can match this up to an input module where you wanna solved
balance the loads you wanna make sure that the resistance here
is a lot lower than the one you are attaching it to so much to the energy
and most to the voltage
control for across the new module so this information
you've got like you can have many modules with just the two attributes
than the resistance and the a.m.
that had an insult each side if you like the output voltage the output resistance
and enables you to have for mochila
circuits taken bill Nagy modulus us really the great thing about
that owns account the next yr to Torreon gonna move onto
pastors and we gonna see this polje divided more often with pastors we stop
stop
looking into filters set church gets more a lot more interesting
okay thanks so much