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Male Speaker: One of the central issues associated with circuit design and analysis is to interface between source and load. First of all the interface is a connection between circuits, you can think of one as a source circuit and the other as a load circuit. You can think of the source as generating signals and delivering at to the load and we want to do is to simplify our analysis when the source circuit is linear.
So, if the source circuit is linear for these two terminal interface then the I, V characteristics that current and then the voltage across the terminals A and B remains the same when we replace it by a Thevenin or Norton equivalent, in other words we take this Thevenin Norton equivalent which is much more simplified than this complex array of sources such as voltage and current sources and our network of resistors.
So, here are equivalent circuits for the source. So, lets say we have a complicated array of resistors and capacitors including current and voltage sources, what we do with that circuit is that we simplify it to a single voltage source and a single equivalent resistance known as the Thevenin equivalent resistance so that we can simplify our analysis when we start connecting the source and load and develop the appropriate interface design when we connect these two circuits.
So once again the Thevenin equivalent replaces this source circuit with the single voltage source and a single resistor. The Norton equivalent on the other hand is used to replace the source circuit with a single current source and the single resistor that is connected in parallel where as the Thevenin equivalent here we have the voltage source and the resistor connected in series and in once again we have a current source and a resistor connected in parallel connected to the terminal points or interface points A and B. Now the key characteristic here is that when we do this replacement with this simplified circuit the I, V characteristics at points A and B remain the same.
Here under the Thevenin equivalent we can replace this Vs with a equivalent Vt notation shown here. So, the Thevenin equivalent voltage source and the Thevenin equivalent resistor Norton equivalent current source and the Norton equivalent resistor. Now let's analyze these two circuits in terms of the I, V characteristics. So, for V in the Thevenin equivalent we have V is equal to Vs right here plus the current through the Thevenin resistor or resistance.
So, that's our current using KVL for this relationship and for this circuit this Thevenin equivalent. On the other hand the current is and the Norton equivalent right here is given as I which is the current due to In and this current enter this node someone will go through the terminals A and B and the other one will go through Rn that will that's simply using Ohm law's V divided by Rn. Now solving for V yields In minus I times Rn or In Rn minus I Rn. Now lets compare it with the one we did here for the Thevenin that's V is equal to In Rn minus I Rn. From this comparison between these two equations we see that Vs, which is really Vt to replace Vs with Vt is equal to In times Rn and that Rt is equal to Rn. So we have these relationships right here to go from one equivalent source to another and we just replace it with the same resistor.
So, if you want to go from a Thevenin to a Norton we just take this series connection and convert it into a parallel connection such that Rn is equal to Rt and In is equal to Vt divided by Rn. Now we can do the same thing going that way where we replace Rt with Rn and then Vt is equal to In times Rn. So, in essence the Norton and Thevenin equivalent are just source transformation techniques. So, we don't have to find all the parameters associated with the circuit once we know Vt and Rt we can easily transform it to In and Rn in the Norton equivalent and vice versa.
When trying to find the Thevenin Norton equivalent is often convenient to replace it with a open circuit voltage and a short circuit current and what do you mean by that. Basically we take our source and we open it that implies that the resistance between terminals A and B is infinity and that implies that the current is equal to zero in this type of open circuit voltage. The short circuit load implies that we have no resistance in other word we just basically place a wire between A and B so the load has a resistance of equal to zero. What does that imply, that means the current, the voltage across here is equal to zero. So, notice these two cases and open load and a short circuit load.
One implies that I is equal to zero for the open load case and the other implies that the voltage across it is equal to zero. So, now we will take a look for an open circuit load, the Thevenin equivalent well since there is no current in the open circuit load we have Rt multiplied by zero current which means there is no voltage drop, since there is no voltage drop across this Thevenin equivalent resistance then the open circuit voltage between A and B is equal to Vt or Thevenin voltage source.
Now we take the same two terminals across A and B and we place a short, where the voltage across these two terminals is zero but we have a short circuit current In because all of the current coming from In has to go through the short circuit since it had zero resistance and Rn has a sort amount of resistance. So, that's the essence of what we mean by a open circuit voltage and a short circuit current.
So, in summary the Thevenin equivalent is equal to for voltage the voltage Thevenin equivalent is equal to the open circuit voltage and the short circuit current is equal to the Norton equivalent. Now our resistance Rt equal to Rn is simply found by taking the open circuit voltage divided by the short circuit current and that's in essence was the Thevenin Norton equivalent does for you is replacing it with simpler circuits and this is how we find it using the open circuit load and a short circuit load, the open circuit load gives you our Voc and our short circuit load gives you Isc and then taking the ratio between these two variables we get our Thevenin equivalent and our Norton equivalent resistance.