A series of videos on the Thevenin and Norton Equaivalent Circuits along with some example circuit analysis. For questions on these and other topics contact Professor Santiago at john@e-liteworks.com.
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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

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