Network Analysis : Network Analysis ALFA PHYSICS CLASSES
Superposition Theorem : Superposition Theorem Eliminate one source of power in the circuit one at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately.
Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all “superimposed” on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active
Example : Example As shown in the circuit we have two sources of power one is 28V battery and other is 7V battery. If we remove the 7V battery the circuit can be redrawn as shown in the figure.
Example : Example If we remove the 7V battery the circuit can be redrawn as shown in the figure.
Analyzing the circuit with 28V we get the following values
Superpose Values : Superpose Values Similarly if we remove the 28V battery, the circuit can be redrawn as shown in the figure.
Superposition Principle : Superposition Principle When superimposing the value of current and voltage we careful about the polarity and the direction of current in each branch of the network
Voltage Superposition : Voltage Superposition
Current Superposition : Current Superposition
Thevenin Theorem : Thevenin Theorem Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load
If we're dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are nonlinear: that is, their opposition to current changes with voltage and/or current. As such, we would call circuits containing these types of components, nonlinear circuits.
Thevenin Theorem : Thevenin Theorem Thevenin's Theorem makes this easy by temporarily removing the load resistance from the original circuit and reducing what's left to an equivalent circuit composed of a single voltage source and series resistance. The load resistance can then be re-connected to this “Thevenin equivalent circuit” and calculations carried out as if the whole network were nothing but a simple series circuit.
Example : Example Consider the circuit as shown in the figure After Thevenin conversion it will look as
How to form Thevenin Equivalent Circuit : How to form Thevenin Equivalent Circuit First, the chosen load resistor is removed from the original circuit, replaced with a break (open circuit): In this case, the original circuit with the load resistor removed is nothing more than a simple series circuit with opposing batteries, and so we can determine the voltage across the open load terminals by applying the rules of series circuits, Ohm's Law, and Kirchhoff's Voltage Law
Equivalent Voltage : Equivalent Voltage
Thevenin Equivalent Circuit : Thevenin Equivalent Circuit The voltage between the two load connection points can be figured from the one of the battery's voltage and one of the resistor's voltage drops, and comes out to 11.2 volts. This is our “Thevenin voltage” (EThevenin) in the equivalent circuit:
Thevenin Equivalent Resistance : Thevenin Equivalent Resistance To find the Thevenin series resistance for our equivalent circuit, we need to take the original circuit (with the load resistor still removed), remove the power sources (in the same style as we did with the Superposition Theorem: voltage sources replaced with wires and current sources replaced with breaks), and figure the resistance from one load terminal to the other
Equivalent Circuit : Equivalent Circuit With the removal of the two batteries, the total resistance measured at this location is equal to R1 and R3 in parallel: 0.8 O. This is our “Thevenin resistance” (RThevenin) for the equivalent circuit:
Solved Values : Solved Values With the load resistor (2 O) attached between the connection points, we can determine voltage across it and current through it as though the whole network were nothing more than a simple series circuit:
Norton Theorem : Norton Theorem Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load. Just as with Thevenin's Theorem, the qualification of “linear” is identical to that found in the Superposition Theorem: all underlying equations must be linear (no exponents or roots).
Norton Theorem : Norton Theorem Contrasting our original example circuit against the Norton equivalent: it looks something like this . . . after Norton conversion . . .
First Norton Step : First Norton Step As before, the first step is to identify the load resistance and remove it from the original circuit:
Norton Theorem : Norton Theorem Then, to find the Norton current (for the current source in the Norton equivalent circuit), place a direct wire (short) connection between the load points and determine the res
ultant current.
Norton Equivalent Circuit : Norton Equivalent Circuit With zero voltage dropped between the load resistor connection points, the current through R1 is strictly a function of B1's voltage and R1's resistance: 7 amps (I=E/R). Likewise, the current through R3 is now strictly a function of B2's voltage and R3's resistance: 7 amps (I=E/R). The total current through the short between the load connection points is the sum of these two currents: 7 amps + 7 amps = 14 amps. This figure of 14 amps becomes the Norton source current (INorton) in our equivalent circuit
Norton Equivalent : Norton Equivalent To calculate the Norton resistance (RNorton), take the original circuit (with the load resistor still removed), remove the power sources (in the same style as we did with the Superposition Theorem: voltage sources replaced with wires and current sources replaced with breaks), and figure total resistance from one load connection point to the other:
Norton Equivalent Circuit : Norton Equivalent Circuit Now our Norton equivalent circuit looks like this: