Ohm's Law

Similarly, when a voltage E is applied across an impedance Z, the resulting current I through the impedance is equal to the voltage E divided by the impedance Z.

Current = Voltage / Impedance

I = E / Z

Similarly, when a current I is passed through an impedance Z, the resulting voltage drop V across the impedance is equal to the current I multiplied by the impedance Z.

Voltage = Current * Impedance

V = IZ

Alternatively, using admittance Y which is the reciprocal of impedance Z:

Voltage = Current / Admittance

V = I / Y

Thevenin's Theorem

Thevenin Equivalent

A circuit containing linear devices (whose current is proportional to the applied voltage) and independent sources can be replaced with a single voltage source with a single series impedance for analysis. This Thevenin equivalent can replace the original complicated subcircuit in the original circuit. The use of the equivalent circuit should simplify (or make possible) the analysis of the original circuit. It should be noted that the equivalent circuit is only equivalent outside the equivalent. You cannot make efficiency calculations of the original subcircuit based on its equivalent.

Figure 1 - Circuit to be analyzed.

Let's find the Thevenin equivalent of the "left half" of the circuit (replacing V1, R1 and R2). Other equivalents are possible, but care must be taken that you don't replace too much of the circuit with the equivalent, leaving points of interest "inside" the equivalent where they are not available for analysis. Figure 2 shows the circuit we wish to "Thevenize". Figure 3 shows how it has been replaced by a single "Thevenin voltage" and a single "Thevenin resistance".

Figure 2 - Circuit to be Thevenized.

Figure 3 - Thevenin equivalent of figure 2

To determine the Thevenin voltage take the original circuit for which the equivalent is desired (figure 2), and place an "imaginary voltmeter" across the two terminals that connected this subcircuit to the remainder of the circuit. In this case, we measure the voltage at the junction of R1 and R2 with respect to ground. This "open circuit voltage" is the Thevenin voltage. In this circuit, it was easily determined using Ohm's Law or using the voltage divider formula (12V*(2K/3K)=8V).

To determine the Thevenin resistance (or, in AC circuits, the Thevenin impedance ), replace all independent voltage sources with zero volt sources (a short) and replace all independent current sources with zero amp sources (an open). Place an "imaginary ohmmeter" the same place we put the voltmeter above. In this case, the shorting of V1 puts R1 in parallel with R2, yielding a Thevenin resistance of 667 ohms. The Thevenin equivalent of figure 2 is shown in figure 3. Figure 4 shows the original circuit with V1, R1 and R2 replaced by their Thevenin equivalent.

Figure 4 - Original circuit with equivalent.