• identify opportunities to use superposition to analyze or design linear circuits.
• use superposition to express the output of a linear circuit as a linear combinations of its inputs.
• identify opportunities for source transformations.
• simplify a dc circuit using source transformations and equivalent resistance.
• identify opportunities to simplify a circuit using Thevinin or Norton equivalent circuits.
• find the Thevinin or Norton equivalent circuit of a given linear circuit.

Reading: Chapter 5.

• Section 5.3 defines superposition shows how it can be used to analyze and electric circuit.

• Here's a surprize: A series voltage source and resistor is equivalent to a parallel current source and resistor. That equivalence, referred to as a "source transformation" is described in Section 5.2.

  • We'll need to pay attention to reference directions as illustrated in Exercises 5.2-1 thru 5.2-4.
  • We now have a collection of equivalent circuits. We have equivalent circuits for series resistors (Section 3.3), parallel resistors (Section 3.4), series voltage sources (Section 3.5) and parallel current sources (Section 3.5).
  • In Example 5.2-2 a circuit is simplified by repeatedly repalcing parts of the circuit with equivalent circuits. Finally, the circuit is reduced to single mesh and is analyzed using KVL.

• Three parameters characterize Thevenin and Norton equivalent circuits. They are the open circuit voltage, v_oc, the short circuit current, i_sc and the Thevenin resistance, R_t.
  • Figures 5.4-3 and 5.4-4, and the associated text, define these three parameters. These definitions are used to determine the values of the parameters for a particular circuit.
  • Figures 5.4-2 and 5.5-1, and the associated text, use these three parameters to construct Thevenin and Norton equivalent circuits.
  • The reference directions of the sources in Figures 5.4-2 and 5.5-1 must correspond the reference directions used to determine v_oc and i_sc in Figures 5.4-3 and 5.4-4. Notice that the terminals have been labeled "a" and "b" in these four figures to make that correspondence.

  • Section 5.4 describes a procedure for determining v_oc, i_sc and R_t from laboratory data. In Section 5.7, MATLAB is used to perform the calculations required by that procedure. In Section 5.8, that same procedure is used to check the laboratory data for consistency.

Lecture Notes:

1. Superposition is a property of linear circuits and systems. It enables us to express the output of a linear circuit as a linear combinations of its inputs. What are the inputs and outputs of an electric circuit?
   • Inputs: The voltages of independent voltage sources and the currents of inpedendent current sources.
   • Output: Any current or voltage. Output are often specified by labeling a paricular voltage or current as v_o or i_o. Sometime meters are used to indicate which voltage or current is the output of a circuit.

2. Circuit analysis using superposition.
3. A lab experiment helps us understand why source transformations work.
4. Okay, we know how to construct a Thevenin equivalent circuit, but what is a Thevenin equivalent circuit?
5. Here's an alternate method for determining the Thevenin or Norton equivalent circuit of a circuit that does not contain dependent sources:
   • Use circuit equivalences repeatedly to simplify the circuit until it consists of a series resistor and voltage source of a parallel resistor and current source.
   • Then: R_t is the resistance of the resistor, v_oc is the voltage of the voltage source and i_sc is the current of the currents.

Examples:

• Using superposition to express the output of a linear circuit as a linear combinations of its inputs.
• Source transformations, together with other circuit equivalences, are used to simplify circuits before analyzing them.
• Here are some examples of finding Thevenin or Norton equivalent circuits. Notice that source transformations and equivalent resistances are used when there are no dependent sources in the given circuit but the definitions of v_oc, i_sc and R_t are used when there are dependent sources.
• We can measure v_oc, i_sc and R_t for a particular circuit by connecting a variable resistor across the output terminals of the circuit and taking some data.

Handouts:

• Superposition.
• "short circuit current" and "open circuit voltage"
• Using source transformations to obtain Thevenin and Norton equivalent circuits.
• Thevenin and Norton equivalent circuits of circuits containing dependent sources.
• Using lab data to obtain Thevenin and Norton equivalent circuits.

On-line Exercises: Signal Processing Superposition Source Transformations Thevenin Equivalent Circuits