EE 101 Fall 2011 Prof. John Vesecky
Lecture 6 Circuit Theorems Outline Notes
Instructor: John Vesecky, Office: BE-239, Office Hours: M (2:30 to class time), Tu 5-6 PM, Friday (after
class until 6 pm) Phone: (831) 459- 4099 E-mail: vesecky@soe.ucsc.edu
Teaching Assistants: Ali Adabi & Patrick Ellis
E-mail: aadabi@gmail.com
E-mail: pbellis@soe.ucsc.edu
Reference reading: Chapter 4 in your textbook
Outline for Lectures 6 & 7 on Circuit Theorems
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Why are we studying this
Linearity Property for Systems
Superposition
Simplifications by Source Transformation
Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer
Why are we studying circuit theorems?
They simplify complex circuits like LM741 Op Amp?
Linearity Property for Systems
System or element describing a linear relationship
between cause and effect.
A linear circuit’s output is linearly related (or directly proportional) to its input. So this means:
→ kv=kiR
Scaling property:
v=iR
Additive property:
v1 = i1 R & v2 = i2 R → v = (i1 + i2) R = v1 + v2
Application to a circuit problem
1
Work your way back from
assuming Io = 1 Amp
Superposition
Definition: the voltage across (or current through) an element in a linear circuit is the
algebraic sum of the voltage across (or currents through) that element due to EACH
independent source acting alone.
Superposition helps us to analyze a linear circuit with more than one independent source by
calculating the contribution of each independent source separately – turn every source off, then
turn each one on by itself, repeat for all independent sources, add up the contributions to the
current or voltage you are investigating and you have it.
v = ? Redraw circuit if needed.
• Independent voltage sources are replaced by 0 V (short circuit)
• Independent current sources are replaced by 0 A (open circuit)
• Dependent sources are left intact because they are controlled by circuit variables.
vo = ?
2
Simplification by Source Transformation
•An equivalent circuit is one whose v-i characteristics are identical with the original
circuit.
•It is the process of replacing a voltage source vS in series with a resistor R by a
current source iS in parallel with a resistor R, or vice versa.
vs = is R
is = vs/R
The source transformation won’t work when
R = 0 for voltage source and R = ∞ for current
source.
3
Thevenin’s Theorem
A linear two-terminal circuit (Fig. a) can be replaced by an equivalent
circuit (Fig. b) consisting of a voltage source VTH in series with a
resistor RTH,
4