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Lecture 4 Overview. More circuit analysis Thevenin ’ s Theorem Norton ’ s Theorem. Announcements. Assignment 0 due Thursday Lab reports due today and tomorrow Physics Colloquium 4pm tommorrow. Method 3: Thevenin and Norton Equivalent Circuits. Léon Charles Thévenin 1857-1926.

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Lecture 4 Overview
• More circuit analysis
• Thevenin’s Theorem
• Norton’s Theorem
Announcements
• Assignment 0 due Thursday
• Lab reports due today and tomorrow
• Physics Colloquium 4pm tommorrow
Method 3: Thevenin and Norton Equivalent Circuits

Léon Charles Thévenin

1857-1926

vTH= open circuit voltage at terminal (a.k.a. port)

RTH= Resistance of the network as seen from port

(Vm’s, In’s set to zero)

Method 3: Thevenin and Norton Equivalent Circuits

Any network of sources and resistors will appear to the circuit connected to it as a voltage source and a series resistance

vTH= open circuit voltage at terminal (a.k.a. port)

RTH= Resistance of the network as seen from port

(Vm’s, In’s set to zero)

Norton Equivalent Circuit

Any network of sources and resistors will appear to the circuit connected to it as a current source and a parallel resistance

Ed Norton – Bell Labs, 1898-1983

Calculation of RT and RN
• RT=RN ; same calculation (voltage and current sources set to zero)
• Remove the load.
• Set all sources to zero (‘kill’ the sources)
• Short voltage sources (replace with a wire)
• Open current sources (replace with a break)
Calculation of RT and RN continued
• Calculate equivalent resistance seen by the load
Calculation of VT
• Remove the load and calculate the open circuit voltage

(Voltage Divider)

Example
• Use Thevenin’s theorem to calculate the current through Resistor R6.
• (solution RTH=6.67Ω, VTH=12V, I=0.95A)
Exercise: Draw the Thevenin Equivalent
• To find RTH remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance.
• To find VTH Remove the load and calculate the open circuit voltage
Exercise: Draw the Thevenin Equivalent
• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.
• To find VTH Remove the load and calculate the open circuit voltage
Exercise: Draw the Thevenin Equivalent
• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.
• To find VTH Remove the load and calculate the open circuit voltage

VAB = 20 - (20Ω x 0.33amps) = 13.33V

Exercise: Draw the Thevenin Equivalent
• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.
• To find VTH Remove the load and calculate the open circuit voltage

VAB = 20 - (20Ω x 0.33amps) = 13.33V

Exercise: Draw the Thevenin Equivalent
• To find RTH kill the sources (short voltage sources, break current sources) and find the equivalent resistance.
• To find VTH Remove the load and calculate the open circuit voltage
Calculation of IN
• Short the load and calculate the short circuit current

(mesh analysis)

(R1+R2)i1 - R2iSC = vs

-R2i1 + (R2+R3)iSC = 0

(KCL at v)

RN=RTH

Source Transformation

Summary: Thevenin’s Theorem

• Any two-terminal linear circuit can be replaced with a voltage source and a series resistor which will produce the same effects at the terminals
• VTH is the open-circuit voltage VOC between the two terminals of the circuit that the Thevenin generator is replacing
• RTH is the ratio of VOC to the short-circuit current ISC; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them.
Summary: Norton’s Theorem
• Any two-terminal linear circuit can be replaced with a current source and a parallel resistor which will produce the same effects at the terminals
• IN is the short-circuit current ISC of the circuit that the Norton generator is replacing
• Again, RN is the ratio of VOC to the short-circuit current ISC; In linear circuits this is equivalent to “killing” the sources and evaluating the resistance between the terminals. Voltage sources are killed by shorting them, current sources are killed by opening them.
• For a given circuit, RN=RTH
Maximum Power Transfer
• Why use Thevenin and Norton equivalents?
• Very easy to calculate load related quantities
• E.g. Maximum power transfer to the load
• It is often important to design circuits that transfer power from a source to a load. There are two basic types of power transfer
• Efficient power transfer: least power loss. Power is usually large (e.g. power utility)
• Maximum power transfer (e.g. communications circuits)
• Want to transfer an electrical signal (data, information etc.) from the source to a destination with the most power reaching the destination. Power is usually small so efficiency is not a concern.
Maximum Power Transfer: Impedance matching

Differentiate w.r.t. RL using quotient rule:

Set to zero to find maximum:

so maximum power transfer occurs when

and

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm

Maximum Power Transfer: Impedance matching

Differentiate w.r.t. RL using quotient rule:

Set to zero to find maximum:

so maximum power transfer occurs when

and

http://circuitscan.homestead.com/files/ancircp/maxpower1.htm