Lecture 5

Source TransformationThevenin Equivalent CircuitNorton Equivalent Circuit

Circuit Techinques

• Ohm’s Law • P=VI• KCL, KVL• Voltage/current divider• Series/parallel resistance• Mesh/Nodal Analysis• Source Transformation• Thevenin/Norton Equivalent Circuit• Superposition Principle• Maximum Power Transfer

Source Transformation

Show that iS=vS/R for any RL

Thevenin Equivalent Circuit

Determine the Thevenin Voltage (VTh)

• If RL=∞ (load across a-b is removed), then Vab=VTH

– RTH does not play a role!

3 Bit Digital to Analog Converter

741 Op-AmpChapter 5

Sample DAC Waveform

Digital Input

DAC Output

Applications

• Most modern audio signals are stored in digital form (e.g. MP3 and CDs) and in order to be heard through speakers they must be converted into an analog signal

Thevenin Equivalent Circuit

Determine VTH

Methods of Finding RTH

• RTH=VTH/iSC

– If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH.

– So RTH=VTh/isc

• If the network contains only independent sources:– Deactivate a voltage source by replacing it with

a short– Deactivate a current source by replacing it with

an open• If the network contains dependent sources– Apply a test source

Calculate the Thevenin Resistance

RTH

If the network contains only independent sources

RTH?

RTH

Methods of Finding RTH

• RTH=VTH/iSC

– If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH.

– So RTH=VTh/isc

• If the network contains only independent sources:– Deactivate a voltage source by replacing it with

a short– Deactivate a current source by replacing it with

an open• If the network contains dependent sources– Apply a test source

Degenerated Common Emitter Amplifier (from last lecture)

What if we drive the base with a small signal?

Vin, m=1 mV Vout, m=46 mV

Mesh Analysis (Last Lecture)

ne=2 essential nodesbe=3 essential branches

3-(2-1)=2 equations

Mesh Analysis (Last Lecture)

1 2

Clockwise around loop 1:+Vin-i1rπ-(i1+i2)RE=0Counter-clockwise around loop 2:i2=gmi1rπ

Vout =-i2RC

Loop 1: clockwiseLoop 2: counter-clockwise

Mesh Analysis (Details)

Determine RTH when a Dependent Source is Present

IT

Methods of Finding RTH

• RTH=VTH/iSC

– If RL=0, the short circuit current from a to b (i.e. iab) should equal to isc=VTh/RTH.

– So RTH=VTh/isc

• If the network contains only independent sources:– Deactivate a voltage source by replacing it with

a short– Deactivate a current source by replacing it with

an open• If the network contains dependent sources– Apply a test source

Another Way to Find RTH

isc

RTH Calculation

• iSC=10V/100 KOhms=0.1 mA

• VTH=10V/2=5V

• RTH=VTH/iSC=5V/0.1 mA=50 KOhms

Norton Equivalent Circuit

• A Norton Equivalent circuit consists of–Short-Circuit Current–Norton Equivalent Resistance,

which is equal to Thevenin Equivalent Resistance

Getting A Norton Equivalent Circuit from Thevenin Equivalent Circuit

Norton Equivalent Circuit

Thevenin Equivalent CircuitVTH

RTH

RTHIN=VTH/RTH

Derivation of Norton Equivalent Circuit

VTH

RTH

RTHIN=VTH/RTH

Extra Credit Assignment

Derive 4.1-4.3

More about the Extra Credit Assignment

Extra Slides on Thevenin

Determine vab

Show that VTH=vab

Determine iSC and RTH

Example 4.10

Determine the Thevenin Equivalent Voltage

Example 4.10

1. Determine the short circuit current 2. Determine RTH

Slides on Source Transformation

RTH

Application

Determine whether the 6V source is absorbing or delivering the power.

Step-by-step simplification

Redundant Resistor (1)

Prove that the left circuit and the right circuit are equivalent for any load resistor.

Redundant Resistor (2)

Prove that the left circuit and the right circuit are equivalent for any load resistor.

Example 4.9

Simplified Circuit