Lecture 5 Source Transformation Thevenin Equivalent Circuit Norton 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-Amp Chapter 5

Sample DAC Waveform DAC Output Digital Input

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 nodes be=3 essential branches 3-(2-1)=2 equations

Mesh Analysis (Last Lecture) 1 2 Loop 1: clockwise Loop 2: counter-clockwise Clockwise around loop 1: +Vin-i1rπ-(i1+i2)RE=0 Counter-clockwise around loop 2: i2=gmi1rπ Vout =-i2RC

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 RTH Thevenin Equivalent Circuit VTH Norton Equivalent Circuit IN=VTH/RTH RTH

Derivation of Norton Equivalent Circuit RTH VTH IN=VTH/RTH 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 Determine the short circuit current 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