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**Lecture 5 Source Transformation Thevenin Equivalent Circuit**

Norton Equivalent Circuit

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**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

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**Source Transformation**

Show that iS=vS/R for any RL

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**Thevenin Equivalent Circuit**

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**Determine the Thevenin Voltage (VTh)**

If RL=∞ (load across a-b is removed), then Vab=VTH RTH does not play a role!

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**3 Bit Digital to Analog Converter**

741 Op-Amp Chapter 5

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Sample DAC Waveform DAC Output Digital Input

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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

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**Thevenin Equivalent Circuit**

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Determine VTH

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**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

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**Calculate the Thevenin Resistance**

RTH

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**If the network contains only independent sources**

RTH?

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RTH

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**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

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**Degenerated Common Emitter Amplifier (from last lecture)**

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**What if we drive the base with a small signal?**

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

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**Mesh Analysis (Last Lecture)**

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

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**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

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**Mesh Analysis (Details)**

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**Determine RTH when a Dependent Source is Present**

IT

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**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

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Another Way to Find RTH isc

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**RTH Calculation iSC=10V/100 KOhms=0.1 mA VTH=10V/2=5V**

RTH=VTH/iSC=5V/0.1 mA=50 KOhms

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**Norton Equivalent Circuit**

A Norton Equivalent circuit consists of Short-Circuit Current Norton Equivalent Resistance, which is equal to Thevenin Equivalent Resistance

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**Getting A Norton Equivalent Circuit from Thevenin Equivalent Circuit**

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

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**Derivation of Norton Equivalent Circuit**

RTH VTH IN=VTH/RTH RTH

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**Extra Credit Assignment**

Derive

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**More about the Extra Credit Assignment**

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**Extra Slides on Thevenin**

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Determine vab Show that VTH=vab

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Determine iSC and RTH

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Example 4.10 Determine the Thevenin Equivalent Voltage

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Example 4.10 Determine the short circuit current Determine RTH

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**Slides on Source Transformation**

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RTH

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**Application Determine whether the 6V source is**

absorbing or delivering the power.

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**Step-by-step simplification**

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Redundant Resistor (1) Prove that the left circuit and the right circuit are equivalent for any load resistor.

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Redundant Resistor (2) Prove that the left circuit and the right circuit are equivalent for any load resistor.

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Example 4.9

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Simplified Circuit

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