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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 i S =v S /R for any R L

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Thevenin Equivalent Circuit

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Determine the Thevenin Voltage (V Th ) If R L =∞ (load across a-b is removed), then V ab =V TH – R TH 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 Digital Input DAC Output

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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 V TH

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Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc 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 R TH

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If the network contains only independent sources R TH ?

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R TH

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Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc 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) n e =2 essential nodes b e =3 essential branches 3-(2-1)=2 equations

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Mesh Analysis (Last Lecture) 12 Clockwise around loop 1: +V in -i 1 r π -(i 1 +i 2 )R E =0 Counter-clockwise around loop 2: i 2 =g m i 1 r π V out =-i 2 R C Loop 1: clockwise Loop 2: counter-clockwise

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Mesh Analysis (Details)

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Determine R TH when a Dependent Source is Present ITIT

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Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc 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 R TH i sc

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R TH Calculation i SC =10V/100 KOhms=0.1 mA V TH =10V/2=5V R TH =V TH /i SC =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 Norton Equivalent Circuit Thevenin Equivalent Circuit V TH R TH I N =V TH /R TH

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Derivation of Norton Equivalent Circuit V TH R TH I N =V TH /R TH

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Extra Credit Assignment Derive 4.1-4.3

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More about the Extra Credit Assignment

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Extra Slides on Thevenin

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Determine v ab Show that V TH = v ab

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Determine i SC and R TH

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Example 4.10 Determine the Thevenin Equivalent Voltage

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Example 4.10 1.Determine the short circuit current 2.Determine R TH

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Slides on Source Transformation

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R TH

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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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