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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

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## Lecture 5

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**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**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**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**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**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**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**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**Determine vab**Show that VTH=vab**Example 4.10**Determine the Thevenin Equivalent Voltage**Example 4.10**Determine the short circuit current Determine RTH**Application**Determine whether the 6V source is absorbing or delivering the power.**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.

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