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Admin for next week: Mid-term date Friday March 20th. •Review lecture Monday (16th). Any requests? •Labs as usual •NO DISCUSSION SECTIONS NEXT WEEK •Extra Office hours • 2-4pm Monday: Dr Holder Sharp Lab 222 • 2-4pm Tuesday: Dr Holder Sharp Lab 222 • 2-4pm Wednesday: Seth Sharp Lab 308 • 2-4pm Thursday: Zach Sharp Lab 320 •Email is also OK – or stop by my office any time Monday or Tuesday •I will be away Wednesday – Friday. •Dr Ji will give Wednesday’s class and the exam. Copyright © 2009 Pearson Education, Inc. Admin: • Assignments: • Fourth assignment due Monday (16th) • Any questions? • Fifth Assignment is posted. • Not due until Monday (23rd), but good exam practice • Three questions on Thevenin circuits Copyright © 2009 Pearson Education, Inc. Thevenin and Norton Equivalent Circuits Any network of sources and resistors will appear to the circuit connected to it as a voltage source and a series resistance vTH= open circuit voltage at terminal (a.k.a. port) RTH= Resistance of the network as seen from port (Vm’s, In’s set to zero) Thevenin and Norton Equivalent Circuits Léon Charles Thévenin 1857-1926 vTH= open circuit voltage at terminal (a.k.a. port) RTH= Resistance of the network as seen from port (Vm’s, In’s set to zero) Norton Equivalent Circuit Any network of sources and resistors will appear to the circuit connected to it as a current source and a parallel resistance Ed Norton – Bell Labs, 1898-1983 The Thevenin and Norton equivalent cicuits are just different representations of the same thing. They are used to simplify circuit analysis RTH=RN VTH=INRTH : so you only usually need IN or VTH Calculation of Thevenin and Norton Resistance (RTH = RN) • RTH=RN ; same calculation (voltage and current sources set to zero) • Remove the load. • Set all sources to zero (‘kill’ the sources) – Short voltage sources (replace with a wire) – Open current sources (replace with a break) • Calculate the equivalent resistance Remove the load. Kill the sources Calculate the equivalent resistance RTH=R3 + R1 || R2 Calculation of the Thevenin Voltage (VTH) • Put the sources back. Remove the load and calculate the open circuit voltage Note: How much current flows through R3? What is the Voltage across R3? The Thevenin equivalent is then just VTH in series with RTH Calculation of the Thevenin Voltage (VTH) • Put the sources back. Remove the load and calculate the open circuit voltage Note: How much current flows through R3? What is the Voltage across R3? Voltage divider! VTH = VR2 = R2 VS R1 + R2 The Thevenin equivalent is then just VTH in series with RTH Exercise: Draw the Thevenin Equivalent as seen by the 40Ω load resistor • To find RTH, remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance. • To find VTH Remove the load and calculate the open circuit voltage Exercise: Draw the Thevenin Equivalent • To find RTH remove the load, kill the sources (short voltage sources, break current sources) and find the equivalent resistance. Exercise: Draw the Thevenin Equivalent • Replace the sources • To find VTH remove the load resistor and calculate the open circuit voltage VAB = 20 - (20Ω x 0.33amps) = 13.33V Exercise: Draw the Thevenin Equivalent • Draw the Thevenin equivalent What about the Norton equivalent? What about the Norton equivalent? But what if we don’t know VTH? Remember – if you suppress the “kilo” in the resistance, the current calculated is in milliAmps STOP HERE for mid-term 1 • Anything you’d like me to cover in detail on Monday? • Requests so far: mesh analysis 2 voltage divider & current divider light bulbs Thevenin