EE100Su08 Lecture 6 July 7th 2008 Outline Today Midterm on Monday 07 14 08 from 2 4 pm Second room location changed to 120 Latimer Questions Chapter 4 wrap up Thevenin and Norton Source Transformations Miscellaneous Maximum Power Transfer theorem Chapter 6 wrap up Capacitors definition series and parallel combination Inductors definition series and parallel combination Chapter 7 Intuitive Introduction EE100 Summer 2008 Slide 1 Bharathwaj Muthuswamy Recap Thevenin Equivalents EE100 Summer 2008 Slide 2 Bharathwaj Muthuswamy RTh Calculation Example 2 Find the Thevenin equivalent with respect to the terminals a b Ix Vx Since there is no independent source and we cannot arbitrarily turn off the dependence source we can add a voltage source Vx across terminals a b and measure the current through this terminal Ix Rth Vx Ix EE100 Summer 2008 Slide 3 Bharathwaj Muthuswamy Norton Equivalent Circuit Any linear 2 terminal 1 port network of indep voltage sources indep current sources and linear resistors can be replaced by an equivalent circuit consisting of an independent current source in parallel with a resistor without affecting the operation of the rest of the circuit Norton equivalent circuit a network of sources and resistors iL vL RL RN iL vL RL b EE100 Summer 2008 iN a b Slide 4 Bharathwaj Muthuswamy I V Characteristic of Norton Equivalent The I V characteristic for the parallel combination of elements is obtained by adding their currents For a given voltage vab the current i is equal to the sum of the currents in each of the two branches a i iN RN b EE100 Summer 2008 I V characteristic of current source i IN i IN Gv v vab i I V characteristic of resistor i Gv Slide 5 Bharathwaj Muthuswamy Finding IN and RN RTh Analogous to calculation of Thevenin Eq Ckt 1 Find o c voltage and s c current IN isc VTh RTh 2 Or find s c current and Norton Thev resistance EE100 Summer 2008 Slide 6 Bharathwaj Muthuswamy Source Transforms Finding IN and RN We can derive the Norton equivalent circuit from a Th venin equivalent circuit simply by making a source transformation RTh vTh a a iL vL RL iN RN iL vL RL b b voc vTh iN RN RTh isc isc RTh EE100 Summer 2008 Slide 7 Bharathwaj Muthuswamy Source Transformations EE100 Summer 2008 Slide 8 Bharathwaj Muthuswamy Source Transformations EE100 Summer 2008 Slide 9 Bharathwaj Muthuswamy Source Transformations EE100 Summer 2008 Slide 10 Bharathwaj Muthuswamy Source Transformations EE100 Summer 2008 Slide 11 Bharathwaj Muthuswamy Maximum Power Transfer Theorem Th venin equivalent circuit Power absorbed by load resistor RTh VTh 2 iL vL RL VTh RL p i RL RTh RL 2 L dp To find the value of RL for which p is maximum set to 0 dRL 2 RL 2 RTh RL dp R R 2 Th L VTh 0 4 dRL RTh RL RTh RL RL 2 RTh RL 0 2 RTh RL EE100 Summer 2008 A resistive load receives maximum power from a circuit if the load resistance equals the Th venin resistance of the circuit Slide 12 Bharathwaj Muthuswamy Summary of Techniques for Circuit Analysis 1 Resistor network Chapter 3 Parallel resistors Series resistors Voltage Divider Current Divider Voltmeters and Ammeters Y delta conversion OPTIONAL EE100 Summer 2008 Slide 13 Bharathwaj Muthuswamy Summary of Techniques for Circuit Analysis 2 Node Analysis Chapter 4 Node voltage is the unknown Solve for KCL Floating voltage source using super node Superposition Leave one independent source on at a time Sum over all responses Voltage off SC Current off OC Mesh Analysis OPTIONAL Loop current is the unknown Solve for KVL Current source using super mesh Thevenin and Norton Equivalent Circuits Solve for OC voltage Solve for SC current Source Transforms Voltage sources in series with a resistance can be converted to current source in parallel with a resistance EE100 Summer 2008 Slide 14 Bharathwaj Muthuswamy Comments on Dependent Sources Node Voltage Method Dependent current source treat as independent current source in organizing node eqns substitute constraining dependency in terms of defined node voltages Dependent voltage source treat as independent voltage source in organizing node eqns Substitute constraining dependency in terms of defined node voltages EE100 Summer 2008 Slide 15 Bharathwaj Muthuswamy Comments on Dependent Sources contd A dependent source establishes a voltage or current whose value depends on the value of a voltage or current at a specified location in the circuit device model used to model behavior of transistors amplifiers To specify a dependent source we must identify 1 2 3 the controlling voltage or current must be calculated in general the relationship between the controlling voltage or current and the supplied voltage or current the reference direction for the supplied voltage or current The relationship between the dependent source and its reference cannot be broken Dependent sources cannot be turned off for various purposes e g to find the Th venin resistance or in analysis using Superposition EE100 Summer 2008 Slide 16 Bharathwaj Muthuswamy Chapters 6 Outline The capacitor The inductor EE100 Summer 2008 Slide 17 Bharathwaj Muthuswamy The Capacitor Two conductors a b separated by an insulator difference in potential Vab equal opposite charge Q on conductors Q CVab stored charge in terms of voltage where C is the capacitance of the structure positive charge is on the conductor at higher potential Parallel plate capacitor area of the plates A m2 separation between plates d m dielectric permittivity of insulator F m capacitance EE100 Summer 2008 A C d F Slide 18 Bharathwaj Muthuswamy A note on circuit variables EE100 Summer 2008 Slide 19 Bharathwaj Muthuswamy Capacitor Symbol or C C C Electrolytic polarized capacitor Units Farads Coulombs Volt typical range of values 1 pF to 1 F for supercapacitors up to a few F Current Voltage relationship dQ dvc dC C vc ic dt dt dt If C geometry is unchanging iC C dvC dt ic vc Note Q vc must be a continuous function of time EE100 Summer 2008 Slide 20 Bharathwaj Muthuswamy Voltage in Terms of Current t Q t ic t dt Q 0 0 t t 1 Q 0 1 vc t ic t dt ic t dt vc 0 C C0 C0 Uses Capacitors are used to store energy for camera flashbulbs in filters that separate various frequency signals and they appear as undesired parasitic elements in circuits where they usually degrade circuit performance EE100 Summer 2008 Slide 21 Bharathwaj Muthuswamy Stored Energy CAPACITORS STORE ELECTRIC ENERGY You might think the energy stored on a capacitor is QV CV2 which has the dimension of Joules But during charging the average
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