Download Thévenin Equivalent Circuit-Introduction to Microelectronic Circuits-Lecture 08 Slides-Electrical Engineering and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 8, Slide 1EECS40, Fall 2003 Prof. King Lecture #8 ANNOUNCEMENTS • HW#2 solutions, HW#3 are posted online • Change in Farhana’s O.H. : Th 5-6 instead of Mo 3-4 • Prof. King will be away next Monday & Wednesday – Guest lecturer: Prof. Neureuther – Prof. King’s office hour on Wed. 9/17 cancelled OUTLINE • Thévenin and Norton equivalent circuits • Maximum power transfer • Superposition Reading Chapter 4.10-4.13 Lecture 8, Slide 2EECS40, Fall 2003 Prof. King Thévenin Equivalent Circuit • Any network of voltage sources, current sources, and resistors can be replaced by an equivalent circuit consisting of an independent voltage source in series with a resistor without affecting the operation of the rest of the circuit. network of sources and resistors ≡ – + VTh RTh RL iL+ vL – a b RL iL+ vL – a b Thévenin equivalent circuit “load” resistor 2 Lecture 8, Slide 3EECS40, Fall 2003 Prof. King I-V Characteristic of Thévenin Equivalent • The I-V characteristic for the series combination of elements is obtained by adding their voltage drops: – + VTh RTh a b i i + vab – v = VTh+ iR I-V characteristic of resistor: v = iR I-V characteristic of voltage source: v = VTh For a given current i, the voltage drop vab is equal to the sum of the voltages dropped across the source (VTh) and the across the resistor (iRTh) v Lecture 8, Slide 4EECS40, Fall 2003 Prof. King Finding VTh and RTh Only two points are needed to define a line. Choose two convenient points: 1. Open circuit across terminals a,b i = 0, vab ≡ voc 2. Short circuit across terminals a,b vab = 0, i ≡ -isc = -VTh/RTh – + VTh RTh + voc = VTh – i v = VTh+ iR vab -isc voc – + VTh RTh isci i 5 Lecture 8, Slide 9EECS40, Fall 2003 Prof. King Comments on Dependent Sources 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. (imaginary device, used to model behavior of transistors & amplifiers) To specify a dependent source, we must identify: 1. the controlling voltage or current (must be calculated, in general) 2. the relationship between the controlling voltage or current and the supplied voltage or current 3. 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 Thévenin resistance). Lecture 8, Slide 10EECS40, Fall 2003 Prof. King RTh Calculation Example #2 Find the Thevenin equivalent with respect to the terminals a,b: 6 Lecture 8, Slide 11EECS40, Fall 2003 Prof. King Networks Containing Time-Varying Sources Care must be taken in summing time-varying sources! Example: 20 cos (100t) 1 kΩ 1 kΩ 10 sin (100t) + – – + [ ] Ω=ΩΩ= +=+ Ω+Ω Ω= 500k1 k1 )90100sin(210)100sin(10)100cos(20 k1k1 k1 Th o Th R tttV Lecture 8, Slide 12EECS40, Fall 2003 Prof. King Norton equivalent circuit Norton Equivalent Circuit • Any network of voltage sources, current sources, and 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. network of sources and resistors ≡RL iL+ vL – a b RL iL+ vL – iN a b RN 7 Lecture 8, Slide 13EECS40, Fall 2003 Prof. King Finding IN and RN • We can derive the Norton equivalent circuit from a Thévenin equivalent circuit simply by making a source transformation: LTh Th L RR vi + = RLRN iL iN + vL – a b – + RL iL+ vL – vTh RTh N LN N L iRR Ri + = sc Th Th N sc oc ThN ; iR vi i vRR ==== a b Lecture 8, Slide 14EECS40, Fall 2003 Prof. King Maximum Power Transfer Theorem A resistive load receives maximum power from a circuit if the load resistance equals the Thévenin resistance of the circuit. L 2 LTh Th L 2 L RRR VRip + == – + VTh RTh RL iL+ vL – Thévenin equivalent circuit ( ) ( ) ( ) ( ) ( ) LTh LThL 2 LTh 4 LTh LThL 2 LTh2 Th 02 02 RR RRRRR RR RRRRRV dR dp L =⇒ =+×−+⇒ = + +×−+= To find the value of RL for which p is maximum, set to 0: Power absorbed by load resistor: LdR dp
