Lecture 4 in EECS40, Fall 2003: Circuit Elements and Kirchhoff's Laws, Slides of Microelectronic Circuits

Download Lecture 4 in EECS40, Fall 2003: Circuit Elements and Kirchhoff's Laws and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 4, Slide 1EECS40, Fall 2003 Prof. King Announcements • Visit the class website to see updated TA section assignments http://www-inst.eecs.berkeley.edu/~ee40 • Lab section 13 (Mondays 6-9PM) is cancelled • Prof. King’s Office Hour tomorrow (Thu. 9/4) will be held from 8:30AM-9:30AM • HW assignments will NOT be accepted in class. Turn in your assignments BEFORE class on Friday in 240 Cory. Lecture 4, Slide 2EECS40, Fall 2003 Prof. King Lecture #4 OUTLINE • Circuit element I-V characteristics • Construction of a circuit model • Kirchhoff’s laws – a closer look Reading (Finish Chapter 2) 2 Lecture 4, Slide 3EECS40, Fall 2003 Prof. King Current vs. Voltage (I-V) Characteristic • Voltage sources, current sources, and resistors can be described by plotting the current (i) as a function of the voltage (v) • Later, we will see that the I-V characteristic of any circuit consisting only of sources and resistors is a straight line. + v _ i Lecture 4, Slide 4EECS40, Fall 2003 Prof. King I-V Characteristic of Ideal Voltage Source 1. Plot the I-V characteristic for vs > 0. For what values of i does the source absorb power? For what values of i does the source release power? 2. Repeat (1) for vs < 0. 3. What is the I-V characteristic for an ideal wire? +_ vs i i + v _ v 5 Lecture 4, Slide 9EECS40, Fall 2003 Prof. King Terminology: Nodes and Branches Node: A point where two or more circuit elements are connected – entire wire Branch: A path that connects two nodes Lecture 4, Slide 10EECS40, Fall 2003 Prof. King Notation: Node and Branch Voltages • Use one node as the reference (the “common” or “ground” node) – label it with a symbol • The voltage drop from node x to the reference node is called the node voltage vx. • The voltage across a circuit element is defined as the difference between the node voltages at its terminals Example: +_ vs + va _ + vb _ a b c R1 R2 – v1 + 6 Lecture 4, Slide 11EECS40, Fall 2003 Prof. King • Use reference directions to determine whether currents are “entering” or “leaving” the node – with no concern about actual current directions Using Kirchhoff’s Current Law (KCL) i1 i4 i3 i2 Consider a node connecting several branches: Lecture 4, Slide 12EECS40, Fall 2003 Prof. King Formulations of Kirchhoff’s Current Law Formulation 1: Sum of currents entering node = sum of currents leaving node Formulation 2: Algebraic sum of currents entering node = 0 • Currents leaving are included with a minus sign. Formulation 3: Algebraic sum of currents leaving node = 0 • Currents entering are included with a minus sign. (Charge stored in node is zero.) 7 Lecture 4, Slide 13EECS40, Fall 2003 Prof. King A Major Implication of KCL • KCL tells us that all of the elements in a single branch carry the same current. • We say these elements are connected in series. Current entering node = Current leaving node i1 = i2 Lecture 4, Slide 14EECS40, Fall 2003 Prof. King KCL Example 5 mA 15 mA i -10 mA 3 formulations of KCL: 1. 2. 3. Currents entering the node: Currents leaving the node: 10 Lecture 4, Slide 19EECS40, Fall 2003 Prof. King A Major Implication of KVL • KVL tells us that any set of elements which are connected at both ends carry the same voltage. • We say these elements are connected in parallel. Applying KVL in the clockwise direction, starting at the top: vb – va = 0 vb = va + va _ + vb _ Lecture 4, Slide 20EECS40, Fall 2003 Prof. King Path 1: Path 2: Path 3: vcva + − + − 3 21 + − vb v3v2 + − + - Three closed paths: a b c KVL Example 11 Lecture 4, Slide 21EECS40, Fall 2003 Prof. King • No time-varying magnetic flux through the loop Otherwise, there would be an induced voltage (Faraday’s Law) Avoid these loops! How do we deal with antennas (EECS 117A)? Include a voltage source as the circuit representation of the induced voltage or “noise”. (Use a lumped model rather than a distributed (wave) model.) • Note: Antennas are designed to “pick up” electromagnetic waves; “regular circuits” often do so undesirably. )t(B v )t(v + − An Underlying Assumption of KVL Lecture 4, Slide 22EECS40, Fall 2003 Prof. King Summary • An ideal voltage source maintains a prescribed voltage regardless of the current in the device. • An ideal current source maintains a prescribed current regardless of the voltage across the device. • A resistor constrains its voltage and current to be proportional to each other: v = iR (Ohm’s law) • Kirchhoff’s current law states that the algebraic sum of all currents at any node in a circuit equals zero. • Kirchhoff’s voltage law states that the algebraic sum of all voltages around any closed path in a circuit equals zero.