* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 2
Yagi–Uda antenna wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Integrating ADC wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Topology (electrical circuits) wikipedia , lookup
Electrical ballast wikipedia , lookup
Wilson current mirror wikipedia , lookup
Charlieplexing wikipedia , lookup
Operational amplifier wikipedia , lookup
Power electronics wikipedia , lookup
Schmitt trigger wikipedia , lookup
Voltage regulator wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Two-port network wikipedia , lookup
Power MOSFET wikipedia , lookup
Surge protector wikipedia , lookup
Opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Rectiverter wikipedia , lookup
Chapter 2 Basic laws SJTU 1 Some Basic Concepts • Branch----- A branch represents a single element such as a voltage source or a resistor. {But usually we think a branch as a path flowing the same current. So maybe includes more than one element.} SJTU 2 Some Basic Concepts •Node-------A node is the point of connection between two or more branches •Loop-------A loop is any closed path in a circuit. •Mesh------A mesh is a loop which does not contain any other loops within it. SJTU 3 KIRCHHOFF’S LAWS • Kirchhoff’s Current Law (KCL): N i k 1 k 0 The algebraic sum of currents entering a node (or a closed boundary) is zero. (Based on the law of conservation of charge) The sum of the currents entering a node = the sum of the currents leaving the node. i1 i2 i3 i4 i5 0 or i1 i3 i4 i2 i5 SJTU 4 i3 KCL also applies to a closed boundary. i6 i4 i2 i7 i i1 5 so i1 i2 i3 i6 i7 0 or i1 i2 i3 i4 i5 0 Note: 1) KCL is available to every node at anytime. 2) KCL is related only to the currents instead of the elements. 3) Pay attention to the current direction. SJTU 5 KIRCHHOFF’S LAWS • Kirchhoff’s Voltage Law (KVL): The algebraic sum of all voltages around a closed path (or loop) is zero. (Based on the principle of conservation of energy) To illustrate KVL, consider the circuit : V1 +V2R1 +V3R2 1k 1k M v k 1 k 0 R3 V1-V2-V3+V4-V5=0 or V2+V3+V5=V1+V4 1k Sum of voltage drops=Sum of voltage rises V4 -V5+ SJTU 6 TWO SORTS OF CONSTRAINTS • 1. Topological constraints Determined by the way of connection among the elements. (Such as KCL KVL) 2. Element constraints Determined by the elements. (VAR) Using two sorts of constraints, we can analysis any lumped circuit (solve out all the voltages and currents). SJTU 7 In a circuit with b branches and n nodes, there are 2b variables should be valued. Then: KCL for n nodes: only n-1 equations are independent. KVL for loops: only b-n+1 equations are independent. (only KVL for meshes) VAR for branches: b equations. So, (n-1)+(b-n+1)+b=2b, 2b equations to value 2b variables. That is called 2b analysis. SJTU 8 SERIES RESISTORS AND VOLTAGE DIVISION • As we know, Series-connected means that the same current flows in them. • The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances. See illustration with 2 resistors: v v1 v2 R1i R2i Ri R R1 R2 R is the equivalent resistance. It can be applied to any number of resistors SJTU 9 P vi v1i v2i R1i 2 R2i 2 Ri 2 P1 P2 The equivalent power of any number of resistors connected in series is the sum of the individual powers. Concept of Equivalent: Be equivalent to the outside, not the inside. Principle of voltage division: if a voltage divider has N resistors(R1,R2,…RN) in series with the source voltage v, the nth resistor(Rn)will have a voltage drop of Rn vn v R1 R2 ... RN SJTU 10 PARALLEL RESISTORS AND CURRENT DIVISION • As we know, Parallel-connected means that the same voltage covers over them. • The equivalent conductance of resistors connected in parallel is the sum of their individual conductances. See illustration with 2 resistors: i i1 i2 G1v G2v Gv G G G G1 G2 G is the equivalent conductance. It can be applied to any number of resistors SJTU 11 P vi vi1 vi2 G1v 2 G2v 2 Gv2 P1 P2 The equivalent power of any number of resistors connected in parallel is the sum of the individual powers. Principle of current division If a current divider has N conductors (G1,G2…GN) in parallel with the source current i, the nth conductor (Gn) will have current Gn in i G1 G2 ... GN SJTU 12 MIXED CONNECTION AND ITS EQUIVALENT RESISTANCE Examples (we combine resistors in series and in parallel) SJTU 13 WYE-DELTA TRANSFORMATIONS Situations often arise in circuit analysis when the resistors are neither in parallel nor in series. d e R12=? SJTU 14 WYE-DELTA TRANSFORMATIONS Y Rb Rc R1 Ra Rb Rc R2 Rc Ra Ra Rb Rc R3 Ra Rb Ra Rb Rc Y R1 R2 R2 R3 R3 R1 Ra R1 R1 R2 R2 R3 R3 R1 Rb R2 R1 R2 R2 R3 R3 R1 Rc R3 SJTU 15 So 2 d e 1 3 Can you imagine another way of transformation? SJTU 16