* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Yagi–Uda antenna wikipedia, lookup

Index of electronics articles wikipedia, lookup

Negative resistance wikipedia, lookup

Regenerative circuit wikipedia, lookup

Josephson voltage standard wikipedia, lookup

Valve RF amplifier wikipedia, lookup

Schmitt trigger wikipedia, lookup

Operational amplifier wikipedia, lookup

Voltage regulator wikipedia, lookup

Power electronics wikipedia, lookup

Wilson current mirror wikipedia, lookup

Switched-mode power supply wikipedia, lookup

Resistive opto-isolator wikipedia, lookup

Power MOSFET wikipedia, lookup

Surge protector wikipedia, lookup

Opto-isolator wikipedia, lookup

Current source wikipedia, lookup

Transcript

Electrical Sources (1/3) • Independent Source: Establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit • Dependent Source: Establishes a voltage or current whose value depends on the value of a voltage or current elsewhere in the circuit (also known as controlled source) • Active Circuit Element: Device capable of generating electric energy • Passive Circuit Element: Device that cannot generate electric energy Principles of Electrical Engineering – I (14:332:221) Chapter 2 Notes 14:332:221, Spring 2004 Electrical Sources (3/3) Electrical Sources (2/3) • Ideal voltage source: A circuit element that maintains a prescribed voltage across its terminals regardless of the current flowing in these terminals • Ideal current source: A circuit element that maintains a prescribed current through its terminals regardless of the voltage across these terminals vs Independent Voltage Source + − Independent Current Source + − vs = ρ i x is i s = α vx Ideal dependent voltage-controlled current source Amperes/Volt (A/V) Ideal dependent current-controlled voltage source Volts/Ampere (V/A) 3 is = β ix Ideal dependent current-controlled current source Dimensionless 14:332:221, Spring 2004 4 Electrical Resistance (2/3) Electrical Resistance (1/3) • Ohm’s Law: v = iR • Resistor: A passive circuit element that impedes the flow of electric charge – v: voltage in volts (V) – i: current in amperes (A) – R: resistance in ohms (Ω) ~ Volts per Ampere (V/A) R – Interaction of moving electrons composing the electric current with the atoms composing the conducting material – Electric energy is converted to thermal energy and dissipated in the form of heat – Different materials offer different degrees of resistance 14:332:221, Spring 2004 Ideal dependent voltage-controlled voltage source + vs = µ vx − Dimensionless 14:332:221, Spring 2004 2 5 + v R i= v R + v − R i=− v R − i i • Conductance (G): Reciprocal of resistance G = 1/R Siemens (S), e.g., R = 8Ω ↔ G = 0.25S 14:332:221, Spring 2004 6 1 Electrical Resistance (3/3) Circuit Switch • Resistive Power Dissipation – Resistor always absorbs power from the circuit – p = vi = (iR)i = i2R = v2/R – Describing power in terms of conductance: p = i2/G = v2G p = vi = (iR )i = i 2 R + v + p = −vi = −(− iR )i = i 2 R v R − Short Circuit: R=0 No current resistance in ON state Open Circuit: R=∞ Infinite resistance to current in OFF state OFF Switch: − i i 14:332:221, Spring 2004 7 14:332:221, Spring 2004 d Fig. 2.15: • To “solve” a circuit, need to know: vs – Voltage across every element – Current in every element 14:332:221, Spring 2004 Fig. 2.18: Multiple elements meeting at a single node a i1 vs + b + ic vc c R1 Rc • E.g., Fig. 2.15, 7 unknowns (Assume vs, R1, Rc and Rl are given) – is, i1, ic, il, v1, vc, vl → Require 7 independent equations – Applying Ohm’s Law, 3 equations provided: • v1 = i1R1 (2.13) • vc = icRc (2.14) • vl = ilRl (2.15) b + 10 Ω 120 V Rl − − c Rc 50 Ω 6A 10 – A reference direction must be assigned to every current at a node – E.g., assign a positive sign to current leaving a node and a negative sign to current entering a node – Recalling again 2.15 and applying KCL • • • • • Node a: is − i1 = 0 (2.16) Node b: i1 + ic = 0 (2.17) Node c: −ic − il = 0 (2.17) Node d: il − is = 0 (2.18) Note: (2.15-2.18) provides only 3 independent equations – n nodes yields n−1 independent equations via KCL – Need 4 more independent equations 14:332:221, Spring 2004 + − + ic vc • Kirchhoff’s Current Law (KCL): The algebraic sum of all currents at any node in a circuit equals zero Rl − − − i1 vs Kirchhoff’s Laws (4/6) + − il vl 14:332:221, Spring 2004 Kirchhoff’s dLaws (3/6) il vl + is R1 9 is + − a • Kirchhoff’s Laws provide algebraic relationships for solving circuits • Node: A point where two or more circuit elements meet + − 8 Kirchhoff’s Laws (2/6) Kirchhoff’s Laws (1/6) vs ON R 11 14:332:221, Spring 2004 12 2 Kirchhoff’s Laws (5/6) Kirchhoff’s Laws (6/6) • Loop: Starting at any arbitrary node, one traces a closed path through selected circuit elements and returns to the original node without passing through any intermediate node more than once • Kirchhoff’s Voltage Law (KVL): The algebraic sum of all the voltages around any loop in a circuit equal zero E.g., Fig. 2.15 has a single loop. Choosing Node d as the starting point and tracing the circuit clockwise yields the loop d→vs→Rl→Rc→Rl→d – Must assign an algebraic sign (reference direction) to each voltage in a loop – E.g., assign a positive sign to a voltage drop and a negative sign to a voltage rise (or visa versa) – Considering again Fig. 2.15 and applying KVL in a clockwise direction: • vl − vc + v1 − vs = 0 (2.20) • Combining (2.13-2.15, 2.16-2.18 and 2.20) yields 7 independent equations that may be applied to solve for the 7 unknowns (is,i1,ic,il,v1,vc,vl) 14:332:221, Spring 2004 13 14:332:221, Spring 2004 14 Reducing the Number of Unknowns • Number of unknowns in Fig. 2.15 may be reduced, thus simplifying the circuit – If know current across a resistor, also know the voltage and visa versa • E.g., Fig. 2.15 need only solve for il, ic, and i1 or alternatively vl, vc and v1. • Knowing the current (or voltage) allows voltage (or current) to be derived via Ohm’s Law – If elements are in series, then the currents through each of the series elements are equal • E.g. in Fig. 2.15: is = i1 = −ic = il • Thus the problem is reduced to solving for a single unknown, is: vs = v1 − vc + vl = is(R1 − Rc + Rl) 14:332:221, Spring 2004 15 3