Lecture 15: Inductor & Capacitor

Transcription

1 ECE 1270: Introduction to Electric Circuits 0 Lecture 15: Inductor & Capacitor Chapter 6 Inductance, Capacitance, and Mutual Inductance Sections

2 EE 1270: Introduction to Electric Circuits 1 Inductor

3 Inductor 2 An inductor consists of a coil of conducting wire (e.g. copper) An inductor is a passive element designed to store energy in its magnetic field Inductor exhibits opposition to the change of current flowing through it: this is known as Inductance (unit=henrys or H).

4 Applications of Inductor Power Transmission Lines and Utility Substation 3 Power Supply Tranceiver PCB Memory Control PCB

5 Circuit Symbol Inductor Basics Practical Inductor 4 An inductor opposes an abrupt change in the current through it (the voltage across an inductor can change abruptly) The ideal inductor does not dissipate energy. It takes power from the circuit when storing energy and delivers power to the circuit when returning previously stored energy A practical, non-ideal inductor has small resistive component, called winding resistance: it dissipates energy. A practical, non-ideal inductor also has small winding capacitance due to the capacitive coupling between the conducting coils. Parasitic resistor and inductor are ignored at low frequencies

6 Inductor v L di dt Where L=inductance [H], i=current [A], v=voltage [V], t=time [s] 5 L Any conductor of electric current has inductive properties and may be regarded as an inductor In order to enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil with many turns of conducting wire N A l 2 where N=the number of turns, l=length, A=cross-sectional area, μ=permeability of the core.

7 Example 6.1: Inductor Current-Voltage Characteristics 6 Q: Find and sketch the voltage across the inductor A: Method 1: Solve the inductor equation, Method 2: Simulate

8 Current in terms of Voltage Across the Inductor Example 6.2 (Omit) 7 Q: Find and sketch the inductor current A: Method 1: Solve the inductor equation, Method 2: Simulate

9 AP6.1a, c, g : Voltage, Current, Power, Energy in Inductor 8

10 Combining Inductors What is L eq for series and parallel combinations? 9

11 P6.22b: Series and Parallel Combination of Inductors 10

12 EE 1270: Introduction to Electric Circuits 11 Capacitor

13 Store Charge in Circuits Applications of Capacitors 12 Welding Machine Power Filter Graphene based Flexible Supercapacitor Battery

14 Power Factor Correction in Transmission Line (Ref) Applications of Capacitors AC Adapters 13

15 Tablets and Smart Phones Applications of Capacitors Capacitor Proximity Switch in Elevators 14

16 Circuit Symbol Capacitor Basics Practical Capacitor 15 A Capacitor opposes an abrupt change in the voltage across it (the current across a capacitor can change abruptly) The ideal capacitor takes power from the ciruit and stores the energy: we denote this operation as, "capacitor charges up..." A practical, nonideal capacitor has a small resistive component, called Equivalent Series Resistance (ESR): it discharges the cap. A practical, noideal inductor also has small Equivlent Series Inductance (ESL) due to the capacitive coupling between the capacitor leads or PCB traces or pads We ignore ESR and ESL at low frequencies

17 Ceramic Capacitor Capacitor Electrolytic Capacitor Surface Mount Capacitor 16 A capacitor consists of two conducting layers separated by dielectic material A capacitor is a passive element designed to store energy in its electric field Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates (unit=farads or F)

18 Capacitor Higher the dielectric* constant, higher the capacitance Smaller the gap, higher the capaictance A C ; d q CV dq dt i C dv dt 17 Where, C=capacitance [F], ε=dielectric constant [N/A 2 ], A=overlapping area [m 2 ], d=gap [m], q=charge accumulated on the plates, i=current across the capacitor Larger the area, higher the capacitance * More info on dielectrics can be found at:

19 AP 6.2 Voltage, Current, Power and Energy in a Capacitor 18 v 0... t 0 v 40e t sin(30000t)... t 0 1) Given the voltage find the capacitor current at t=0 2) Find the power delivered to the capacitor at t=π/80 ms 3) Find the energy stored in the capacitor at t=π/80 ms

20 Combining Capacitors What is C eq for series and parallel combinations? 19

21 P6.27: Series and Parallel Combination of Capacitors 20 Q: How do you combine two parallel caps with different voltages?

22 Always Remember!! An inductor will act as a short at DC (low frequency) and open at AC (high frequency) 21 low frequency high frequency A capacitor will act as an open at DC (low frequency) and short at AC (high frequency) low frequency high frequency