ECE 1270 Introduction to Electric Circuits Suketu Naik

0ECE 1270: Introduction to Electric Circuits

Lecture 15:

Inductor & Capacitor

Chapter 6

Inductance, Capacitance, and

Mutual Inductance

Sections 6.1-6.3

ECE 1270 Introduction to Electric Circuits Suketu Naik

1EE 1270: Introduction to Electric Circuits

Inductor

ECE 1270 Introduction to Electric Circuits Suketu Naik

2Inductor

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).

ECE 1270 Introduction to Electric Circuits Suketu Naik

3Applications of Inductor

Power Transmission Lines and Utility Substation

Power

SupplyTranceiver PCB Memory Control PCB

ECE 1270 Introduction to Electric Circuits Suketu Naik

4Inductor Basics

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

Circuit Symbol Practical Inductor

ECE 1270 Introduction to Electric Circuits Suketu Naik

5Inductor

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

dt

diLv

Where L=inductance [H],

i=current [A],

v=voltage [V],

t=time [s]

where N=the number of turns,

l=length, A=cross-sectional area,

μ=permeability of the core.

l

ANL

2

ECE 1270 Introduction to Electric Circuits Suketu Naik

6Example 6.1: Inductor Current-Voltage Characteristics

Q: Find and sketch the voltage across the inductor

A: Method 1: Solve the inductor equation, Method 2: Simulate

ECE 1270 Introduction to Electric Circuits Suketu Naik

7Current in terms of Voltage Across the Inductor

Q: Find and sketch the inductor current

A: Method 1: Solve the inductor equation, Method 2: Simulate

Example 6.2 (Omit)

ECE 1270 Introduction to Electric Circuits Suketu Naik

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

ECE 1270 Introduction to Electric Circuits Suketu Naik

9Combining Inductors

What is Leq for series and parallel combinations?

ECE 1270 Introduction to Electric Circuits Suketu Naik

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

ECE 1270 Introduction to Electric Circuits Suketu Naik

11EE 1270: Introduction to Electric Circuits

Capacitor

ECE 1270 Introduction to Electric Circuits Suketu Naik

12Applications of CapacitorsStore Charge in Circuits

Welding Machine Power FilterGraphene based Flexible Supercapacitor

Battery

ECE 1270 Introduction to Electric Circuits Suketu Naik

13Applications of CapacitorsPower Factor Correction in

Transmission Line (Ref) AC Adapters

ECE 1270 Introduction to Electric Circuits Suketu Naik

14Applications of CapacitorsTablets and Smart Phones Capacitor Proximity Switch

in Elevators

ECE 1270 Introduction to Electric Circuits Suketu Naik

15Capacitor Basics

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

Circuit Symbol Practical Capacitor

ECE 1270 Introduction to Electric Circuits Suketu Naik

16Capacitor

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)

Ceramic Capacitor Surface Mount

Capacitor

Electrolytic Capacitor

ECE 1270 Introduction to Electric Circuits Suketu Naik

17Capacitor

Higher the dielectric* constant, higher the capacitance

Smaller the gap, higher the capaictance

Larger the area, higher the capacitance

;d

AC

Where, C=capacitance [F], ε=dielectric

constant [N/A2], A=overlapping area

[m2], d=gap [m], q=charge accumulated

on the plates, i=current across the

capacitor

dt

dVCi

dt

dq

CVq

* More info on dielectrics can be found at: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html

ECE 1270 Introduction to Electric Circuits Suketu Naik

18AP 6.2 Voltage, Current, Power and Energy in a Capacitor

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

0)...30000sin(40

0....0

15000

ttev

tv

t

ECE 1270 Introduction to Electric Circuits Suketu Naik

19Combining Capacitors

What is Ceq for series and parallel combinations?

ECE 1270 Introduction to Electric Circuits Suketu Naik

20P6.27: Series and Parallel Combination of Capacitors

Q: How do you combine two parallel caps with different

voltages?

ECE 1270 Introduction to Electric Circuits Suketu Naik

21Always Remember!!

An inductor will act as a short at DC (low frequency) and open at

AC (high frequency)

A capacitor will act as an open at DC (low frequency) and short

at AC (high frequency)

low frequency

high frequency

low frequency

high frequency