chapter 9johnston/ee204_pdf_slides/chapters 8-10/ch09.pdfchapter 9 capacitors. basics of a capacitor...

Chapter 9Chapter 9Capacitors

Basics of a Capacitor

• In its simplest form, a capacitor is an electrical

device constructed of two parallel plates separated

by an insulating material called the dielectric

• In the neutral state, both plates have an equal • In the neutral state, both plates have an equal

number of free electrons

• When a voltage source is connected to the

capacitor, electrons are removed from one plate and

an equal number are deposited on the other plate

• No electrons flow through the dielectric (insulator)

FIGURE 9-1 The basic capacitor.

Thomas L. Floyd

Electronics Fundamentals, 6e

Electric Circuit Fundamentals, 6e

Copyright ©2004 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

All rights reserved.

Illustration of a capacitor storing charge

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Equivalent circuit for a no ideal capacitor

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No Current flows through a capacitor except for undesired leakage current.

How a Capacitor Stores Energy

• A capacitor stores energy in the form of an

electric field that is established by the opposite

charges on the two plates

• A capacitor obeys Coulomb’s law:• A capacitor obeys Coulomb’s law:

A force exists between two point-source charges

that is directly proportional to the product of the

two charges and inversely proportional to the

square of the distance between the charges

The electric field stores energy in a capacitor. The beige area indicates the dielectric.

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Lines of force are created by opposite charges

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The unit for Capacitance is the Farad (F)

1 Farad = 1 Coloumb/1V

Usually specified un Micro-Farads (uF)

Characteristics of a Capacitor

• Capacitance is directly proportional to the physical size of the plates as determined by the plate area

• Capacitance is inversely proportional to the distance between the plates

• The measure of the dielectric material’s ability to establish • The measure of the dielectric material’s ability to establish an electric field is called the dielectric constant. Capacitance is directly proportional to the dielectric constant

• The measure of how much voltage a capacitor can handle across it’s plates is called dielectric strength or breakdown voltage. All capacitors specify a safe voltage at which to operate the capacitor.

• Most capacitors have a very thin dielectric and a very large plate area (often stacked or rolled up).

Capacitance is directly proportional to plate area (A)

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Less plate area = Less Capacitance

Capacitance is inversely proportional to the distance d between the plates

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More distance between plates = Less Capacitance

Charging a capacitor

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Uncharged Cap

Appears as a short

the instant the switch

is closed

Charging Cap

Current drops and

voltage across cap

rises

Charged Cap

Appears as an open

All current stops and

VC = VS

No current except for

leakage current and

capacitor stores the

charge

Discharging a Capacitor

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Current reverses:

High at first then

drops as voltage

drops

Back to where it

started

•This phenomenon often makes it appear that current is passing through the cap

•It does not

•The reversing current goes back to the supply

Fixed Capacitors

• Stacked-foil mica capacitors are made of alternate layers of metal foil and thin

sheets of mica

• Silver mica are formed by stacking mica sheets with silver electrode material

screened on them

• Range from 1pF to 0.1 uF @ 2500V• Range from 1pF to 0.1 uF @ 2500V

Low Capacitance @ High Voltage

Fixed Capacitors

• Ceramic capacitors provide very high dielectric

constants, and relatively large capacitance in a

small physical size

• Capacitance ranges are from 1pF to 2.2µF @ • Capacitance ranges are from 1pF to 2.2µF @

2500V

Medium Capacitance @ High Voltage

(a) Typical ceramic capacitors with radial leads. (b) Construction view

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Up to 2.2uF @ 6kVMedium Capacitance @ Very High Voltage

Electrolytic Capacitors

• Two common types of electrolytic

capacitors are Aluminum and Tantalum

electrolyticselectrolytics

• Safety Warning: The voltage polarity of

these devices must be observed, as reversal

of polarity will usually result in complete

destruction of the capacitor

Electrolytic Capacitors

• Electrolytic capacitors have higher capacitance but

lower voltage ratings and higher leakage current

• They come in capacitance values from 1µF to

200,000 µF, with voltage ratings to 350 V200,000 µF, with voltage ratings to 350 V

High Capacitance @ Low (Polarized) Voltage

Basic construction of axial-lead tubular plastic-film dielectric capacitor.

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Electrolytic capacitors

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Construction view of a typical “tear drop” shaped tantalum electrolytic capacitor

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“Tear Drop” shaped tantalum electrolytic capacitor.

Variable Capacitors

• Variable capacitors are used in circuits when there

is a need to adjust the capacitance value

• Ceramic or mica is a common dielectric

• Capacitance is changed by plate separation

FIGURE 9-16 Schematic symbol for a variable capacitor.

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Schematic symbol for a variable capacitor.

Variable Air Capacitor

•Air Capacitors are used in high frequency (RF)

applications

•The space between the plates (air) is the dielectric

•This is an example of a variable air capacitor probably

used in a radio tuner

Series Capacitors

• When capacitors are connected in series, the total capacitance is less than the smallest capacitance value

• This is because the effective plate separation increases

11

1/C1 + 1/C2 + 1/C3 + … + 1/Cn

Capacitors in series produce a total capacitance that is less than the smallest value

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CT = 76.7pF

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•In a DC Circuit, current stops flowing when the smallest cap is charged

•Vs = VC1 + VC2

FIGURE 9-22 P 406

Capacitor Voltages – The smallest cap holds the largest voltage

And versa visa (The smallest cap charges first halting all current flow)

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V x = (CT/Cx)VS

Parallel Capacitors

• The total parallel capacitance is the sum of all

capacitors in parallel

CT = C1 + C2 + C3 + … + Cn

• This is because the effective plate area increases

FIGURE 9-24

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CT = 560 pF

FIGURE 9-26

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CT = .133uF

FIGURE 9-23 P 407 Capacitors in parallel produce a total capacitance that is the sum of the individual capacitances.

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•Current doesn’t stop until all caps are charged

•VC1 = VC2

RC Time Constant

• The voltage across a capacitor cannot

change instantaneously because a finite time

is required to move charge from one point is required to move charge from one point

to another (limited by circuit resistance)

• The time constant of a series RC circuit is a

time interval that equals the product of the

resistance and the capacitance

ττττ = RC

Current and voltage in a charging and discharging capacitor

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Charging and Discharging• The charging curve is an increasing exponential

• The discharging curve is a decreasing exponential

• It takes 5 time constants to change the voltage by

99% (charging or discharging), this is called the

transient timetransient time

Charge and discharge curves shown together

Charge v

Charge i

Discharge v & i

Formulas for instantaneous charging and discharge

voltages and currents* = On Quiz

General Instantaneous Charging Voltage Formula:(Determine Instantaneous Voltage Charging From an Initial Instantaneous Value)

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Determine Instantaneous Voltages Charging From 0V *

Determine Instantaneous Voltages Discharging to 0V *

Determining the instantaneous voltage during

capacitor charge

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Determine the Instantaneous Voltage across the capacitor at 50 uS

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Determining the instantaneous voltage during capacitor

discharge

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Determine the capacitor voltage 6 ms after the switch is closed

The capacitor is charged

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Capacitive Reactance, XC

• Capacitive reactance (XC) is the opposition to

sinusoidal current, expressed in ohms

• The rate of change of voltage is directly related to

frequencyfrequency

• As the frequency increases, the rate of change of

voltage increases, and thus current ( i ) increases

• An increase in i means that there is less opposition

to current (XC is less)

• XC is inversely proportional to i and to frequency

The current in a capacitive circuit varies directly with the frequency of the source

voltage

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Because the voltage rate of change is higher at higher frequencies,

the capacitive current increases proportionately with the frequency

For a fixed voltage and frequency, the current varies directly with the capacitance

value

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Relationship of Capacitance and Current

Formula for X

Rate of change of a sine wave increases when frequency increases

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Formula for XC

FIGURE 9-41 P 418

Determine XC in the circuit below

1 kHz

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1 kHz

Ohm’s Law for Capacitors

Vrms = I XC

Irms = Vrms/Xc

Xc = VrmsI

Determine the RMS Current in the circuit below

Approx. Equivalent Circuit

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Capacitors in ac Circuits

• When a sine wave signal is applied to a capacitor,

the instantaneous capacitor current is equal to the

capacitance times the instantaneous rate of change

of the voltage across the capacitor of the voltage across the capacitor

• This rate of change is a maximum positive when

the rising sine wave crosses zero

• This rate of change is a maximum negative when

the falling sine wave crosses zero

• The rate of change is zero at the maximum and

minimum of the sine wave

The rates of change of a sine wave

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The higher the rate of voltage change, the higher the capacitor current

Analysis of Capacitive ac Circuit

• The current leads the voltage by 90° in a purely capacitive ac circuit (ICE)

• This is because:

– Current in a capacitor is dependent upon the rate of voltage change

– The highest rate of change in voltage is when it crosses zero

VC ≈ VS

voltage is when it crosses zero volts.

• This is also when the capacitor is closer to being discharged and easily accepts higher current change.

– The least rate of change in voltage is near the peak voltage

– There is zero rate of change in voltage at peak.

• This is also when the capacitor is closest to being charged and doesn’t easily accept much current change.

Close

to

Charged

Close

to

Discharged

Close

to

Charged

Close

to

Discharged

Current is always leading the capacitor voltage by 90°

IC

+90o (Lead)

VS, VC

0o (Reference)

Vector Diagram

Close

to

Charged

Close

to

Discharged

Close

to

Charged

Close

to

Discharged

Power in a Capacitor(Purely Capacitive Circuit)

• Energy is stored by the capacitor during a portion of the voltage cycle; then the stored energy is returned to the source during another portion of the cycle

• True power (P ) is zero, since no energy is • True power (Ptrue) is zero, since no energy is consumed by the capacitor. It just shifts back and forth between the cap and the source.

• Reactive Power (Pr)The overall rate at which a capacitor stores and returns energy. Unit: (VAR)

• Instantaneous power (p) is the instantaneous product of v and i at any given time.

FIGURE 9-45 Power curve for a capacitor.

Reactive Power Formulas

True Power (Ptrue) = 0•There is no energy dissipation, just energy transfer (Except for leakage current)

•The current just shifts back and forth between the cap and the source

(Reactive)

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Instantaneous Power:

•Power is 0 when either V or I are 0

•Power is maximum when V or I are equal (positive or negative)

•Power Frequency is 2X the source frequency

Reactive Power Formulas

Instantaneous Values

FIGURE 9-46Determine the true power and reactive power for the circuit below

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Ptrue = 0

Capacitor Applications

• Since capacitors “pass” ac (Signals) and do not

pass DC, they are used for DC blocking and ac

signal coupling between circuit stages

• Capacitors are used for filtering in power supplies• Capacitors are used for filtering in power supplies

• Capacitors are used to eliminate unwanted ac

signals

An application of a capacitor used to block DC and couple ac in an amplifier

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Capacitors “Pass AC and Block DC”

(Pass Signals/Changing Current and Block DC)

Biased SignalUn-Biased Signal

FIGURE 9-55 Capacitively coupled amplifier.

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Basic block diagram and operation of a dc power supply

Capacitors can also be used to filter out unwanted signals or ripple

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Half-wave and full-wave rectifier operation

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Basic operation of a power supply filter capacitor

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The capacitance of the filter capacitor(s) is usually fairly large

Example of the operation of a bypass capacitor

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Unwanted Signal is “Passed” or”Shunted” to ground

Input

Output

More Capacitor Applications

• Capacitors are used in filters, to select one ac signal

with a certain specified frequency from a wide

range of signals with many different frequencies

– For example, the selection of one radio station and – For example, the selection of one radio station and

rejecting the others (High/Low/Bandpass Filters)

• Capacitors are used in timing circuits to generate

time delays, based on the RC time constant

• Dynamic memories used in computers are simply

very tiny capacitors used as a storage element

Checking a capacitor with an analog ohmmeter. This check shows a good capacitor.

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A typical capacitance meter. (Courtesy of B+K Precision)

Capacitance meters are also included in most modern multimeters too

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