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Chapter 1

Resistors, Capacitors, an

Inductor

by Glen Ball

10.1 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1.1 Resistor Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1.2 Combining Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1.3 Types of Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.2 Network Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.3 Characteristics of Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4 Types of Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.1 Film Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.2 Paper Foil-Filled Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.3 Mica Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.4 Ceramic Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.5 Electrolytic Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.6 Suppression Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2.4.7 Supercapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1 Types of Inductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.1 Air Core Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.2 Axial Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.3 Bobbin Core Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.4 Ceramic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.5 Epoxy-Coated Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.6 Ferrite Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.7 Laminated Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.8 Molded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.9 MPP Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.10 Multilayer Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.3.1.11 Phenolic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.12 Powdered Iron Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.13 Radial Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.14 Shielded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.15 Slug Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.16 Tape Wound Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.1.17 Toroidal Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3.2 Impedance Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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10.3.3 Ferrite Beads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.3.4 Skin Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.3.5 Shielded Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.4 Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.5 Resonant Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272


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Resistors, Capacitors, and Inductors

10.1 Resistors

Resistance is associated with the phenomenon of energydissipation. In its simplest form, it is a measure of theopposition to the flow of current by a piece of electricmaterial. Resistance dissipates energy in the form ofheat; the best conductors have low resistance and

produce little heat, whereas the poorest conductors havehigh resistance and produce the most heat. For example,if a current of 10 A flowed through a resistance of 1 ,the heat would be 100 W. If the same current flowedthrough 100 , the heat would be 10,000 W, which isfound with the equation

(10-1)

where,Pis the power in watts,Iis the current in amperes,

R is the resistance in ohms.

In a pure resistancei.e. one without inductance orcapacitancethe voltage and current phase relation-ship remains the same. In this case the voltage dropacross the resistor is

(10-2)

where,Vis the voltage in volts,Iis the current in amperes,R is the resistance in ohms.

All resistors have one by-product in common whenput into a circuit, they produce heat because power isdissipated any time a voltage, V, is impressed across aresistanceR. This power is calculated from Eq. 10-1 or

(10-3)

where,Pis the power in watts,Vis the voltage in volts,R is the resistance in ohms.

Changing the voltage, while holding the resistanceconstant, changes the power by the square of thevoltage. For instance, a voltage change from 10 V to12 V increases the power 44%. Changing the voltagefrom 10 V to 20 V increases the power 400%.

Changing the current while holding the resistanceconstant has the same effect as a voltage change.Changing the current from 1 A to 1.2 A increases the

power 44%, whereas changing from 1 A toincreases the power 400%.

Changing the resistance while holding the voconstant changes the power linearly. If the resistandecreased from 1 k to 800 and the voltage remthe same, the power will increase 20%. If the resis

is increased from 500 to 1 k , the powerdecrease 50%. Note that an increase in resistance ca decrease in power.

Changing the resistance while holding the cuconstant is also a linear power change. In this exaincreasing the resistance from 1 k to 1.2 k incrthe power 20%, whereas increasing the resistance1 k to 2 k increases the power 100%.

It is important in sizing resistors to take into acchanges in voltage or current. If the resistor remconstant and voltage is increased, current also incrlinearly. This is determined by using Ohms Law

10-1 or 10-3.Resistors can be fixed or variable, have tolerfrom 0.5% to 20%, and power ranges from 0.1hundreds of watts

10.1.1 Resistor Characteristics

Resistors will change value as a result of apvoltage, power, ambient temperature, frequency chmechanical shock, or humidity.

The values of the resistor are either printed oresistor, as in power resistors, or are color coded o

resistor, Fig. 10-1. While many of the resistoFig. 10-1 are obsolete, they are still found in granold radio you are asked to repair.

Voltage Coefficient. The voltage coefficientis thof change of resistance due to an applied voltage, in percent parts per million per volt (%ppm/V)most resistors the voltage coefficient is negativeis, the resistance decreases as the voltage increHowever, some semiconductor devices increase in tance with applied voltage. The voltage coefficivery high valued carbon-film resistors is rather and for wirewound resistors is usually negligible.

tors are resistive devices designed to have a voltage coefficient.

Temperature Coefficient of Resistance. The temture coefficient of resistance (TCR) is the rate of chin resistance with ambient temperature, usually sta

parts per million per degree Celsius (ppm/C). Mtypes of resistors increase in value as the temperincreases, while others, particularly hot-molded ctypes, have a maximum or minimum in their resis

P I2R=

V IR=

PV

2

R------=


5/33

244 Chapter 10

curves that gives a zero temperature coefficient at sometemperature. Metal film and wirewound types havetemperature coefficient values of less than 100 ppm/C.Thermistors are resistance devices designed to have alarge temperature coefficient.

The percent temperature coefficient of resistance is

(10-4)

where,TCR is the temperature coefficient in percent per C,R is the resistance at reference temperature,ris the resistance at test temperature,TR is the reference temperature in C,TTis the test temperature in C.

It is better to operate critical resistors with a limitedtemperature rise.

Noise. Noise is an unwanted voltage fluctuation gener-ated within the resistor. The total noise of a resistoralways includes Johnson noise, which depends only onresistance value and the temperature of the resistanceelement. Depending on the type of element and itsconstruction, total noise may also include noise caused

by current f low and by cracked bodies and loose endcaps or leads. For adjustable resistors, noise is alsocaused by the jumping of the contact over turns of wireand by an imperfect electrical path between the contactand resistance element.

Hot-Spot Temperature. The hot-spot temperature isthe maximum temperature measured on the resistor dueto both internal heating and the ambient operatingtemperature. The maximum allowable hot-spot temper-ature is predicated on the thermal limits of the materialsand the resistor design. The maximum hot-spot temper-ature may not be exceeded under normal operatingconditions, so the wattage rating of the resistor must belowered if it is operated at an ambient temperaturehigher than that at which the wattage rating was estab-lished. At zero dissipation, the maximum ambienttemperature around the resistor may be its maximumhot-spot temperature. The ambient temperature for aresistor is affected by surrounding heat-producingdevices. Resistors stacked together do not experiencethe actual ambient temperature surrounding the outsideof the stack except under forced cooling conditions.

Carbon resistors should, at most, be warm to touch,40C (140F), while wirewound or ceramic resistors aredesigned to operate at temperatures up to 140C(284F). Wherever power is dissipated, it is imperativethat adequate ventilation is provided to eliminateFigure 10-1. Color codes for resistors.

Multiplier

1st significant figure2nd significant figure

Body Dot System

1st significant figure

2nd significant figureMultiplier

Tolerance Multiplier


Multiplier Tolerance


ToleranceBody-End Band System

Multiplier Tolerance


Dot Band System

Multiplier MultiplierTolerance Tolerance

2nd significant figure 2nd significant figure1st significant figure 1st significant figure

Color Band System

Resistors with black body are composition, noninsulated.

Resistors with colored body are composition, insulated.

Wirewound resistors have the 1st color band double

width.

Multiplier


2nd significant figure

Miniature Resistor System

Body-End-Dot System

Carbon composition Carbon film

3rd significant figure

Black 0 1

Brown 1 10 1% 1.0Red 2 100 2% 0.1Orange 3 1000 3% 0.01Yellow 4 10,000 4% 0.001Green 5 100,000 Blue 6 1,000,000 Violet 7 10,000,000 Gray 8 100,000,000 White 9 Solderable*Gold 0.1 5% Silver 0.01 10% No Color 20%

Color Digit Multiplier Tolerance Failure Rate

TCRR r( )100TR TT( )R

---------------------------=


6/33


thermal destruction of the resistor and surroundingcomponents.

Power Coefficient. The power coef f icient i s theproduct of the temperature coefficient of resistance andthe temperature rise per watt. It is given in percent perwatt (%/W), and is the change in value resulting fromapplied power.

Ac Resistance. The acresistance value changes withfrequency because of the inherent inductance andcapacitance of the resistor plus the skin effect, eddycurrent losses, and dielectric loss.

Ambient Temperature Effect. W h en o p e ra t i n g aresistor in free air at high ambient temperature, the

power capabilities must be derated, Fig. 10-2. Free air isoperation of a resistor suspended by its terminals in freespace and still air with a minimum clearance of one footin all directions to the nearest object.

Grouping. Mounting a number of resistors in closeproximity can cause exc essive temperature riserequiring derating the power capabilities, Fig 10-3. Thecurves are for operation at maximum permissible hotspot temperature with spacing between the closest

points of the resistors. Derating could be less if operatedat less than permissible hot spot temperature.

Enclosure. Enclosures create a rise in temperature dueto the surface area, size, shape, orientation, thickness,

material and ventilation. Fig. 10-4 indicates the eon a resistor enclosed in an unpainted steel sheet

box, 0.32 inches thick without vents. Determininderating is often by trial and error.

f

Figure 10-2. Resistor derating for elevated ambient temper-ature. Courtesy Ohmite Mfg. Co.

100

80

60

40

20

00 40 80 120 160 200 240 280 320 360 400

Ambient temperature riseoC

%ratedwattage

U.L. - NEMA - Industrial Standard

Mil R-26

Figure 10-3. Power derating for grouping resistors. tesy Ohmite Mfg. Co.

Figure 10-4. Effect of the size of an enclosure on a 53/4 inch 6

1/2 inch resistor. Courtesy of Ohmite Mfg

12

11

10

9

8

7

6

5

4

3

2

140 50 60 65 70 75 80 85 90 95 1

% of single unit free air rating

Numberofresistorsingroup

1 inch space

2 inch space

3/4 inch space

300

200

100

0

0 25 50 75 100% rated load

TemperatureriseoC

500

400

300

200

100

0

A

B

C

D

E

A. Resistor in 33/8 inch 33/8 inch 8 inch box.

B. Resistor in 513/16 inch 513/16 inch 12

3/4 inch bo

C. Resistor in free air.

D. Box temperaturesmall.

E. Box temperaturelarge.

F. Unpainted sheet metal box, 0.32 inch thick steel,

no vents.

F


7/33

246 Chapter 10

Forced Air Cooling. Resistors and components can beoperated at higher than rated wattage with forced aircooling, Fig. 10-5. The volume of cooling air requiredto keep the resistor temperature within limits can befound with the equation

(10-5)

where,

Volume of airis in cubic feet per minute,

Tis the permissible temperature rise in degrees F,KW is the power dissipated inside the enclosure in

kilowatts.

Air density at high altitudes causes less heat to bedissipated by convection so more forced air would berequired.

Pulse Operation. A resistor can usually be operatedwith a higher power in the pulse mode than in a contin-uous duty cycle. The actual increase allowed dependson the type of resistor. Fig. 10-6 is the percent of contin-uous duty rating for pulse operation for a wirewoundresistor. Fig. 10-7 is the percent of continuous dutyrating for pulse operation for typical NEMA dutycycles. Fig. 10-8 shows the percent of continuous dutyrating for pulse operation of a 160 W vitreous enam-

eled resistor.

10.1.2 Combining Resistors

Resistors can be combined is series or parallel orseries/parallel.

Resistors in series. The total resistance of resistorsconnected in series is the summation of the resistors.

(10-6)

The total resistance is always greater than the largestresistor.

Figure 10-5. Percent of free air rating for a typical resistorcooled by forced air. Courtesy of Ohmite Mfg. Co.

Volume of air 3170T------------KW=

400

350

300

250

200

150

1000 500 1000 1500

Air velocityft/min

%r

atedwatts

Figure 10-6. Effect of pulse operation on wirewound resis-tors. Courtesy of Ohmite Mfg. Co.

Figure 10-7. Percent of continuous duty rating for pulseoperation of small and medium size vitreous enameledresistors. Courtesy of Ohmite Mfg. Co.

Figure 10-8. Percent of continuous duty rating for pulseoperation of a 160 W vitreous enameled resistor. Courtesy

of Ohmite Mfg. Co.

15

30

45

75

70

75

15

15

15

15

10

5

OnOffSeconds

0 100 200 300 400 500 600 700 800% of rated load

1000

700

500

300

200

100

7050

30

20

10

75

3

2

11 2 5 710 20 50 100 200 500 1k 2k 5k 10k

Off times

Ontimes

125%

200%

500%

1000%

10 W

50 W

1000

700

500

300

200

100

7050

30

20

10

75

3

2

1

1 2 5 710 20 50 100 200 500 1k 2k 5k 10kOff times

Ontimes

125%

150%

200%

500%

!000%

RT R1 R2 Rn+ +=


8/33


Resistors in Parallel. The total resistance of resistorsin parallel is

(10-7)

If two resistors are in parallel use:

(10-8)

When all of the resistors are equal, divide the valueof one resistor by the number of resistors to determinethe total resistance. The total resistance is always lessthan the smallest resistor.

To determine the value of one of the resistors when

two are in parallel and the total resistance and oneresistor in known, use

(10-9)

10.1.3 Types of Resistors

Every material that conducts electrical current has resis-tivity, which is defined as the resistance of a material toelectric current. Resistivity is normally defined as theresistance, in ohms, of a 1 cm per side cube of the mate-

rial measured from one surface of the cube to the oppo-site surface. The measurement is stated in ohms percentimeter cubed (/cm3). The inverse of resistivity isconductivity. Good conductors have low resistivity, andgood insulators have high resistivity. Resistivity isimportant because it shows the difference betweenmaterials and their opposition to current, making it

possible for resistor manufacturers to offer productswith the same resistance but differing electrical, phys-ical, mechanical, or thermal features.

Following is the resistivity of various materials:

Carbon-Composition Resistors. Carbon-compositionresistors are the least expensive resistors and are widely

used in circuits that are not critical to input noise anot require tolerances better than 5%.

The carbon-composition, hot-molded version iscally the same product it was more than 50 yearsBoth the hot- and cold-molded versions are madea mixture of carbon and a clay binder. In some ver

the composition is applied to a ceramic core or ature, while in the inexpensive version, the compois a monolithic rigid structure. Carbon-composresistors may be from 1 to many megohm0.14 W. The most common power rating is W W with resistance values from 2 22 M.

Carbon-composition resistors can withstand hsurge currents than carbon-film resistors. Resisvalues, however, are subject to change upon absorof moisture and increase rapidly at temperatures above 60C (140F). Noise also becomes a factor carbon-composition resistors are used in audio

communication applications. A carbon-core resistoexample, generates electrical noise that can reducreadability of a signal or even mask it completely.

Carbon-Film Resistors. Carbon-film resistorleaded ceramic cores with thin films of carbon apCarbon film resistors offer closer tolerances and btemperature coefficients than carbon composition tors. Most characteristics are virtually identicamany general purpose, noncritical applications whigh reliability, surge currents, or noise are not crfactors.

Metal Film Resistors. Metal film resistors are didevices formed by depositing metal or metal oxideon an insulated core. The metals are usually enichrome sputtered on ceramic or tin oxide on ceor glass. Another method of production is to scre

paint powdered metal and powdered glass that is min an ink or pastelike substance on a porous cersubstrate. Firing or heating in an oven bonds the rials together. This type of resistor technology is ccermet technology.

Metal film resistors are most common in the 101 M range and 18 W to 1 W with tolerances of1

The TCR is in the 100 ppm/C range for alltechnologies. Yet there are subtle differences:

Cermet covers a wider resistance range and hahigher power than nichrome deposition.

Nichrome is generally preferred over tin oxide upper and lower resistance ranges and can prTCRs that are lower than 50 ppm/C.

Tin oxide is better able to stand higher power dition than nichrome.

Material ResistivityAluminum 0.0000028

Copper 0.0000017

Nichrome 0.0001080

Carbon (varies) 0.0001850

Ceramic (typical) 100,000,000,000,000 or (1014)

RT1

1R1------ 1

R2------

1Rn------+ +

----------------------------------------=

RTR1 R2

R1 R2+------------------=

R2RT R1

R1 RT------------------=


9/33

248 Chapter 10

Wirewound Resistors. Wirewound resistors haveresistive wire wound on a central ceramic core. One ofthe oldest technologies, wirewounds provide the bestknown characteristics of high temperature stability and

power handling ab il ity. Nichrome, Manganin , andEvanohm are the three most widely used wires for wire-

wound resistors.W i rewo u n d r e s i s t o r s a r e u s u a l l y i n t h e

0.1 250 k range. Tolerance is 2% and TCR is10 ppm/C.

Wirewound resistors are generally classed as poweror instrument-grade products. Power wirewounds,capable of handling as much as 1500 W, are woundfrom uninsulated coarse wire to provide better heatdissipation. Common power ratings are 1.5 W, 3 W,5 W, 8 W, 10 W, 20 W, 25 W, 50 W, 100 W, and 200 W.

Instrument-grade precision wirewound resistors aremade from long lengths of finely insulated wire. After

winding, they are usually coated with a ceramicmaterial.

All wirewound resistors are classed as air-coreinductors and the inductive reactance alters the highfrequency resistive value. This problem is directly

proportional wi th frequency. Specia l windings areuseful to cancel reactance at audio frequencies. Becauseof the severity of the problem, these resistors cannot beused at high frequencies.

Noninductive Resistors. Non-inductive resistors areused for high frequency applications. This is accom-

plished by utilizing the Ayrton-Perry type of wiring, i.e.two windings connected in parallel and wound in oppo-site directions. This keeps the inductance and distrib-uted capacitance at a minimum. Table 10-1 is acomparison of MEMCOR-TRUOHM type FR10, FR50,VL3 and VL5 resistors.

Resistor Networks. With the advent of printed circuitboards and integrated circuits, resistor networks becamepopular. The resistive network may be mounted in asingle-in-line package (SIP) socket or a dual-in-line

package (DIP) socketthe same as the ones used forintegrated circuits. The most common resistor networkhas 14 or 16 pins and includes 7 or 8 individual resistorsor 12 to 15 resistors with a common terminal. In mostresistor networks the value of the resistors are the same.

Networks may also have special value resistors and inter-connections for a specific use, as shown in Fig. 10-9.

The individual resistors in a thick-film network canhave a resistance value ranging from 10 to 2.2 Mand are normally rated at 0.125 W per resistor. Theyhave normal tolerances of2% or better and a tempera-

ture coefficient of resistance 100 ppm/C from 55Cto +125C (67F to +257F).

Thin-film resistors are almost always specializedunits and are packaged as DIPs or flatpacks. (Flatpacksare soldered into the circuit.) Thin-film networks usenickel chromium, tantalum nitride, and chromiumcobalt vacuum depositions.

Variable Resistors. Variable resistors are ones whosevalue changes with light, temperature, or voltage orthrough mechanical means.

Photocells (Light-Sensitive Resistors). Photocells areused as offon devices when a light beam is broken oras audio pickups for optical film tracks. In the latter, thesound track is either a variable density or variable area.Whichever, the film is between a focused light sourceand the photocell. As the light intensity on the photocellvaries, the resistance varies.

Table 10-1. Inductance Comparison of Standard and

Non-Inductive Windings.

Approximate Frequency Effect

Stock inductive

winding

Non-inductive

winding

Type Resistance

()LS

(H)

LS

(H)

CP

(F)

FR10 (10 W) 25 5.8 0.01

100 11.0 0.16

500 18.7 0.02

1000 20.8 0.75

5000 43.0 1.00

FR50 (50 W) 25 6.8 0.05

100 >100.0 0.40

500 >100.0 0.31

1000 >100.0 1.10

5000 >100.0 1.93

VL3 (3 W) 25 1.2 0.02

100 1.6 0.07

500 4.9 0.47

1000 4.5 0.70

5000 3.0 1.00

VL5 (5 W) 25 2.5 0.08

100 5.6 0.14

500 6.4 0.03

1000 16.7 0.65

5000 37.0 0.95

Courtesy Ohmite Mfg. Co.


10/33


Photocells are rated by specifying their resistance atlow and high light levels. These typically vary from600 110 k (bright), and from 100 k200 M

(dark). Photocell power dissipation is between 0.005 Wand 0.75 W.

Thermistors. Thermistors, thermal-sensitive resistors,may increase or decrease their resistance as tempera-ture rises. If the coefficient of resistance is negative, theresistance decreases as the temperature increases; if

positive, the res istance increases with an increase intemperature. Thermistors are specified by how theirresistance changes for a 1C change in temperature.They are also rated by their resistance at 25C and bythe ratio of resistance at 0C and 50C. Values varyfrom 2.5 1 M at room temperature with powerratings from 0.11 W.

Thermistors are normally used as temperature-sensingdevices or transducers. When used with a transistor, theycan be used to control transistor current with a change intempera tu re . As the t rans i s to r hea t s up , theemitter-to-collector current increases. If the power supplyvoltage remains the same, the power dissipation in thetransistor increases until it destroys itself through thermalrunaway. The change in resistance due to temperature

change of the thermistor placed in the base circuitransistor can be used to reduce base voltage and, fore, reduce the transistor emitter to collector curren

properly matching the temperature coefficients of thdevices, the output current of the transistor can befairly constant with temperature change.

Varistors. Varistors (voltage-sensitive resistorsvoltage-dependent, nonlinear resistors which symmetrical, sharp breakdown characteristics sim

back-to-back Zener diodes. They are designed forsient suppression in electrical circuits. The trancan result from the sudden release of previously senergyi.e., electromagnetic pulse (EMP)orextraneous sources beyond the control of the cdesigner, such as lightning surges. Certain semicotors are most susceptible to transients. For exampleand VLSI circuits, which may have as many as 2components in a 0.25 inch 0.25 inch area,

damage thresholds below 100 J.The varistoris mostly used to protect equip

from power-line surges by limiting the peak voacross its terminals to a certain value. Abovevoltage, the resistance drops, which in turn tenreduce the terminal voltage. Voltage-variable resor varistors are specified by power dissip(0.25 1.5 W) and peak voltage (30300 V).

Thermocouples. While not truly a resistor, thermples ar e used fo r temperat ure meas urement. operate via the Seebeck Effect which states tha

dissimilar metals joined together at one end prodvoltage at the open ends that varies as the temperatthe junction varies. The voltage output increases atemperature increases. Thermocouples are rugged, rate, and have a wide temperature range. They require a exitation source and are highly responThermoouples are tip sensitive so they measurtemperature at a very small spot. Their output issmall (tens to hundreds of microvolts, and is nonlrequiring external linearization in the form of coldtion compensation.

Never use copper wire to connect a thermocou

the measureing device as that constitutes anthermocouple.

Resistance Temperature Detectors. RTDs are accurate and stable. Most are made of platinumwound around a small ceramic tube. They can bemally shocked by going from 100C to 195times with a resulting error less than 0.02C.

RTDs feature a low resistance-value chantemperature (0.1 /1C. RTDs can self heat, ca

Figure 10-9. Various types of resistor networks.

1

2

3

4

5

7 8

9

10

11

12

13

14

6

1

2

3

4

5

7 8

9

10

11

12

13

14

6

1

2

3

4

5

7

8

9

10

11

12

13

14

6


11/33

250 Chapter 10

inaccurate readings, therefore the current through theunit should be kept to 1 mA or less. Self heating canalso be controlled by using a 10% duty cycle rather thanconstant bias or by using an extremely low bias whichcan reduce the SNR. The connection leads may causeerrors if they are long due to the wire resistance.

Potentiometers and Rheostats. Th e r e s i s t an ce o f po ten ti ometers (pots), and rheostats is varied bymechanically varying the size of the resistor. They arenormally three terminal devices, two ends and onewiper, Fig. 10-10. By varying the position of the wiper,the resistance between either end and the wiper changes.Potentiometers may be wirewound or nonwirewound.The nonwirewound resistors usually have either a carbonor a conductive plastic coating. Potentiometers or potsmay be 300 single turn or multiple turn, the mostcommon being 1080 three turn and 3600 ten turn.

Wirewound pots offer TCRs of50 ppm/C andtolerances of5%. Resistive values are typically10 100 k, with power ratings from 1 W to 200 W.

Carbon pots have TCRs of 4 0 0 p p m/ C to800 ppm/C and tolerances of20%. The resistiverange spans 50 2 M, and power ratings are gener-ally less than 0.5 W.

Potentiometers may be either linear or nonlinear, asshown in Fig. 10-11. The most common nonlinear potsare counterclockwise semilog and clockwise semilog.The counterclockwise semilog pot is also called anaudio taper pot because when used as a volume control,it follows the human hearing equal loudness curve. If alinear pot is used as a simple volume control, only aboutthe first 20% of the pot rotation would control theusable volume of the sound system. By using an audiotaper pot as in F ig. 10-11 curve C2, the entire pot isused. Note there is only a 10%20% change in resis-tance value between the common and wiper when the

pot is 50% rotated.

Potentiometers are also produced with various tapsthat are often used in conjunction with loudnesscontrols.

Potentiometers also come in combinations of two ormore units controlled by a single control shaft orcontrolled individually by concentric shafts. Switches

with various contact configurations can also be assem-bled to single or ganged potentiometers and arranged foractuation during the first few degrees of shaft rotation.

A wirewound potentiometeris made by windingresistance wire around a thin insulated card, Fig.10-12A. After winding, the card is formed into a circleand fitted around a form. The card may be tapered, Fig.10-12B, to permit various rates of change of resistanceas shown in Fig 10-11. The wiper presses along the wireon the edge of the card.

Contact Resistance. Noisy potentiometers have been aprob lem that has plagued audio ci rcui ts for year s.Although pots have become better in tolerance andconstruction, noise is still the culprit that forces pots to

be replaced. Noise is usually caused by dirt or, in thecase of wirewound potentiometers, oxidation. Manycircuits have gone up in smoke because bias-adjustingresistors, which are wirewound for good TCR, oxidizeand the contact resistance increases to a point where it ismore than the value of the pot. This problem is most

Figure 10-10. Three terminal potentiometer.

High

Low

Wiper

Low

High

Wiper

Low

Rear view

Figure 10-11. Tapers for six standard potentiometers inresistivity versus rotation.

100

80

60

40

20

00 10 20 30 40 50 60 70 80 90 100Left terminal

Percent clockwise rotationRight terminal

C5

C3

C6

C1C4

C2

Linear taper, general-purpose control for television

picture adjustments. Resistance proportional to

shaft rotation.

Left-hand semilog taper for volume and tone

controls. 10% of resistance at 50% rotation.

Right-hand semilog taper, reverse of C2. 90% of

resistance at 50% of rotation.

Modified left-hand semilog taper for volume and

tone controls. 20% of resistance at 50% of rotation.

Modified right-hand semilog taper, reverse of C4.

80% of resistance at 50% of rotation.

Symmetrical straight-line taper with slow resistance

change at either end. Used principally as tone

control or balance control.

C1.

C2.

C3.

C4.

C5.

C6.

%resistance

Percent counter-clockwise rotation

100 90 80 70 60 50 40 30 20 10 0


12/33


noticeable when trying to adjust a bias voltage with an

old oxidized pot.Sometimes the pot can be cleaned by spraying it with

a contact cleaner or silicone and then vigorouslyrotating it. Usually, however, it is best to replace it

because anything else is only temporary.Any dc voltage present on the pot is also a source of

noise. Such voltage is often produced by leaky couplingcapacitors at the input connector or output circuit of thewiper, allowing dc voltage to appear at the wipercontact. If there is a resistance between the resistor andthe wiper, the dc current flowing through the wipercontact to the output stage will create a voltage drop.

Because the wiper is moving, the contact resistanceconstantly changes creating what looks like a varying acvoltage. Using Fig. 10-13, the value at VLoad, whether acor dc, can be calculated with Eqs. 10-10 and 10-11. Ifthe wiper resistance is 0i.e., a perfect potthe outputvoltage VLoadis

(10-10)

where,

If a pot wiper has a high resistance,Rw, the outputvoltage VLoadis

(10-11)

where,

.

10.2 Capacitors

Capacitors are used for both dc and ac applicationdc circuits they are used to store and release energyas filtering power supplies and for providindemand, a single high voltage pulse of current.

In ac circuits capacitors are used to bloc

allowing only ac to pass, bypassing ac frequencidiscriminating between higher and lower ac frecies. In a circuit with a pure capacitor, the currenlead the voltage by 90.

The value of a capacitor is normally written ocapacitor and the sound engineer is only requirdetermine their effect in the circuit.

Where capacitors are connected in series withother, the total capacitance is

(1

and is always less than the value of the smacapacitor.

When connected in parallel, the total capacitanc

(1

and is always larger than the largest capacitor.When a dc voltage is applied across a gro

capacitors connected in series, the voltage drop athe combination is equal to the applied voltagedrop across each individual capacitor is inve

proportional to its capaci tance, and assuming capacitor has an infinitely large effective shunt tance, can be calculated by the equation

(1

where,VC is the voltage across the individual capacitor i

series (C1, C2,Cn) in volts,

Figure 10-12. Construction of a wirewound resistor.

Wiper

Wiper

End viewA. Fixed card wirewound resistor.

B. Tapered card wirewound resistor.

VLo ad V1Ry

R1 Ry+------------------

=

RyR2RLo ad

R2 RLo ad+--------------------------=

VLo ad VwRLo ad

Rw RLo ad+---------------------------

=

Vw V1R2 Rw RLo ad+( )

R2 Rw RLo ad+ +---------------------------------------

=

Figure 10-13. Effects of wiper noise on potentio

output.

Vin

C1

C2

RLeakage

R2

R1

RW

RLoad

V1

VW VLoad

CT1

1

C1

------1

C2

------ 1

Cn

------+ +-----------------------------------------=

CT C1 C2 Cn+ +=

VC VACX

CT------

=


13/33

252 Chapter 10

VA is the applied voltage in volts,CX is the capacitance of the individual capacitor under

consideration in farads,CTis the sum of all of the capacitors in series.

When used in an ac circuit, the capacitive reactance,

or the impedance the capacitor injects into the circuit, isimportant to know and is found with the equation:

(10-15)

where,XCis the capacitive reactance in ohms,fis the frequency in hertz,Cis the capacitance in farads.

To determine the impedance of circuits with resis-tance, capacitance, and inductance, see Section 10.4.

Capacitance is the concept of energy storage in anelectric field. If a potential difference is found betweentwo points, an electric field exists. The electric field isthe result of the separation of unlike charges, therefore,the strength of the field will depend on the amounts ofthe charges and their separator. The amount of worknecessary to move an additional charge from one pointto the other will depend on the force required and there-fore upon the amount of charge previously moved. In acapacitor, the charge is restricted to the area, shape, andspacing of the capacitor electrodes, sometimes knownasplates, as well as the property of the material sepa-

rating the plates.When electrical current flows into a capacitor, a force

is established between two parallel plates separated by adielectric. This energy is stored and remains even afterthe input current flow ceases. Connecting a conductoracross the capacitor provides a plate-to-plate path bywhich the charged capacitor can regain electron balance,that is, discharge its stored energy. This conductor can

be a resistor, hard wire, or even ai r. The value of aparallel plate capacitor can be found with the equation

(10-16)

where,Cis the capacitance in farads,x is 0.0885 whenA and dare in cm, and 0.225 whenA

and dare in inches, is the dielectric constant of the insulation,Nis the number of plates,A is the area of the plates,dis the spacing between the plates.

The work necessary to transport a unit charge fromone plate to the other is

(10-17)where,e is the volts expressing energy per unit charge,

kis the proportionality factor between the work neces-sary to carry a unit charge between the two plates andthe charge already transported and is equal to 1/Cwhere Cis the capacitance in farads,

gis the coulombs of charge already transported.

The value of a capacitor can now be calculated fromthe equation

(10-18)

where,q is the charge in coulombs,e is found with Eq. 10-17.

The energy stored in a capacitor is found with theequation

(10-19)

where,Wis the energy in joules,Cis the capacitance in farads,Vis the applied voltage in volts.

Dielectric Constant (K). The dielectric constant is theproperty of a given material that determines the amountof electrostatic energy that may be stored in that material

per uni t volume for a given vol tage. The value of Kexpresses the ratio of a capacitor in a vacuum to oneusing a given dielectric. The K of air is 1 and is the refer-ence unit employed for expressing K of other materials.If K of the capacitor is increased or decreased, the capac-itance will increase or decrease respectively if otherquantities and physical dimensions are kept constant.Table 10-2 is a listing of K for various materials.

XC1

2fC-------------=

Cx N 1( )A[ ]

d--------------------------------

1310=

Table 10-2. Comparison of Capacitor Dielectric

Constants

Dielectric K (Dielectric Constant)

Air or vacuum 1.0

Paper 2.06.0

Plastic 2.16.0

Mineral oil 2.22.3

Silicone oil 2.72.8

e kg=

Cq

e---=

WCV

2

2----------=


14/33


The dielectric constant of materials is generallyaffected by both temperature and frequency, except forquartz, Styrofoam, and Teflon, whose dielectricconstants remain essentially constant. Small differencesin the composition of a given material will also affectthe dielectric constant.

Force. The equation for calculating the force of attrac-tion between the two plates is

(10-20)

where,Fis the attractive force in dynes,A is the area of one plate in square centimeters,Vis the potential energy difference in volts,Kis the dielectric constant,Sis the separation between the plates in centimeters.

10.2.1 Time Constants

When a dc voltage is impressed across a capacitor, atime (t) is required to charge the capacitor to a voltage.This is determined with the equation:

(10-21)

where,tis the time in seconds,R is the resistance in ohms,Cis the capacitance in farads.

In a circuit consisting of only resistance and capaci-tance, the time constant tis defined as the time it takesto charge the capacitor to 63.2% of the maximumvoltage. During the next time constant, the capacitor ischarged or the current builds up to 63.2% of theremaining difference of full value, or to 86.5% of thefull value. Theoretically, the charge on a capacitor or thecurrent through a coil can never actually reach 100%

but is considered to be 100% after five time constants

have passed. When the voltage is removed, the citor discharges and the current decays 63.2% perconstant to zero.

These two factors are shown graphically in10-14. Curve A shows the voltage across a capawhen charging. Curve B shows the capacitor vo

when discharging. It is also the voltage acrosresistor on charge or discharge.

10.2.2 Network Transfer Function

Network transfer functions are the ratio of the outpinput voltage (generally a complex number) for a type of network containing resistive and rea

elements. The transfer functions for networks consof resistance and capacitance are given in Fig. 1The expressions for the transfer functions onetworks are:

A is j or j2f,B isRC,C isR1C1,D isR2C2,n is a positive multiplier,fis the frequency in hertz,Cis in farads,

R is in ohms.

10.2.3 Characteristics of Capacitors

The operating characteristics of a capacitor deterwhat it was designed for and therefore where it isused.

Capacitance (C). The capacitance of a capacinormally expressed in microfarads (F or 106 fa

Quartz 3.84.4

Glass 4.88.0

Porcelain 5.15.9

Mica 5.48.7

Aluminum oxide 8.4

Tantalum pentoxide 26.0

Ceramic 12.0400,000

Table 10-2. Comparison of Capacitor Dielectric

Constants (Continued)

Dielectric K (Dielectric Constant)

FAV

2

K 1504S( )2

---------------------------=

t RC=

Figure 10-14. Universal time graph.

Pe

rcentofvoltage

orcurrent

100

80

60

40

20

00 1 2 3 4 5

A

B

TimeRC or L/R

A. Voltage across Cwhen charging.B. Voltage across Cwhen discharging.


15/33

254 Chapter 10

Figure 10-15. Resistance-capacitance network transfer functions.

Network Transfer function Network Transfer function

1 + AB

1 + AB

1 + AB

n(1 + AB)

1 + AB

1 + AB

(1 + AB)2

1 + AB

1 + AB

1

1

1

1

1 + 2AB

1 + 2AB

1 + 3AB

AB

3 + 2AB

AB

AB

AB

AB

3 + AB

2 + AB

2 + AB

(1 + AB)2

1 + 3AB + A2B2

1 + 3AB + A2B2

1 + 3AB + A2B2

1 + 3AB + A2B2 1 + 3AB + A2B2

2 + 5AB + A2B2

2 + 5AB + A2B2

Input

Input

Input

Input

Input

Input

Input

Input

Input

Input

Input Input

Input

Input

Input

Input

Input

Input

Input

Input

Input

Input Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

Output

1 + 5AB +6A2B2 + A3B3

1 + 3AB

n(3 + AB)3(1 + n) + 2nAB

A3B3

1 + (C D + R1C2)A + CDA2

CDA2

1 + (C D + R1C2)A + CDA2

(1 = n) + nAB

R2(1 + AC)

(R1 +R2) + (R1D + R2C)A

R

C

C

R

C C

R R

R

C R

C C C

R R R

R

C

C

R

C R

RC

C R

R C

RR C

R

C

C R

C C

nR

R R

C CR

C R

R C

R

R

C

C

R R

CR

C

C

RnR

R

R

C

C

RC

R

R

C

C

RR

C

R1 R2

C1 C2

C1 C2

R1 R2

C2

C1

R2

R1

R


16/33


or picofarads (pF or 1012 farads) with a stated accuracyor tolerance. Tolerance is expressed as plus or minus acertain percentage of the nominal or nameplate value.Another tolerance rating is GMV (guaranteed minimumvalue), sometimes referred to as MRV (minimum ratedvalue). The capacitance will never be less than the

marked value when used under specified operatingconditions but the capacitance could be more than thenamed value.

Equivalent Series Resistance (ESR). All capacitorshave an equivalent series resistance expressed in ohmsor milliohms. This loss comes from lead resistance,termination losses, and dissipation in the dielectricmaterial.

Equivalent Series Inductance (ESL). The equivalentseries inductance can be useful or detrimental. It doesreduce the high-frequency performance of the capacitor.

However, it can be used in conjunction with the capaci-tors capacitance to form a resonant circuit.

Dielectric Absorption (DA). Dielectric absorption isa reluctance on the part of the dielectric to give upstored electrons when the capacitor is discharged. If acapacitor is discharged through a resistance, and theresistance is removed, the electrons that remained in thedielectric will reconvene on the electrode, causing avoltage to appear across the capacitor. This is alsocalled memory.

When an ac signal, such as sound, with its high rate

of attack is impressed across the capacitor, time isrequired for the capacitor to follow the signal becausethe free electrons in the dielectric move slowly. Theresult is compressed signal. The procedure for testingDA calls for a 5 min capacitor charging time, a 5 sdischarge, then a 1 min open circuit, after which therecovery voltage is read. The percentage of DA isdefined as the ratio of recovery to charging voltagetimes 100.

Insulation Resistance. Insulation resistance is basi-cally the resistance of the dielectric material, and deter-mines the period of time a capacitor, once charged witha dc voltage, will hold its charge by a specified

percentage. The insulation resistance is generally veryhigh. In electrolytic capacitors, the leakage currentshould not exceed

(10-22)

where,IL is the leakage current in microamperes,Cis the capacitance in microfarads.

Maximum Working Voltage. All capacitors hmaximum working voltage that should not be exceThe capacitors working voltage is a combination dc value plus the peak ac value that may be apduring operation. For instance, if a capacitor has 1applied to it, and an ac voltage of 10 Vrms or 17 V

applied, the capacitor will have to be capable of standing 27 V.

Quality Factor (Q). The quality factorof a capacthe ratio of the capacitors reactance to its resistancspecified frequency. Q is found by the equation

(1

where,fis the frequency in hertz,Cis the value of capacitance in farads,R is the internal resistance in ohms.

Dissipation Factor (DF). The dissipation factorratio of the effective series resistance of a capaciits reactance at a specified frequency and is giv

percent. It is also the reciprocal ofQ. It is, therefsimilar indication of power loss within the capaand, in general, should be as low as possible.

Power Factor (PF). The power factorrepresenfraction of input volt-amperes or power dissipated capacitor dielectric and is virtually independent ocapacitance, applied voltage, and frequency.PF

preferred measurement in describing capacitive lin ac circuits.

10.2.4 Types of Capacitors

The uses made of capacitors become more variemore specialized each year. They are used to filter,couple, block dc, pass ac, shift phase, bypass,through, compensate, store energy, isolate, supnoise, and start motors, among other things. Wdoing this, they frequently have to withstand adconditions such as shock, vibration, salt spray, extemperatures, high altitude, high humidity, and rtion. They must also be small, lightweight, and reli

Capacitors are grouped according to their dielmaterial and mechanical configuration. Becausemay be hardwired or mounted on circuit boards, cators come with leads on one end, two ends, or they

be mounted in a dual-in-line (DIP) or single in(SIP) package. Figs. 10-16 and 10-17 show the vatypes of capacitors, their characteristics, and their codes.

IL 0.04C 0.30+=

Q1

2fCR-----------------=


17/33

256 Chapter 10

10.2.4.1 Film Capacitors

Film capacitors consist of alternate layers of metal foil,and one or more layers of a flexible plastic insulating

Figure 10-16. Color codes for tubular and disk ceramiccapacitors.

Color Digits

Black 0 0 1 2.0 pF 20% 0 0.0 1Brown 1 1 10 0.1 pF 1% 33 10Red 2 2 100 2% 75 1.0 100Orange 3 3 1000 3% 150 1.5 1000Yellow 4 4 230 2.0 10,000Green 5 5 0.5 pF 5% 300 3.3 +1Blue 6 6 470 4.7 +10Violet 7 7 750 7.5 +100Gray 8 8 0.01 0.25 pF 150 to 1500 +1000White 9 9 0.1 1.0 pF 10% +100 to 75 +10,000Gold Silver

Capacitance in picofarads

Temperature coefficient

1st & 2nd significant digit

Capacitance multiplier

Tolerance

1st & 2nd significant digitCapacitance multiplier

Tolerance

Temperature coefficient multiplier


1st & 2nd significant digit

Capacitance multiplier

Tolerance


Five dot color coderadial lead

Five dot color codeaxial lead

Six dot color coderadial lead


1st & 2nd digits

Multiplier Multiplier

Tolerance

Five dot color code Three dot color code

Tubular Ceramic Capacitors

Ceramic Disk Capacitor

Rated dc voltage

Positive

Positive lead (longer)

4735 V

Capacitance (MF)

Ceramic Disk Capacitor

MultiplierTemperature coefficient

10 pF >10 pFTolerance

ppoC5 dot 6 dot

Sig. Fig. Multiplier1st 2nd

Figure 10-17. Color codes for mica capacitors.

Black 0 0 1 20% 100Brown B 1 1 10 1% 55oC to +85CRed C 2 2 100 2% 300Orange D 3 3 1000 55C to +125CYellow E 4 4 10,000 500Green F 5 5 5%Blue 6 6Violet 7 7

Gray 8 8White 9 9Gold 0.1 0.5% 1000Silver 0.01 10%

Color Char. Digits Multiplier Tolerance dc Operating1st 2nd working temperature

voltage range

White EIA identifier indicates mica capacitor



Indicator style (optional)

MultiplierCapacitance tolerance

Characteristic

White EIA identifier indicates mica capacitor



Indicator style (optional)

MultiplierCapacitance tolerance

Characteristic

dc working voltage

Operating temperature

Identifier (white)

Nine Dot System

Six Dot System

Characteristic Temperature coefficient Maximumof capacitance (ppm/oC) capacitance drift

B Not specified Not specifiedC 200 0.5% +0.5pFD 100 0.3% +0.1pFE 20(+100) 0.3% +0.1pFF 0 to +70 0.5% +0.1pF

Mica Capacitor Characteristics


18/33


material (dielectric) in ribbon form rolled andencapsulated.

10.2.4.2 Paper Foil-Filled Capacitors

Paper foil-filled capacitors consist of alternate layers ofaluminum foil and paper rolled together. The paper may

be saturated with oil and the assembly mounted in anoil-filled, hermetically sealed metal case. These capaci-tors are often used as motor capacitors and are rated at60 Hz.

10.2.4.3 Mica Capacitors

Two types ofmica capacitors are in use. In one type,

alternate layers of metal foil and mica insulation, arestacked together and encapsulated. In the silvered-micatype, a silver electrode is screened on the mica insula-tors that are then assembled and encapsulated. Micacapacitors have small capacitance values and areusually used in high frequency circuits.

10.2.4.4 Ceramic Capacitors

Ceramic capacitors are the most popular capacitors forbypass and coupling appl icat ions because of thei r

variety of sizes, shapes, and ratings.Ceramic capacitors also come with a variety ofK

values or dielectric constant. The higher theKvalue, thesmaller the size of the capacitor. However, highK-valuecapacitors are less stable. High-Kcapacitors have adielectric constant over 3000, are very small, and havevalues between 0.001 F to several microfarads.

When temperature stability is important, capacitorswith aKin the 10200 region are required. If a high Qcapacitor is also required, the capacitor will be physi-cally larger. Ceramic capacitors can be made with a zerocapacitance/temperature change. These are called nega-tive-positive-zero (NPO). They come in a capacitancerange of 1.0 pF0.033 F.

A temperature-compensated capacitor with a desig-nation of N750 is used when temperature compensationis required. The 750 indicates that the capacitance willdecrease at a rate of 750 ppm/C with a temperaturerise or the capacitance value will decrease 1.5% for a20C (68F) temperature increase. N750 capacitorscome in values between 4.0 pF and 680 pF.

10.2.4.5 Electrolytic Capacitors

The first electrolytic capacitorwas made in Germaabout 1895 although its principle was discovered 25 years earlier. It was not until the late 1920s

power supplies replaced batteries in radio receiversaluminum electrolytics were used in any quantitiesfirst electrolytics contained liquid electrolytes. Twetunits disappeared during the late 1930s whedrygeltypes took over.

Electrolytic capacitors are still not perfect.temperatures reduce performance and can even felectrolytes, while high temperatures can dry themand the electrolytes themselves can leak and corrodequipment. Also, repeated surges over the working voltage, excessive ripple currents, andoperating temperature reduce performance and shcapacitor life. Even with their faults, electrolytic cators account for one-third of the total dollars spe

capacitors, probably because they provide high catance in small volume at a relatively low cost per mfarad-volt.

During the past few years, many new and impdevelopments have occurred. Process controlsimproved performance. Better seals have assured llife, improved etching has given a tenfold increavolume efficiencies, and leakage characteristicsimproved one hundredfold.

Basic to the construction of electrolytic capacitthe electrochemical formation of an oxide film on a surface. Intimate contact is made with this oxide fi

means of another electrically conductive materialmetal on which the oxide film is formed serves aanode or positive terminal of the capacitor; the oxidis the dielectric, and the cathode or negative termieither a conducting liquid or a gel. The most commused basic materials are aluminum and tantalum.

Aluminum Electrolytic Capacitors. Aluminum

trolytic capacitors use aluminum as the base matThe surface is often etched to increase the surfaceas much as 100 times that of unetched foil, resulthigher capacitance in the same volume.

The type of etch pattern and the degree to whicsurface area is increased involve many carecontrolled variables. If a fine etch pattern is desirachieve high capacitance per unit area of foil fovoltage devices, the level of current density and timfoil is exposed to the etching solution will bdifferent from that required for a coarse etch paThe foil is then electrochemically treated to form aof aluminum oxide on its surface. Time and cudensity determine the amount of power consumed


19/33

258 Chapter 10

process. The oxide film dielectric is thin, usually about15 /V. When formed on a high purity aluminum foil, ithas a dielectric constant between 7 and 10 and an equiv-alent dielectric strength of 25 million volts per inch(25 106 V/inch).

The thickness of the oxide coating dielectric is deter-

mined by the voltage used to form it. The workingvoltage of the capacitor is somewhat less than thisformation voltage. Thin films result in low voltage, highcapacitance units; thicker films produce higher voltage,lower capacitance units for a given case size.

As a capacitor section is wound, a system of paperspacers is put in place to separate the foils. This

prevents the possibility of direct shorts between anodeand cathode foils that might result because of roughsurfaces or jagged edges on either foil. The spacer mate-rial also absorbs the electrolyte with which the capacitoris impregnated, and thus assures uniform and intimate

contact with all of the surface eccentricities of theetched anode foil throughout the life of the capacitor.The cathode foil serves only as an electrical connectionto the electrolyte which is in fact the true cathode of theelectrolytic capacitor.

The electrolyte commonly used in aluminum electro-lytic capacitors is an ionogen that is dissolved in andreacts with glycol to form a pastelike mass of mediumresistivity. This is normally supported in a carrier of high

purity craft or hemp paper. In addition to the glycol elec-trolyte, low resistivity nonaqueous electrolytes are usedto obtain a lower ESR and wider operating temperatures.

The foil-spacer-foil combination is wound into acylinder, inserted into a suitable container, impreg-nated, and sealed.

Electrical Characteristics. The equivalent circuit ofan electrolytic capacitor is shown in Fig. 10-18. Aand B are the capacitor terminals. The shunt resis-tance,Rs, in parallel with the effective capacitance,C, accounts for the dc leakage current through thecapacitor. Heat is generated in the ESR if there isripple current and heat is generated in the shunt resis-tance by the voltage. In an aluminum electrolyticcapacitor, the ESR is due mainly to the spacer-electro-lyte-oxide system. Generally it varies only slightlyexcept at low temperatures where it increases greatly.L is the self-inductance of the capacitor caused byterminals, electrodes, and geometry.

Impedance. The impedance of a capac i to r i sfrequency dependent, as shown in Fig. 10-19. Here,ESR is the equivalent series resistance, XC is thecapacitive reactance,XL is the inductive reactance,andZis the impedance. The initial downward slope

is a result of the capacitive reactance. The trough(lowest impedance) portion of the curve is almosttotally resistive, and the rising upper or higherfrequency portion of the curve is due to the capac-itors self-inductance. If the ESR were plotted sepa-rately, it would show a small ESR decrease withfrequency to about 510 kHz, and then remain rela-tively constant throughout the remainder of thefrequency range.

Leakage Current.Leakage currentin an electrolyticcapacitor is the direct current that passes through a

capacitor when a correctly polarized dc voltage isapplied to its terminals. This current is proportional totemperature and becomes increasingly importantwhen capacitors are used at elevated ambient temper-atures. Imperfections in the oxide dielectric filmcause high leakage currents. Leakage currentdecreases slowly after a voltage is applied and usuallyreachessteady-state conditions after 10 minutes.

If a capacitor is connected with its polarity back-ward, the oxide film is forward biased and offers verylittle resistance to current flow, resulting in highcurrent, which, if left unchecked, will cause over-

heating and self destruction of the capacitor.The total heat generated within a capacitor is the

sum of the heat created by theI2R losses in the ESRand that created by theILeakage Vapplied.

Ac Ripple Current. The ac ripple currentrating isone of the most important factors in filter applica-tions, because excessive current produces a greaterthan permissible temperature rise, shortening capac-itor life. The maximum permissible rms ripple

Figure 10-18. Simplified equivalent circuit of an electrolytic

capacitor.

Figure 10-19. Impedance characteristics of a capacitor.

ESR C L

B

Rs

A

XCXL

Capacitorresonantfrequency

Z

XC

ESR

Effectiveimpedance

ofcapacitor

XL

ESR

Impedance curve

represents sum ofESR and XL or XC


20/33


current for any capacitor is limited by the tempera-ture within the capacitor and the rate of heat dissipa-tion from the capacitor. Lower ESR and longer cansor enclosures increase the ripple current rating.

Reverse Voltage. Aluminum electrolytic capacitorscan withstand a reverse voltage of up to 1.5 V

without noticeable effect from its operating charac-teristics. Higher reverse voltages, when applied overextended periods, will lead to some loss of capaci-tance. Excess reverse voltages applied for short

periods will cause some change in capacitance butmay not lead to capacitor failure during the reversevoltage application or during subsequent operation inthe normal polarity direction.

A major use of large value capacitors is forfiltering in dc power supplies. After a capacitor isfully charged, when the rectifier conductiondecreases, the capacitor discharges into the load until

the next half cycle, Fig. 10-20. Then on the nextcycle the capacitor recharges again to the peakvoltage. The e shown in the illustration is equal tothe total peak-to-peak ripple voltage. This is acomplex wave which contains many harmonics of thefundamental ripple frequency and is the ripple thatcauses the noticeable heating of the capacitor.

This can be mathematically determined or theripple current through the capacitor can be measured

by insert ing a low impedance true rms ammeter inseries with the capacitor. It is very important that theimpedance of the meter be small compared with that

of the capacitor, otherwise, a large measurement errorwill result.

Standard Life Tests. Standard life tests at ratedvoltage and maximum rated temperatures are usuallythe criteria for determining the quality of an electro-lytic capacitor. These two conditions rarely occursimultaneously in practice. Capacitor life expectancyis doubled for each 10C (18F) decrease in oper-ating temperature, so a capacitor operating at room

temperature will have a life expectancy 64 timeof the same capacitor operating at 85C (185F)

Surge Voltage. The surge voltage specificationcapacitor determines its ability to withstand thetransient voltages that occur during the sta

period of equipment. Standard tests specify a sh

and long off period for an interval of 24 houmore; the allowable surge voltage levels are us10% above the rated voltage of the capacitor10-21 shows how temperature, frequency, timeapplied voltage affect electrolytic capacitors.

Tantalum Capacitors. Tantalum electrolyticsbecome the preferred type where high reliabilitlong service life are paramount considerations.

Most metals form crystalline oxides thanonprotecting, such as rust on iron or black oxi

Figure 10-20. Capacitor charge and discharge on a

full-wave rectifier output.

E

$e

Figure 10-21. Variations in aluminum electrolytic chaistics caused by temperature, frequency, time, and a

voltage. Courtesy of Sprague Electric Company.

Cap

Frequency

DF

Frequency

ESR

Frequency

Z

Frequency

Cap

Time

DF

Time

= Increased or highor later

Z,ESR,

C

(normalized) Z

ESR

C

Temperature25C

Ripplecurrent

capability

Temperature

F

ailurerate

Temperature

VoltageLeakagecurrent

Failurerate

% Rated voltage


21/33

260 Chapter 10

copper. A few metals form dense, stable, tightlyadhering, electrically insulating oxides. These are theso-called valve metals and include titanium, zirco-nium, niobium, tantalum, hafnium, and aluminum.Only a few of these permit the accurate control ofoxide thickness by electrochemical means. Of these,

the most valuable for the electronics industry arealuminum and tantalum.The dielectric used in all tantalum electrolytic

capacitors is tantalum pentoxide. Although wet foilcapacitors use a porous paper separator between theirfoil plates, its function is merely to hold the electro-lyte solution and to keep the foils from touching.

The tantalum pentoxide compound possesses highdielectric strength and a high dielectric constant. Ascapacitors are being manufactured, a film of tantalum

pentoxide is applied to their electrodes by an electro-lytic process. The film is applied in various thick-

nesses and at various voltages. Although transparentat first, it takes on different colors as light refractsthrough it. This coloring occurs on the tantalum elec-trodes of all three types of tantalum capacitors.

Rating for rating, tantalum capacitors tend to haveas much as three times better capacitance/volumeefficiency than aluminum electrolytic capacitors,

because tantalum pentoxide has a dielectric constantof 26, some three times greater than that of aluminumoxide. This, in addition to the fact that extremely thinfilms can be deposited during manufacturing, makesthe tantalum capacitor extremely efficient with

respect to the number of microfarads available perunit volume.The capacitance of any capacitor is determined by

the surface area of the two conducting plates, thedistance between the plates, and the dielectricconstant of the insulating material between the plates.

The distance between the plates in tantalum elec-trolytic capacitors is very small since it is only thethickness of the tantalum pentoxide film. The dielec-tric constant of the tantalum pentoxide is high, there-fore, the capacitance of a tantalum capacitor is high.

Tantalum capacitors contain either liquid or solidelectrolytes. The liquid electrolyte in wet-slug andfoil capacitors, usually sulfuric acid, forms thecathode or negative plate. In solid-electrolyte capaci-tors a dry material, manganese dioxide, forms thecathode plate.

The anode lead wire from the tantalum pelletconsists of two pieces. A tantalum lead is embeddedin, or welded to, the pellet, which is welded, in turn,to a nickel lead. In hermetically sealed types, thenickel lead is terminated to a tubular eyelet. An

external lead of nickel or solder-coated nickel issoldered or welded to the eyelet. In encapsulated or

plastic-encased designs , the nickel lead, which iswelded to the basic tantalum lead, extends throughthe external epoxy resin coating or the epoxy end fillin the plastic outer shell.

Foil Tantalum Capacitors. Foil tantalum capacitorsare made by rolling two strips of thin foil, separated bya paper saturated with electrolyte, into a convolute roll.The tantalum foil, which is to be the anode, is chemi-cally etched to increase its effective surface area,

providing more capacitance in a given volume. This isfollowed by anodizing in a chemical solution underdirect voltage. This produces the dielectric tantalum

pentoxide film on the foil surface.Foil tantalum capacitors can be manufactured in dc

working voltage values up to 300 V. However, of thethree types of tantalum electrolytic capacitors, the foil

design has the lowest capacitance per unit volume. It isalso the least often encountered since it is best suited forthe higher voltages primarily found in older designs ofequipment and requires more manufacturing operationsthan do the two other types. Consequently, it is moreexpensive and is used only where neither a solid electro-lyte nor a wet-slug tantalum capacitor can be employed.

Foil tantalum capacitors are generally designed foroperation over the temperature range of55C to+125C (67F to +257F) and are found primarily inindustrial and military electronics equipment.

Wet-Electrolyte Sintered Anode Tantalum Capaci-tors. Wet-electrolyte sintered anode tantalum capaci-

tors often called wet-slugtantalum capacitors, use apellet of sintered tantalum powder to which a lead hasbeen attached. This anode has an enormous surface areafor its size because of its construction. Tantalum powderof suitable fineness, sometimes mixed with bindingagents, is machine-pressed into pellets. The second stepis a sintering operation in which binders, impurities, andcontaminants are vaporized and the tantalum particlesare sintered into a porous mass with a very large internalsurface area. A tantalum lead wire is attached bywelding the wire to the pellet. (In some cases, the lead isembedded during pressing of the pellet before sintering.)

A film of tantalum pentoxide is electrochemicallyformed on the surface areas of the fused tantalum parti-cles. The oxide is then grown to a thickness determined

by the applied voltage.Finally the pellet is inserted into a tantalum or silver

container that contains an electrolyte solution. Mostliquid electrolytes are gelled to prevent the free move-ment of the solution inside the container and to keep the


22/33


electrolyte in intimate contact with the capacitorcathode. A suitable end seal arrangement prevents theloss of the electrolyte.

Wet-slug tantalum capacitors are manufactured in aworking voltage range up to 150 Vdc.

Solid-Electrolyte Sintered Anode Tantalum Capaci-

tors. Solid-electrolyte sintered anode tantalum capaci-

tors differ from the wet versions in their electrolyte.Here, the electrolyte is manganese dioxide, which isformed on the tantalum pentoxide dielectric layer byimpregnating the pellet with a solution of manganousnitrate. The pellets are then heated in an oven and themanganous nitrate is converted to manganese dioxide.

The pellet is next coated with graphite followed by alayer of metallic silver, which provides a solderablesurface between the pellet and its can.

The pellets, with lead wire and header attached, areinserted into the can where the pellet is held in place by

solder. The can cover is also soldered into place.Another variation of the solid-electrolyte tantalum

capacitor encases the element in plastic resins, such asepoxy materials. It offers excellent reliability and highstability for consumer and commercial electronics withthe added feature of low cost.

Still other designs of solid tantalum capacitors, asthey are commonly known, use plastic film or sleevingas the encasing material and others use metal shellswhich are back filled with an epoxy resin. And, ofcourse, there are small tubular and rectangular molded

plastic encasements as well.

Tantalum Capacitors. In choosing between the threebasic types of tantalum capacitors, the circuit designercustomarily uses foil tantalum capacitors only wherehigh voltage constructions are required or where there issubstantial reverse voltage applied to a capacitor duringcircuit operation.

Wet-electrolyte sintered anode capacitors, orwet-slug tantalum capacitors, are used where the lowestdc leakage is required. The conventional silver candesign will not tolerate any reverse voltages. However,in military or aerospace applications, tantalum cases areused instead of silver cases where utmost reliability isdesired. The tantalum-cased wet-slug units will with-stand reverse voltages up to 3 V, will operate underhigher ripple currents, and can be used at temperaturesup to 200C (392F).

Solid-electrolyte designs are the least expensive for agiven rating and are used in many applications wheretheir very small size for a given unit of capacitance isimportant. They will typically withstand up to 15% ofthe rated dc working voltage in a reverse direction.

They also have good low temperature performcharacteristics and freedom from corrosive electrol

10.2.4.6 Suppression Capacitors

Suppression capacitors are used to reduce interfe

that comes in or out through the power line. Theeffective because they are frequency dependent ithey become a short circuit at radio frequencies, wiaffecting low frequencies. Suppression capacitoidentified as X capacitors and Y capacitors. Fig. shows two examples of radio interference suppreFig.10-22A is for protection class I which winclude drills and hair dryers. Fig.10-22B is for prtion class II where no protective conductor is connto the metal case G.

X Capacitors. X capacitors are used across the mto reduce symmetrical interference where a failuthe capacitori.e., the capacitor shorts outwicause injury, shock or death.

Y Capacitors. Y capacitors are used between aconductor and a cabinet or case to reduce asymme

Figure 10-22. Radio frequency suppression with X capacitors. Courtesy of Vishay Roederstein.

G

N

L

P

Lin

Cy

Cy

Cx

G

N

L

Li

Cy

Cy

Cx

A. Protective class I

B. Protective class II


23/33

262 Chapter 10

interference. Y capacitors have high electrical andmechanical specifications so they are much less likelyto fail.

XY Capacitors. When used together they are calledXY capacitors.

10.2.4.7 Supercapacitors

Supercapacitors, Ultracapacitors, more technicallyknown as electrochemical double-layer capacitors, areone more step beyond the electrolytic capacitors. Thecharge-separation distance in ultracapacitors has beenreduced to literally the dimensions of the ions within theelectrolyte. In supercapacitors, the charges are not sepa-rated by millimeters or micrometers (microns) but by afew nanometers or from electrostatic capacitors to elec-trolytic capacitors to ultracapacitors. The charge-separa-

tion distance has in each instance dropped by threeorders of magnitude, from 103 m to 106 m to 109 m. How a Supercapacitor Works. An supercapacitor

or ultracapacitor, also known as a double-layer capac-itor, polarizes an electrolytic solution to store energyelectrostatically. Though it is an electrochemicaldevice, no chemical reactions are involved in itsenergy storage mechanism. This mechanism is highlyreversible and allows the ultracapacitor to be chargedand discharged hundreds of thousands of times.

An ultracapacitor can be viewed as two nonreac-tive porous plates, or collectors, suspended within an

electrolyte, with a voltage potential applied across thecollectors. In an individual ultracapacitor cell, theapplied potential on the positive electrode attracts thenegative ions in the electrolyte, while the potential onthe negative electrode attracts the positive ions. Adielectric separator between the two electrodes

prevents the charge from moving between the twoelectrodes.

Once the ultracapacitor is charged and energystored, a load can use this energy. The amount ofenergy stored is very large compared to a standardcapacitor because of the enormous surface areacreated by the porous carbon electrodes and the smallcharge separation of 10 angstroms created by thedielectric separator. However, it stores a muchsmaller amount of energy than does a battery. Sincethe rates of charge and discharge are determinedsolely by its physical properties, the ultracapacitorcan release energy much faster (with more power)than a battery that relies on slow chemical reactions.

Many applications can benefit from ultracapaci-tors, whether they require short power pulses or

low-power support of critical memory systems.Using an ultracapacitor in conjunction with a batterycombines the power performance of the former withthe greater energy storage capability of the latter. Itcan extend the life of a battery, save on replacementand maintenance costs, and enable a battery to be

downsized. At the same time, it can increase avail-able energy by providing high peak power whenevernecessary. The combination of ultracapacitors and

batteries requires additional dc/dc power electronics,which increases the cost of the circuit.

Supercapacitors merged with batteries (hybridbattery) will become the new superbattery. Just abouteverything that is now powered by batteries will beimproved by this much better energy supply. Theycan be made in most any size, from postage stamp tohybrid car battery pack. Their light weight and lowcost make them attractive for most portable elec-

tronics and phones, as well as for aircraft and auto-mobiles.

Advantages of a Supercapacitor

1. Virtually unlimited life cyclecycles millions oftimes10 to 12 year life.

2. Low internal impedance.3. Can be charged in seconds.4. Cannot be overcharged.5. Capable of very high rates of charge and discharge.

6. High cycle efficiency (95% or more).

Disadvantages of a Supercapacitor:

1. Supercapacitors and ultra capacitors are relativelyexpensive in terms of cost per watt.

2. Linear discharge voltage prevents use of the fullenergy spectrum.

3. Low energy densitytypically holds one-fifth toone-tenth the energy of an electrochemical battery.

4. Cells have low voltages; therefore, serial connec-tions are needed to obtain higher voltages, whichrequire voltage balancing if more than threecapacitors are connected in series.

5. High self-dischargethe self-discharge rate isconsiderably higher than that of an electrochem-ical battery.

6. Requires sophisticated electronic control andswitching equipment.

A supercapacitor by itself cannot totally replace thebattery. But, by merging a supercapacitor and a batterytogetherlike a hybrid battery, it will be possible for


24/33


supercapacitors to replace the battery as we know ittoday.

Presently supercapacitors need batteries to store theenergy and are basically used as a buffer between the

battery and the device. Supercapacitors can be chargedand discharged hundreds of thousands of times where a

battery cannot do that. Calculating Backup Time. To calculate the desired

backup time the supercapacitor will provide if thepower goes off, the starting and ending voltage on thecapacitor, the current draw from the capacitor, andthe capacitor size must be known.

Assuming that the load draws a constant currentwhile running from VBACKUP, then the worst-case

backup time in hours would use the equation:

(10-24)where,Cis the capacitor value in farads,VBA CK UP STA RT is the initial voltage in volts. The

voltage applied to VCC, less the voltage drop fromthe diodes, if any, used in the charging circuit,

VBACKUPMINis the ending voltage in volts,IBA CK UP MA X is the maximum VBA CK UP current in

amperes.

For example, to determine how long the backuptime will be under the following conditions:

0.2 F capacitor VBACKUPSTARTis 3.3 V

VBACKUPMINis 1.3 V

IBACKUPMAXis 1000 nA, then:

10.3 Inductors

Inductance is used for the storage of electrical energy ina magnetic field, called magnetic energy. Magneticenergy is stored as long as current keeps flowingthrough the inductor. The current of a sine wave lags thevoltage by 90 in a perfect inductor. Figure 10-23 showsthe color code for small inductors.

10.3.1 Types of Inductors

Inductors are constructed in a variety of wdepending on their use.

10.3.1.1 Air Core Inductors

Air core inductors are either ceramic core or phe

core.

10.3.1.2 Axial Inductor

An axial inductor is constructed on a core with cotric leads on opposite ends, Fig.10-24A. The core rial may be phenolic, ferrite, or powdered iron.

10.3.1.3 Bobbin Core Inductor

Bobbin core inductors have the shape of a bobbimay come with or without leads. They may be e

axial or radial, Fig. 10-24B.

10.3.1.4 Ceramic Core

Ceramic core inductors are often used in frequency applications where low inductance, lowlosses, and high Q values are required. Ceramic hmagnetic properties so there is no increase in pe

bility due to the core material.

Backup time

C VBA CK UP ST AR T VBA CK UP MI N( )

IBA CK UP MAX-------------------------------------------------------------------------------------

3600-------------------------------------------------------------------------------------=

Backup time

0.2 3.3 1.3( )

106

---------------------------------

300---------------------------------=

111.1 h=

Figure 10-23. Color code for small inductors (in H).

Mil spec (if requiredlarger band)

1st digit

2nd digit

Multiplier

Tolerance (narrower)

Color 1st 2nd Multiplier Tolerance

Black 0 0 1Brown 1 1 10Red 2 2 100Orange 3 3 1000Yellow 4 4 10,000Green 5 5Blue 6 6Violet 7 7Gray 8 8White 9 9Gold 5%

Silver 10%No band 20%

Inductancedigits


25/33

264 Chapter 10

Ceramic has a low thermal coefficient of expansionallowing high inductance stability over a high operatingtemperature range.

10.3.1.5 Epoxy-Coated Inductor

Epoxy-coated inductors usually have a smooth surfaceand edges. The coating provides insulation.

10.3.1.6 Ferrite Core

Ferr it e cores can be easily magnetized. The coreconsists of a mixture of oxide of iron and other elements

such as manganese and zinc (MnZn) or nickel and zinc(NiZn). The general composition is xxFe2O4 where xxis one of the other elements.

10.3.1.7 Laminated Cores

Laminated cores are made by stacking insulated lamina-tions on top of each other. Some laminations have thegrains oriented to minimize core losses, giving higher

permeability. Laminated cores are more common intransformers.

10.3.1.8 Molded Inductor

A molded inductorhas its case formed via a moldingprocess, creating a smooth, well-defined body withsharp edges.

10.3.1.9 MPP Core

MPP, or moly perm alloy powder, is a magnetic materialwith a inherent distributed air gap, allowing it to storehigher levels of magnetic flux compared to other mate-rials. This allows more dc to flow through the inductor

before the core saturates.The core consists of 80% nickel, 23% molyb-

denum, and the remaining percentage iron.

10.3.1.10 Multilayer Inductor

A multilayer inductorconsists of layers of coil betwee

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