RF Ceramic Chip Capacitors in High RF Power Applications

8/18/2019 RF Ceramic Chip Capacitors in High RF Power Applications

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In today’s world of wireless communica-tions systems there are a myriad of highRF power applications that necessitate theuse of high quality specialized ceramic chipcapacitors. These demands require the de-

signer to carefully ac-

count for factors suchas device power dissi-pation and maximumcurrent and voltageratings as well as ther-mal resistance andtemperature rise dur-ing normal circuit op-eration. This articlehighlights some of themost essential ele-ments needed for se-lecting capacitor prod-ucts suitable for these

applications.

POWER DISSIPATION

In order to deter-mine the device powerdissipation of a ceramiccapacitor operating in

an RF power application the circuit designermust consider several critical factors. Amongthe most prominent are the equivalent seriesresistance (ESR) and maximum operating cir-

cuit current (Imax). The thermal resistance of the capacitor (θC) as well as the thermal char-acteristics of the mounting surface are also key factors that should be taken into account whileattempting to establish the power rating for agiven capacitor. All of these areas are ad-

dressed in this article.The actual power dissipated by a capacitor(PCD) in an RF power application is readily determined by calculating the product of therms circuit current squared (IC

2) and ESRsuch that

PCD = IC2 × ESR

The ESR takes into account all of the lossesincurred by the dielectric material, electrodes,terminations and termination to electrode in-terfaces. It is interesting to note that capaci-tors that exhibit ultra-low ESR as well as high vol tage breakdown characteris tics (such as

porcelain types) are especially well suited forhigh RF power applications.

A Capacitor Power Dissipation Example

Consider the following example consistingof a 51 pF RF porcelain chip coupling capaci-tor used in the power output stage of a

RF CERAMIC CHIP

CAPACITORS IN HIGH RF

POWER APPLICATIONS

TUTORIAL

RICHARD FIOREDIRECTOR OF RF APPLICATIONS ENGINEERING American Technical Ceramics Corp. (ATC)Huntington Station, NY

“To ensure the highest level of

reliability in high RF power

design applications, factors

such as maximum device

power, maximum voltage and

current ratings, thermal

characteristics of all circuit

devices and various ways that

heat is removed should betaken into account before

being incorporated into the

end product design.”

Reprinted with permission of MICROWAVE JOURNAL® from the April 2000 issue.©2000 Horizon House Publications, Inc.


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cellular base station operating at 900MHz, as shown in Figure 1. The RFpower is 60 W in a 50 W system; the

coupling capacitor has an ESR of 0.061 W at 900 MHz. The total RFcurrent in this application is deter-mined using

l P

Z

A

C =

=

=

60

50

1 09.

Therefore, the total power dissipatedin the capacitor is

PCD = IC2 × ESR

= (1.09)2 × (0.061)= 0.072 W (72 mW)

This example illustrates the impor-tance of the relationship betweenESR and the total power dissipatedby the capacitor. Here, the power dis-sipated by the capacitor due to its in-ternal losses represents 72 mW or0.12 percent of the total power ap-plied to the capacitor. This low loss isachieved by utilizing low ESR RF ce-ramic capacitors in these applications.Recent advances in materials technol-ogy have enabled the realization of lower ESR, further reducing thepower dissipated by the capacitor.

CURRENT RATING

The maximum current rating as-signed to a capacitor by the manufac-turer is stated in one of two ways: volt-age limited or power dissipation limit-ed. The rating that applies depends onthe capacitance value and operatingfrequency for a given application. If thecapacitor’s current rating (IC) in a par-ticular application is limited by voltageit can be calculated using the relation-ship between the rms voltage rating of the capacitor and the capacitive reac-tance. Accordingly, the maximum cur-rent for the voltage limited operatingcondition is directly proportional to the

capacitor rms voltage rating and inversely proportional to its reactance:

where

X C = 1/2πfC

Therefore, ICV = V rms × 2πfC.

As the operating frequency or ca-pacitance is increased, a region on thecurrent curve is entered where the nu-merical value of the voltage limitedcurrent is equal to that of the current

limited by power dissipation. This con-dition occurs at the intersection of thedotted and solid lines as shown in Fig-

ure 2. At frequencies above this inter-section point the current rating is de-termined solely by the power dissipa-tion limit. In this region the maximumcurrent is calculated using

I P

ESRCP

d= max

where

Pdmax= maximum power dissipationof the device as defined inreference to a givenmounting surface withknown thermalcharacteristics

Hence, in this region the maximum

current is now limited by the capaci-tor’s power dissipation limit. Regard-less of the specified power rating (asomewhat relative term), a capacitorexhibiting low ESR is always desir-able for providing an optimum devicecurrent rating.

VOLTAGE RATING

Maximum voltage ratings are de-termined predominantly by the di-electric strength or voltage break-down characteristics of the dielectricmaterial. As an example, porcelain di-

electrics exhibit a breakdown voltagethat typically exceeds 1000 V/mil of dielectric thickness and is virtually constant over the specified operatingtemperature range. Other dielectricsfabricated from barium titaniate(BaTiO3) based materials for exam-ple will exhibit lower breakdown volt-age characteristics due to differencesin their chemical and microstructuralcompositions, as shown in Figure 3.

A voltage breakdown also may occuron the outside of the device package.In this instance, the applied voltage is

large enough compared to the length of the external path (termination to termi-nation) in air to produce a flashover.Other factors that may promote an ex-ternal breakdown are surface contami-nation as well as environmental factorssuch as humidity and sharp edges, es-pecially in the immediate areas of theterminations. One method of testingfor dielectric strength is to submersethe test sample in an insulating oil bath,thereby eliminating the incidence of external flashover failure.

THERMAL RESISTANCE

The thermal resistance of a ceram-ic capacitor operating in a given ap-plication is a key factor that must beknown in order to establish the device power rating Pdmax. Knowingthe length of the heat flow path, thethermal gradient and the perpendicu-lar area, as shown in Figure 4, makesit possible to determine the thermalresistance θ.

R T

P S

ESR = 0.072 Ω

50 Ω

C = 51 pF

IC (rms)LOAD

F ig. 1 Current flow through a capacitor with series loss element.

100

10

1

0.1 100010010CAPACITANCE (pF)

(SOLID LINE SEGMENTS REPRESENTCURRENT ICV LIMITED BY VOLTAGE.

DOTTED LINE SEGMENTS REPRESENT CURRENT ICP LIMITED BY POWER

DISSIPATION.)

1000 MHz 500 MHz 30 MHz

10.1

R M S C U R R E N T ( A )

Fig. 2 The relationship between current IC , capacitance and frequency for an ATC series100 case B capacitor.

D I E L E C T R I C S T R E N G T H

( V )

DIELECTRIC THICKNESS (mils)

Mg TiO3 BaTiO3 AIR

Fig. 3 Voltage vs. dielectric thickness.

2

TUTORIAL

American Technical Ceramics • www.atceramics.com


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The thermal resistance for a givencapacitor structure with length L andcross-sectional area A can be ex-pressed by the relationship

Thermal conductance λ is expressedas

where

λ = coefficient of thermalconductivity for the subjectmaterial

L = length of the thermal path (cm)A = cross-section area perpendicular

to the heat path (cm2)

Note that multiplying [W/(°C)(cm)]by 0.2389 converts the units tocal/(°C)(sec)(cm). In addition, thethermal conductivity λ is essentially constant over the normal tempera-ture range of 25° to 125°C.

From this expression it can be readi-ly seen that the thermal resistance isproportional to the length of the heatflow path and inversely proportional tothe thermal conductivity and the cross-

sectional area perpendicular to the heatflow path. This relationship suggeststhat the aspect ratio of the capacitor,that is, the ratio between width andlength, plays an important role in thedetermination of the thermal resist-ance. The power dissipation of the device can be determined from the ther-mal resistance expression by establish-ing the temperature differential acrossthe heat flow path and dividing by θ.Hence, the maximum power dissipa-tion is expressed as

where

Pd = power dissipated at area A (W)T2 = temperature of cross-section

area A (perpendicular to heatflow) (°C)

θλ

λ

=

= °

L

A

L

A

C

W

4 186

0 2389

.

.

λ =°( )( )

=°( )( )( )

W

C cm

cal

C cmsec

P T T

T W

dC

=

= ( )

2 1–

θ

θ∆

T1 = temperature at a cross-sectionarea at a distance L from area A(°C)

L = length of path between areas(cm)

θC = thermal resistance of path acrosscapacitor length L (°C/W)

The thermal model used for calcu-lating the maximum power dissipa-

tion of a ceramic capacitor typically takes into account the thermal resist-ance of the capacitor and its mount-ing surface. This model assumes thatheat is removed mainly by conduc-tion through the capacitor’s termina-tions and external leads. Since heatremoval by radiation and convectionis disregarded in this model, a safety factor for maximum power dissipa-tion therefore is established. Themodel further assumes that the ther-mal resistance of the capacitor’s ter-minations is insignificant compared

to the ceramic body and, hence, isdisregarded. The effects of themounting surface also are disregard-ed and an infinite heat sink is as-sumed for the temperature rise calcu-lation shown in Figure 5.

TEMPERATURE RISE

The maximum change in tempera-ture along the heat flow axis is re-ferred to as the temperature rise orthermal gradient. The hypotheticaldetermination of temperature rise asa function of RF current is not always

straightforward. To get a reasonablehandle on this value the designermust account for the ESR and ther-mal resistance of the capacitor as wellas its mounting surface.

Given the ESR and current in anapplication, the capacitor’s power dis-sipation PCD as well as the heat gen-erated in the capacitor can be calcu-lated. The thermal resistance of thecapacitor and its external connectionsto a heat sink also can be ascertainedand, hence, the temperature riseabove the ambient can be estab-lished. Assuming an infinite heat sinkand a capacitor with zero manufac-turing flaws, the temperature rise canbe calculated using

ΔT = T1 – T2= θ (IC

2 × ESR)= θ × PCD (0°C)

Figure 6 shows the relationship be-tween the capacitor’s power dissipa-

tion and the change in the capacitocase temperature.

HEAT TRANSFER METHODS

Heat may transfer either to from the boundaries of a ceramic pacitor structure in several waHeat transfer occurs only whentemperature difference exists btween the capacitor and its immeate surroundings. Heat is transferrby conduction, convection and radtion, which may occur separatelyin combination.

Thermal Conduction

Heat energy transferred by coduction takes place in ceramic capator structures essentially at the termnation areas. In this case, heat trafer takes place because there

AREA A

T 2

T 1L

H E A T

F L O W

Fig. 4 Heat flow path, thermal gradient antermination area of a ceramic capacitor.

HEAT SOURCE

PLANE

θc = THERMAL RESISTANCE OF CAPACITOθhs = THERMAL RESISTANCE OF HEAT SINK

θhsθc

Fig. 5 The thermal model of a capacito mounted on a heat sink.

5

3.75

2.5

1.25

PCD (watts)

0 25 50

TEMPERATURE RISE ( °C)

75 100

Fig. 6 PCD as a function of temperatu

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physical contact between the capaci-tor terminations and the points of connection on the board surface. En-ergy transfer by conduction occurs inthe direction of decreasing tempera-ture and is due to the temperaturegradient along the length of the heatflow path.

On the molecular level, conduc-tion can be thought of as the transferof energy from a more energeticthermal state to a less energetic ther-mal state. Therefore, as moleculescollide with each other energy istransferred in the form of heat fromthe more energetic to the less ener-getic molecules. This heat transfer isdue to the random movement of mol-ecules and the interactions betweenthem within the two thermal gradi-ents. As the temperature increases,the activity or interaction betweenthe molecules also increases. Thesemolecules collide with each otherand, hence, transfer energy in theform of heat.

From Fourier’s law of heat con-duction the conduction process canbe quantified as a heat flux rate equa-tion. The law states that the rate of heat flow through a solid homoge-neous structure is directly propor-tional to the area of a section at rightangles to the direction of heat flow path and to temperature differencesper unit length along the path of heatflow, as shown in Figure 7 . Thus,

where

dQ/dt = rate of heat flow per unittime

A = cross-sectional area at rightangle to the direction of heat flow path

dT/dx = temperature gradient perunit length along heat flow path

λ = thermal conductivity of the

materialNote that the negative sign associated with λ indicates that the heat flowsconductively from high to low tem-peratures, or against the temperaturegradient.

Thermal Convection

Energy transfer between a solid sur-face and moving air in the immediate

dQ

dt

AdT

dx= – λ

From this expression it can be seenthat the cooling process is exponen-tial, that is, rapid at first, then levelsoff. Hence, this characteristic may bethought of as the thermal time con-stant of an object. The temperature of the object T now can be directly ex-pressed at time t (s). In Newton’s law of cooling, t is the variable where TA,k and C are constants. In order to de-termine the temperature of the objectat a given time, all of the constantsmust have numerical values.

Thermal Radiation

Thermal radiation is energy emit-ted by matter and transported by electromagnetic waves or photons. While the transfer of energy by convection or conduct ion requires thepresence of a medium, electromag-netic waves do not require a mediumto propagate and will transfer heatenergy most efficiently in a vacuum.

The total energy at which radiationmay be emitted from a surface asphotons per second by a square cen-timeter of an ideal black body radia-tor is equal to the temperature raisedto the fourth power. This energy emission results from changes in theelectron configurations of the atomsor molecules of the radiating object.

Stefan-Boltzmann’s law gives themaximum heat flux at which radiationmay be emitted from a surface. Thelaw takes the form

E = σ T4

where

T = temperatureσ = a constant

From this equation it can be seenthat a small increase in temperatureproduces a very large increase inemitted radiation energy. If the

surroundings is commonly referred toas convection. The heat transfer due toconvection is an interactive combina-tion of diffusion or molecular motion inthe dielectric material and the bulkmovement of the surrounding air.There are basically two types of convection heat transfers: natural (free)and forced. Natural convection cur-rents are induced by forces due to dif-ferences in variations between the device surface temperature and the sur-rounding ambient temperature; that is,heat is directly picked up by the air andtransported away. Natural or free convection is caused by air movement dueto thermal gradients between an object(in this case a ceramic capacitor) and itssurrounding ambient environment.

Forced convection heat flow is in-duced by external means, such as acooling fan. Heat transfer coefficientsdue to forced flow are generally greaterthan that of natural convection flow. Inmost cases the free convection may beneglected when there is forced airflow,hence forced convection provides thegreater effect for convection cooling.

Newton’s law of cooling is used tomodel the temperature change of anobject that is at some initial elevatedtemperature placed in an environ-ment of a lower temperature. Thelaw states that the rate at which a warm body cools is approximately proportional to the temperature dif-ference between the temperature of

the warm object and the temperatureof its immediate surroundings. Thus,

where

T = temperature of the object attime t

TA= temperature of the surroundingenvironment (ambienttemperature)

k = constant of proportionality t = time variable (s)

Solving the differential equation for Tmeans placing T on one side and t onthe other, such that

Integrating both sides producesln(T – TA) = kt + C

and solving for T gives

T = ekt+C + TA

dT

dtk T TA= ( )–

dT

T Tk dt

A–=

AREA A dQdt

T T + dT

d x

H E A T

F L O W

Fig. 7 Heat flow through a solid homogeneous structure.

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T R I M L I N E

temperature is doubled, the energy emitted increases by a factor of 16.The surface emissivity indicates how efficiently the surface of a given object will emit radiation energy relative to anideal black body radiator. The idealblack body has an emissivity referenceequal to 1.0. Just as surfaces emit ener-gy, another surface can absorb a por-tion of that energy. The surface prop-erties of various materials will affectthe amount of heat radiated.

The intensity of radiation is definedas the rate of emitted energy per unitof surface area through a unit solid an-gle. The radiation from a surface hasdifferent intensities in different direc-tions. The intensity of radiation alongthe normal to the surface is known asthe intensity of normal radiation.

When thermal radiation strikes asolid object, portions of the energy can be absorbed, reflected or trans-mitted through the object. This ener-gy is dispersed in various proportionsdepending on the surface emissivity and density of the material, as shownin Figure 8. The portion of the inci-dent radiation that is absorbed by theobject is its absorptivity α. Anotherportion of the incident radiation en-ergy will be reflected and is referredto as reflectivity ρ. Lastly, the portionof the radiated energy that is trans-mitted though the object is referredto as transmissivity τ. The sum of all

of these portions of the radiated en-ergy is unity and, therefore,

α + ρ + τ = 1

APPLICATION CONSIDERATIONS

This article has highlighted severalmajor factors to consider while de-signing circuit elements for high RFpower applications. Some of the mostimportant considerations relate di-rectly to such things as ESR, thermalresistance of the device(s), mountingsurface characteristics and heat re-

moval. These factors are associated with the overall thermal managementof the entire design and should neces-sitate careful assessment of all circuitelements and their contribution to theoverall thermal load on the design.Some of the guidelines for these con-siderations are summarized below.• It is always prudent to select capac-

itor products with ultra-low ESRand dissipation factor characteris-tics, especially concerning thermalmanagement considerations of highRF power designs. This choice will

ensure the most efficient operationand minimize the amount of heatgenerated in the application.

• The thermal resistance of the ca-pacitor’s mounting surface and heatsink should be as low as possible.Since the heat is primarily conduct-ed by the capacitor’s terminationsto the metallic contact points onthe board, it is important to evalu-ate characteristics such as thermalconductivity of all materials in- volved as well as board trace di-mensions and material thickness at

the points of contact.• Since the greater part of the heat

transfer is predominantly throughthe terminations of the capacitor,the thermal path of a ceramic chipcapacitor may be further improvedby the use of external leads such assilver microstrip ribbon. The rib-bon leads will serve to bleed heataway from the capacitor more effi-ciently. The leads also may serve asa mechanical strain relief, especial-ly in situations where the coeffi-cient of thermal expansion between

the capacitor and the board materi-al is significantly mismatched. Thesilver lead stock is tailored to the

width of the capacitor body, makit suitable for this purpose.

• The overall thermal managementthe entire design must be judiciouevaluated. Devices such as powFETs and active gain blocks as was other passives in an applicati will provide additional sources heat during operation and there

add to the overall thermal load of design module. Care must be takto account for the impact of all of heat sources in the final design.

• Using capacitor assemblies themploy several capacitors in parlel will serve to greatly extend tcurrent and power rating ovesingle capacitor. Assemblies thutilize ruggedized porcelain capator building blocks in various cobinations will greatly extend the pacitance, voltage and current hadling capabilities. For example, t

equal value capacitors in paral wil l yield approximately one-hthe ESR of one capacitor athereby afford virtually twice tcurrent handling capability, an a vantage that is difficult to ignore

CONCLUSION

To ensure the highest level of rebility in high RF power design applitions, factors such as maximum devpower, maximum voltage and curreratings, thermal characteristics of circuit devices and various ways th

heat is removed should be taken inaccount before being incorporated inthe end product design. In additi when selecting ceramic chip capacitfor these applications it is prudentfirst evaluate the ESR of the particucapacitor(s) at the application operatfrequency. Knowing the ESR alo with the network impedance will allthe designer to perform quick calcutions of the power dissipated by the pacitor. This consideration is equaimportant for all other circuit elemein the application. Proper design w

emphasis on thermal management whelp to ensure efficient and troubfree operation.

DIELECTRICBLOCK

REFLECTED RADIATIONINCIDENT RADIATION TRANSMITTED RADIATION

Fig. 8 Thermal radiation dispersion.

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TUTORIAL

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ATC has made every effort to have this information as accurate as possible. However, no responsibility is assumed by ATC for its use, nor for any infringements of rights of third parties which may result from its use. ATC reserves the right to revise the content or modify its product without prior notice.

© 2000 American Technical Ceramics Corp. All Rights Reserved. ATC # 001-942 Rev. C; 4/05

RF Ceramic Chip Capacitors in High RF Power Applications

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