CERAMIC CAPACITORS

127

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General characteristics

Page revised 06/20

When the frequency is enough low and ESR negligible:

Z ≈ (1/Cq

) (4)

Then IVm ≈ 2∏ x WVDC x √2 x f x C (5)

I.2.2. Power Dissipation Limit

The maximum RMS current for the power dissipation limited operating condition is di-

rectly proportional to the maximum power dissipation of the device and the Equivalent

Series Resistance:

IP(RMS) =

√Pdmax.

ESR

(6)

Pdmax. is the maximum power dissipation of the device as defined in reference to a

given mounting surface with known characteristics. The thermal resistance (VC) of a

ceramic capacitor operating in a given application is a key factor to establish the device

power rating:

Pdmax. =

Tmax.–Tamb.

VC

(7)

I.2.3. Maximum current

The maximum current is :

I max = minimum (

d Ip(RMS), Ivm)

Considering the general trend of the current with the frequency:

(5) shows that Ivm increases with the frequency

(6) shows that Ip(RMS) decreases with the frequency (ESR increases with

frequencies in a general trend with skin effect)

Therefore typically the maximum current is limited

• By Ivm at low frequencies

• By Ip(RMS) at higher frequencies

I.3. HEAT TRANSFER

I.3.1. Thermal Convection

Convection is a heat transfer produced by the motion of a mass of fluid such as air or

water when the heated fluid is caused to move away from the source of heat, carrying

energy with it. Convection above a hot surface occurs because at constant pressure,

hot air expands, becomes less dense, and rises.

I.3.2. Thermal Radiation

Radiation is a heat transfer produced by the emission of electromagnetic waves which

carry energy away from the emitting object. For ordinary temperatures, the radiation

is in the infrared region of the electromagnetic spectrum. The relationship governing

radiation from hot objects is called the Stefan-Boltzmann law:

P =

e x j x A x (T4 –Tc4) (8)

Where:

P is the net radiated power

e is the emissivity coefficient (1 for ideal radiator)

j is the Stefan’s constant (5.6703.10-8 W/m2.K4)

A is the radiating area

T is the temperature of radiator

TC is the ambient temperature

I.3.3. Thermal Conduction

Conduction is a heat transfer by means of molecular agitation within a material without

any motion of the material as a whole. If one end of a metal rod is at a higher tempera-

ture, then energy will be transferred down the rod toward the colder end because the

higher speed particles will collide with the slower ones with a net transfer of energy to

the slower ones.

For a heat transfer between two flat surfaces, such as heat loss through the wall of a

house, the rate of conduction heat transfer is:

Q

= k

x A x (Thot –Tcold)

t

d

(9)

Where:

Q is the heat transferred with the time t

k is the thermal conductivity of the barrier

A is the conducting area

T is the temperature

d is the thickness of the barrier

Conceptually, the thermal conductivity can be thought as the rate of heat loss per unit

area to the rate of change of temperature.

(10)

The net heat transfer is in the opposite direction of the temperature gradient

For a stationary state and without internal heat source: [1]

_

2

T= 0 therefore for one dimensional equation T = Ax +B (A and B are constants)

Considering the following capacitor where

Tmax. is the maximum temperature of capacitor (°C) located at the center of the

capacitor

Tamb. is the application ambient temperature in operating conditions (°C) located at

both terminations if the thermal transfer of the connections is enough efficient.

Temperature profile inside the capacitor

The thermal resistance Vc of the capacitor is composed on two parallel thermal resis-

tance V:

General Information