1/48

Passive components and circuits - CCP

Lecture 9

2/48

Content Capacitors

Short history Electrical properties Clasification Parameters Marking Codification Choosing the type of a capacitor

3/48

Web addresses

http://en.wikipedia.org/wiki/Capacitor#Hydraulic_model http://www.interq.or.jp/japan/se-inoue/e_capa.htm http://www.illinoiscapacitor.com/ http://www.americancapacitor.com/ http://www.uoguelph.ca/~antoon/gadgets/caps/caps.html http://www.williamson-labs.com/ http://micro.magnet.fsu.edu/electromag/java/varcapacitor/ http://www.capacitorindustries.com/ http://www.tpub.com/neets/book2/index.htm

4/48

The capacitor – history and tendencies 1745 first capacitor – Pieter van

Messchenbroek – Universitaty of Lyden – known also as Lyden jar.

Tendencies of evolution: Increase the specific capacitance Decrease dimensions Increase the voltages to which they

can be submitted

5/48

The capacitance - dependency with the geometry

d

A

- - - - -

+ + + +

Parallel plates

d

AC o

a

b L

r

+Q

-Q

Cylindrical plates

abL

C o

ln

2

a

b

+Q-Q

Spherical plates

ab

abC o

4

pF/m

6/48

The influence of the dielectric material In the behavior of the capacitor an important role has the

isolating material (the dielectric) placed between the metallic plates.

With its relative permittivity r it increases the capacitance of the capacitor:

With the electric field at which its breakdown appears (electric rigidity) the voltage that can be applied to the capacitor is limited .

d

ACCC r 000;

7/48

Permitivity - complex dimension dependent on the frequency

The real part characterizes the energy accumulation in the capacitor;

The imaginary part characterizes the energy dissipated in the capacitor;

Their ratio is the tangent of the loss angle:

log(/0)

*=’+i ’’

'

")(

tg

'0d

'0

8/48

The properties of the dielectrics

9/48

Capacitor – equivalent electric scheme

CRj1

RLjRZ

p

ppsC

Cj

1LjRZ psC

Equivalent circuit

Equivalent circuit at high frequencies

10/48

Capacitor – the frequency characteristic

10%

10%

sR

psp RRR

CL

1

p0 03,0 CR

2

p

L

C

1

CZ

Capacitive area

11/48

Parallel connected capacitors

Sometimes in electronic circuits, two capacitors appear connected in parallel, one with very high value and one with very small value.

In this situation the smaller capacitance compensates the inductive component of the higher capacitance.

+

C 1 C 2

10 10 n

C 1 C 2

1010

L1 L2 <L1

n

12/48

The modulus of the capacitors’ impedances

13/48

Modification of the modulus of the equivalent impedance at high frequency

14/48

Clasification – constructive criterion Discrete

Fixed Variable

Embedded (included in the structure) On the board On the ceramic sub-layer (multichip modules – MCM) On the integrated circuits

15/48

Discrete capacitors - clasification

Fixed unpolarized

polarized

Variable with dielectric air

trimmers

16/48

Parameters of fixed capacitors Parameters printed most of the times

The nominal capacitance The tolerance of the nominal value The nominal voltage

Parameters that characterize the non-ideal capacitors The loss resistance The loss angle tangent

Parameters that characterize the influence of the medium The temperature coeficient

Parameters of performance The interval of functioning temperatures The specific capacitance The frequency domain of functioning

17/48

The nominal capacitance and its tolerance For capacitors with values under 1F this parameter

respects the series of normalized values E6, E12, E24, ... with their corresponding tolerances.

Obtaining capacitors with small tolerances is a lot more difficult than in the case of resistors.

For capacitors of high values (especially electrolytic ones) we have the following normalized values: 1, 2, 3, 4, 5, 8, 16, 25, 32, 64. Their tolerance varies between larger limits: t[-40%; +100%].

18/48

The nominal voltage Vn Represents the maximum continuous voltage (or the

maximum value of the effective value of an alternative voltage) that can be applied at the terminals of the capacitor in a long functioning regime at the superior limit of temperature.

Exceeding the value of this parameter brings the capacitor in the situation of risk of breakdown of the dielectric.

The value of this parameter is chosen with a coefficient of safety k[1,5; 3] smaller than a test voltage (close to the breakdown voltage) to which the capacitor is submitted. The safety coefficient covers the phenomena of “aging” that can appear in case of some dielectrics.

19/48

The nominal voltage Vn

The values of this parameter are realized in a series of standardized values: 6, 12, 16, 25, 63, 70, 100, 125, 250, 350, 450, 500, 630, 1000 volts.

For some electrolytic capacitors this parameter is printed on the body.

For the other types of capacitors it can be deduced from the size of the capacitor.

20/48

The isolating resistance - Riz

Characterizes the imperfections of the properties of isolator of the used dielectric.

It is defined as the ratio between the continuous voltage applied on the capacitor and the continuous current that flows through it.

Typical values: 104M for ceramic capacitors, 102-105 for plastic coat capacitors.

21/48

The isolating resistance – equivalent parameters

The parameter, isolating resistance, can be deduced from other two parameters that can be specified for capacitors, especially for the high value ones (electrolytic):

The specific time constant:

Leakage current (DC):

izn RC

iz

nf R

VI

22/48

The tangent of the loss angle Represents the ratio between the active power that is

dissipated in the capacitor and its reactive power when on its terminals is applied a sinusoidal voltage:

This parameter is also the ratio between the currents that are closing through the isolation resistance and through the nominal capacitance when a sinusoidal voltage is applied:

iznn

iz

r

a

RCVC

RV

P

Ptg

1

2

2)( 2

2

iznCn

Riz

RCI

Itg

1

)(

23/48

The tangent of the loss angle tg() – is dependent on the pulsation, this is why it is

indicated in the catalog at the pulsation to which it was measured and the capacitance of the capacitor.

For an ideal capacitor this parameter is zero. In the case of real capacitors it should be as small as possible.

Depending on the technology of manufacturing the capacitor, this parameter can take values between 10-5 (mica or ceramic capacitors) and 0,25 (the electrolytic ones).

In catalogs there can be indicated an equivalent parameter, the quality factor, representing the inverse of the tangent of the loss angle:

iznRCtg

Q

)(

1

24/48

The temperature coefficient Apears printed in case of some capacitors. Depending on this

parameter, the capacitors can be divided in different classes. The parameter is defined as follows:

For most of the capacitors this parameter can be considered constant only for a limited interval of temperatures.

In catalogs, it can be defined in parts per million per degree Celsius:

dT

dC

CC 1

C][ppm/1 o

0

0

0 TT

CC

CC

25/48

Performance parameters

The functioning temperature interval varies a lot from one technology to another: -10oC +70oC for capacitors with paper, -40oC +125oC for the electrolytic capacitors with tantalum.

The domain of the functioning frequencies is limited by the behavior of the dielectric and by the inductive behavior. In the case of the ceramic capacitors, the domain extends up to GHz order, and the electrolytic capacitors up to tens of KHz.

The specific capacitance characterizes the performances of the technology, being defined as the ratio between the nominal capacitance and the volume of the capacitor.

26/48

Marking the capacitors

Marking refers to the way in which the information printed on the capacitors is coded. Marking with the code of letters and figures Marking with the code of colors

Marking the capacitors brings more variety than marking the resistors. The information printed on the capacitor differs a lot from one technological type to another.

27/48

Marking with the code of letters and figures

On some capacitors the nominal value and the nominal voltage can be printed clearly and the tolerance is expressed with standardized letters (presented for resistors too).

B0,1%; C0,25%; D0,5%; F1%; G2%; H2,5%; J5%; K10%; M20%

28/48

Marking with the code of letters and figures Another code that can be

seen is the one with three figures and a letter. The first two figures represent the digits of the nominal value, the third, the multiplier for 1 pF, and the letter, the tolerance.

474J Value 47, multiplier 104, tolerance 5% => 470nF, tolerance 5%

29/48

Marking with the code of colors

There can appear different prints: With three colors – only the value of the nominal capacitance With four colors With five colors – they can have different meanings from one

type of capacitor to another

For some ceramic capacitors the temperature coefficient can be indicated by the body color.

It is recommended to consult the equivalence tables for each type of capacitor.

30/48

Exemple for ceramic capacitors

31/48

Exemple for mica and paper capacitors

32/48

Exemple for capacitors with mica

33/48

Exercises – identify the type and the parameters of the following capacitors

34/48

Codification of the capacitors The catalog codes (romanians) contain information structured

on four fields: Field I – the constructive type suggested by a code of letters; Field II – the technological family and the capsule used

(code of figures); Field III – the value of the nominal capacitance; Field IV – the value of nominal voltage;

Examples: MZ 32.02 10n/25 – ceramic capacitor multilayer type II, 10

nF, 25V; CTS-P 10.96 10/50 – electrolytic capacitor with tantalum,

10F, 50V.

35/48

Choosing the type of the capacitors According to the requirements of the application in which

the capacitors are used, they are chosen from different technological families.

The frequency domain in which the capacitance is used,

establishes the technological type required. A short characterization of the main technological types

can be a reference point in selecting capacitors.

36/48

Choosing the type of the capacitors

d

AC 0 rε

010 110 210 310 410 510 610 710 810 910 f

electro litice cu Al

electro litice cu Ta

cu hârtie cu hârtie m etalizatã

ceram ice K m are

m icã, ceram ice cu pierdere m icã

polistiren

Electrolytic with Al

Electrolytic with Ta Mica and ceramic with low losses

With paper With metalized paper

Ceramic with high K

polystyrene

37/48

Ceramic capacitors type I Properties:

The dielectric is a ceramic made of magnesium silicates with r[5-200];

Stability at temperature variation;

Parameters: Small and very small tolerances;

Cn [0,8pF-27nF]; Riz>10G; tg()<15x10-4;

Small temperature coefficients and linear behavior;

Aplications: in industrial and professional equipments where temperature stability is important, they can be used ay high frequencies too.

38/48

Ceramic capacitors type II Properties:

The dielectric is a ceramic with high electric permeability , r up to 15000;

Highest specific capacitances in the domain pF şi nF; Parameters:

Medium tolerances ; Cn [33pF-100nF]; Riz>3G; tg()<0,035; Undefined temperature coeficients ; High nominal voltages;

Aplications: in industrial and professional equipments where the accent is put on miniaturization, in decoupling and filtering, used at high voltages, do not have high frequency limits.

39/48

Capacitors with plastic coat (film) - with polystyrene (stiroflex) or with myler Properties:

The dielectric is the thin sheet of plastic coat film on which the plates are placed (Al pellicle).;

The thin sheet is rolled, this way obtaining high specific capacitances (myler), but also parasite inductances ;

Parameters: Medium tolerances ; Cn [47pF-6,8F]; tg() small at the ones with stiroflex and high and

temperature dependent at the ones with myler; Small temperature coefficients at the ones with stiroflex;

Aplications: in equipments for general usage, at decoupling and filtering, have limited the frequency domain due to the inductive component.

40/48

Capacitors with paper Properties:

The dielectric, a special paper, called capacitor paper , on which the plates are placed;

Although the paper is special, it can modify its properties (electric rigidity) due to humidity;

Parameters: High tolerances (20%); Cn [10nF-20F]; tg() high and highly dependent on

the temperature; Small specific capacitance, therefore larger dimensions; Instable with temperature and humidity;

Applications: in power circuits, decoupling, starting engines, in applications where high capacitances are necessary and electrolytic capacitors can’t be used, only at low frequencies.

41/48

Capacitors with mica

Properties: The dielectricis mica and the plates are thin sheets of tin,

electrolytic cooper or aluminum; Due to the technology they are very expensive;

Parameters: Medium tolerances ; Cn [1pF-100nF]; tg()<15x10-4; Very high nominal voltages, up to 35KV; Very stable with temperature;

Applications: in professional circuits where a good stability with temperature is required, in circuits where very high voltages appear.

42/48

Electrolytic capacitors with aluminum Technology:

the dielectric is obtained by oxidation of the aluminum plates surface;

a plate consists of a thin shit of aluminum, and the other of a conducting solution called electrolyte;

the electrolyt can be impregnated in a sub-layer (paper), obtaining dry or semidry capacitors.

43/48

Electrolytic capacitors with aluminum Properties:

Very thin oxide layer, limits the value of the voltage to which the capacitor can be submitted;

High specific capacitances are obtained by increasing the surface of the plates; The limited possibilities of control over the surface of the plates and over the

thickness of the dielectric determines the manufacturing of capacitors with high tolerances;

Parameters: High tolerances [-20% +100%] for the miniature ones and [-20% +50%] for the

high capacitance ones;

Cn [1F-200 F] – miniature, Cn [1ooF-10mF] – high capacitance; Nominal voltages up to 350V (miniature) and 450V (high capacitance ); High parasite elements;

Aplications: in industrial circuits, only at low frequency.

44/48

Electrolytic capacitors with tantalum Properties:

The superior mechanic properties of tantalum allow the using of thinner sheets;

The relative permittivity of the Ta oxide is double as compared to the Al oxide;

Parameters: High tolerances [-20% +30%] for the drop ones (picătură) and [-20%

+20%] for the professional ones ;

Cn [0,1F-680 F] – drop, Cn [100F-330 F] – professional; Nominal voltages up to 50V (drop) and 63V (professional); tg() smaller than for the ones with Al; Parasite elements smaller than for the ones with Al.

Aplications: in industrial circuits, up to the frequency of 10KHz.

45/48

Electrolytic un-polarized capacitors Properties:

Are manufactured with tantalum, constructively consisting of two tantalum capacitors connected in series to which the dielectric is the common plate;

By series connection, the specific capacitance decreases; Parameters:

Tolerance [-20% +20%] Cn [4,7F-150 F]; Nominal voltages up to 10V; tg() is very small;

Aplications: in circuits where high capacitances are required but polarized capacitors can’t be used, nor the ones with paper; they can’t be used for high voltages and neither over 20KHz.

+ +

m e ta lic p la te (T a )m e ta lic p la te (T a )

E le c tro ly te

46/48

Usage of electrolytic capacitors

The “plus” sign indicates that, in the circuit, the plate must always be connected to a higher potential than the other one.

On the capacitor there is a mark either for the positive terminal or for the negative. If is not marked, the capacitor body is connected to the negative terminal.

If the condition vC>0 is not fulfilled, the capacitor can be destroyed due to overheating.

+

V C V C V C

V C >0

electrolitoxidmetal Electrolyte

47/48

Problem On a capacitor body, the following parameters are marked:

1 µF and 63V. From the datasheet we can get the following parameters: tg=0.001, determinated at the 50Hz frequency, and T= 0.002 [1/oC].

1. May we connect the capacitor directly to the power system, if the environment temperature is 50 oC (motivate the answer)?

2. How is the capacitor impedance if at its terminal is applied a voltage source with vI=5 +20 sin(100t) [V]?

3. The capacitor is connected in series with a 10 K resistor. How the waveform of the voltage across the capacitor looks after 10 ms? The previous voltage source is applied on the RC series circuit.

48/48

Problem For the capacitor from the circuit, the

following parameters are extracted from datasheet:

Temperature domain -40oC ~ +85oC Tolerance ±20% Nominal capacitance 1µF The tangent of loss angle 0,02 at 1KHz

and 25 oC Nominal voltage 250 VDC

Calculate the insulation resistance. Draw the equivalent circuit Represent the modulus of the transfer

function vo/vi.

CRvi vo

1K