V. Bande, Applied Electronics Department (English version)-> Information for students Lecture 9 1 Passive Electronic

V. Bande, Applied Electronics Departmentwww.ael.utcluj.ro (English version)-> Information for students

Lecture 9

1

Passive Electronic Components and Circuits (PECC)

Capacitors

http://www.ael.utcluj.ro/

CapacitorsShort historyElectrical PropertiesClassificationParametersMarking Choosing capacitors criteriaVariable resistorsSpecial capacitors – nonlinear capacitors

Capacitors

History

• 1745 – the first capacitor – Pieter van Messechenbroek – Leyden University – also known as Leyden Jar.

• General evolution trends:

Increasing the specific capacitance

Size reducing

Increasing the maximum voltages


Capacitors

Electrical properties

Capacitance vs geometry dependency

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

e0=8,85419 pF/m


• A very important role of the capacitor behavior is played by the insulting material (dielectric) displaced between the metallic plates of every capacitor.

The dielectric influence

• Through its electrical field value at which the dielectric is breakthrough (electrical rigidity), the voltage that can be applied at the capacitor’s terminals can be limited.

d

ACCC r 000;

• Through its relative electrical permittivity, εr the capacitor’s capacitance can be controlled.


• The real part characterizes energy accumulation inside the capacitor.

Electrical permittivity – complex quantity

'0d

'0

*=’+i ’’

log(/0)

• The imaginary part characterizes energy dissipation inside the capacitor.

• The ratio between the imaginary part and the real part is called loss-angle tangent.

'

")(

tg


Dielectric properties


The capacitor – the electrical equivalent model

CRj1

RLjRZ

p

ppsC

Cj

1LjRZ psC


The capacitor – the frequency characteristic

10%

10%

zona capacitivã

sR

psp RRR

CL

1

p0 03,0 CR

2

p

L

C

1

CZ


Parallel connection

+

C1 C2

10 10 n

C1 C2

1010

L1 L2 <L1

n

• Sometimes, in electronic circuits, you can find a low-value capacitor connected in parallel with a high value capacitor.

• In this situation, the lower value capacitor compensates the inductive component from the other capacitor (the higher value one).


The capacitors impedance module


The equivalent capacitor impedance module – high frequency


Capacitors

Classification

Constructive criteria

• Discrete

• Embedded

Fixed

Variable

At the PCB level

At the ceramic substrate level

Inside integrated circuits

Classification

• Fixed

• Variable

Non-polarized

Polarized

With air as dielectric

Trimmers


Capacitors

Parameters

• For capacitors with the capacitance lower then 1μF, the nominal capacitance respects the normalized series E6, E12, E24, etc., with their designated tolerances.

Nominal capacitance and its tolerance (discrete capacitors)

• For capacitors with higher capacitances (especially for electrolytic capacitors), the following normalized values are being used: 1, 2, 3, 4, 5, 8, 16, 25, 32, 64. Their tolerance can be found in larger the usual domains: tє[-40%; +100%].

• Obtaining low tolerances capacitors is more difficult as for resistances.

Parameters

• The nominal voltage represents the maximum DC voltage (or the maximum value of the effective voltage for an alternative voltage) which can be applied at the capacitor’s terminals for a prolong functionality regime at the superior temperature limit without breaking the capacitor.

Nominal voltage, Vn

• Choosing this value takes into consideration a safety coefficient kє[1.5;3] lower then a test voltage (test voltage – a voltage closer but lower then the dielectric breakdown voltage) for the capacitor. The safety coefficient covers the situations on which the capacitor’s dielectric is affected by the so called aging.

• Exceeding the value for the above parameter can concur to dielectric breakdown.

Parameters

• The nominal voltage respects as well a normalized value series: 6, 12, 16, 25, 63, 70, 100, 125, 250, 350, 450, 500, 630, 1000 volts.

Nominal voltage, Vn

• For the other capacitors, this parameter can be deduced from the capacitor’s dimensions.

• For certain electrolytic capacitors, this parameter is printed on their body.

Parameters

• The insulating resistance characterizes the insulating dielectric material imperfections

The insulating resistance

• Typical values: 104 MΩ for ceramic capacitors, 102 - 105 MΩ for the plastic film capacitors.

• Can be defined as the ratio between the DC voltage applied at the capacitor’s terminals and the DC current that flows through it.

Parameters

• The insulating resistance parameter can be deduced from other two parameters which are clearly specified for the capacitors (for most higher value capacitors – especially the electrolytic capacitors):

The insulating resistance – equivalent parameters

The specific time constant:

The leakage current (ro: curent de fuga):

izn RC

iz

nf R

VI

Parameters

• The loss angle tangent represents the ration between the active power which its being dissipated by the capacitor and the reactive power of the capacitor when a sinusoidal voltage is applied at the capacitor’s terminals:

Loss-angle tangent

iznn

iz

r

a

RCVC

RV

P

Ptg

1

2

2)( 2

2

• The loss angle tangent represents also the ration between the currents that flow through the insulating resistance, respectively through the nominal capacitance when a sinusoidal voltage is applied at the capacitor’s terminals:

iznCn

Riz

RCI

Itg

1

)(

Parameters

• The loss angle tangent is frequency dependent. That is why, in the electronic data-sheets, the loss-angle tangent is indicated in respect with the frequency at which the capacitor was measured.

Loss-angle tangent

• For an ideal capacitor, this parameter should be zero. For real capacitor is desirable that the loss-angle tangent to be as lower as possible.

• Typical values: 10-5 (ceramic or mica capacitors), 0.25 for electrolytic capacitors

• In some datasheets, you can find an equivalent parameter instead of the loss-angle tangent – quality factor:

iznRCtg

Q

)(

1

Parameters

• It is printed only for certain capacitors. Following this parameter, the capacitors can be divided in different categories.

Temperature coefficient

• The temperature coefficient is defined as follows:

dT

dC

CC 1

• For most of the capacitors, this parameter can be considered constant only for a limited temperature domain.

• In some datasheets it is specified as parts per million per Celsius degree:

C][ppm/1 o

0

0

0 TT

CC

CC

Parameters

• The temperature domain differs from a technology to another: from -10°C to +70°C for paper dielectric capacitors, from -40°C to +125°C for the tantalum electrolytic capacitors.

Performance parameters:

• The frequency domain is limited by the dielectric behavior and by the inductive parasitic component. For the ceramic capacitors the frequency domain reaches GHz values, for the electrolytic capacitors only to tens of kHz.

• The specific capacitance characterizes the technology performances, being defined as the ration between the nominal capacitance and the capacitor’s volume.


Capacitors

Marking

• The capacitors marking refers at the procedure with the help of which the information printed is encrypted.

Marking using letter and digit codes.

Marking using the capacitors color code.

• In comparison with the resistors, the marking procedure is more diversified. The information printed on each capacitor differs from a technology type to another.

Marking


• On certain capacitors, the nominal value of the capacitance and the nominal value of the voltage can be printed clearly, respectively for the tolerance you will find the standardized letters (as for the resistors):

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

Marking


• Another procedure consists in printing a code with 3 digits and a letter. First to digits represent the nominal value digits. The third digit represents the multiplier in respect with the 1pF value. The letter represents the tolerance.

474JValue 47,

multiplier 104, tolerance 5%

Cn = 470nF, tolerance 5%

Marking

Marking using capacitors color code.

• There can be various procedures:

Three colors – only the nominal capacitance.

Four colors.

Five colors – can have different meaning from a capacitor to another.

• For certain ceramic capacitors, the temperature coefficient can be printed as well on the capacitor’s body.

• In is recommended to review the datasheets for every capacitor type.


Capacitors

Choosing capacitors criteria

• Depending on every application requirements, the capacitors are being chosen from different technological families.

• The frequency domain in which the capacitor will be used establishes the technological type of the capacitor.

• A way of choosing the proper capacitor by application is to characterize the main technological types.


d

AC 0ε r

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


Ceramic capacitors – constructive approach

1 - plates, 2 - ceramic dielectric

3 - terminals


Type I ceramic capacitors

• Properties:

The dielectric – magnesium silicate ceramic based with εrє[5-200].

High stability with the temperature variation.

• Parameters:

Low and very low tolerances;

Cn є[0.8pF-27nF]; Riz>10GΩ; tg(δ)<15x10-4; Low temperature coefficients and linear behavior;

• Applications: in industrial and professional equipment, where the temperature stability is mandatory. Can be also used for high frequency applications.


Type II ceramic capacitors

• Properties:

The dielectric – high electrical permittivity ceramic (εr can reach 15000.

Very high specific capacitances in the pF and nF domains.

• Parameters:

Medium tolerances;

Cn є[33pF-100nF]; Riz>3GΩ; tg(δ)<0.035; Undefined temperature coefficients and high nominal

voltages.• Applications: in industrial and professional equipment,

where the miniaturization is mandatory, decoupling and filtering applications. Very used at high voltages and frequencies.


Plastic film capacitors – constructive approach


Plastic film capacitors – with polystyrene or myler

• Properties:

The dielectric – plastic film foil on which the plates are being deposited as an aluminum foil.

The foil is rolled resulting high specific capacitances (myler) but also high parasitic inductances.

• Parameters:

Medium tolerances;

Cn є[47pF-6.8μF]; Low tg(δ) for the polystyrene capacitors, respectively temperature dependent loss-angle tangent for the myler capacitors.

Low temperature coefficients for polystyrene capacitors.• Applications: in general use equipment for decoupling and

filtering applications. Limited frequency domain due to the inductive parasitic component.


Paper capacitors

• Properties: The dielectric – special paper (e.g.

capacitor paper) on which the plates are being deposited. Even though the paper has special properties, the paper is strongly affected by humidity.• Parameters:

High tolerances (20%). Cn є[10nF-20μF]; High tg(δ) strongly

dependent with the temperature.

Unstable with the temperature and humidity.• Applications: in high power circuits,

decoupling, engines starting applications, in applications where large capacitances are needed and electrolytic capacitors cannot be used, low frequencies only.

Low specific capacitance so large dimensions.


Mica capacitors

• Properties: The dielectric – mica ant the plates are tin, electrolytic

copper or aluminum foil.

High price due to high technology requirements.

• Parameters:

Medium tolerances.

Cn є[1pF-100nF]; tg(δ) < 15x10-4.

Very good stability with the temperature.

• Applications: in professional circuits where temperature stability is mandatory and in very high voltage applications.

Very high nominal voltages, up to 35 kV.


Aluminum electrolytic capacitors

• Technology:

The dielectric is obtained by oxidizing the aluminum foil surface.

One plate is the aluminum foil and the other is a conductive liquid called electrolyte.

The electrolyte can be impregnated in a substrate (paper) obtaining dry or semi-dry capacitors.


Aluminum electrolytic capacitors

• Properties: The low thickness of the oxide layer limits the voltage at

which the capacitor can be connected.

High specific capacitances can be obtained by growing the plates surface by roughening (ro: asperizare).

• Parameters: High and very high tolerances [-20%;+100%] for small

capacitances and [-20%;+50%] for the larger capacitors. Cn є[1μF-200μF] –small capacitors, Cn є[100μF-10mF] –

large capacitors.

• Applications: in industrial circuits only at low frequency.

High nominal voltages, up to 350V (small capacitors) and up to 450 (large capacitors).

High parasitic elements.


Non – polarized electrolytic capacitors

• Properties: Tantalum based. From the constructive point of view are

two tantalum capacitors connected in series where the dielectric is the common plate.

Series connection lowers the specific capacitance.

• Parameters: Tolerances [-20%;

+20%]. Cn є[4.7μF-150μF].

• Applications: in circuits where high capacitance values are needed and polarized and paper capacitors cannot be used. Not recommended at high voltages or at frequencies higher then 20 kHz.

Nominal voltages up to 10V. Low loss-angle tangent.

+ +

a rm ă tu ră m e ta l ic ă (T a )a rm ă tu ră m e ta l ic ă (T a )

e le c tro l it


Tantalum electrolytic capacitors

• Properties: Tantalum superior mechanical properties allow using a

low thickness foil. The tantalum relative permittivity is twice the aluminum

relative permittivity.

• Parameters: High tolerances [-20%;+30%] for small capacitors (“drop”)

and [-20%;+20%] for the professional capacitors. Cn є[0.1μF-680μF] –small capacitors, Cn є[100μF-330μF] –

professional capacitors.

• Applications: in industrial circuits up to 10kHz.

Nominal voltages up to 50V (small capacitors) and up to 63V (professional capacitors).

Lower parasitic elements in comparison with the aluminum electrolytic capacitors.


Using electrolytic capacitors

• The “+” sign suggest that that plate must be connect in a circuit in a higher potential point that the “-” plate!

+

VC VC VC

VC >0

electrolitoxidmetal

• Every capacitor has printed or marked either the positive terminal either the negative one. If the marking misses, then the capacitor casing is connected to the negative terminal.

• If you don’t follow the above connection, the capacitor will be overheated and will blow up!


Capacitors

Variable capacitors

Variable capacitors with air as a dielectric

• Consist in a succession of plates – fixed (stator) and mobile (rotor). The rotor plates are interlocked with the stator plates. The mobile plates rotation will lead in a variable superposed surface of the plates (lower or higher). In this way, the capacitance can be modified.

• Applications: filtering applications for selectivity purposes.

• The big difference between potentiometers and variable capacitors is that the variable capacitors have only 2 terminals. Thus, it can be used only in rheostat topology.

Variable capacitors

Parameters

• Parameters similar with fixed capacitors:

Nominal capacitance (related with the maximum value of the capacitance).

Nominal capacitance’s tolerance.

Loss-angle tangent.

Insulating resistance.

Breakdown voltage.

Temperature coefficient.

Variable capacitors

Specific parameters

The effective rotation angle.

Residual capacitance.

Maximum capacitance variation (Cn-Crez).

The capacitance variation law:

The mobile plate’s rotation momentum.

Reversibility.

ngleaotationrαCCfC rezn ;,,

Variable capacitors

Trimmers

• Are equivalent with semi-adjustable resistors.

• The dielectric can be: air, ceramic or even organic.

• Their capacitance is being modified when the equipment is powered up or during a periodically checking procedure.

• Trimmers have very low capacitances. Usually in the pF domain.


Capacitors

Special capacitors – non-linear capacitors

Varicap diodes

• The capacitance varies function of the DC voltage applied at its terminals.

• The varicap diodes are being used in selective filtering applications, mechanical control (used for adjustable capacitors) being replaced by an electric control – the DC voltage applied at the varicap diode’s terminals.

• Are polarized capacitors.

Problem

On a capacitor, the following parameters are being printed: 1μF and 63V. From its datasheet, the following parameters are extracted: tg(δ) = 0.001, measured at the Romanian electrical network frequency and αT=0.002[1/°C].

• Can the capacitor be connected directly at the electrical network if the environment temperature is 50°C? Sustain your answer.• What is the impedance module of the capacitor if the voltage vI(t)=5+20sin(100t) [V] is being applied at its terminals?

• The capacitor is connected in series with a 10kΩ resistor. How does the voltage across the capacitor look after 10ms from the moment when the previous voltage was applied at the series connection above?

Problem

For the capacitor from the figure below, the following parameters are being extracted from its datasheet:

• Temperature domain: [-40°C;+85°C].• Tolerance: 20%.

• Nominal capacitance: 1μF.

• Loos-angle tangent: 0.02 at 1kHz and 25°C.• Nominal voltage: 250VDC.

CRvi vo

1K

Please determine the value for the insulating resistance.

Draw the equivalent circuit. Plot the modulus of the vO/vI

function.

Documents

V. Bande, Applied Electronics Department (English version)-> Information for students Lecture 9 1 Passive Electronic