1. V. Bande, Applied Electronics Department www.ael.utcluj.rowww.ael.utcluj.ro (English version)-> Information for students Lecture 9 1 Passive Electronic Components and Circuits (PECC) Capacitors

2. Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

3. 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

4. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

5. Electrical properties  Capacitance vs geometry dependency d A - - - - - + + Parallel plates a b L r +Q+Q -Q-Q Cylindrical plates a b +Q+Q -Q-Q Spherical plates    pF/m

6. Electrical properties 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. Through its relative electrical permittivity, ε r the capacitor’s capacitance can be controlled.

7. Electrical properties The real part characterizes energy accumulation inside the capacitor.  Electrical permittivity – complex quantity  *=  ’+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.

8. Electrical properties  Dielectric properties

9. Electrical properties  The capacitor – the electrical equivalent model

10. Electrical properties  The capacitor – the frequency characteristic

11. Electrical properties  Parallel connection 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).

12. Electrical properties  The capacitors impedance module

13. Electrical properties  The equivalent capacitor impedance module – high frequency

14. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

15. Classification  Constructive criteria Discrete Embedded  Fixed  Variable  At the PCB level  At the ceramic substrate level  Inside integrated circuits

16. Classification Fixed Variable  Non-polarized  Polarized  With air as dielectric  Trimmers

17. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

18. 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.

19. 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, V n 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.

20. 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, V n 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.

21. Parameters The insulating resistance characterizes the insulating dielectric material imperfections  The insulating resistance Typical values: 10 4 MΩ for ceramic capacitors, 10 2 - 10 5 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.

22. 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 ):

23. 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 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:

24. 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:

25. 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: 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:

26. 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.

27. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

28. 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.

29. Marking  Marking using letter and digit codes. 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): B  0,1%; C  0,25%; D  0,5%; F  1%; G  2%; H  2,5%; J  5%; K  10%; M  20%

30. Marking  Marking using letter and digit codes. 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. Value 47, multiplier 10 4, tolerance 5% C n = 470nF, tolerance 5%

31. 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.

32. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

33. 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.

34. Choosing capacitors criteria

35.  Ceramic capacitors – constructive approach 1 - plates, 2 - ceramic dielectric 3 - terminals

36. Choosing capacitors criteria  Type I ceramic capacitors Properties:  The dielectric – magnesium silicate ceramic based with ε r є[5-200].  High stability with the temperature variation. Parameters:  Low and very low tolerances;  C n є[0.8pF-27nF]; R iz >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.

37. Choosing capacitors criteria  Type II ceramic capacitors Properties:  The dielectric – high electrical permittivity ceramic (ε r can reach 15000.  Very high specific capacitances in the pF and nF domains. Parameters:  Medium tolerances;  C n є[33pF-100nF]; R iz >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.

38. Choosing capacitors criteria  Plastic film capacitors – constructive approach

39. Choosing capacitors criteria  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;  C n 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.

40. Choosing capacitors criteria  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%).  C n 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.

41. Choosing capacitors criteria  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.  C n 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.

42. Choosing capacitors criteria  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.

43. Choosing capacitors criteria  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.  C n є[1μF-200μF] –small capacitors, C n 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.

44. Choosing capacitors criteria  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%].  C n 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.

45. Choosing capacitors criteria  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.  C n є[0.1μF-680μF] –small capacitors, C n 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.

46. Choosing capacitors criteria  Using electrolytic capacitors The “+” sign suggest that that plate must be connect in a circuit in a higher potential point that the “-” plate! 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!

47. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

48. 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.

49. 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.

50. Variable capacitors  Specific parameters  The effective rotation angle.  Residual capacitance.  Maximum capacitance variation (C n -C rez ).  The capacitance variation law:  The mobile plate’s rotation momentum.  Reversibility.

51. 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.

52. Capacitors Short history Electrical Properties Classification Parameters Marking Choosing capacitors criteria Variable resistors Special capacitors – nonlinear capacitorsCapacitors

53. 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.

54. 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 v I (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?

55. 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: 250V DC.  Please determine the value for the insulating resistance.  Draw the equivalent circuit.  Plot the modulus of the v O /v I function.