Lecture 9
Capacitors
Passive Electronic Components and Circuits (PECC)
V. Bande, Applied Electronics Department
www.ael.utcluj.ro (English version)-> Information for students
1
Capacitors
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear 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
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear capacitors
Electrical properties
 Capacitance vs geometry dependency
-Q
A
++++
d
----Parallel plates
C
o A
d
+Q
r
a
-Q
a
+Q
b
b
L
Cylindrical plates
C
2 o L
b
ln  
a
08,85419 pF/m
Spherical plates
ab
C  4 o
ba
Electrical properties
 The dielectric influence
• A very important role of the capacitor behavior is played by the
insulting material (dielectric) displaced between the metallic
plates of every capacitor.
• Through its relative electrical permittivity,
capacitance can be controlled.
A
C   r  C0 ; C0   0 
d
εr
the capacitor’s
• 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.
Electrical properties
 Electrical permittivity – complex quantity
• The
real
part
characterizes
energy
accumulation inside the
capacitor.
• The
imaginary
part
characterizes
energy
dissipation inside the
capacitor.
• The ratio between the
imaginary part and the
real part is called lossangle tangent.
"
tg ( ) 
'

'
d0

*=’+i ’’
'
0
log(/0)
Electrical properties
 Dielectric properties
Electrical properties
 The capacitor – the electrical equivalent model
Z C  R s  jL p 
Rp
1  jR p C
Z C  R s  jL p 
1
jC
Electrical properties
 The capacitor – the frequency characteristic
ZC
Rp  Rs » Rp
10%
L
zona capacitivã
1
C
10%
Rs
2
Rp  C

0, 3   0
0 
1
LpC
Electrical properties
 Parallel connection
• Sometimes, in electronic
circuits, you can find a lowvalue capacitor connected in
parallel with a high value
capacitor.
C1
10 
C2
10 
C2
10 n
+
• In this situation, the lower
value capacitor compensates
the inductive component
from the other capacitor (the
higher value one).
C1
10 n
L1
L2 <L1
Electrical properties
 The capacitors impedance module
Electrical properties
 The equivalent capacitor impedance module – high frequency
Capacitors
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear capacitors
Classification
 Constructive criteria
• Discrete
 Fixed
 Variable
• Embedded
 At the PCB level
 At the ceramic substrate level
 Inside integrated circuits
Classification
• Fixed
 Non-polarized
 Polarized
• Variable
 With air as dielectric
 Trimmers
Capacitors
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear capacitors
Parameters
 Nominal capacitance and its tolerance (discrete capacitors)
• For capacitors with the capacitance lower then 1μF, the nominal
capacitance respects the normalized series E6, E12, E24, etc., with
their designated tolerances.
• Obtaining low tolerances capacitors is more difficult as for
resistances.
• 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%].
Parameters
 Nominal voltage, Vn
• 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.
• Exceeding the value for the above parameter can concur to
dielectric breakdown.
• 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.
Parameters
 Nominal voltage, Vn
• 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.
• For certain electrolytic capacitors, this parameter is printed on
their body.
• For the other capacitors, this parameter can be deduced from the
capacitor’s dimensions.
Parameters
 The insulating resistance
• The insulating resistance characterizes the insulating dielectric
material imperfections
• Can be defined as the ratio between the DC voltage applied at the
capacitor’s terminals and the DC current that flows through it.
• Typical values: 104 MΩ for ceramic capacitors, 102 - 105 MΩ for the
plastic film capacitors.
Parameters
 The insulating resistance – equivalent 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 specific time constant:
 The leakage current (ro: curent de fuga):
  Cn  Riz
Vn
If 
Riz
Parameters
 Loss-angle tangent
• 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:
V2
tg ( ) 
Pa

Pr
2 Riz
1

V 2 Cn Riz
Cn
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:
I Riz
1
tg ( ) 

I Cn Cn Riz
Parameters
 Loss-angle tangent
• 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.
• 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:
1
Q
 Cn Riz
tg ( )
Parameters
 Temperature coefficient
• It is printed only for certain capacitors. Following this parameter,
the capacitors can be divided in different categories.
• The temperature coefficient is defined as follows:
1 dC
C  
C dT
• 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:
1 C  C0
C  
[ppm/ o C]
C0 T  T0
Parameters
 Performance 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.
• 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
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear 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
 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%
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.
474J
Value 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
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear 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.
Choosing capacitors criteria
A
C  εr 0
d
electrolitice cu Al
electrolitice cu Ta
micã, ceramice cu pierdere micã
cu hârtie
cu hârtie metalizatã
ceramice K mare
polistiren
10 0
101
102
103
104
105
106
107
108
109
f
Choosing capacitors criteria
 Ceramic capacitors – constructive approach
1 - plates,
2 - ceramic dielectric
3 - terminals
Choosing capacitors criteria
 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.
Choosing capacitors criteria
 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.
Choosing capacitors criteria
 Plastic film capacitors – constructive approach
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;
 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.
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%).
 Cn є[10nF-20μF]; High tg(δ) strongly dependent
with the temperature.
 Low specific capacitance so large dimensions.
 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.
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.
 Cn є[1pF-100nF]; tg(δ) < 15x10-4.
 Very high nominal voltages, up to 35 kV.
 Very good stability with the temperature.
• Applications: in professional circuits where temperature stability
is mandatory and in very high voltage applications.
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 semidry capacitors.
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.
 Cn є[1μF-200μF] –small capacitors, Cn є[100μF-10mF] – large
capacitors.
 High nominal voltages, up to 350V (small capacitors) and up to
450 (large capacitors).
 High parasitic elements.
• Applications: in industrial circuits only at low frequency.
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%].
 Cn є[4.7μF-150μF].
 Nominal voltages up to 10V.
 Low loss-angle tangent.
electrolit
armătură metalică (Ta)
+
armătură metalică (Ta)
+
• 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.
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.
 Cn є[0.1μF-680μF] –small capacitors, Cn є[100μF-330μF] –
professional capacitors.
 Nominal voltages up to 50V (small capacitors) and up to 63V
(professional capacitors).
 Lower parasitic elements in comparison with the aluminum
electrolytic capacitors.
• Applications: in industrial circuits up to 10kHz.
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!
metal
• If you don’t follow the above
connection, the capacitor will be
overheated and will blow up!
electrolit
+
V
• 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.
oxid
C
V
V
C
C >0
V
C
Capacitors
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear 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.
• 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.
• Applications: filtering applications for
selectivity purposes.
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:
C  f Cn , Crez ,  ; α  rotation angle
 Reversibility.
 The mobile plate’s rotation momentum.
Variable capacitors
 Trimmers
• Are equivalent
resistors.
with
semi-adjustable
• Their capacitance is being modified when
the equipment is powered up or during a
periodically checking procedure.
• The dielectric can be: air, ceramic or even
organic.
• Trimmers have very low capacitances.
Usually in the pF domain.
Capacitors
Capacitors
Short history
Electrical Properties
Classification
Parameters
Marking
Choosing capacitors criteria
Variable resistors
Special capacitors – nonlinear 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.
 Please determine the value for the
insulating resistance.
 Draw the equivalent circuit.
 Plot the modulus of the vO/vI
function.
vi
C
R
1K
vo