©Paul R. Godin prgodin @ gmail.com

Capacitance

Capacitance 1

DIGI-260

Capacitance 1.1

Capacitance

Capacitance

• Capacitance affects digital electronics in various ways: – Used for timing elements such as monostables, astables and other time-based circuits – Used in filters for supply noise and external noise – Affects digital transmission, digital design and circuit board design – Used in some types of memory circuits – Used in detection and sensor circuits

Capacitance 1.2

Capacitance

Capacitance

• Capacitance is storage of an electrical charge, measured in Farads.

• It is a property where an arrangement of conductors and an insulator can store an electrical charge if a voltage difference exists between them.

Capacitance 1.3

Capacitance

Capacitors

• Capacitors are devices designed to hold an electrical charge.

• Capacitors are based on electrostatic principles where a force of attraction or repulsion exists between charged bodies.

Capacitance 1.4

Capacitance

Basic Model of an Atom

Electron (-) Proton (+) Neutron (no charge) Nucleus Orbit (path of the spinning electrons) Capacitance 1.5

Capacitance

Electro-statically charged particles

Capacitance 1.6

Capacitance

Electrostatic Fields

Coulomb’s Law of electrostatic attraction.

F



kQ

1

Q

2

d

2

Where: F = force (Newtons) Q 1 , Q 2 = charges (Coulombs) d = distance between the charges (meters) K = dielectric constant of the insulator Capacitance 1.7

Capacitance

Capacitors

• Capacitors consist of two conductors usually in the form of plates, separated by an insulator (dielectric).

• Increasing the plate size can be accomplished by rolling it up into a smaller package, or stacking plates.

Capacitance 1.8

Capacitance

Capacitors

The plates hold the charge.

- - + + + + + +

Attraction The charge is held on the plates because the negative and positive charges are attracted to each other. Without a conductive path connecting them, the charge remains on the plates.

Capacitance 1.9

- - + + + + + + Capacitance

Capacitors Maximum Voltage

Voltage Capacitors have a maximum voltage rating. If the voltage is great enough current will arc through the dielectric, destroying the capacitor.

Capacitance 1.10

Capacitance

Capacitor

• Symbols:

Non-Polarized Polarized

• Letter Symbol: C • Unit of Measure: Farads (F) – Typical: µF, ηF, ρF

Variable Capacitance 1.11

Capacitance

Factors Affecting Capacitance

Plate size – The larger the plates the more charge can be held Separation between the plates – The larger the separation between the plates the less the attraction between the plates. Less charge.

The insulator – The insulating material between the plates affects the attraction between the plates

Capacitance 1.12

Capacitance

Factors Affecting Capacitance

• Plate size (measured in meters 2 ) • Separation between the plates (in meters) • The dielectric constant of the insulator – measured as Permittivity, symbol ε, unit 

Dielectric

Vacuum Air Teflon Paraffin paper Rubber Tranformer oil Mica Procelain Bakelite Glass Water Ceramic 

r

1.0

1.0006

2.0

2.5

3.0

4.0

5.0

6.0

7.0

7.5

80.0

7500.0

Relative permittivity of materials

Capacitance 1.13

Capacitance

Calculating Capacitance

• The formula for calculating capacitance from physical characteristics: C  A   r  ( 8 .

85 d  10  12 F / m ) A = Area of the plates, in meters 2 ε r = Relative Permittivity (no unit of measure...it’s a ratio) 8.85 x 10 -12 F/m = permittivity in a vacuum, in Farads/meter d = distance between plates, in meters

Capacitance 1.14

Capacitance

Examples

1. Calculate the capacitance of a plate capacitor that has a plate area of 0.02

2 meters, a plate separation of 0.01 meters and uses glass as a dielectric.

2. What happens to the capacitance if the distance between the plates is doubled?

3. What happens if the area of the plates is doubled?

Capacitance 1.15

Capacitance

Types of Capacitors

• Non-polarized: – Mica, glass, polyester, ceramic, air, other plastic • Polarized: – electrolytic, tantalum • Variable – air – ceramic or mica often called trimmers

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Capacitance

Capacitors in Series, Parallel

• Capacitance in parallel: values are added – Think of it as making bigger plates – C T = C 1 + C 2 • Capacitors in series: reciprocals are added 1 C T  1 C 1  1 C 2

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Capacitance

Capacitor Charge and Discharge in DC Applications

Capacitance 1.18

Capacitance

Capacitor Charge

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Capacitance

Charge Cycle: Initial State

• Initial state: The capacitor is in a discharged state

Capacitance 1.20

Capacitance

Charge Cycle: Initial charge state

• Charge state: At the moment the switch is closed the capacitor act like a short circuit. The electrons see empty plates and it has no voltage across it (think KVL). All of the voltage of the source appears across the resistor.

Capacitance 1.21

Capacitance

Charge Cycle: Charge state

++++ ++++ --- ----

• Charge state: As the electrons begin to fill the plates on the capacitor a voltage develops across it. • Voltage across the resistor correspondingly drops as the voltage across the capacitor increases. Current is reduced.

Capacitance 1.22

Capacitance

Charge Cycle: Final Charge state

++++ ++++ ---- ----

• Charge state: Once the capacitor has developed the full applied voltage the current drops to 0. There is no more current flowing in the circuit. The capacitor is an open circuit, and the voltage across the capacitor equals the applied voltage (KVL).

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Capacitance

Charged

++++ ++++ --- ----

• The capacitor retains the charge after being disconnected from the source.

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Capacitance

Capacitor Discharge

Capacitance 1.25

Capacitance

Discharge: Initial State

++++ ++++ --- ----

• The capacitor acts like a source. The resistor has the capacitor voltage across it.

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Capacitance

Discharge: Discharge State

++++ ----

• As the capacitor charge becomes depleted, the voltage drops. The voltage across the resistor correspondingly drops.

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Capacitance

Discharge: Final State

• The capacitor has depleted its charge, current and voltages are all at 0.

Capacitance 1.28

Capacitance

Transient Time

• Capacitor charge and discharge cycles take time. • The size of the capacitor and of the resistor will have a direct impact on this time.

– The resistor limits the current and therefore affects the time it takes to fully charge or discharge the capacitor – The capacitor size determines the amount of current it requires over time to achieve full charge or full discharge state • The time it takes for a capacitor to go from an initial state to a final state is called transient time.

Capacitance 1.29

Capacitance

Time Constant

• A unit of time for charging or discharging a capacitor can be expressed as a time constant tau:   RC  either fully charged or fully discharged.

• Each tau represents 63.2% of change to the capacitor voltage.

Capacitance 1.30

% charge

Capacitance

Charge Curve

Tau

Capacitance 1.31

Capacitance

Numerical values for Tau

4.5

5 5.5

6 2 2.5

3 3.5

4 Tau Discharge 0 0.5

1 0.607

1 1.5

0.368

0.223

0.135

0.082

0.050

0.030

0.018

0.011

0.007

0.004

0.002

Charge 0 0.393

0.632

0.777

0.865

0.918

0.950

0.970

0.982

0.9891

0.993

0.996

0.998

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Capacitance

Charge Equation

• The capacitor charges exponentially v C  E  1  e  t / RC  – Where: • • E = potential applied to the capacitor

е

= natural log (2.718) • t = elapsed time • RC = tau = resistor • capacitor

Capacitance 1.33

Capacitance

Discharge Curve

Capacitance 1.34

Capacitance

Discharge Equation

• The capacitor discharges exponentially v C  Ee  t / RC – Where: • • E = potential applied to the capacitor

е

= natural log (2.718) • t = elapsed time • RC = tau = resistor • capacitor

Capacitance 1.35

Capacitance

Universal Charge-Discharge Curves

Capacitance 1.36

Capacitance

Example

• A series circuit has a 50kΩ resistor and a 10µF capacitor, with a voltage source of 5 volts. Assuming an initial charge of 0, calculate: – tau – the time to achieve what is considered full charge – the voltage across the capacitor 0.2 seconds after the source is applied.

Capacitance 1.37

Capacitance

Example Solution

• A series circuit has a 50kΩ resistor and a 10µF capacitor, with a voltage source of 5 volts. • Solutions: v C – tau = 50,000 x 0.000 01 = 0.5

– full charge = 5 tau = 5 x 0.5 = 2.5 seconds  – the voltage across the capacitor 0.2 seconds after the source is applied = E  1  e  t / RC   5 ( 1  e  0 .

2 / 0 .

5 )  5 ( 1  0 .

67 )  5 ( 0 .

33 )  1 .

65 V

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Capacitance

END ©Paul R. Godin prgodin @ gmail.com

Capacitance 1.39