Chapter 9 Capacitors
Basics of a Capacitor In its simplest form, a capacitor is an electrical device constructed of two parallel plates separated by an insulating material called the dielectric In the neutral state, both plates have an equal number of free electrons When a voltage source is connected to the capacitor, electrons are removed from one plate and an equal number are deposited on the other plate No electrons flow through the dielectric (insulator)
FIGURE 9-1 The basic capacitor.
Illustration of a capacitor storing charge
Equivalent circuit for a no ideal capacitor No Current flows through a capacitor except for undesired leakage current.
How a Capacitor Stores Energy A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates A capacitor obeys Coulomb s law: A force exists between two point-source charges that is directly proportional to the product of the two charges and inversely proportional to the square of the distance between the charges
The electric field stores energy in a capacitor. The beige area indicates the dielectric.
Lines of force are created by opposite charges The unit for Capacitance is the Farad (F) 1 Farad = 1 Coloumb/1V Usually specified un Micro-Farads (uf)
Characteristics of a Capacitor Capacitance is directly proportional to the physical size of the plates as determined by the plate area Capacitance is inversely proportional to the distance between the plates The measure of the dielectric material s ability to establish an electric field is called the dielectric constant. Capacitance is directly proportional to the dielectric constant The measure of how much voltage a capacitor can handle across it s plates is called dielectric strength or breakdown voltage. All capacitors specify a safe voltage at which to operate the capacitor. Most capacitors have a very thin dielectric and a very large plate area (often stacked or rolled up).
Capacitance is directly proportional to plate area (A) Less plate area = Less Capacitance
Capacitance is inversely proportional to the distance d between the plates More distance between plates = Less Capacitance
Charging a capacitor Uncharged Cap Appears as a short the instant the switch is closed Charging Cap Current drops and voltage across cap rises Charged Cap Appears as an open All current stops and V C = V S No current except for leakage current and capacitor stores the charge
Discharging a Capacitor Current reverses: High at first then drops as voltage drops Back to where it started This phenomenon often makes it appear that current is passing through the cap It does not The reversing current goes back to the supply
Fixed Capacitors Stacked-foil mica capacitors are made of alternate layers of metal foil and thin sheets of mica Silver mica are formed by stacking mica sheets with silver electrode material screened on them Range from 1pF to 0.1 uf @ 2500V Low Capacitance @ High Voltage
Fixed Capacitors Ceramic capacitors provide very high dielectric constants, and relatively large capacitance in a small physical size Capacitance ranges are from 1pF to 2.2µF @ 2500V Medium Capacitance @ High Voltage
(a) Typical ceramic capacitors with radial leads. (b) Construction view Up to 2.2uF @ 6kV Medium Capacitance @ Very High Voltage
Electrolytic Capacitors Two common types of electrolytic capacitors are Aluminum and Tantalum electrolytics Safety Warning: The voltage polarity of these devices must be observed, as reversal of polarity will usually result in complete destruction of the capacitor
Electrolytic Capacitors Electrolytic capacitors have higher capacitance but lower voltage ratings and higher leakage current They come in capacitance values from 1µF to 200,000 µf, with voltage ratings to 350 V High Capacitance @ Low (Polarized) Voltage
Basic construction of axial-lead tubular plastic-film dielectric capacitor.
Electrolytic capacitors
Construction view of a typical tear drop shaped tantalum electrolytic capacitor Tear Drop shaped tantalum electrolytic capacitor.
Variable Capacitors Variable capacitors are used in circuits when there is a need to adjust the capacitance value Ceramic or mica is a common dielectric Capacitance is changed by plate separation
FIGURE 9-16 Schematic symbol for a variable capacitor. Schematic symbol for a variable capacitor.
Variable Air Capacitor Air Capacitors are used in high frequency (RF) applications The space between the plates (air) is the dielectric This is an example of a variable air capacitor probably used in a radio tuner
Series Capacitors When capacitors are connected in series, the total capacitance is less than the smallest capacitance value This is because the effective plate separation increases 1 1/C 1 + 1/C 2 + 1/C 3 + + 1/C n
Capacitors in series produce a total capacitance that is less than the smallest value C T = 76.7pF
In a DC Circuit, current stops flowing when the smallest cap is charged V s = VC 1 + VC 2
Capacitor Voltages The smallest cap holds the largest voltage And versa visa (The smallest cap charges first halting all current flow) FIGURE 9-22 P 406 V x = (C T /C x )V S
Parallel Capacitors The total parallel capacitance is the sum of all capacitors in parallel C T = C 1 + C 2 + C 3 + + C n This is because the effective plate area increases
FIGURE 9-24 C T = 560 pf
FIGURE 9-26 C T =.133uF
FIGURE 9-23 P 407 Capacitors in parallel produce a total capacitance that is the sum of the individual capacitances. Current doesn t stop until all caps are charged V C1 = V C2
RC Time Constant The voltage across a capacitor cannot change instantaneously because a finite time is required to move charge from one point to another (limited by circuit resistance) The time constant of a series RC circuit is a time interval that equals the product of the resistance and the capacitance τ = RC
Current and voltage in a charging and discharging capacitor
Charging and Discharging The charging curve is an increasing exponential The discharging curve is a decreasing exponential It takes 5 time constants to change the voltage by 99% (charging or discharging), this is called the transient time
Charge and discharge curves shown together Charge v Charge i Discharge v & i
Formulas for instantaneous charging and discharge voltages and currents * = On Quiz General Instantaneous Charging Voltage Formula: (Determine Instantaneous Voltage Charging From an Initial Instantaneous Value) Determine Instantaneous Voltages Charging From 0V * Determine Instantaneous Voltages Discharging to 0V *
Determining the instantaneous voltage during capacitor charge Determine the Instantaneous Voltage across the capacitor at 50 us
Determining the instantaneous voltage during capacitor discharge Determine the capacitor voltage 6 ms after the switch is closed The capacitor is charged
Capacitive Reactance, X C Capacitive reactance (X C ) is the opposition to sinusoidal current, expressed in ohms The rate of change of voltage is directly related to frequency As the frequency increases, the rate of change of voltage increases, and thus current ( i ) increases An increase in i means that there is less opposition to current (X C is less) X C is inversely proportional to i and to frequency
The current in a capacitive circuit varies directly with the frequency of the source voltage Because the voltage rate of change is higher at higher frequencies, the capacitive current increases proportionately with the frequency
For a fixed voltage and frequency, the current varies directly with the capacitance value Relationship of Capacitance and Current
Rate of change of a sine wave increases when frequency increases Formula for X C
Determine X C in the circuit below FIGURE 9-41 P 418 1 khz
Ohm s Law for Capacitors V rms = I X C I rms = V rms /X c X c = V rms I
Determine the RMS Current in the circuit below Approx. Equivalent Circuit
Capacitors in ac Circuits When a sine wave signal is applied to a capacitor, the instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor This rate of change is a maximum positive when the rising sine wave crosses zero This rate of change is a maximum negative when the falling sine wave crosses zero The rate of change is zero at the maximum and minimum of the sine wave
The rates of change of a sine wave The higher the rate of voltage change, the higher the capacitor current
Analysis of Capacitive ac Circuit The current leads the voltage by 90 in a purely capacitive ac circuit (ICE) This is because: Current in a capacitor is dependent upon the rate of voltage change The highest rate of change in voltage is when it crosses zero volts. This is also when the capacitor is closer to being discharged and easily accepts higher current change. The least rate of change in voltage is near the peak voltage There is zero rate of change in voltage at peak. This is also when the capacitor is closest to being charged and doesn t easily accept much current change. Close to Discharged Close to Charged V C V S Close to Discharged Close to Charged
Current is always leading the capacitor voltage by 90 I C +90 o (Lead) V S, V C 0 o (Reference) Vector Diagram Close to Discharged Close to Charged Close to Discharged Close to Charged
Power in a Capacitor (Purely Capacitive Circuit) Energy is stored by the capacitor during a portion of the voltage cycle; then the stored energy is returned to the source during another portion of the cycle True power (P true ) is zero, since no energy is consumed by the capacitor. It just shifts back and forth between the cap and the source. Reactive Power (P r )The overall rate at which a capacitor stores and returns energy. Unit: (VAR) Instantaneous power (p) is the instantaneous product of v and i at any given time.
True Power (P true ) = 0 There is no energy dissipation, just energy transfer (Except for leakage current) The current just shifts back and forth between the cap and the source FIGURE 9-45 Power curve for a capacitor. (Reactive) Reactive Power Formulas Instantaneous Power: Instantaneous Values Power is 0 when either V or I are 0 Power is maximum when V or I are equal (positive or negative) Power Frequency is 2X the source frequency
Determine the true power and reactive power for the circuit below FIGURE 9-46 P true = 0
Capacitor Applications Since capacitors pass ac (Signals) and do not pass DC, they are used for DC blocking and ac signal coupling between circuit stages Capacitors are used for filtering in power supplies Capacitors are used to eliminate unwanted ac signals
An application of a capacitor used to block DC and couple ac in an amplifier Un-Biased Signal Biased Signal Capacitors Pass AC and Block DC (Pass Signals/Changing Current and Block DC)
FIGURE 9-55 Capacitively coupled amplifier.
Basic block diagram and operation of a dc power supply Capacitors can also be used to filter out unwanted signals or ripple
Half-wave and full-wave rectifier operation
Basic operation of a power supply filter capacitor The capacitance of the filter capacitor(s) is usually fairly large
Example of the operation of a bypass capacitor Input Output Unwanted Signal is Passed or Shunted to ground
More Capacitor Applications Capacitors are used in filters, to select one ac signal with a certain specified frequency from a wide range of signals with many different frequencies For example, the selection of one radio station and rejecting the others (High/Low/Bandpass Filters) Capacitors are used in timing circuits to generate time delays, based on the RC time constant Dynamic memories used in computers are simply very tiny capacitors used as a storage element
Checking a capacitor with an analog ohmmeter. This check shows a good capacitor.
A typical capacitance meter. (Courtesy of B+K Precision) Capacitance meters are also included in most modern multimeters too