In previous tutorials, we discussed setting up an electronics laboratory and learned rudimentary knowledge about resistors. Continuing with the discussion about passive components, let's talk about the capacitor.
Let's start with a fictitious circuit
Imagine a purely resistive circuit driven by an ideal voltage source or an ideal current source. In such a fictitious ideal circuit, purely resistive components (of purely resistive load circuit) have fixed voltage drops in a short time. Once the circuit is powered, the voltage drops across the components become constant and constant currents flow through them at all times.
Let's get back to reality
Virtually no electronic or electrical circuit behaves like our fictional circuit. There are no purely resistive components (even resistors show some reactance), ideal voltage sources, or ideal current sources. Even though a resistive circuit is powered by a constant voltage source or a constant current source, it goes through a transient state before reaching a fixed and stable state. Thus, all circuits and their components on application of a voltage or current experience changes in voltage or current through them. A course can reach a stable state only after some time.
DC circuits and DC signals
Broadly speaking, electrical signals can be classified as DC and AC signals. Any voltage or current source is a two-terminal device that can conduct current in two directions in any circuit. A DC circuit is a circuit in which current flows in only one direction from the voltage or current source that drives it. Thus, DC signals can be defined as electrical signals with fixed polarity and in which voltage and current change only in one direction. There is no polarity inversion or change in the direction of the current in the source that drives the circuit.
Practically, DC is a generalized term. It may also refer to a DC component of an electrical signal or the DC behavior of an electrical or electronic component. A DC signal can have voltage or current varying with time, but it never involves reversing the polarity of the voltage or reversing the direction of the current.
AC Circuits and AC Signals
A voltage source that supplies voltage in which the polarity keeps reversing alternatively is called an AC voltage source. Similarly, a current source that supplies current in which the direction continues alternating is called an AC source. A circuit powered by an AC voltage source or an AC source has an inversion of voltage polarity and current trend alternatively. Such circuits, where voltage and current change direction periodically, are called AC circuits. An AC signal can be defined as an electrical signal in which the voltage polarity and current direction alternate periodically. The voltage and current rise to a peak value, fall to zero reversing direction, rise again to a peak value in the opposite direction, and then fall to zero reversing direction. This continues until the signal remains active.
Signals, DC circuits and AC circuits
Changes in the magnitude (and direction) of voltage and current are all for the good. If the signals do not change over time, they are of no practical use. After all, electronics is about processing electrical signals. DC circuits process electrical signals in which voltage and/or current change in only one direction. AC circuits process electrical signals in which voltage and current change magnitude and keep changing direction alternatively.
More opposition to current : capacitance and inductance
Similar materials and electronic components show some natural opposition to current flow. This is defined by “resistance”. They also oppose any change in the magnitude and direction of the current. This is defined as “inductance”. Inductance comes from an opposing magnetic field induced in materials and electronic components in response to changing or alternating current.
Similarly, electronic materials and components present opposition to current due to opposing electric fields induced due to retention or storage of charge carriers by them. This is defined as “capacitance”. Resistance remains present in both DC and AC circuits and exhibits signal behavior similar to DC and AC signals. Only AC or DC circuits with pulsating DC signals show inductance and capacitance. In DC circuits involving constant DC signals, inductance and capacitance are not very significant (and are also unwanted).
While resistance dissipates electrical energy in the form of heat, inductance and capacitance temporarily store electrical energy in the form of magnetic and electric fields, respectively, and return it to the circuit again in the form of electrical energy. Therefore, there is no loss of energy due to inductance or capacitance, unlike the case of resistance.
Capacitance
Capacitance is the property of materials or electronic components by which they can temporarily store electrical charge. Capacitance is the amount of charge stored by an electronic entity per unit volt of applied potential difference.
C = Q/V
Where,
C = Capacitance (in Farad)
Q = Stored charge (in Coulombs)
V = Applied voltage (in Volts)
Obviously, a component with greater capacitance can store a more significant amount of charge per unit of applied voltage. Not all materials or components can store charge in response to an applied potential difference. Some special insulating materials that can polarize in response to applied potential difference have capacitance. These electronic materials are called dielectric materials or simply dielectrics. Fortunately, air or vacuum can serve as a dielectric medium, allowing the electric field to be established between two conductors in response to an applied voltage.
Devices designed to store charge in an electric field in response to applied potential difference (voltage) are called capacitors. The simplest capacitor can be two metal plates (electrodes) separated by air or vacuum. If the two boards are shorted together, they are nothing more than a connecting wire. The presence of air or vacuum, a dielectric medium, between the plates makes this assembly capable of storing electrical charge with some potential difference (voltage).
Therefore, any capacitor is a configuration of two electrodes (conductive materials) separated by a dielectric medium. The unit of capacitance is Farad (Coulomb/Volt), named after Michael Faraday. The property of a dielectric medium that determines the charge stored per unit volume upon application of unit voltage is called permittivity. The permittivity of free space or vacuum is a constant called absolute permittivity equal to 8.85×10 -12 Farad/Meter. The permittivity of a dielectric medium with respect to the absolute permittivity is called relative permittivity or dielectric constant. The capacitance of a capacitor depends on the permittivity of the dielectric medium used in it, the shape, size and construction of the capacitor.
Capacitance Unit
Farad is too large a unit to express standard capacitance. Thus, the capacitance of standard capacitors is expressed in submultiples of Farad such as Microfarad (10 -6 F), Nanofarad (10 -9 F) and Picofarad (10 -12 F).
Capacitor signal analysis
Let's first look at the behavior of a capacitor in a DC circuit. Capacitors are designed to temporarily store charge in a circuit. The simplest DC circuit with a capacitor can be a capacitor connected to a voltage source via a switch. A resistor (remember bleeder resistors) can be connected in parallel to the capacitor via another switch to discharge the capacitor.
Initially, there is no potential difference across the capacitor and let us assume that no charge is initially stored in the capacitor. When the voltage source is connected to the capacitor, a potential difference of equal voltage is applied to the capacitor. In response to an applied voltage, the dielectric medium of the capacitor begins to polarize and store charge in the form of an electric field. The following equation gives the charge that the capacitor can store:
Q = CV
Therefore, the current through the capacitor is given by the following equation:
l = dQ/dt
= d(CV)/dt
= CdV/dt
And the voltage across the capacitor is given by the following equation:
dV = I/C . dt
So, ∫dV = 1/C * ∫i.dt
= 1/C * 0 ∫ t i.dt
Capacitor Charging
The voltage across the capacitor is proportional to the charge stored by it and inversely proportional to the capacitance of the capacitor. Charge is not stored instantly within the capacitor in response to an applied voltage. When voltage is applied to the capacitor, it acts as a short circuit and maximum current flows through it. The current through the capacitor decreases exponentially with the charge stored by it and the voltage across it increasing at the same rate. The current through the capacitor stops when the voltage across the capacitor increases equal and opposite to the applied voltage. Now, the capacitor acts as an open circuit and no current flows through it while an equal and opposite voltage develops across it. Therefore, current flows through the capacitor only until the voltage across it changes. Once the voltage across the capacitor becomes constant (equal and opposite to the applied voltage), there is no current flowing through it. The voltage across the capacitor remains even when no current flows through it, as the rate of change of voltage across the capacitor is proportional to the current and inversely proportional to the capacitance; the greater the capacitance of a capacitor, the slower the rate of voltage change (voltage rise) across it.
Capacitor discharge
Once the capacitor has equal and opposite voltage, it is fully charged, holding a charge equal to CV, and no current flows through it. There will be no change in current or voltage through the capacitor until the applied voltage is changed or varied. Therefore, in a constant DC circuit, the capacitor will become fully charged (exponentially) and will eventually become an open circuit. Now it needs to be discharged by short-circuiting its terminals or using a bleeder resistor. Either way, a discharge current flows through the capacitor in the opposite direction of the charging current. Like the charge current, the discharge current is initially maximum and decreases exponentially. The voltage across the capacitor also decreases exponentially along with the discharge current. The discharge current stops when the voltage across the capacitor is reduced to zero.
The capacitor in the AC circuit
Now, let's assume the voltage source is AC. As a sinusoidal voltage source, the applied voltage will be given by the following equation:
V = V I sin (ωt)
Where,
V = waveform voltage at an instant
V i = Peak voltage of the waveform
ω = Frequency of the waveform
t = instant of time
The following equation will give the current through the capacitor:
i = CdV/dt
= Cd(V i sin(ωt))/dt
=ωCV i cos(ωt)
= I I cos(ωt) where I I =ωCV I
= I sin (ωt + 90°)
The opposition to current by the capacitor is called capacitive reactance. The following equation gives this:
Xc = V/I
=V I /I I OR V rms /I rms
= 1/ωC
We can then see that the current through the capacitor of an AC circuit drives the voltage at 90° or 1/4 the frequency as the applied voltage increases to the peak value, the capacitor charges and the charging current decreases exponentially from the value maximum to zero while the voltage across the capacitor increases exponentially, increasing equal and opposite to the applied voltage. Thus, at the 90° phase angle of the applied voltage signal (1/4 of the signal frequency), the charging current through the capacitor was reduced to zero (from maximum) and the voltage across the capacitor increased from zero to peak voltage.
As the applied voltage drops from the peak value to zero, a current in the reverse direction flows through the capacitor, which rises from zero to a maximum value. The voltage across the capacitor drops along with the applied voltage, reducing it to zero and discharging the capacitor. Therefore, at a phase angle of 180° of the applied voltage signal (1/2 of the signal frequency), the discharge current (here, current in the reverse direction due to the decrease in applied voltage) flows in the opposite direction, rising from zero to the maximum value and the voltage across the capacitor drops from the peak value to zero.
Now the applied voltage signal reverses polarity and the applied voltage increases from zero to the peak value in the opposite direction. This again starts charging the capacitor, increasing the voltage across the capacitor equal and opposite to the peak voltage (in the reverse direction) and reducing the current through the capacitor from the peak value to zero. Thus, at a phase angle of 270° of the applied voltage signal (3/4 of the signal frequency), the voltage across the capacitor increased to a peak value with opposite polarity, and the current through the capacitor flowing in the opposite direction drops to zero from the peak value (in the reverse direction).
As the applied voltage falls from the peak value to zero in reverse polarity, a current flows through the capacitor in a positive direction, increasing from zero to a peak value, and the voltage across the capacitor (in reverse polarity) drops from peak value to zero. This discharges the capacitor. Thus, at a 360° phase angle of the applied voltage signal (completion of one cycle of the AC signal), the voltage across the capacitor fell back to zero, discharging the capacitor, and the current through the capacitor rose again to peak value in a positive direction. The AC response of a capacitor can be illustrated through the following signal diagram:
Graph showing voltage and current through a capacitor in an AC circuit (Image: Electronics Tutorials).
The signal behavior of a capacitor can be summarized as follows:
1) A capacitor is intended to temporarily store charge in a circuit, which returns to the circuit when discharging. The stored charge is returned as a discharge current in the opposite direction of the charge current.
2) Whenever the voltage applied to a capacitor in any direction increases, the capacitor gets charged. The current passing through it decreases exponentially and the voltage passing through it increases exponentially until it equals the applied voltage. When charging, the voltage across the capacitor develops opposite to the applied voltage and current, always in the direction of the applied voltage (and opposite to the voltage developed across the capacitor).
3) Whenever the voltage applied to a capacitor in any direction decreases, the capacitor discharges. The current through it increases exponentially and the voltage across it decreases exponentially until the capacitor is either fully discharged or discharged to the lowest level, depending on the drop in the applied signal. When discharging, the voltage across the capacitor develops along the direction of the initially applied voltage. The current is always in the opposite direction to the initially applied voltage (load voltage).
4) Current flows through the capacitor until the voltage applied to it changes. Increasing voltage charges the capacitor and decreasing voltage discharges the capacitor. The voltage across the capacitor remains even though no current flows through it until it is discharged due to a decrease in applied voltage, or discharged through a resistor (or load), or by a short circuit.
5) In an AC circuit or in response to an AC signal, the current through the capacitor always carries the voltage across it by 90°. The current through the capacitor depends not only on the capacitance and the rate of change of voltage, but also on the frequency of the applied signal.
6) The opposition to current by a capacitor (capacitive reactance) is inversely proportional to its capacitance and the frequency of the applied voltage. The greater the capacitance of a capacitor, the lower its capacitive reactance. Likewise, the higher the frequency of the applied voltage signal, the lower its capacitive reactance. The capacitor acts as an open circuit for a constant DC signal after charging to a peak level. Therefore, a capacitor can be used to block DC signals or DC components of electrical signals. Similarly, due to the frequency dependence of capacitive reactance, capacitors can be used to filter AC signal frequencies.
7) Since capacitors store charge temporarily, they are used in electrical memories.
In the next article, we will discuss different types of capacitors and their applications.