Capacitors

Capacitance (C) is the measure of a capacitor’s ability (capacity) to store an electric charge on its plates. A capacitor is an electrical component that consists of two conductors (plates) separated by an insulator called the dielectric.

The voltage rating of a capacitor, often labeled as WVDC for Working Voltage Direct Current, is the maximum voltage that can safely be applied across the capacitor without arcing, or voltage breakdown, occurring in the dielectric. The difference of potential between the capacitor’s plates creates a stress on the atomic structure of the dielectric. If the voltage is too high, electrons will be torn from their orbits in the dielectric material, producing an electric arc. A small carbon path known as a puncture is created. A punctured capacitor is not useable as the puncture creates a leakage path for current between the plates.

When a capacitor is connected to a DC voltage source, electrons accumulate on the negative plate. The other plate becomes positively charged by electrostatic conduction . The presence of the negative charge (surplus electrons) on one plate repels negative charges (electrons) off the neighboring plate. Thus, the opposite plate receives an equal, though opposite, positive charge of “holes”. A hole is a vacant spot in the valence shell of an atom where an electron may be captured.

The amount of capacitor charge is determined by the amount of applied voltage and the capacitance, in Farads, of the capacitor. When a DC voltage is first applied, the capacitor acts like a short and demands a great amount of current. At this first instant of time when voltage is applied, the circuit resistance is the main limiting factor to current flow. Current flow will be at its greatest. As capacitor charge increases, the rate of charge decreases as the voltage across the capacitor approaches the source voltage. When the source voltage is reached, current flow stops. Remember that there is actually no current flowing from one plate of the capacitor to the other. There are only free electrons moving onto and leaving the plates by the leads. As like charges repel (electrons have a negative charge), the plate with an excess of electrons will repel electrons from the other plate giving it a positive charge.

AC Capacitor Current A capacitor is able to pass alternating current even though there is an insulator between the plates (no actual current path). In an RC (resistive/capacitive) transient circuit, the capacitor charge current will flow until the capacitor is fully charged, and discharge current will flow until the capacitor is fully discharged. When an alternating voltage is applied to the plates of a capacitor, the capacitor’s plates are forced to follow repeated cycles of charge and discharge.

The RC Time Constant It takes time for a capacitor to charge through a circuit resistance. Capacitors do not charge at a linear rate, they charge at an exponential rate. The RC Time Constant (t) formula is



One time constant is equal to the product of the circuit resistance times the capacitance. A capacitor will reach a full charge and show the source voltage after a period of 5 time constants. This applies to every capacitor in every circuit, and applies to inductors as well! For example, a 5 uF capacitor, charging through a 1 KW resistor will have a time constant equal to 5 E-6 X 1K = .005 seconds, or 5 milliseconds. Therefore, with this capacitor/resistance combination, the capacitor will reach full charge and show the full source voltage in 5 X 5 milliseconds or 25 milliseconds.

In the first 5 ms, the capacitor will reach 66.6% of the total charge; it will reach 86% after 10 ms, 95% after 15 ms, 98% after 20 ms, and 99% after 25 ms. As you can see, the rate of charge slows as the capacitor takes on charge and the voltage across the cap approaches the source voltage. After 5 time constants, current flow stops, and capacitor voltage equals the source voltage.

RC Highpass Filter An RC highpass filter would consist of a capacitor connected in series with a load. In our case, this would be a speaker voice coil, which is a reactive load. For the purposes of our discussion, we will consider our load to be non-inductive and therefore non-reactive.

What we refer to as the crossover frequency of a first- order, high pass filter, is generally called the cutoff frequency (fco) or half-power point, in electronics terminology. This is the frequency at the output of the filter whose power has dropped by half or -3 dB as compared to the source voltage. This is the voltage that is dropped across the capacitor and therefore not across the load. The formula for calculating the -3 dB down point is



The crossover frequency will be the reciprocal of 6.28 times the value of the capacitor times the resistance of the load. For example, if we placed a 3 uF capacitor in series with an 8-ohm speaker, we would expect the crossover frequency or -3 dB down point to be the reciprocal of 6.28 X 3 E -6 X 8W or 6.63 KHz. Frequencies above 6.63 KHz would be passed, frequencies below will be rolled off at a rate of 6 dB per octave. Run this load/frequency combination in BassBox and see if it doesn’t call for a 3 uF cap!

Voltage/Current Phase Relationship Current “leads” the voltage in a capacitive circuit. Remember that when voltage is first applied to the capacitor, current flow is at a maximum because the capacitor initially looks like a short. This is why our 1 Farad stiffening caps come with a resistor to slow the initial charge rate. This ensures that fuses in the line are not blown, and a large spark does not mark the connector or cause a fire in the presence of combustible fumes. At the instant a sinusoidal AC voltage reaches its positive peak (90°), voltage beings to appear across the capacitor. It rises and falls sinusoidally just like the current. This phase relationship is maintained through the 360° cycle of the sine wave. Therefore, current leads the voltage in a capacitive circuit by 90°.

Frequency Response A capacitor in series with a speaker acts as a highpass filter. The longer the period of the frequency applied, the longer the signal will cause the capacitor to charge and discharge. If the frequency of the applied AC signal is high enough, the signal will change polarity before the capacitor begins to show a voltage drop across itself. If capacitor voltage does not have the opportunity to build across the capacitor, it will be “invisible” to the AC signal. The lead/lag relationship between current and voltage still applies.

It should now stand to reason that the higher the frequency, the easier it will pass a capacitor. Often capacitors are sold as “bass blockers”. The lower frequencies have a longer period which causes a voltage drop to appear across the capacitor before the current changes direction. If the voltage at these frequencies are dropped across the capacitor, they are effectively “blocked” from the speaker. There must be a voltage or potential difference between the speaker voice coil leads for current to flow through the voice coil and create an output from the speaker.

Inductors

The terms inductor, coil, and choke are synonymous. A coil is a winding of insulated wire around a core, be it air, paper, iron, etc. The core material of the coil has a definite affect on the value of the inductor. Other specifications affecting inductance are the thickness of the wire used, the diameter and length of the coil, and the number of turns of wire. The wire in a coil must be insulated or current will flow across from turn to turn and the device will act like a short.

Coils and capacitors serve opposite functions in electronic circuits, and you will notice that much of the math involved with capacitors is very similar, though opposite or reciprocal, to that for inductors. The idea of time constants and charge/discharge rates apply to coils in the same fashion as they do to capacitors.

XL = 2pfL

Notice the similarity between the reactance formulas for XC and XL. They are the mathematical opposite, in that the XC is divided into 1. It should follow that the two devices have the complete opposite affect on circuit operation.

As capacitors pass AC and block DC, a coil blocks AC and passes DC. When current passes through a conductor, flux lines or magnetic lines of force form around the conductor. Conversely, if a conductor is passed through flux lines, current is induced to flow in the conductor (generator action) in a predictable polarity. The relative motion between the flux lines and the conductor causes current to flow. Alternating current provides this relative motion between the flux lines and the conductors. The number and density of the flux lines around a conductor depends upon the amount of current flowing and the applied voltage, among other things.

You will remember that the current flow and rate of charging slows as a capacitor approaches the applied source voltage. A coil is the complete opposite. The instant that a voltage is applied to a coil, there is the immediate appearance of magnetic flux lines. As flux lines “grow” from one turn of wire, they cut across the adjacent windings. By cutting through the adjacent windings (relative motion), they induce a voltage there. So each turn of wire in the coil induces current to flow in the adjacent turns. It is extremely important that you understand that this “self-induced” current goes against the current flow and voltage polarity that produced it! Once again, the relative motion of the flux lines produces a voltage that is in the opposite polarity of the voltage that produced it. We call this phenomenon reactance, and it produces a “counter electromotive force” or CEMF.

The instant voltage is applied to the coil, the coil reacts trying to push current in the opposite direction. At that first instant that voltage is applied, the full source voltage appears immediately across the coil due to immediately high impedance, and there is virtually no current flow as the induced CEMF prevents or impedes it. The source voltage immediately appears across the coil. Completely opposite from a capacitor!

With a DC voltage is applied to a coil, the flux lines move outward from the conductor and stop. So long as they are “growing” outward, they are cutting adjacent turns of wire and creating CEMF, and the coils looks like an open with no current flowing. Once the flux lines slow and stop moving, the CEMF falls away and current beings to flow. The voltage across the coil begins to drop. So as you can see, it is a change in current that causes a coil to react. When there is no change in current, there is no CEMF, and the coil acts like a short and passes the current virtually unimpeded.

When the DC voltage to the coil is removed, it reacts in a similar way, though reversed. When the voltage is removed, current flow stops, and the flux lines collapse and cut back through the adjacent turns of wire. Because the flux lines are now collapsing and moving back toward the wire, the voltage induced is now forward and in the same direction as the original applied voltage. It is said that coils resists a change in current flow. When the current increases, CEMF is produced. When the current decreases, (forward) EMF is produced, resisting the change. Capacitors are, again, the opposite. They resist a change in voltage. When voltage goes up, it takes time for the capacitor to increase its charge. When voltage goes down, the cap more or less acts like a battery and tries to maintain the voltage until its charge falls away.

This charge and discharge, CEMF and EMF, occurs according to the time constant of the coil, just as it does with a capacitor. 66.6% of the voltage across the coil will fall away during the first TC after DC is removed, and so forth.

Inductor Voltage/Current Phase Relationship Voltage “leads” the current in an inductive circuit. When voltage is first applied to the coil, it immediately reacts with a CEMF that prevents current from flowing. The entire source voltage shows across the coil immediately. When the sine wave reaches 90°, the inductor voltage begins to drop away and current flow begins to rise. Therefore, the voltage always leads the current in an inductive circuit by 90°.

A single coil in series with the speaker will act as a low pass filter. Remember that it is the rate of current change that causes a coil to react. Bass frequencies have a lower rate of change in current flow than do higher frequencies. The higher the frequency, the greater the rate of current change and the more the coil will create a CEMF to the input EMF. Low frequency passes across the coil, high frequency causes a greater rate of change in current flow and causes a reverse voltage to appear across the coil. Frequencies that develop a reverse voltage drop across the coil will not create a voltage across the speaker’s voice coil.

RCL Filters These filters use a capacitor and a coil to block or filter unwanted frequencies, and you probably know them as “second order” having a rolloff rate of -12 dB per octave, as opposed to a -6 dB slope for just a capacitor or coil.

Capacitors and coils react to changing current and voltages, some of which cause the device to impede current flow. We call this phenomenon reactance, and as it impedes current flow, it is measured in ohms. You can calculate the reactance, in ohms, that a capacitor or coil is producing using Ohm’s Law, if you know the current through, and voltage drop across the device. The symbol for reactance is X. XL is inductive reactance, Xc is capacitive reactance.

Let’s consider the second order, lowpass RCL filter. In this network, the coil is in series with the speaker load, and capacitor is paralleled across it. Low frequency moves across the coil unimpeded, but will not go across the capacitor to ground for reasons you should already understand. The current moves through the voice coil of the speaker and creates an output. High frequency creates a voltage drop across the coil and is blocked. The high frequencies that do come across the coil are passed to ground across the capacitor and do not create a voltage drop across the voice coil. This action by the capacitor is what creates the steeper slope over the use of just a coil in a first-order network.

So how is the cross over frequency established? Based upon the values of capacitor and coil used, there will be a certain frequency at which the inductive reactance, in ohms, is the same as the capacitive reactance. As both devices now represent the same ohmic value and the same impedance to current flow, it should follow that the capacitor will show the same voltage drop as the coil.

If you look at the circuit diagram, you will see that the capacitor and coil are in series with one another, and the speaker is paralleled across the capacitor. When XL equals XC, in ohms, the current flow will be the same through the two devices as they are in series, and the voltage drop across the two devices will be equal. At this particular frequency, the capacitor and coil are trading a charge back and forth (resonating), and are acting resistively in the circuit. One half of the source voltage dropped across each.

Since the speaker is paralleled across the capacitor, it sees the same voltage as the capacitor. Since the capacitor has one half of the source voltage dropped across it at “resonance”, the speaker is only seeing the capacitor voltage. If the speaker is only receiving one half of the voltage, it is down -3 dB from those frequencies in the passband that would cause the full source voltage to show across the capacitor and speaker voice coil. This is the cutoff frequency (fco), half power point, or the cross over frequency. Higher frequencies are blocked more and more by the coil, and what does come through is passed to ground by the capacitor. Lower frequencies pass across the coil, are blocked from ground by the capacitor, and therefore go through the voice coil.
Because the voice coil is paralleled across the capacitor, the impedance of the speaker does affect circuit operation. This is why we must know the impedance of the speaker load when calculating capacitor and inductor values for cross over networks.

Swapping positions of the capacitor and coil in our RCL circuit will cause the network to become a highpass filter. The crossover frequency will be the same.

Inductive and Capacitive Coupling Another common use for capacitors and coils is for “coupling”. A common place to see inductive coupling is at the output of a tube-type amplifier. The output impedance of the 6L6 power triode tube is about 1.2KW. I should stand to reason that this tube could not drive an 8W load, and would surely burn up trying. A transformer is used to impedance-match and couple or connect the AC signal to the load.

A Class A single-ended amplifier uses an output transistor or tube that is biased to be half way between cutoff and saturation with no input signal. So even with no input, it is flowing a lot of current and dissipating power. This DC current is blocked from reaching the speaker by a coupling capacitor. If it were allowed to reach the speaker, it would load the voice coil seriously. As capacitors block DC, only the AC signal will go across the capacitor to drive the speaker.

Large-value capacitors are used in power supplies in electronic devices such as power amplifiers to filter out the ripple from rectified AC, which is actually DC that varies from ground reference to a peak voltage at 120 Hz. Remember that capacitors resist a change in voltage. These large-value capacitors are also referred to as “reservoir capacitors” as they can give up current for a heavy transient with less resistance than the rectifier circuit. This is precisely what our automotive “stiffening” capacitors do to prevent flickering lights and poor bass response.

Comparing Capacitors and Inductors

Inductors	Capacitors
Unit of measure is the Henry	Unit of measure is the Farad
Passes DC	Blocks DC
Opposition to AC increases with freq.	Opposition to AC decreases with freq.
Energy is stored in a magnetic field	Energy is stored in an electric field
Stray capacitance between windings	Stray inductance in wire leads, plates
Some R in the windings	Some R in the leads and plates
Acts like an open the instant V is applied	Acts like a short the instant V is applied