As we move toward the end of our discussion of car audio electrical theory, we need to talk about capacitance and inductance and how the characteristics of those phenomena interact with AC and DC signals. There’s no doubt that these are advanced concepts, but even a basic understanding of how capacitors and inductors work is fundamental to a thorough understanding of mobile electronics systems.

What Is a Capacitor?

A capacitor is a two-terminal electronic component that stores energy. Capacitors are made of two metallic plates that are separated by an electrical insulator. When we apply a voltage to one terminal of the capacitor, the electrons on one plate will impose a force on the opposite plate to create an opposite charge. The result is that the plates have equal and opposite charges and thus, maintain an electric field. Because the plates in a capacitor are very close together, they can store a large amount of energy for their overall size.

Capacitors are quantified in units of farads. A farad is defined as one coulomb of charge on each plate, resulting in a voltage of one volt across the terminals.

Capacitors in DC Circuits

Capacitors are, at their most basic function, a device that stores a microscopic magnetic field between its plates. When we apply a DC voltage to a discharged capacitor, it appears as a short circuit for an instant as the magnetic and electric fields start to form between its plates. As the capacitor starts to store energy, it increases in effective resistance, and the amount of current flowing through the device is reduced. Once the capacitor has equalized with the supply voltage, almost no current passes through the device.

When we remove the supply voltage from a capacitor, it will attempt to maintain the voltage across the terminals. It is this characteristic that makes capacitors an ideal solution to reduce variations in voltage. Capacitors resist changes in voltage.

Inside the amplifiers in our car audio systems, capacitors are used to store large amounts of energy at the rail voltage. When there is a sudden demand for current that exceeds the capability of the power supply, the capacitors will release energy to maintain their initial voltage. This characteristic helps to stabilize the voltage of the amp during dynamic transients. This same concept applies to “stiffening capacitors” used on the 12V feed to your amplifier. When implemented using high-quality components, the addition of a large capacitor can help to provide transient current to the amp.

The Capacitor in AC circuits

In alternating current circuits, capacitors take on an interesting phenomenon of “virtual resistance.” As we know, capacitors don’t like to change voltage, yet an AC signal is one that is defined as ever-changing. Depending on the relationship between the capacitor value and the frequency of the AC signal, some amount of the current is allowed to pass through the cap.

If we attempt to measure the resistance of a capacitor with a conventional multimeter, we’ll find it shows an extremely high value. For AC signals, we use the formula Xc = 1 / (2 x 3.1416 x F x C) to calculate the effective resistance, where F is the frequency of the signal and the C is the value of the capacitor in farads. Because this resistance is not present in DC signals, we call it capacitive reactance.

If we wanted to create a simple filter circuit to limit the amount of low-frequency signal going to a speaker, we could wire a non-polarized capacitor in series with the speaker. To calculate the frequency at which the cap starts to reduce bass going to the speaker, we can rearrange the above equation to F = 1 / (2 x 3.1416 x R x C), where R is the same value as the speaker resistance. For a four-ohm speaker and a capacitor with a value of 200 uF (microfarads), we get a frequency of 198.9 Hz. At this frequency, the capacitor appears to have the same reactance as the speaker, and the signal that is going to the speaker is reduced by 50 percent. Because capacitance is inversely proportional to frequency, the impedance of the capacitor increases as frequency decreases. At 99 Hz, the reactance is 8 ohms, at 50 Hz, it’s 16 ohms, and so on. This phenomenon simultaneously reduces the current supplied by the amplifier and acts as a voltage divider between the cap and the speaker.

A capacitor in series with a speaker is known as a first-order high-pass filter. It reduces the output of the speaker at a rate of -6dB per octave as you move away from the crossover frequency as defined above. Capacitors are suitable as filters for midrange and high-frequency drivers in passive designs and as protection devices for tweeters in active designs.

What Is an Inductor?

In the simplest of terms, an inductor is a coil of wire that creates a magnetic field based on the amount of current flowing through it. Many inductors feature iron cores to increase the intensity of the magnetic field. Where a capacitor resists changes in voltage, an inductor resists changes in current flow. We know from our previous article on magnetism that current flowing through a conductor creates a magnetic field around that conductor. If we wrap the conductor in a loop, the proximity of the loops to one another intensifies the magnetic field.

Also from our previous article, we also know that a magnetic field can impose a voltage on a conductor. If the current in an inductor tries to change, the magnetic field attempts to create a voltage across the device to maintain the current flow.

A good analogy for an inductor is a flywheel on a motor. Once you have established a specific rotational speed, it takes a large amount of work to increase or decrease its speed. Inductors work the same way with current. They resist changes in current flow. Inductors are rated using the unit henry (H). A henry is defined as the opposition to electrical current flow through a device that results in one volt of electromotive force to appear across the terminals.

Inductors in Electrical Circuits

In most applications, we don’t want inductors in a 12V DC circuit because they resist changes in current flow. For a variable load such as an amplifier, a large amount of inductance in the supply wiring would result in an unstable supply voltage as the current requirements change.

There are some cases where inductors are used in combination with a capacitor to act as a noise filter.

In an AC circuit, inductors allow low-frequency signals to pass through the device with little to no effect. If we wire an inductor in series with a speaker, it acts as a high-pass filter. Unlike a capacitor, in a DC circuit, an inductor appears as a short circuit with very little resistance. To an AC signal, we can calculate the reactive inductance of a capacitor using the equation Xl = 1 x 3.1416 x F x L, where F is frequency and L is inductance in henries.

If we want to use an inductor as a high-pass filter, we can determine the effective crossover point by swapping the Xl for the resistance of the speaker. In this example, we’ll use an inductor with a value of 6 mH (millihenries) and a speaker with a nominal impedance of 4 ohms. There, the -3dB point of the filter circuit would be F = 4 / (2 x 3.1416 x 0.006), or 106.1 Hz. This value of inductor would make a good low-pass filter for a woofer. Just as with a capacitor in series with a speaker, an inductor acts as a first-order filter and reduces output at a rate of -12dB per octave as frequency increases from the crossover point.

Other Cases of Inductance and Capacitance

Anytime two conductors are parallel to each other and in close proximity, there will some level of capacitance. Many overly exuberant enthusiasts talk about capacitance in interconnect cables. While this is a factor, the microscopic changes (if indeed any are perceptible) can be compensated for during the tuning process of the system. When it comes to buying high-quality interconnects, noise rejection and overall design durability should be your top goals.

The voice coil winding in the speakers we use has a certain amount of inductance. This characteristic reduces high-frequency output by reducing current flow at high frequencies. Because speakers are dynamic, their parameters change as the speaker cone moves. In the same way that having an iron core in an inductor increases inductance as compared to an air-core design, the inductance of a speaker voice coil increases when the cone assembly moves rearward into the basket. The T-yoke in the center of the speaker increases the strength of the magnetic field created by the current in the voice coil. Likewise, as the speaker moves forward, the inductance decreases. These position-based inductance distortions can cause a high-frequency warbling effect that can be detrimental to the reproduction of your music. One solution is to implement an under-hung voice coil design where the gap is taller than the coil winding. The drawback to this design is that the voice coil is often small and lacks power handling. Another option is to include a copper pole piece cap to reduce the magnetic field and minimize distortion. A copper cap is an expensive option but offers excellent performance benefits.

Car Audio Electrical Theory

For now, this is the end of our series of articles on car audio electrical theory. We hope you’ve enjoyed learning about the physics behind how your car audio system works. Our goal is to educate enthusiasts so that they can make educated purchases and upgrades to their mobile sound system. If you have any questions, drop by your local mobile electronic specialist retailer. They can help you design an upgrade that will truly transform your commute into an enjoyable listening experience.

This article is written and produced by the team at www.BestCarAudio.com. Reproduction or use of any kind is prohibited without the express written permission of 1sixty8 media.

Furthering our discussion about car audio electrical theory brings us to a discussion of how the flow of electricity through a conductor creates magnetic fields around the conductor. Understanding the relationship between current flow and magnetism is crucial to understanding how a speaker works.

History of Electromagnetism

The first documented correlation between electricity and magnetism came from Gian Domenico Romagnosi, a 19^th-century Italian legal scholar who noticed that a magnetized needle moved in the presence of a voltaic pile (the predecessor to a battery). Hans Christian Ørsted observed a similar occurrence in April 1820. He was setting up materials for an evening lecture and noticed that a compass needle changed directions when he connected a battery to a circuit. Neither Romagnosi nor Ørsted could explain the phenomenon, but they knew there was a defined relationship.

In 1873, James Clark Maxwell released a publication titled A Treatise on Electricity and Magnetism, which explained the presence of four effects:

1. Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: Unlike charges attract, like ones repel.
2. Magnetic poles (or states of polarization at individual points) attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: Every north pole is yoked to a south pole.
3. An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire. Its direction (clockwise or counter-clockwise) depends on the direction of the current in the wire.
4. A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved toward or away from it; the direction of current depends on that of the movement.

What Causes a Magnetic Field when Electricity Flows?

Electricity is the movement of electrons into and out of a conductor. One electron enters the end of a conductor, bumps into another electron, and so on until a different electron leaves the other end of the conductor and enters the load.

Because there are effectively more electrons in the conductor when current is flowing, the balance of negatively charged electrons to positively charged ions is upset and thus causes an imbalance in the magnetic field around the conductor.

We could devote thousands of words to explaining how atoms work. But in short, the core of an atom has a core of positively charged protons with a bunch of negatively charged electrons circling this core. When there is no flow of current, an atom doesn’t have a magnetic field because the quantity and path of the electrons around the protons are balanced. When we bump an electron out of an atom and into another, the atoms become imbalanced and thus produce a net magnetic field.

An Explanation On a Larger Scale

When electricity flows from the positive terminal of a battery to the negative, a magnetic field is created around the conductor. If you look at the image below, you will see the direction of the magnetic field relative to the flow of power.

In schools, this is often referred to as the right-hand rule. If you wrap your right hand around a conductor with your thumb extended upward in the direction of current flow (putting positive below your hand and negative above), your fingers point in the direction of the magnetic field.

Keep in mind that for audio signals, the polarity of the current changes from positive to negative in the same way that the vibrations produced by someone talking or playing an instrument pressurize and rarefy the air to produce sound.

How Magnetism Makes a Speaker Work

Conventional moving coil loudspeakers use a coil of wire (called a voice coil) and a fixed magnet. The electricity from the amplifier flows through the voice coil and creates a magnetic field. The polarity of the magnetic field pulls the voice inward or pushes it out in an amount proportional to the strength of the magnetic field.

The diagram below shows the force exerted on the voice coil with the current flowing through the positive half of the audio waveform.

This diagram shows the force exerted on the voice coil with the current flowing through the negative half of the audio waveform.

As the polarity of the current reverses, so too does the force exerted on the voice coil, which is attached to the speaker cone through the voice coil former.

Magnetism Isn’t Always Beneficial

Regarding speakers, we rely on and need magnetic fields for them to work. With that said, magnetism doesn’t always work in our favor.

If there is a large amount of current flowing through a conductor, there will be a strong magnetic field around that conductor. If we place another conductor in that magnetic field, a voltage will be produced across the second piece of wire.

In our vehicles, many devices such as fans, sensors, the alternator, lighting control modules and computers create magnetic fields containing high-frequency noise. When an improperly shielded interconnect passes through one of these fields, it can pick up that noise and produce a voltage on the conductor. This phenomenon is why it’s important for your installer to run the interconnect cables and often the speaker wires in your car away from sources of electrical noise.

Consult Your Local Mobile Electronic Installation Experts

When it’s time to upgrade the sound system in your vehicle, visit your local specialized mobile enhancement retailer. They have the training and experience to ensure your new audio system will sound great and be free of unwanted noise!

In our next article, we are going to talk about inductance and capacitance and how those characteristics affect high-frequency electrical signals.
This article is written and produced by the team at www.BestCarAudio.com. Reproduction or use of any kind is prohibited without the express written permission of 1sixty8 media.

In our ongoing discussion of car audio electrical theory, we need to discuss some of the characteristics of alternating current signals. These points of discussion include the concept of amplitude and frequency. Understanding the concept of frequency is crucial to developing an understanding of how the components in our audio systems work.

The Concept of Signal Amplitude

Thankfully, we are going to start off easy with a discussion of signal amplitude. When it comes to the ability of an AC signal to do work, just as with a DC power source, more amplitude (or level) means that more work can be done.

In a DC power source, the amplitude is fixed at a certain level. In our cars, this level is around 12 volts. In our homes, the voltage at the wall receptacle is 120V. High-power devices like an electric stove, a clothes dryer or an air conditioner are typically powered by 240V to reduce the amount of current required to make these devices operate.

When we want to reproduce sound, we need to supply an audio signal from an amplifier to the voice coil of a speaker. Ignoring the design limitations of a speaker, supplying more voltage results in the cone moving farther and thus producing more sound.

If our amplifier is producing 1 volt rms of signal to a speaker with a nominal impedance of 4 ohms, then the speaker is receiving 0.25 watts of power (calculated using the equation P = V^2 ÷ R). If we increase the voltage to 2 volts, the power at the speaker is now 1 watt ((2×2) ÷ 4). If the voltage increases to 10 volts, the power is now 25 watts.

If we were to look at the two signals described above (1Vrms and 2Vrms) on an oscilloscope (a device that shows voltage relative to time), you would see the following:
Just a reminder: The RMS value of a sine wave is 0.707 times its peak value. In the case of these waveforms, the peak values would be 1.414 and 2.818 volts.

The Concept of Frequency

Signals Containing Multiple Frequencies

Let’s step back a bit and look at the fundamentals of analyzing the frequency content of a signal. The graph you see below shows a single 1kHz signal.

The “stuff” you see at the bottom of the screen is noise. Every signal contains some amount of noise. For this graph, we can see that the 1kHz signal is recorded at a level of 0dB and that the loudest noise component is almost 170dB quieter. This low amplitude makes the noise level irrelevant.

What can be difficult to understand is that a signal can be, and often is, made up of many different frequencies. This graph shows an audio signal that contains 1kHz and 2kHz signals.

Almost every audio signal we hear comprises an infinite number of frequencies. The relative level of these frequencies is what makes one person’s voice sound different than another’s or makes a piano sound different than a guitar.

These two frequency response graphs show a piano and a guitar both playing Middle C with a frequency of 256 Hz.

The red line represents the response of the guitar, showing a peak at 256 Hz, a strong harmonic at 512 Hz and an intermodulation peak at 768Hz.

The green line shows the frequency response of a piano playing the same 256 Hz middle C note. It has significantly more harmonic content with harmonics and intermodulation peaks above and below the fundamental.

Audio Measurement Waveforms

Two waveforms are commonly used to test audio equipment and audio signals. The first is called a white noise signal. This signal includes random audio signals at all frequencies up to the cutoff of the recording medium (in this case, 22.05kHz or our 44.1kHz sampling rate WAV file). Each frequency is the same in terms of amplitude. We can use this signal along with a real-time analyzer to measure the frequency response of audio components.

Here is the frequency response plot of a white noise signal:

Another important signal is called pink noise. We use this signal when measuring the frequency response of a speaker. Unlike white noise that contains signals at equal levels at all frequencies, pink noise has an equal amount of signal energy per octave. When looked at in the frequency domain, the level decreases at a rate of 10dB per octave as frequency increases.

When you play pink noise through a set of speakers and measure the response with a microphone, you will be looking for a flat waveform.

Frequency Response of a Loudspeaker

Let’s take a high-quality, 6.5-inch coaxial speaker with a specified efficiency of 89dB when supplied with pink noise at a level of 2.83V and measured at a distance of 1 meter. A value of 2.83 volts happens to work out to 2 watts using the P = V^2/R equation.

While this specification works when we feed the speaker a pink noise signal, it doesn’t tell us how loud the speaker is at a specific frequency. For that, we need a frequency response graph.

This frequency response graph shows us how much sound energy this speaker will produce when driven by a pink noise signal.

This particular driver has a gentle dip around 1kHz, some emphasis in the mid-bass region between 80 and 150Hz and a gently rising response above 2kHz to improve off-axis performance. In a car, this speaker sounds amazing!

The Bonus Signal – A Square Wave

OK, strap on your space suit, thinking cap or whatever will help you understand the following. We are going to look at a square wave. A square wave is a waveform that combines harmonics (multiples) of a fundamental frequency to create a waveform of a specific shape. The waveform appears to have two values, one high and one low. It’s for this reason that people incorrectly assume that these are Direct Current (DC) levels.

The formula to create a square wave is made up of multiple odd-ordered harmonics of the fundamental frequency. If you have a 30Hz square wave and look at it in the frequency domain, you can see these harmonics.

When an amplifier is pushed beyond its output voltage limit, it creates a square wave. There is no DC content in the signal, but it IS full of high-frequency harmonic content.

Using an Excel spreadsheet created by Alexander Weiner from Germany, here are six graphs that show how a square wave is created by adding odd-ordered harmonics to a fundamental signal. For a perfect waveform, we need an infinite number of harmonics.

The yellow line shows a single sine wave with no harmonics.

The yellow waveform adds the third harmonic of the fundamental frequency.

The yellow waveform adds the third and fifth harmonic of the fundamental frequency.

The yellow waveform adds the third, fifth and seventh harmonic of the fundamental frequency.

The yellow waveform shows the 100 odd-ordered harmonics as well as the fundamental frequency.

In this graph, we have the fundamental frequency and 256 odd-ordered harmonics added together.

If you have ever wondered why tweeters seem to the be the first to fail when an amp is driven into clipping or distortion, the reason is the addition of high-frequency information to the audio signal. Where we might have been feeding one or two watts to a tweeter with music, a square wave or a waveform containing significant harmonics contains a great deal more high-frequency information.

We hope this wasn’t too much to information for a single article. Understanding waveform amplitude and frequency content are crucial to any discussion of a mobile audio system. In our next article, we are going to discuss the flow of electricity through a conductor and the associated magnetic field that is created.

This article is written and produced by the team at www.BestCarAudio.com. Reproduction or use of any kind is prohibited without the express written permission of 1sixty8 media.