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.

In our ongoing series of articles about car audio electrical theory, we are going to introduce the concept of alternating current power sources and signals. Understanding the basics of AC is crucial to understanding how a mobile audio system works. This article uses a lot of references to the electricity delivery systems used in our homes and offices to help establish a basic understanding of AC circuits. We’ll build on this foundation in this and subsequent articles to help form an understanding of the complexities of AC systems.

The Difference Between AC and DC

The voltage produced by the electrical system in our vehicles is called direct current. The electrons flow in one direction from one terminal of the battery to the other (except when we are recharging the battery). While there are changes in the voltage level as we add loads to the circuit, or when the alternator starts recharging the battery, the direction of current flow to the electric and electronic devices in the vehicle never changes.

Conversely, the power supplied by your local electric company to drive the lights and appliances our homes and at work is called alternating current. It has this name because the flow of electrons changes direction 60 times a second. Yes, this sounds weird. Who would want their power to go back and forth? Don’t fret; we’ll explain it all shortly. Just keep reading.

Power Loss in Transmission Wires

Researchers believe that the first electrical power source was a clay pot that contained tin plates and an iron rod. If filled with an acidic solution like vinegar, a voltage would be produced on the metal terminals. The belief is that this first battery was created more than 2,000 years ago. All batteries are direct current power sources.

Using electricity to do work started to become popular in the late 1800s, and as such, the need to deliver electricity to homes and offices became necessary. The problem with delivering power over long distances is voltage loss in the wires because of their resistance.

As we know from Ohm’s law and the power calculations we have recently discussed, the power in a circuit is directly proportional to the current and voltage (P = I x V) in the circuit. Power is also proportional to the square of current in the circuit relative to the resistance (P = I^2 x R). If we can transmit power with more voltage and less current, less power is wasted in the transmission wires.

Adoption of Alternating Current

A significant benefit of alternating current power supplies in commercial and residential applications is that it is easy to change the relationship between voltage and current using a transformer. A transformer is a device that uses magnetic fields to increase or decrease the voltage to current ratio. For example, an ideal 2:1 transformer would convert 10 volts and five amps of AC to five volts and 10 amps.

George Westinghouse is credited with the popularization of the delivery of AC power to homes, thanks to being awarded the contract to supply power to light the 1893 World’s Fair Columbian Exposition. Westinghouse used transformers based on patents he purchased from Lucien Gaulard and John Dixon Gibbs. Gaulard and Gibbs invented the transformer in London in 1881.

The output of a generator in a nuclear, coal or hydroelectric plant is 20 to 22 kilovolts. This voltage is stepped up to between 155,000 to 765,000 volts using a transformer for distribution around the state or province. Most of the high-voltage towers you see along the highway or in clearings have around 500,000 volts flowing through the three power conductors.

Each city or portion of a city will have some type of electrical substation where the electricity from these high-voltage lines is stepped down to lower voltages for distribution around different neighborhoods. These voltages are usually in the 16kV range to maintain an adequate level of transmission efficiency over these short to moderate distances. Transformers in enclosures at the side of the road or installed underground convert that voltage to the 120V feeds that run to the electrical panels in our homes.

By way of an example, let’s look at 1 mile of 8 AWG stranded cable. According to the American Wire Gauge standard, 1 mile of 8 AWG copper wire will have a maximum resistance of 3.782 ohms and an ideal resistance of 3.6 ohms.

If we want 5,000 watts of power delivered through this mile of cable, there will be some energy lost to the resistance in the cable. If we transmit our power at 240 volts, there will be 20.83 amps of current flowing in the cable. With a resistance of 3.6 ohms, the cable itself causes a loss of 1562.5 and we lose 75 volts across the cable. Clearly, low-voltage signal transmission over long distances doesn’t work.

If we increase the voltage up to 16,000 volts, the power loss in the cable drops to 0.3125 watts and we only lose 1.125 volts to the cable.

High-voltage transmission lines are how electric companies can deliver megawatts of electricity over long distances with minimal power loss. At 500,000 volts, we can transmit 1 megawatt of electricity over 100 miles and lose only 720 volts. That’s 0.144 percent!

OK, enough about the relationship of AC power and voltage. Let’s talk about audio systems.

A First Look at Audio Signals

Unlike the 60Hz AC waveform that feeds our homes, audio signals contain voltage information that mimics the changes in air pressure that we would perceive as sound. In most cases, sounds are recorded using a microphone that works in the opposite way a speaker does. Sound energy moves a small diaphragm that includes a coil of wire. The coil of wire moves past a fixed magnet. The motion of the coil through the magnetic field induces a voltage in the wire. The distance the diaphragm moves determines the amplitude of the voltage signal. Louder sounds produce higher voltages.

Below is a picture of an audio waveform as seen on an oscilloscope. The person speaking said the word audio.

Understanding Power in Alternating Current Circuits

The basic concept of power in an AC circuit is the same as for a DC circuit, but some calculations need to be completed before we can apply Ohm’s law. We’ll look at the 120V, 60Hz residential power supply to explain the math in the simplest of terms.

To measure power, we need to look at the amount of work completed over a given period. In the case of a light bulb plugged into an outlet, the filament doesn’t care which direction current is flowing, but the amount of light and heat created depends on the amplitude of the voltage supplied. The work done by the bulb is calculated by the number of electrons that flow through the bulb for a given amount of time.

To determine the work done by an AC voltage, we need to calculate the value of that signal that does the same amount of work as a DC voltage. This value is called the RMS or root mean square value and is 1/sqrt 2, or 0.70711 for sine waves. For our 120V power feed coming out of the wall, 120V volts is the RMS voltage. The peak voltage is about 167.7 volts. To be clear, the value of 0.70711 only works for a sinusoidal waveform. The RMS value of a square wave is 1.0 and for a symmetrical triangle wave is 0.577.

By definition, the RMS AC voltage can perform the same amount of work as DC voltage of the same value.

The image below shows a single cycle of a sinusoidal waveform. The peak voltage is 167.7 volts, and the two orange lines define the RMS value of 120V.

Basic Understanding of Alternating Current Sources and Signals

For this article, the takeaway is that the audio waveforms on the preamp and speaker wires in our stereo system are alternating current signals. In the next article, we will discuss the concept of frequency and amplitude in more detail.

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.

We’ll continue our introduction to the basics of car audio electrical theory by talking about wiring loads in series and parallel. Understanding the characteristics of each wiring option and how it relates to power delivery and current consumption is crucial in choosing the right speakers for your sound system. All reputable mobile enhancement retailers know the basics of series and parallel wiring by heart and can help you get the right combination of speakers or subwoofers to ensure optimum performance from your sound system.

Electrical Circuit Review

At this point, you should be familiar with the basic concept of wiring a load to a power source. In our cars, this could be something as simple as plugging a USB phone charger into the center console or having your installer integrate an amplifier into the electrical system in your vehicle.

The most basic of electrical circuits has a single power source and a single load. The two devices are connected together with the positive terminal of the source connected to the positive terminal of the load and likewise for the negative terminals. Current flows from the power source, through the load and back to the opposite terminal of the source.

Wiring Loads in Parallel

Any device we wire to the electrical system in our cars and trucks is considered to be wired in parallel with other loads. The positive connections all go to the same source of electricity, and the ground connections are all effectively connected to the same terminal of the battery.

The first and most important characteristic of loads wired in parallel is that the voltage across all of those loads is equal.

Knowing this makes it easy to calculate the current through each load using the equation I = V ÷ R. We can also calculate the power dissipated by each load using the equation P = V^2 ÷ R.

In the diagram above, we see two loads connected to a common 12-volt power source. Load 1 has a resistance of 20 ohms and Load 2 has a resistance of 15 ohms. Using the equations above, we can calculate that 0.6 amp of current flows though the 20-ohm load and 0.8 amp flows through the 15-ohm branch. Likewise, the 20-ohm branch dissipates 7.2 watts of energy and the 15-ohm branch dissipates 9.6 watts.

The power source needs to provide a total of 1.4 amps of current to the circuit.

Calculating the Resistance of Loads In Parallel

An important part of understanding parallel loads and how they affect the power drawn from the supply is a required understanding of how to calculate the net resistance of multiple loads in parallel.

The formula to calculate the total resistance multiple loads wired in parallel is 1/Rt = 1/R1 + 1/R2 + 1R3 and so on, until you have included all the loads.

For our 15- and 20-ohm loads in the example, the math would be: 1/Rt = 1/20 + 1/15, or 1/Rt = 0.05 + 0.06667. This works out to 1/Rt = 0.11667 which works out to 8.571 ohms.

There are a few shortcuts you can take to calculate resistance when multiple loads of the same value are used. Look at the following circuit:

In this circuit, all four loads are 8 ohms. We can do the math and see that the net resistance is 2 ohms. Where all the loads in the circuit are the same, we can simply divide the resistance of each by the number of loads.

So, 1/8 + 1/8 + 1/8 + 1/8 = 8 ÷ 4 = 2

Please remember, this only works when all the load resistances are identical.

Wiring Loads in Series

The second option in terms of wiring loads together is to wire them in series. The schematic below shows two loads wired in series with a voltage source.

In a series circuit, the current through all the loads is the same. The voltage drop across the loads is dependent on the total current flowing in the circuit at the value of the individual load resistance.

Another trait of series circuits that makes them very easy to work with is that the total circuit resistance is equal to the sum of all the loads. The equation is Rt = R1 + R2 + R3 and so on until all the loads are considered. For our example with the 15- and 20-ohm resistors, the total resistance in a series circuit would be 35 ohms. The current through the circuit is calculated using the I = V ÷ R equation, which would be 12 ÷ 35, or 0.343 amp for this circuit.

To calculate the voltage across each load, we can multiply the current times the resistance for each value from the V = I x R equation. The voltage across R1 is 6.857 volts and the voltage across R2 is 5.143 volts. Not coincidentally, the sum of these two voltages is equal to our supply voltage of 12 V.

In automotive applications, the problem with wiring loads in series is that the total power supplied to the circuit depends on the resistance of each component in the circuit. This makes predicting results for dynamic loads very difficult. Where we do occasionally wire loads in series is when we connect subwoofers to an amplifier or in the rare occasion we are using passive crossover components with a speaker.

Series-Parallel Wiring for Subwoofers

Let’s use the example of an amplifier designed to produce its rated power into a 4-ohm load. If we want to connect a single subwoofer to the amp, it should have a nominal impedance of 4 ohms. Depending on the brand of subwoofer you are looking at, you may have a single voice coil 4-ohm sub available, a dual 2-ohm configuration or a dual 8-ohm.

If you choose a dual 2-ohm woofer, the voice coils will need to be wired in series before the positive and negative connections are attached to the amplifier. If you use the dual 8-ohm sub, the coils need to be wired in parallel.

What if we want to wire multiple subwoofers to a single amplifier channel? In this case, the net impedance still needs to be 4 ohms. You can use a pair of single voice coil 2-ohm subs or a pair of dual 4-ohm subs. The pair of 2-ohm subs would be wired in series and then to the amp. The dual 4-ohm subs would have their individual voice coils wired in series, then the two subwoofers would be wired in parallel to the amplifier.

You will note that we switched the power source in this diagram to an AC source. You can think of that as your amplifier. We didn’t want anyone calling us out for suggesting that you connect your subwoofers to your battery.

You can continue wiring multiple subwoofers in simultaneous series and parallel loads until you run out of trunk space, so long as the net results keeps the amp happy with a 4-ohm load.

Choose the Right Subwoofers for Your Amplifier

Understanding the basics of series and parallel wiring is instrumental in ensuring you get the right subwoofer combination for your amplifier, or the right amplifier for your choice of subwoofers. Your local mobile electronics specialist retailer can help ensure you get the right solution for your application and install it so that it sounds great. In the next car audio electrical theory article, we will introduce the concept of alternating current.

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.