Tech Today: Amplifier Power, Frequency and Speaker Power Ratings

WORDS BY DAVID MACKINNON

Over the years, several amplifier manufacturers have created four- and six-channel amplifiers designed to produce dramatically different amounts of power from each pair of channels. My first interaction with an amplifier like this was back in 2005 with a Lightning Audio Strike-Series S2.800.4 four-channel. This amp was rated to produce 50 watts of power from the front channels and 150 watts from the rear channels.

Why Stagger Power Production Capabilities?

It could have been Lightning Audio’s intention that you powered the tiny 3.5-inch speakers in the front of your Monte Carlo or Mustang with the 50-watt channels and a set of 6x9’s from the 150-watt channels. No matter what they had in mind, they were on to something. Read on to find out why this is an idea that could do with some revisiting.

Signal Power Versus Frequency Have you ever sat and stared at a frequency response graph of pink noise? No? Just me? Okay, pretend I didn’t ask.

Pink noise is the test signal we use to make acoustic measurements of an audio system using a real-time analyzer (RTA) and a microphone. A pink noise signal is comprised of sine waves

of varying frequencies at very specific amplitudes. What makes pink noise unique is that each octave has the same amount of energy as the adjacent octaves.

When you look at pink noise in the spectral domain (a frequency versus amplitude graph), it slopes downward at a rate of 10dB per decade as frequency increases.

Explained differently, pink noise has the same amount of energy the octave between 100Hz and 200Hz (let’s call that 100 steps) as it does between 1,000Hz and 2,000Hz (which would be 1,000 steps). As there are ten times as many steps, each step has 1/10th the energy.

A frequency response analysis of a pink noise test track created at a 192kHz sampling frequency

Don’t Phunk with My Heart by The Black Eyed Peas

Go Your Own Way by Fleetwood Mac

A pink noise track divided into frequency bands suitable for our simulated four-way audio system.

Measuring Audio System Response

If you play pink noise through a sound system and measure the results with an RTA, you will see a flat line. Since the human hearing system perceives and compares sound amplitudes in octaves (doubling or halving of frequency), it makes sense that a seemingly ‘flat’ human response to a sound would follow the same octave-based energy distribution philosophy that’s used to create Pink Noise. Said another way—pink noise best represents the way our brain interprets sounds.

Pink Noise and Music

It’s not only test tones that follow this philosophy of decreasing energy as frequency increases. The music we listen to in our cars and on the radio follows suit. Below are the averaged frequency response graphs for four different songs. You can see the downward slope.

The Power Required to Reproduce Audio

Let’s think about the power required to reproduce what we would call a flat audio response from a sound system. Knowing that the energy density in the pink noise test signal drops off at a rate of 10dB per decade means that we need 1/10th as much power to drive our speakers every time the frequency is multiplied by ten. If we have 100 watts a 100Hz, we only need 10 watts at 1kHz to produce the same output (assuming the speaker has flat frequency response). Following that logic, we only need one watt at 10kHz to produce the same output level.

We’ll get into the details shortly of how to put these theories into practice. Suffice it to say, from a perspective of physics, if you had a 1,000 watt amplifier driving a subwoofer that plays below 80Hz, then you would only need 10 watts to power a super-tweeter (of the same efficiency) playing from eight kHz and up to produce the same perceived output level.

Let’s look at the power distribution required in a semi-realworld four-way audio system design. We’ll use an example of a 500-watt subwoofer amp and set the low-pass filter at 80Hz at -24dB per octave.

Next, we’ll run a mid-bass driver from 80Hz to 300Hz using similar slopes, a midrange speaker from 300Hz to 3kHz and let a tweeter play from 3kHz and up. We’ll make this a worst-case scenario and not boost the subwoofer level by the normal ~10dB that most people enjoy (which is why the mid-bass and subwoofer crossovers can be at the same frequency).

If we look closely at the response graph above, you’ll see that the peak power requirement of the mid-bass driver (orange curve) is down four dB from the peak of the subwoofer. The midrange driver (yellow curve) is down roughly 10.5dB and the tweeter (green curve) is down 21dB. If we convert these numbers to power ratios, our mid-bass driver needs 200 watts, our midrange driver needs 45 watts and our tweeter needs a mere four watts.

This example doesn’t take into account the fact that there are two of each high-frequency driver in the system, nor does it allow for equalizer boost just above each driver’s crossover point. This example also doesn’t take into account cabin gain in terms of subwoofer system efficiency. The sole purpose of this example is to explain the laws of physics in relation to the power required to reproduce audio with respect to frequency. Once you have a grasp on this, you can continue to the next part of the article.

A graphical representation of sine wave energy verses pink noise energy

Let’s Talk About Speaker Power Ratings

One of the least understood concepts in the car audio industry is related to how speaker power handling specifications are created, and perhaps, why so darned many speakers are damaged each year—day? Hour? Thanks to Andy Wehmeyer from Audiofrog, we are going to explain how speaker power ratings work.

Speaker power handling specifications typically describe the amount of pink noise (or modified pink noise) a speaker can handle in terms of thermal capacity. The original specifications were created for full-range home audio speakers, and as such, were tested using full-bandwidth (20Hz to 20kHz) pink noise signals.

Of course, if you fed 100 watts of full-bandwidth pink noise into a tweeter, it would last less a half-second before ripping itself apart. It also stands to reason that the thermal capacity of a tiny one-inch diameter by the 0.1-inch tall voice coil in a tweeter won’t be able to dissipate the same amount of heat as a three-inch voice coil that’s an inch tall as found in a large subwoofer. Thermal power handling is directly tied to the physical size of the voice coil assembly.

Speakers, especially smaller ones, are tested using pink noise, and the test is conducted in a specified frequency range. For a tweeter, the test signal may be passed through a high-pass filter at 2,500Hz. All good, right? Here’s where the size of the voice coil and its thermal capacity start to make sense.

How Speakers Get Their Power Ratings

Let’s say you have asked a laboratory to test the power handling capabilities of four prototype speakers. The samples include a 10-inch subwoofer, a 6.5-inch woofer, a four-inch midrange and a oneinch tweeter. You want them to test the sub to confirm it can handle 500 watts of power and the rest of the drivers need to handle 100 watts of power.

As part of the test configuration, as a manufacturer, you will have to specify what high-pass filters should be applied to the test signal. For the subwoofer, it can run full range. We’ll choose some arbitrary examples and pick 60Hz for the woofer, 100Hz for the midrange and for the tweeter, you specify 2,500Hz.

Finally, you have to specify the length of the test and the pass and fail criteria. Most companies test for eight to 10 hours, but some extend the test to more than 100 hours. The pass or fail criteria for some companies is a simple matter of the speaker continuing to play or failing.

Other companies have far more stringent quality control standards, such as requiring the Thiele-Small parameters of the driver cannot change by more than 10 percent from the beginning to the end of the test after the speaker has had time to cool off.

Distortion vs. Power of a High-Quality Class AB Amplifier

Distortion vs. Power of a High-Quality Class D Amplifier.

For comparison, a distortion vs power output graph of a low-quality Class ABamplifier. This egregiously bad amplifier produces more than one percentdistortion below one watt of output.

Speaker Power Handling Test Procedure

The test begins with the speaker being mounted on a baffle and connected to an amplifier. The test stimulus will be set with a sine wave that represents the voltage required to produce the power level you want to test for. For our subwoofer, at 500 watts, we need 44.72 volts, assuming the voice coil has a four-ohm impedance. Once the level is set, the pink noise track is played and the timer starts.

For the woofer, mid and tweeter, the setup is the same. We want 100 watts, so the test amplifier will be set to produce 20 volts, then the filter is applied and the pink noise is played.

Now, think carefully about the shape of the pink noise signal. It slopes down at 10 dB per decade above 20Hz. The test signal is set with a sine wave at a level representative of the energy produced by the pink noise below 20Hz.

If we filter the signal at 60Hz, the peak level is down 3.5dB, which is less than half the power. It’s 44.7 percent, to be exact. So, we are testing this speaker with 44.7 watts of power to give it a 100-watt standardized rating.

When our four-inch midrange is filtered above 100Hz, it receives about 6dB less energy than the sub, which equates to 25 watts. Finally, filtered way up at 2,500Hz, the tweeter level is down 19.5dB from our peak <20Hz level, and only receives 11 watts of power to pass a 100-watt power handling rating test.

Look back at the chart that shows the pink noise energy distribution in our four-way audio system. Remember that the pink noise signal produces a theoretically flat acoustic response.

If you don’t believe me, connect an oscilloscope to a fully active audio system and play pink noise (NOT SINE WAVES!) and look at the average level going to each speaker. You’ll see there’s less and less voltage (and consequently power) as frequency increases.

Setting Up Your Audio System Destroys Speakers

We’ve seen countless examples of people using sine-waves to set the sensitivity controls on their amplifier. If you play a 0dB sine wave at 1kHz into your four-inch, four-ohm midrange at a level of 20 volts, that’s 100 watts of power.

Think back to our discussion about how pink noise is shaped. You have just exceeded the power rating of that speaker by a factor of four. It might continue to play long enough to set up the system, but then again, it might not. Keep reading…

Pink Noise Power

Working out the amount of energy in a pink noise signal and dealing with the amplitude of that signal gets a little tricky. I’ve created an image that serves only as a graphical representation of a concept and does not specifically follow the laws of physics. The image below shows the average energy in a pink noise signal on the blue trace. By comparison, a 1kHz sine wave (green trace) demonstrates the same perceived peak power level. The sine wave signal crosses the pink noise curve at a level of -15dB.

Considering our explanation of power testing above, a speaker rated to handle 100 watts of power at 1kHz and up is testing with a mere 3.2 watts of power. Feeding a 100-watt sine wave into a speaker that’s rated for 3.2 watts is going to smell bad, really fast.

Keep this in mind when using test equipment to set up your audio system. Setting gains at 1kHz doesn’t always equate to having the right amount of power once the operating bandwidth and power ratings of the speakers are considered.

Making the Most of Car Audio Amplifier Power Ratings

Back to our discussion about amplifiers with staggered power ratings. I want to show you two graphs. These are Total Harmonic Distortion versus Amplifier Power Output measurements I performed on two high-quality amplifiers. Amplifier designers and engineers use graphs like these (and many more) to fine-tune their designs. Good product development folks use this information to select vendors, approve designs and help quantify what a particular amplifier will sound like in a specific application or operating range.

As you can see, the distortion produced by these amplifiers decreases as the output level increases. This (completely normal) behavior is due to crossover distortion and noise. Crossover distortion doesn’t have anything to do with the high- and low-pass filters in the amp. It’s a phenomenon associated with the transition of the output signal from the positive output devices to the negative device. Because this distortion is essentially fixed in level, as the signal level increases, the effect of crossover distortion decreases.

When you are designing a high-end audio system, you want to choose amplifiers that produce as little distortion as possible. Every car audio manufacturer rates their amplifiers at their minimum distortion level, and few (if any) have the fortitude to provide graphs like these.

If you know your midrange speakers and tweeters only need 45 or five watts of power, you are better off using a 75-watt per channel amplifier as opposed to one rated for 250 watts. Why? Because in most cases the crossover distortion is lower as the amplifier gets closer to reaching its maximum output level.

Car Audio Physics

I know this was a lot of ground to cover in a single article. It would have been easier to spread this information over a few articles, but they’d be small, and really, the information delivered would be the same.

If you have questions or want more examples, track me down on any of the big industry Facebook groups and ask. I’d be honored to help.