October 2021

Amplifier Power Ratings From The Ground Up, Part 3
The final part of our series offers practical conclusions and key takeaways.
Article By Pat Brown Of SynAudCon

Figure 1: The amplifier's function is to reproduce a voltage waveform (larger pic).

  With this article, I wrap up a three-part series on amplifier power ratings. In Parts 1 and 2, I presented some relevant theory to understand what amplifier power ratings mean. In this final installment, I'll present some practical conclusions.

It's All About Waveforms
A wave editor presents a graphical representation of the voltage amplitude of a waveform versus time (Figure 1). The voltage waveform originates from a microphone, recording, electronic musical instrument, PC, etc. The function of each stage of the signal chain is to modify this waveform. This might include gain, equalization, delay and a host of other signal processes. By the time it gets to the power-amplifier input, only one modification remains: gain. Some of these voltage modifications are to introduce compensations or corrections to the loudspeaker's response. That's why the amplifier must preserve the voltage fidelity.

The amplifier's primary job is scaling. To do that accurately, there must be a linear relationship between its input and output waveforms. That allows the function of the amplifier to be expressed by a simple gain figure (dB) and a simple power rating in Watts (W).

The waveform is a complete time record of the signal voltage. The moment-by-moment variations include signal peaks. When integrated over time, there is an average level. The averaging is done to determine the root-mean-square (RMS) value, which, in turn, reveals the signal power that the waveform generates. Because the amplifier's job is to exactly reproduce the waveform, it must have sufficient voltage swing to pass the signal peaks, as well as sufficient current output to produce the RMS voltage across the loudspeaker's impedance.

How Many Watts Do I Require?
This is one of the most common questions in audio, and it's one of the most difficult to pin down to a simple answer. As an aid, I offer you a gift — namely, a freeware calculator to perform the math. The CAFViewer can be downloaded from caf.prosoundtraining.com (Figure 2). Although mainly developed as an app for presenting amplifier specifications, it includes a lineup of useful calculators. For amplifier sizing chores, I refer you to the Low-Z and High-Z calculators (circled on Figure 2).

Figure 2: CAFViewer home screen, with particular calculators circled. Note the URL for download (larger image).

The Loudspeaker Power Rating
All loudspeakers have a power rating that results from measuring the RMS voltage of a standard noise spectrum (e.g., IEC 60268-1). The E_max(RMS) is the maximum continuous RMS voltage based on thermal criteria (power compression). It is measured with an RMS voltmeter. The amplifier used to perform the test must be sufficiently large that its output voltage can grow incrementally over the duration of the test until E_max(RMS) is reached. In other words, the amplifier must not clip or limit prior to the loudspeaker reaching its thermal limit. The amplifier must also source sufficient current to satisfy the demands of the loudspeaker's impedance. Insufficient voltage swing or current flow results in distortion, and that would indicate that a larger amplifier will be required to perform the test.

The voltage tells the story. It is common practice to present this voltage in Watts by using a rated loudspeaker impedance (e.g., eight Ohms). Squaring and dividing by eight gives E_max(RMS) as a wattage. This is just a math trick. It's not reallya wattage because the loudspeaker's rated impedance is not its actual impedance. This extra step does no harm so long as it doesn't obfuscate the value of E_max(RMS). It is E_max(RMS) that the loudspeaker thermal test determines, and this value must be known to set an RMS limiter to protect the loudspeaker.

Figure 3: Important fields in the low-Z calculator (larger image).

Amplifier Sizing: Bottom Up
The amplifier's eight-Ohm sine-wave rating is important. In the low-Z calculator, it is always shown in red text on the amplifier graphic, calculated from the entered voltage. This serves as a useful reference when modifying the other variables. It clarifies the difference between rated and actual power.

To use the low-Z calculator, start by entering the loudspeaker's continuous-power rating under the loudspeaker graphic. Leave the impedance set to the default eight Ohms. The calculator will determine the E_max(RMS) from the entry. The amplifier section must be able to produce this E_max(RMS) with enough voltage swing for the signal peaks.

Like real-world amplifiers, the one in the calculator is rated with a sine wave (either continuous or burst). The default 3dB crest factor (CF) must be increased for real-world program. Note that, as the CF increases, the RMS voltage from the amplifier decreases. This might force you to increase the amplifier size in order to achieve the target E_max(RMS). Figure 4 shows the CFs of common program types.

Figure 4: Required peakroom for various types of audio program.

A little experimentation will reveal that "peakroom" is expensive. For most applications, we could neither afford nor justify the 20dB figure used in recording studios and other critical-listening environments. This forces a compromise, and possibly the need for a peak limiter ahead of the amplifier. From Figure 5, you can see that a 300W amplifier is required to feed 17V_RMS of pink noise to a loudspeaker.

Figure 5: A 300W amplifier producing 17VRMS of pink noise has no headroom (larger image).

A related (and important) point is that a 300W amplifier that's passing 17V_RMS of pink noise (12dB CF) is operating with no headroom. Headroom is what's left above the signal peaks. The same amplifier passing 17V_RMS of EN-50532 noise (6dB CF) would have an additional 6dB of headroom. The distinction between peakroom and headroom is important. When the peaks hit the rails, there is no headroom!

This is the "bottom-up" way of sizing an amplifier. It is what's used when the loudspeaker's E_max(RMS) is the starting point.

Amplifier Sizing: Top Down
Next, I will phrase the question in a different way. We have an amplifier with an eight-Ohm sine (or burst) rating of 300W into eight Ohms. What is the maximum power that it can deliver to a loudspeaker?

Because it's the same question, we can use the same calculator (see Figure 5). Increase the default 28V_RMS until "300" is displayed on the amplifier graphic. Next, increase the CF to the expected value. Increasing the CF decreases the RMS voltage and resultant power. I'll assume pink noise and make it 12dB. The calculator determines that the amplifier will be producing about 17V_RMS, which is about 38W into eight Ohms. Yes, it takes a 300W amplifier to produce 38W when leaving 12dB of peakroom. As I wrote earlier, peakroom is expensive!

To summarize, amplifier sizing based on the loudspeaker's thermal power rating is done "from the bottom up." Amplifier sizing based on the amplifier's power rating is done "from the top down."

Why Eight Ohms?
I suggest using the calculator's default eight-Ohms settings unless you have a specific reason to change them. The reasons for this suggestion are as follows:

1. Most low-Z amplifiers behave as an ideal voltage source when loaded to eight Ohms. That means that the input and output voltage have a linear relationship that can be expressed as a simple gain figure in decibels and/or power rating in Watts.

2. At lower impedances, the amplifier's voltage might drop or limit in a dynamic, load-dependent way if it's pushed to the point of clipping. This is due to the amplifier running out of current. That makes the output voltage dependent on the load impedance, the signal type or both. Under such conditions, an amplifier's behavior cannot be conveyed by a gain figure or power rating. We can still do the calculations as an estimate, but you'd have to hook it up and listen for the dynamic details.

3. If a loudspeaker is rated at four Ohms (or lower), it's likely only that low over a small part of its bandwidth. This might not excessively load the amplifier for broadband program material, which is what most amplifiers must pass. In other words, the amplifier's voltage into four Ohms might be essentially the same as its voltage into eight Ohms. This certainly is true if you stay well below clipping.

Our calculations assume amplifier linearity, where the amplifier's behavior is expressible as a simple gain figure in decibels or as a one-number wattage rating. This might not be the case when the amplifier is excessively loaded and pushed hard. It might survive, but you'd have to try it "in situ" to assess its performance under such conditions. That's one reason why two amplifiers that have the same power rating can sound the same at low playback levels but sound quite different when loaded down and pushed hard.

Startling Conclusions
The calculations reveal some realities as regards the amplifier-to-loudspeaker relationship. They include the following:

1. If you buy an amplifier that's large enough to deliver the loudspeaker's E_max(RMS) you likely won't be able to afford 20dB of peakroom for most sound-reinforcement applications. This is mostly due to the long distances over which we must project the sound. The inverse-square law will exact its toll on the L_P.

2. If you buy an amplifier that's large enough to reach the loudspeaker's linear peak excursion limit (X_max), then it will be able to toast the loudspeaker completely if driven to full output by a medium CF (or lower) waveform.

As such, and as with most things audio, a compromise is required when sizing an amplifier.

Cookbook Amplifier Sizing
A defensible guideline for sizing an amplifier is as follows:

1. Determine the loudspeaker's E_max(RMS). This might be as simple as looking it up on a spec sheet. In some cases, you'll have to determine it from the loudspeaker's power rating. Be careful here! If the power rating is exaggerated, so, too, will the calculated E_max(RMS) be. You can always get the true E_max(RMS) from the loudspeaker's Generic Loudspeaker Library (GLL) or Common Loudspeaker File Format (CLF) data file.

2. Square and divide by eight. This yields a reference power for sizing the amplifier.

3. Double it to determine the minimum suggested amplifier size. This will yield an amplifier with 6dB of peakroom above E_max(RMS). With a peak limiter in line, this might be enough peakroom for some applications, but it's likely to sound pretty "squashed." At least it won't burn up the loudspeaker, though.

4. Each additional doubling of the amplifier size will yield an additional 3dB of peakroom. As such, 9dB of peakroom requires four times the loudspeaker's continuous rating, 12dB requires eight times and so on. This can really drain your bank account, but it's how it works. Yes, it's better to have more, but it's also expensive.

5. Regardless of the amplifier size selected, you must not exceed the loudspeaker's E_max(RMS), as determined in step 1.

In a nutshell, if the loudspeaker's power rating is based on an accurate E_max(RMS), then the amplifier should be four to eight times that rating if you desire to produce its maximum L_P with a reasonable amount of peakroom.

The four-times-rated power guideline is very common. In practice, if you size your amplifier this way, and then keep the amplifier out of clipping, you'll be operating well below both E_max(RMS) and the loudspeaker's peak limits. Your loudspeaker should have a long, happy life! This "recipe" certainly increases the loudspeaker's reliability and reduces tech-support calls. However, it won't produce the maximum L_P of which the loudspeaker is capable, based on its thermal limits. It's good engineering practice to design systems that don't have to be pushed to their maximum output level on a regular basis.

Amplifier-Configuration Summary
Armed with the earlier-discussed principles, you can figure out how any amplifier configuration works. Looking at Figure 6, "A" shows a selector switch found on the back of a popular amplifier. I've chosen it because it represents most all of the methods used to interface amplifiers to loudspeakers. All amplifiers support one or more of these configurations. Note that two of the settings are for direct-connected "low-Z" loads. Three of the settings are for driving transformer distributed systems.

Figure 6: Amplifier load-selection switch.

The ΔdB column shows the level difference that you'll hear if you connect a loudspeaker and switch between the settings. Before you do so, set the amplifier for a very low playback level.

What follows are the specifics for each setting:

Eight Ohms: Reference setting for all direct-connected, low-Z loads at eight Ohms or higher.

Four Ohms: Voltage is -3dB relative to the eight-Ohm setting. This doubles the available current to drive very-low-Z loads. Note that, if you don't require the extra current, you have sacrificed 3dB of level.

25V: For driving 25V distribution transformers. Total of taps should not exceed 60W.

70V: For driving 70V distribution transformers. Total of taps should not exceed 60W.

100V: For driving 100V distribution transformers. Total of taps should not exceed 60W.

Clearly, the voltage and impedance specifications reveal more than the power ratings for deploying this amplifier.

A different manufacturer might offer the amplifier as shown in "B" (see Figure 6). The four-Ohm, eight-Ohm and 25V settings have been combined into a single eight-Ohm selection. Is this legit? What follows is the reasoning: There's only 1dB difference between the eight-Ohm and 25V settings. That means that the eight-Ohm setting can drive a 25V line directly, with no noticeable change in level. For broadband program material, the output voltage of the eight-Ohm setting might not drop when loaded with a real-world, four-Ohm load for reasons that I cited earlier. If this is the case, then a physical four-Ohm setting that reduces the voltage to allow more current might not be considered necessary.

Figure 7: The IO Matrix of an amplifier's performance (larger image).

Key Takeaways
The "deliverable" from amplifier to loudspeaker is voltage fidelity, not wattage. That voltage can be expressed in Watts using a rated impedance for the loudspeaker.

The only way to change the wattage to a loudspeaker is to change the applied voltage. That's because the loudspeaker's impedance is fixed. If you view power as the deliverable, then you might do things, such as ganging multiple loudspeakers onto a single amplifier channel, "to get more Watts."

An amplifier's wattage rating might oversimplify the amplifier's performance. It can make amplifiers that are quite different appear superficially to be the same.

A power rating doesn't convey the same information as the voltage and load impedance, even though they're mathematically related. For the same reason, you can't shop for a "wall wart" for an electronic widget knowing only the required power. You must first know the voltage, and then the required current. Although multiplying these yields a power rating, the power rating alone doesn't convey the required information.

At least three waveforms are required to describe an amplifier's performance fully. A burst waveform reveals the amplifier's E_max for a sine wave. That is the value used for drawing-board sizing calculations and assumes a medium- to high-CF waveform. A continuous sine wave reveals the amplifier's ability to source current. That value is useful for assessing the lowest impedance the amplifier can drive when passing low-CF waveforms (e.g., heavily compressed program). A noise waveform provides a picture of real-world performance and is necessary to size circuit breakers and cooling systems. For a properly sized amplifier, this should be near the loudspeaker's E_max(RMS), if you intend to drive the loudspeaker to its maximum L_P.

The IO Matrix presents a complete picture of the amplifier's behavior (Figure 7). Power ratings are fine for quick estimates and water-cooler chatter. However, the IO Matrix reveals the details of the amplifier-to-loudspeaker interface. It provides all the necessary information to deploy the amplifier in various configurations, for various loads and signal types.

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