From The Bench

by Tom Lees

**This Article Was Originally Published On: July 1st, 2014 #Issue 14. **

In this column, we are going to address the issue of power, and more pertinently, the concept of burst power. Let’s kick some things off with some definitions. Here at *Bass Gear Magazine*, we use the term “burst power” to refer to the ability of some amplifiers to deliver power for a short duration at a power output level greater than the amplifier’s ability to output continuous power, without increasing the distortion introduced into the signal.

There are many ways to define burst power, but we use the CEA 2006/490A standard. The idea behind our burst power test is to apply a 1kHz sine wave that is modulated with a square wave to transition between two main output levels. “Huh?” Think of it as a 1kHz sine wave that is at full output level for 20 cycles, then the signal is attenuated by 20dB for 480 cycles. This pattern repeats as necessary. Don’t worry if you do not fully understand decibels; we will touch on that below.

Check this out; a 1kHz sine wave repeats its cycle 1,000 times per second. That means that each cycle takes 1/1000 or 0.001 seconds. Thus, our burst signal is at maximum output for 20 ms. The signal then drops 20dB for 480 ms. This pattern thus takes about ½ second, and it repeats until our test is complete.

The key to our burst testing is that we establish a target distortion level that we are focusing on. For our purposes, we use the same distortion level that is chosen for our continuous power test. This number can vary, depending upon the amplifier we are testing, and is set to account for the intentional character of the overall amp. For instance, a tube amplifier may test at 5% THD+N, whereas a precise, clean solid state amplifier may tested at 1% THD+N level.

We then crank up the amplifier, such as by turning up the master volume or equivalent, and apply our burst signal. The level of our burst signal is varied until we find the maximum output level at the target distortion level.

Basically, we record the output power for each of the 20 cycles that occur at the maximum signal level. We throw away the first nine cycles to forgive amps for spurious results caused by initial transients, and analyze the remaining 11 cycles. The 480 cycles at 20dB down are there to allow the amplifier some time to recover from our burst before the pattern is repeated.

One thing to note right away: if an amplifier cannot burst for the full 20 ms, it will be penalized by our test, because in our test, the last 11 cycles of the burst are the most important. Also, an amplifier that can sustain a burst longer than 20 ms is not rewarded by our test.

Are you still hanging with me? Good, let’s move on.

Continuous Power is the maximum output level that an amplifier can sustain for longer than a burst. We say this because some amplifiers can output the maximum continuous level for as long as the musician needs it. However, we are starting to see some amplifiers that kick in thermal protection right at, or just before the amplifier hits its maximum – in some cases, the amplifier can only sustain its continuous level for a few seconds before thermal shutdown kicks in.

We need to get one thing clear before we continue. We are in no way trying to draw any correlation between burst power and amplifier “quality.” To the contrary, the utilization of burst power is simply one design consideration that is factored into a particular design. Different amplifier designers take different approaches to address the problem of amplifying dynamic signals.

“Problem? I did not know there was a problem.” Well, there is and there isn’t. Let’s put some examples to work to show why we may care about burst power, and examples why it may not be “all that.”

First, we need to create a fiction. I have a fictional amplifier that is capable of an absolute maximum output of 500 watts at 1% THD+N into a 4-ohm load. Using the formula:

** P=V ^{2}/R (Equation 1)**

We know that to squeeze out the maximum amount of power, our amplifier must supply a 44.72 Vrms signal at 1% THD+N (or less) to the 4-ohm load. In our fictional amplifier, any voltage over 44.72 Vrms will cause too much distortion for our example specification.

Recall that a voltage can be expressed in at least four ways, including peak to peak, + peak, – peak, and rms. For this simple analysis, assume that a wave is plotted with amplitude on the Y-axis and time on the X-axis. Further, assume that the wave is centered at zero amplitude (i.e., no DC offset).

To find the peak to peak voltage, take one cycle of the wave, find the highest point and the lowest point, and that difference is the peak to peak voltage.

To find the +peak voltage, take one cycle of the wave, and find the most positive peak.

To find the –peak voltage, take one cycle of the wave, and find the most negative peak.

To find the rms voltage, first note that rms (root mean square) is essentially the quadratic mean. The rms value represents the energy under the wave and better represents the ability of the wave to do work – in our case, provide power. To simplify our quick and dirty math, we make a first assumption, that our wave is a sinusoid. The equation for rms for a sinusoid is:

** Vrms=1/sqrt(2) * Vpeak (Equation 2)**

We simplify this to Vrms=0.707 * Vpeak. Note that this equation is inaccurate for other waveshapes, such as square waves, pulse trains, triangles, sawtooth waves, etc. However, for the fictional world of our article, it’s good enough.

Take a look at *Fig. 1*. This is an oscilloscope capture of a slap line in *E* performed on our Editor-in-Chief’s modified Lotus bass (a fantastic-sounding instrument, IMHO, with a single split-coil P-bass pickup). Roughing this out, it looks like the peak voltage is about 1.7 V peak, which occurs at about 2.8 seconds. Let’s also say that most of the signal (excluding the peaks) falls under 600 mV peak. It is worth observing here that the output of the Lotus is asymmetric. For instance, the largest negative going peak is about -1.5 Vpeak at about 1.15 seconds and that peak occurs on a different slapped note than the 1.7 Vpeak.

** FIG.1** Lotus E Slap Scope

Getting back on track, for this discussion, we will convert our peak voltages to rms and say that our largest spike is 1.7 Vpeak * 0.707 or about 1.2 Vrms. Now, to amplify 1.2 Vrms to the maximum power of our fictional amplifier, we need a gain of about 31.4dB, so we dial up our fictional amplifier to a gain of 31.4dB.

“Whoa, there! Weren’t we talking about voltages? Where did this ‘dB stuff’ come from?”

In amplifiers, it is often convenient to talk about level changes in terms of decibels (dB). The equation we use for this is:

** Level Change in dB = 20 log(Vout/Vin) (Equation 3)**

If the result is positive, we call that amplification or gain. If the result is negative, we call that attenuation.

In this case, the level change = 20 log(44.72 (max voltage out)/1.2 (max voltage in))=31.4dB. Under these conditions, at about 2.8 seconds into our line, we eeked out the ideal maximum 500 watts of our amplifier. Sweet. But what about the rest of the signal?

Now, watch this. We said that the better part of this slap line falls somewhere under 600 mVrms peak. The average is actually less than this, but the math is purely for illustration, so we pick this value for convenience. That is about 600 mVpeak * 0.707 or about 424.2 mVrms. Now, the gain of our amplifier has not changed. So, applying a gain of 31.4dB of gain, we get a voltage of 15.8 Vrms out from our fictional amplifier. Hint: to get 15.8, use equation 3 and solve for Vout.

Going back to Equation 1, we now see that the output power of our fictional amplifier at our new level is: output power = (15.8 Vrms)^{2}/4 ohms = approximately **62 watts.** Crikeys, that stinks. Keep in mind that for the lower signals, the output power is even less.

“But hey, we started out with a 500-watt amp. What gives?” I will tell you what gives … your bass does not output perfect sine waves at a constant output level. Now, in the context of your particular application, this may be okay. Alternatively, there could be issues of you getting lost in the mix.

Take a look at *Fig. 2*. Let’s play the same game. We will use the same fictional amp and the same real Lotus bass. However, this time, instead of playing a slap line in *E*, we have a walking blues line in *A*, with some wide, ringing notes, and much more finger finesse than thumb-thwacking action.

**FIG. 2 Lotus Walk in A Scope**

The peak note looks to be about -650 mVpeak, with most of our notes around 400mVpeak (or less). Converting to rms, we see that our maximum signal is about -460 mVrms. To keep things simple, we take the absolute value and compute the gain that we need to get to the limits of our amplifier. We need a gain of about:

Gain = 20 log (44.72/0.460) = 39.8dB

We can assume that the amplifier is capable of this much gain, and we need to turn our amp up, relative to our first example with reference to *Fig. 1*. So, at about 700 ms into our walking line, we eek out our full 500 watts. Sweet.

Now, taking 350 mVpeak as an approximation of the remaining parts of the line, we end up at about 247.5 mVrms. Applying our gain of 39.7dB, we get an output voltage of about 24.2 Vrms, or about 146 watts. Hey, that’s not 500 watts, but it sure the heck is better than 62 watts.

“So what is it? Do I have a 62-watt amp, a 146-watt amp, a 500-watt amp, or something else?”

Well, the truth is, you have an amplifier that is capable of producing 500 W into a 4 ohm load for an input signal at a given amplitude. Thus, any lackluster performance is due to the dynamics of the instrument and performance. On the other hand, that dynamic range is what contributes to the difference between “music” and sine waves. As such, we do not want to require that the musician change instruments or style.

__Burst Power to the Rescue:__

Assume that we change the design of our fictional amplifier. Now, for a small interval of time (e.g., under 1 second), we can actually exceed our rated 500 watts. After our burst time, we need to drop back down to the 500-watt maximum to allow the amplifier time to reset.

“Great. How much ‘burst power’ do I need?”

Go back to our slap line in *Fig. 1*. Since we are in a fictional world, I am going to assume that a user wants to run our average continuous level of 424.2 mVrms at our full 500 watts. To do so, the amplifier needs a gain of:

20 log (44.72/0.424.2) = 40.6dB

We can assume this is no problem for our amplifier, since our amplifier is fictional. But recall, our peak was 1.2 Vrms. Now, to amplify that peak without introducing additional distortion, we need an output voltage of 128.6 V rms. That is over * 4,100 watts*!

Okay, we can play the same game for the walking bass line of *Fig. 2*. Since we are in a fictional world, I am going to assume that a user wants to run our average continuous level of 247.5 mVrms at our full 500 watts. To do so, the amplifier needs a gain of:

20 log (44.72/0.0.247.5) = 45.1dB

Once again, we can assume this is no problem for our amplifier. Here, our peak was 460 mVrms. Now, to amplify that peak without introducing additional distortion, we need an output voltage of 83.1 Vrms. That is over * 1,700 watts*!

I hope that you can see that the subject of burst power is extremely variable. For instance, the above examples are for a single bass, a single musician and only two examples of different playing style.

Moreover, we have not even addressed *how *we go about providing this extra oomph. What I hope readers take away, here, is that this is not a trivial task to ask manufacturers to take on. Everyone is going to have personal preferences and approaches in how to deal with burst power. Moreover, the topology of the particular amplifier is going to provide opportunity and limitation.

__Real World Examples:__

Now that the problem is framed, we are going to take a look at several real world amplifiers that we have on hand here at the Amp Lab to see what they can do. Note, all measurements were taken with the amplifiers driving a 4-ohm non-inductive dummy load.

__Example 1:__

Up first is a contender from the class-D topology. The character of this amplifier slanted on the squeaky clean side, so we tested the amplifier at about 1% THD+N. We measured:

740 watts; 1% THD+N filtered 20Hz-20kHz; 680 mVrms 1kHz sin Input Continuous

930 watts; 1% THD+N filtered 20Hz-20kHz; 770 mVrms 1kHz sin Input Burst

The above suggests that with this amplifier, there are about 200 watts on tap for bursts. However, with reference to *Fig. 3*, it can be seen that the amplifier comes out of the gate swinging with nice, clean burst power. However, about halfway through the 20-cycle burst, the amplifier starts to run out of energy. The burst drops off in amplitude, and begins to show signs of distortion, especially at the peaks of the last few cycles.

** FIG. 3** Example 1 Class D Amplifier

__Example 2:__

Up next is a heavyweight contender from the all-tube topology. The character of this amplifier slanted on the “tubey,” yet clean side, so we tested the amplifier at about 2.5% THD+N. We measured:

275 watts; 2.5% THD+N filtered 20Hz-20kHz; 120 mVrms 1kHz sin Input Continuous

370 watts; 2.5% THD+N filtered 20Hz-20kHz; 135 mVrms 1kHz sin Input Burst

The above numbers suggest that this tube amplifier is capable of generating about 100 watts of extra burst power. With reference to *Fig. 4*, it can be seen that the amplifier starts off strong, with nice, clean burst power and maintains a consistent amplitude and distortion level throughout the burst signal. The last few cycles arguably show a little sign of clipping, but this is minimal. So, with a tube amplifier, we see less available dynamic power, but the amplifier has the ability to preserve the burst in both level and distortion.

** FIG. 4** Sample 2 Tube Amplifier

__Example 3:__

Up next is a solid state contender. The character of this amplifier slanted on the gritty side for solid state due to some tube-like preamp character, so we tested the amplifier at 1.6 % THD+N. We measured:

400 watts; 1.6% THD+N filtered 20Hz-20kHz; 120 mVrms 1kHz sin Input Continuous

620 watts; 1.6% THD+N filtered 20Hz-20kHz; 150 mVrms 1kHz sin Input Burst

With reference to *Fig. 5*, it appears as if our solid state contender one-ups both the class-D and tube amplifier. Our solid state amplifier bursts at over 200 watts above its measured continuous power output. As *Fig. 5* illustrates, the amplifier maintains the burst signal throughout its duration, with minimal drop off in amplitude. Moreover, the burst signal appears to remain substantially clean.

** FIG. 5** Sample 3 Solid State Amplifier

__Example 4:__

Up next is another class-D amplifier, this time with a tube preamplifier. The character of this amplifier slanted on the gritty side, so we tested the amplifier at 6.6 % THD+N. We measured:

306 watts; 6.6% THD+N filtered 20Hz-20kHz; 240 mVrms 1kHz sin Input Continuous

398 watts; 6.6% THD+N filtered 20Hz-20kHz; 247 mVrms 1kHz sin Input Burst

With reference to *Fig. 6*, it appears that our tube preamp/class-D amplifier can generate just under 100 watts of burst power. The burst signal remains at about the same distortion level, appearing clean and rounded along the edges through the entire 20 cycles of the burst. However, the amplitude consistently drops off after the initial burst.

** FIG. 6** Sample 4 Hybrid Tube Preamp Class D Amplifier

In our tiny survey, we looked at four different amplifiers, each with a different approach to burst power. We saw four completely different results and characteristics. However, we also note that individual playing style, choice of instrument, use of effects, etc., can have a significant impact upon what is required of the amplifier.

We have just begun the discussion of burst power. There is much more to get into, and I hope to do so in future issues. At any rate, keep on jamming and don’t get too caught up in this numbers game. This stuff is fun for the academics and, of course, for practice using that math crap that in school you were convinced had no practical use.