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Tube Amplifiers Explained, Part 10: Understanding Distortion

Part of a blog series Tube Amplifier Circuits Explained


It’s time to try and cover the topic of distortion. It certainly sounds like a bad thing for a high fidelity amplifier, but what exactly is it? Let’s take a closer look, and we may dispel a myth or two in the process. First, I should say that there are multiple types of distortion, and I will mainly be discussing one type here—harmonic distortion, which is commonly analyzed in an amplifier—and even this we will only just begin to explore.


In a perfect amplifier, we would have an input voltage that varies over time (the audio signal) and an amplified output voltage that varies over time exactly proportional to the input voltage but at a larger amplitude. We want this to be a linear relationship: Vout = Vin * gain, no matter what level of Vin. As the input voltage rises, the larger output voltage rises proportionally.

But in the real world things are not perfect. Perhaps over the range of possible voltages, the tube is doing its best (c’mon give the guy a break!) but as the input voltage on the grid moves up and down, the output voltage on the anode is changing in a similar, but not exactly identical way across all voltage levels. Perhaps we would expect 1V input to result in 10V output, but the amplifier actually puts out 9.5V.


This non-linearity of the range of output voltages relative to the range of input voltages is distortion. This is an attribute of all tube amplifiers, and some might argue part of their “tube sound.” In that respect, zero distortion might not actually be the goal, but certainly we want the output to be as close a representation of the original as possible, so we will aim to have relatively low distortion.


Ok, so how can we visualize and understand distortion even more? First, I want to emphasize one important point. The amplifier has no idea about the concept of an audio signal or sine wave, which incorporates time. The tube is not first listening to your Bob Dylan song and then playing it back to you louder, nor is it looking at a sine wave for a millisecond or two and then recreating a new sine wave afterward, hopefully similar. The amplifier sees an input voltage at a point in time and puts out an output voltage at that exact point in time, or close enough to consider instantaneous. This will be important as we get into visualizing distortion and discussing feedback. We use sine waves to communicate concepts of frequency and distortion, but the behavior of the amplifier occurs at a single point in time. That said, there are elements of time in the ability of the amplifier to react quickly to fast changes in voltage and demands on current in order to perform its job properly at the present point in time, but the point I’m making is that we need to consider distortion of a sine wave as an effect that we observe over time, but that is happening at any given instant.


Now let’s reintroduce the concept of time and consider a sine wave as a voltage changing over time, and the output voltage isn’t perfectly identical in shape to the input sine wave. Remember how we drew a straight load line, expecting that variation of the grid voltage would cause the anode voltage to swing up and down on that line. But if the characteristics of the tube means the grid lines are not evenly spaced apart, then we can’t expect the output to be a perfect replica. Two examples are illustrated below, where grid curves are either closer together at one end, or at both ends, causing non-linearity.

Examples of harmonic distortion

If grid curves are wider on one side than another, gain is asymmetrical, creating even-order harmonic distortion:

If grid curves are wider in the center than at the extremes, this causes symmetrical odd-order harmonic distortion:

You can see in these examples that an equal change in grid voltage would not cause a proportionally equal change in anode voltage at all areas of the load line. When the gain is asymmetrical around the operating point, the output waveform will be misshapen, or distorted, on one side but not the other. This will cause a type of harmonic distortion that is even-order. If the non-linear effect is symmetrical on both sides of the waveform, then this causes odd-order harmonic distortion.


You might also consider what happens if the operating point were too far to the left or right on the load line, or if the input signal were too large relative to the span of grid curves—if the input voltage pushes into saturation (near or above 0 volts on the grid) or down to cutoff (deeply negative grid curves, with low or no current), then obviously the output signal will be extremely distorted and a sine wave would appear as flattened on top or bottom. This is what we would refer to as clipping. Guitar amplifiers operate closer to these conditions to achieve a desirable overdrive or distortion sound, but obviously in a hifi amplifier, this is undesirable.


Now, we’re finally ready to look at harmonic distortion another way to visualize these even and odd-order harmonics! I love this part, because the natural world, physics and math are sometimes like magic.


The sine wave that we input is at a frequency, let’s say 1000 Hz. We can call this the fundamental frequency (FF). Multiples of this frequency are the harmonics: the second harmonic is 2x the fundamental frequency, or 2000 Hz; the third harmonic is 3x the fundamental frequency, or 3000 Hz; and so on…fourth, fifth, etc.


An output sine wave that has been distorted by a non-linear amplifier will have a waveform that doesn’t look exactly like the original sine wave. And this distorted waveform is equal to the fundamental frequency plus some combination of harmonics at lower amplitudes. See the charts below that are illustrative examples if we took a pure sine wave input and add a second or third harmonic at lower amplitude. The output is a combination of those frequencies added together.


Distorted waveforms In both examples here, the blue distorted waveform is equivalent to the combination of the input sine wave and a second or third-order harmonic (at 2x or 3x the frequency).

Are you getting it? The distorted waveform is the same as multiple sine waves at different frequencies and amplitudes added together.[1] Going back to our amplifier, it’s important to re-emphasize: the output waveform is distorted due to various causes, and this is equivalent to a fundamental frequency plus harmonics. We could be tempted to have a mental image that the harmonic frequencies are created in some other way and then added to the original signal, with harmonics as the cause of a distorted output. I suggest this is not the best way to think about it. Remember how I pointed out that amplification is happening instantaneously. The waveform is distorted because gain is not uniform across all input levels, and when that happens, we can watch a waveform over time that can be described as the original fundamental frequency plus harmonics. The net effect is, however, exactly the same as if we did truly have multiple sine waves generated at different frequencies, amplitudes and phases and combined together.


What this means is we have a way to measure the harmonic distortion of the amplifier. While you could look at the waveform on an oscilloscope and subjectively say, “well, it looks pretty close to a sine wave,” and this is fine for basic observation and detection of significant distortion, we can do better.


Since the distorted waveform is identical to multiple sine waves at different frequencies, we can measure and visualize the amplitudes of those harmonic frequencies. Here’s where we need a new graph: instead of showing amplitude versus time of a waveform, we can show amplitude versus frequency. A frequency analyzer can do this for us. Below is an illustrative chart demonstrating measurements of harmonic distortion on the frequency spectrum.

You’ll see this uses decibels for the vertical amplitude, with a 1000 Hz fundamental frequency at a certain level, and the second harmonic is much lower about 50 dB below the FF. The third harmonic is lower still, and very tiny amounts of higher order harmonics. This is typical of a single-ended tube amplifier: most distortion is second and third harmonic.


We could then calculate a summary measure to add up all these harmonics and this is what you see reported as Total Harmonic Distortion (THD) usually as a percentage of the fundamental frequency. High quality modern solid state amplifiers will have extremely low values, like 0.01% THD. Tube amplifiers by nature will typically have higher THD and harmonic distortion will nearly always be proportional to output level—higher volume (higher grid voltage change) will have more distortion.


We have not yet discussed what harmonic distortion means in terms of how the amplifier sounds. How much distortion would be audible? What does second-order harmonic distortion sound like versus third-order or higher? You can find examples online or create your own if you have computer software or signal generators, to hear a sine wave with a second or third harmonic mixed in. You will notice that second and third order harmonics have distinct tonal qualities. In music, doubling the frequency is the same as a one octave higher note, and some will argue that a second-harmonic is “better” or more acceptable in sound because it is “in tune” whereas some odd-order harmonics are not musically related. There is much debate on this and conflicting tests and research about people’s perceptions of which sounds better. There is typically consensus that lower-order harmonics (second and third) are more acceptable than excess amounts of higher order harmonics.


On the subject of how much THD is acceptable, again there is much debate and probably the answer is: it depends, on many factors—the type of distortion, source, etc. Purists will say it should be as close to zero as possible. Some research was done years ago that gave clues many people may not be able to detect it audibly below 0.75% and that it may not be noticed or considered interfering with the sound until 2-3% or even higher with complex sources such as music.[2] This enters into complex or subjective areas of what people believe sounds good or not, learned experience of critical listening, variability in human hearing, etc.


Measure or Listen?

I believe in measurements to help understand performance of the amplifier or speakers. I’ve learned too often my ears play tricks on me and my own psychology can lead me to think something sounds good because I want it to (or vice versa). Remember also that one of the most critical parts of how it sounds is your speakers. There’s a whole other world of speaker selection (or DIY design!) and room environment and treatments to think about, and that’s all part of the fun of this hobby. But remember, at the end of the day, if you can play a system and it sounds good to you, you win!


I should emphasize again that there is much depth to this topic and I’m only covering some simple concepts to explain it. There are other types of distortion, such as intermodulation distortion, that can be important, too. For now, I hope you will at least understand some basics of harmonic distortion, examples of how it could be caused and how we can see or measure it.


You may be asking now what we can do to control distortion, and the next post will cover the use of negative feedback.

[1] Harmonics may also be at a different phase than the fundamental frequency, but this is not introduced here. For illustrative reasons, the second order harmonic shown here is offset by 90 degrees in phase. [2] Check out the Radiotron Designer’s Handbook , published in the 1950s and available online in PDF, for some interesting information about distortion, among other things.

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