Linearity

May 1, 2021
 by Paul McGowan

The term linearity as it applies to amplification suggests a ruler-flat straight line. That is, for a given input voltage we expect a mathematical relationship with the output voltage that can be graphically expressed as a straight line.

So, for example, with an amplifier designed with a gain of 10, for 1 volt in, we expect exactly 10 volts out at every frequency. Easy peasy. Only, that isn’t what happens with amplifying elements.

Neither transistors nor vacuum tubes are natively linear with voltage or frequency, yet we expect them to perform as if they were.

Here’s a simple graph of input vs. output voltage of an amplifying element. Note how only part of its response is a straight line.

And this graph only covers voltage. A similar graph displaying input vs. output frequency is even worse.

What to do.

There are numerous ways designers have of overcoming a device limitation. For instance, a transistor’s input vs. output is very non-linear at input levels below half a volt. So, imagine you’re trying to amplify the tiny output voltage of a phono cartridge—maybe 0.005 volts. Yikes! That’s so low the amplifying device wouldn’t even recognize it!

The answer to that problem is simple and straightforward. We pre-apply to the transistor a steady, small, “turn-on” voltage. Now, when we next add the tiny voltage from the phono cartridge, the transistor will add that voltage to the steady voltage and we get a linear output response we can count on. At the device output, we remove the steady “turn-on” voltage and, what’s leftover, is a perfect bigger version of the tiny phono cartridge output.

Bingo!

That process I just described is known in engineering circles as adding bias. And yes, you guessed it, the amount of that bias is categorized in familiar classes of operation like B, AB, and A. Remember? Class A or Class AB are well-known terms to audiophiles. They describe how much a device is constantly turned on with that steady turn-on voltage we will eventually throw away when we extract what we really want, the amplified output signal.

And, since today’s Saturday and we can write a longer post, how do we throw away that steady voltage? Well, in vacuum tube amplifiers and simple transistor amplifiers, we place a blocking capacitor. What it blocks is that unwanted turn-on voltage (DC) and what it lets pass is the desired amplified audio signal. The quality and construction of that blocking capacitor has an enormous impact on how the eventual sound we hear is. (Of course, there are other means of doing this, I use this simple example only for means of explanation).

But that covers only one aspect of what we must do to make a non-linear device like a vacuum tube or transistor perform the way we wish. Other tools in the belt include feedback, both local and global, and many tricks of the trade all in service of getting a non-linear device closer to the ideal of linear.

And yes, all that we do impacts sound quality.

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10 comments on “Linearity”

  1. Ah, music to my ears.
    The HEGEL ‘Sound Engine II’ topology is the most fascinating technology that I’ve read about lately.
    I’m sure that Pass Labs, McIntosh, PS Audio, Ayre, Gryphon, Krell, Benchmark, Audio Research, etc, etc. all have their own way of dealing with linearity & hence the distortion issues.
    Ultimately the combination of source & loudspeaker; regenerator & cables; ears & brain & indeed available funds ($$$) & room acoustics will be what makes the final personal judgment of whether the sound of the reconstituted music being processed by any specific amplifier pleasing to us as individuals…or not.

    1. As far back as the 80’s there were some folks who were using detection and summing the output against the input and using an inverse waveform back into the input side to cancel both gain stage distortion and transistor crossover distortion with vanishingly low THD results. It’s been around for a while.

    2. The Hegel Sound Engine II is a dynamic “feed forward” system rather than a feedback system. In the Hegel view, injecting the correction signal all the way back at the input of a gain stage is not the way to go, but rather to feed forward the correction to the next gain stage. https://youtu.be/BOo-kCfEuAY

  2. Both feedback and feed forward were both developed by the same man working for AT&T to clean up long distance transmissions. He preferred feed back to feed forward since it was simpler to implement but then he wasn’t dealing with the band width and fidelity of today’s audio.

  3. There is no such thing as a perfect amp, a perfect speaker, a perfect microphone, a perfect cable, a perfect cartridge, etc. etc…

    Yet, we keep trying to somehow arrange the sum ( actually the convolution ) of all of these imperfections to yield the perfect sound.

    We are very silly people.

    1. I have been constantly preaching about no such thing as true perfection and I have come to the conclusion that I have not been considering the difference between literal perfection and figurative perfection. A quote from the Dalai Lama: “ True perfection seems imperfect, yet it is perfectly itself“.

      At the moment I’m listening to the Analog Productions recording on vinyl of ‘Sonny Meets Hawk’ and I must say that it’s very close to literal perfection at least to me.

  4. Brings back all the load-line calculation memories for various tubes during my radio training back in the 60’s.
    My Avo Mk1 tube characteristic meter is of the same vintage, one of the few things in life that doesn’t change happily.

  5. Too much global negative feedback can adversely influence the phase response of the amplifier. This is likely the main problem with applying lots of global feedback to get the distortion numbers to “measure good” but misses the critical sensitivity of the human ear/brain to detect phase shift that’s frequency dependent.

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