The sound of DistortionThe sound of Distortion Pete Millett ETF.04 AgendaAgenda Who I am EE101: A brief tutorial AC Signals Transfer Functions Fouriers Theorem Time Domain vs. Frequency Domain the FFT Harmonic Distortion What is it? Spectra vs. transfer functions: real amplifiers THD, audibility, and masking The “Magic Box” How it works Settings for the demonstration Listening demonstration Whos Pete Millett?Whos Pete Millett? 44 years old, started playing with electronics when I was 8 Ivy-league engineering school dropout Worked as an electronics engineer for almost 25 years Currently work as a hardware engineer designing “consumer imaging products” for a “large US-based computer and consumer electronics company” (damn the lawyers!) Designing tube audio stuff for about 10 years Design headphone amps for HeadRoom (www.headphone.com) Occasionally write for AudioXpress magazine Live in Colorado, USA Contact: pmilletthotmail.com Website: pmillett.addr.com EE101EE101 AC signalsAC signals An AC signal is a voltage (or current) that changes over time AC signals can be periodic like a sine or square wave, or not, like music A signal can be viewed on an oscilloscope, which shows amplitude vs. time Amplitude Time More signalsMore signals In audio, we typically look at signal voltages to evaluate circuits A pure, single- note tone is a sine wave Amplitude Whereas music can be a very complex waveform. Time Transfer functionsTransfer functions The function of an amplifier (or any device) can be represented with a graph of “input vs. output” This is called a “transfer function” This graph shows a perfect linear transfer function I.e., the output equals the input Output Input Nonlinear transfer functionsNonlinear transfer functions Real amplifiers have imperfections, resulting in nonlinearities in their transfer functions This is the transfer function of a real (bad!) P-P amplifier Output Input Fouriers TheoremFouriers Theorem “Any periodic signal is composed of a superposition of pure sine waves, with suitably chosen amplitudes and phases, whose frequencies are harmonics of the fundamental frequency of the signal” What this means is that you can break down a waveform, like a musical note, into a combination of sine waves whose frequencies are integral multiples (x2, x3, x4, etc.) or harmonics - of a single fundamental frequency. A little math:A little math: This shows the fundamental and first two harmonics added together in the series that makes up a square wave, which is represented in the equation above Time domain and the FFTTime domain and the FFT A signal can be represented in the time domain, as on an oscilloscope A signal can also be represented in the frequency domain, as on a spectrum analyzer. This transformation is called a “Fourier Transform” An FFT is a “Fast Fourier Transform”. Amplitude Time Frequency Signals in time vs. freq.Signals in time vs. freq. A pure tone, a sine wave, is represented by a single peak at one frequency As we saw before, a square wave is composed of all odd harmonics; e.g., a 1 kHz square wave is made up of 1kHz, 3kHz, 5kHz, etc. Time domainFrequency domain Harmonic DistortionHarmonic Distortion Harmonic Distortion: Harmonic Distortion: DefinitionDefinition A textbook definition: Harmonic distortion: In the output signal of the device, distortion caused by the presence of frequencies that are not present in the input signal. What does THAT mean? If you put a signal at one distinct frequency (i.e., a sine wave) into a device (like an amplifier), any signals appearing at the output of the device that are at a different frequency are harmonic distortion products Another way to look at it: the signal at the output should have the same frequency-domain makeup as the input Harmonics: Even vs. OddHarmonics: Even vs. Odd Even harmonics (2nd, 4th, etc.) result from asymmetrical nonlinearities of a transfer function Odd harmonics (3rd, 5th, etc.) result from symmetrical nonlinearities of a transfer function The transfer function of real devices like amplifiers generally have both symmetrical and asymmetrical characteristics Single-ended circuits are asymmetrical, so they tend to create more even harmonics Push-pull circuits are symmetrical, so they tend to create more odd harmonics HD: A perfect amplifierHD: A perfect amplifier A perfect amplifier If we had a perfect amplifier, the output would be an exact copy of the input, only larger: it would have a linear transfer function If you input a pure sine wave into such an amplifier, you would get a pure sine wave out of the amplifier Such an amplifier would have no harmonic distortion InputTransfer FunctionOutput Spectrum HD: Real amplifiersHD: Real amplifiers A real amplifier A real amplifier has a somewhat nonlinear transfer function If you input a pure sine wave into such an amplifier, you would get the original sine wave, plus distortion products at other frequenci