Written by Blaine LaCross and Andrew Park
Introduction - What is SINAD?
Editor's note - there is an additional companion piece to this article titled "Simulating Amplifier Distortion" where you can hear examples of real-world products.
SINAD, also known as THD+N, is very commonly quoted in a number of audio discussions. This term is generally brought up in relation to amplifier or other source equipment performance - but what is it? How relevant is it to what we hear? Let’s examine how SINAD works, and in this article we’ll explain why it’s not a useful measure or indicator of performance at all.
SINAD is short for “Signal to Noise And Distortion”. It’s the ratio between the signal - the stuff we want to hear, like the music we play - to all the other things we don’t want in the sound. It’s also sometimes expressed as THD+N, or “total harmonic distortion plus noise”, which is the ratio of the noise and distortion to the signal - the same thing the other way around.
As the name suggests, SINAD is a sum of two broad groups of things we don’t want in the sound: Noise, and distortion. Noise is just what it sounds like: noises leaking into your music, which can range from the “hum” of your AC power, to the “hiss” of white noise. There are a lot of potential sources of noise out there, and they can distract from what you actually want to listen to, particularly if you’re listening quietly.
Distortion, the other part, is similar to noise in that it’s an addition to your music. Unlike noise, however, distortion is produced by your music interacting with the flaws of the system. This means that distortion will be related in level to the signal causing it, whereas - as anyone who’s heard hiss on their IEMs will know - noise can be loud without anything playing at all.
Harmonic distortion is the distortion of a single frequency sine wave. It is frequencies that are multiples of the fundamental. For example, a fundamental tone of 1000hz, would have 2000hz, 3000hz, 4000hz, 5000hz, as its 2nd, 3rd, 4th and 5th harmonics. A distortionless amplifier or speaker fed a 1khz tone will only put out 1khz, but any nonlinear system will produce some amount of additional frequencies in the form of harmonic distortion, which will be related to the input in both level and frequency.
Since SINAD is a ratio to the sum of noise and distortion, it can be 'dominated' by one of the two if it is much higher. Because a 20dB difference is a tenfold change, the ratio doesn't change much between an amplifier with -80dB THD and -100dB noise, and one with -80dB THD and no noise at all. The following are examples of SINAD, one with distortion dominated equipment and the other with noise dominated equipment.
Here you see the fundamental tone (the strongest tone) at 1khz, with three harmonic distortion products (the lower three tones). Those three are 2nd, 3rd, and 4th harmonics.
Here distortion is completely dominated by noise in SINAD - even though some harmonics are visible, they are not impacting the SINAD score at all due to the high noise
SINAD combines distortion and noise because it is a very old measurement - about a century old, in fact. In the early 1900s, it was difficult and expensive to separate out different types of signal problems, so SINAD and THD+N, which summed them all together and compared them to the desired output, became dominant. Measurements of SINAD could be done quickly and consistently even on very simple equipment, and their adoption paved the way for some very early innovations in audio technology.
However, because SINAD simply combines all of the unwanted parts of the signal into one number, it has trouble capturing what we hear. As early as 1950, there were suggestions to improve the calculation to better match subjective sound quality, but ultimately simplicity and inertia won out, and SINAD remains the same to this day.
Why is it bad to just sum things together though? Let’s start with a bit about how distortion and human hearing works to start explaining that.
In order to demonstrate the downsides of using SINAD as an indicator for sound quality or equipment performance, let's take a closer look at distortion in general. Consider the following 1khz sine wave test tone:
Unlike music, which has a massive number of different frequencies, sines are “pure tones”. Because you know that a sine wave is supposed to have energy at just one frequency, you can easily tell that anything at any other frequency is either distortion or noise, and that’s how SINAD does it. As mentioned above, when a sine wave is distorted, it produces “harmonics” - multiples of its frequency.
For example, here's what a 1khz fundamental sounds like with its 2nd harmonic (2khz) being played at the same time at the same level: