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In the digital world, "clipping" would occur when a signal passes above 0db.

But if you are dealing with analog equipment, is there a certain "ceiling" that tends to "brickwall" the signal down as well? Does this have anything to do with Line-Level?

What happens beyond that level, does distortion starts to get introduced? Could the signal, in theory, be amplified in a series of daisy-chained volume / gain devices to go way beyond the normal levels?

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You're right in that when your digital signal "clips" at 0dB, it's an absolute maximum limit. 16-bit audio has 2^16 possible volume levels, and once you get to 2^16, there's no higher number to express your sound, so it maxes out, or clips.

With analog signals, your "clipping" limit is less well defined. The term distortion in an amplifier just refers to non-linear response, (and it so happens that's when you get your nasty harmonics and crackle). So distortion is harder to define when it becomes unacceptable and destroys the sound for a listener.

To look at why distortion happens, let's take a look at amplifiers. A perfect amplifier takes in a signal, and multiplies it by a constant factor. In theory if you chain a load of perfect amplifiers together, you could get unlimited volume. However, real amplifiers need to get their power from somewhere...

Your limitation is the voltage of the power supply on the amplifier - if your amplifier circuit is powered by 10V, it will amplify a 0.1V signal to a 5V signal happily, but as your signal gets near 10V, it will start to distort, up until the point where it reaches 10V and you loose all your signal's information. The graph below approximates an amplifier's response. For small voltage inputs (x near 0) you have a diagonal line, so the output (y) is linear, directly proportional to the input. As X gets big though, the graph flattens out as the amplifier reaches its supply limit, so you reach a maximum output Y, and hear distortion. Amplifier response

Expensive amplifiers have a more linear response, and are less prone to distortion, but your "ceiling" is the maxiumum voltage across the amplifier, or the maximum current it can draw.

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With analog equipment, if the signal level rises above the maximum input level of the equipment, it will begin to distort. The corresponding output level may or may not continue to increase, depending on the equipment. At some point, you will begin to damage the equipment.

Equipment that has Line-Level inputs will typically not accept levels much beyond Line-Level. Other equipment varies based on the input type and configuration.

Daisy chaining volume / gain devices would certainly increase the level of the signal. A good example of this is connecting a microphone through a preamp and then through an amplifier. If you increase the signal level too much, you will run into the problem explained above.

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I can't comment yet, so I'm posting this as an answer. Regarding 0dB as highest level in the digital domain, you might be interested in reading Søren Nielsen and Thomas Lund's paper called "0dBFS+ Levels in Digital Mastering(PDF)" (AES 109th convention). It shows a quite interesting phenomenon taking place in some equipment. Here's the abstract:

A sine tone at 0dBFS is often believed to be the maximum level obtainable from a digital medium. Therefore it is typically the maximum level digital filters and analog circuitry in consumer equipment is aimed at reproducing.

As we have showed in previous papers, inter-sample peaks may be considerably higher than 0dBFS.

This paper examines the sonic consequences when 0dBFS+ signals are reproduced in typical consumer equipment. The performance of a variety of domestic CD players exposed to such signals are presented and evaluated.

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