# What do you call the dynamic range of a variable gain amp?

Dynamic range is the ratio of the largest signal a system can process to the noise floor of that system.

If the system has variable gain, though, then you could interpret this two ways:

1. Fixed gain case: Dynamic range = (biggest signal at some gain x / noise floor at same gain x)
2. Variable gain case: Dynamic range = (biggest signal at minimum gain / noise floor at maximum gain)

I'd generally assume definition 1 for an electronic circuit, where you're picking the best gain to minimize noise while maximizing signal and then measuring both at the same gain. However, when people say the human ear has a dynamic range of 140 dB, they're using definition 2, since the human ear has variable gain. Likewise for human eye.

When measuring mic preamps or ADCs with variable gain stages, I could use either definition.

Questions:

1. If the term "dynamic range" really only applies to one of these cases, is there a name for the other thing?
2. If the term "dynamic range" can ambiguously refer to both cases, are there unambiguous terms for each case?

Example using the term "SNR":

Human Ear Range (Instantaneous) 85
Human Ear range (Total) 120

Definitions of dynamic range based on filtering out a -60 dB tone imply that the gain is fixed:

The EIAJ standard measurement for dynamic range is done by reading THD+N at an input amplitude of –60dB ... inverting the polarity of the THD+N reading, and adding 60dB.

-
If dynamic range is the ratio between largest and smallest signals a system can process, then your 2nd choice seems like the correct one for the system. But you could also talk about the "dynamic range at a fixed gain of XX dB" or something to get the first choice. – The Photon Apr 9 '12 at 18:46

Dynamic Range tests are always done at a fixed test level. If you have variable gain, it only means you might have a best case and worst case scenario when it comes to variable noise levels and fixed output levels. Noise Figures are the better way to determine the noise floor of each stage and with gain in each stage, you can determine your dynamic range , best case and worst case.

In reality you want some headroom to reduce HD and IMD, also the human ear's dynamic range has nothing to do with the amplifier's range except that it will most certainly have a wider dynamic range (unless you have hearing loss). What is most important is will you be able to hear the noise when it should be silent between music. So SNR becomes more important. If you have a dynamic range of a rock band amp to match your ears then lets say its 100dB but if your SNR is only 50dB from other sources of noise it wont matter.

More importantly, even if the ear has a dynamic range of 100dB and instantaneous range of 80dB will you be able to hear a triangle 80 dB down from the foreground music? Not likely I suggest unless you have a very narrow band hearing you won't be able to discriminate the trombone player turning the page of his sheet music on a direct cut CD while the rest of the symphony is blaring an overture, so your "discrimination" level at high outputs and your SNR of music at very low levels will ultimately determine your overall quality of sound reproduction. Keep in mind HD & IMD is usually only 40~60dB down.

If you have any hearing loss that raises the noise floor or at least the detection threshold. For more elaborate theory on dynamic range and how they hope to apply this to better hearing aids, read this university level research ... discussion & conclusion Effects of stimulus level on nonspectral frequency discrimination by human subjects.

-

Dynamic range refers to the difference between the maximum signal a system can handle and the noise floor for a specific system configuration. If the gain of the system is fixed, there is no difficulty with this definition. If the gain of the system can be varied, then the dynamic range becomes a function of the system gain. The use of the word "dynamic" means that it refers to the system capability in processing a signal at one point in time, in other words for one specific gain. Since the gain can only be varied statically, you cannot claim increased dynamic range by having a variable gain. For example, if you have a 10-bit A/D converter in the system, the dynamic range is generally taken as approximately 6 dB X the number of bits or 60 dB in this case. If you put a variable gain amplifier (say with 0 to 40 dB gain in front of this A/D converter, you can't claim the dynamic range of the system is increased by 40 dB. The advantage of the variable gain amplifier is the ability to set the system dynamic range over a given voltage range. For example, if the maximum input of the A/D converter is 10 volts, then the dynamic range of the system with the variable gain amplifier can be shifted from 10 millivolts to 10 volts with the amplifier gain set to 0 dB, to 0.1 millivolts to 100 millivolts with the amplifier gain set to 40 dB. In both cases, the dynamic range remains at 60 dB but the static range has increased to 100 dB.

-

Ok, cutting to the chase and writing a concise answer:

1. Dynamic range is a loose concept, and as such it cannot be defined generically in terms of a gain. It is the ratio between the maximum and the minimum value of a quantity (that can be the output audio power from an amplifier, the radiant power that can be sensed by a photographic camera sensor, etc) and the specific context will dictate if you have to compare things at specific gains or at different gains.

2. It makes no sense to talk about the "noise floor" of our auditory system.

3. Using your first definition, restated to indicate that you're calculating the ratio between powers, you would calculate the best signal-to-noise ratio a amplifier can output.

The dynamic range of a variable amp gain would fit your second "definition". But by all means that is not the definition of dynamic range. It's merely how you would interpret the real loose definition and calculate it.

-
When talking about a device, your definition of the ratio between the maximum and minimum that it can "perceive" would seem to match OP's 2nd definition. – The Photon Apr 9 '12 at 1:39
The problem is that he defines it as having to be calculated at maximum and minimum gain, and that just makes sense in one very specific context. That's the case of a sensor, but not the general case, and definitely, for me, not a "definition" per se – Castilho Apr 9 '12 at 2:06
OP is asking how to calculate it in that specific context, not necessarily the general definition. – The Photon Apr 9 '12 at 2:27
@ThePhoton: I don't know, this looks to me like a long answer that doesn't really say anything in particular. I wish there were others to choose from. – endolith Apr 9 '12 at 18:39
Signal to noise ratio and dynamic range are not the same thing. Signal-to-noise is calculated with an arbitrary signal level that is not usually equal to the maximum. Why wouldn't it make sense to talk about our auditory system's noise floor? It has one. – endolith Apr 9 '12 at 21:33