Iliah Borg
Forum Pro
Old habits, in "Soviet school" E was reserved for electrostatic field in EMF equation, V (and sometimes U) appeared in Ohm's Law as electric potential difference
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Units of dynamic range
- Thread starter TN Args
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thank you both of you!Iliah is correct. Let me unpack that for you, Jonas.
One Bel is one factor of ten in power. The relationship between power, P, and current, I, and voltage, V, is as follows:
P = E * I
Now, let's assume that the voltage is measured across a resistance of R. Ohm's law states that:
E = I * R
Let's solve that for I:
I = E / R
Now let's plus that into the power equation:
P = E * E / I, or P = E^2 / I
That's where the V^2 that Iliah is talking about comes from. Some engineers, like me, use E to indicate a voltage. Some, like Iliah, use V. Po-tay-to, po-tah-to.
So 1 Bel is a factor of ten in power (log10(10) = 1), and a factor of 3.162 in voltage (2*log10(3.162) = 1.
A decibel is one tenth of a Bel, so, if we have a power ratio of x, it's
10 * log10(x) decibels
If we have a voltage ratio of y, it's
20 * log10decibels
If we raise the voltage to 3.162 times what it was before, the power goes up by:
20*log10(3.162) = 10 dB
If we raise the power to 10 times what it was before, the relationship is:
10*log10(10) = 10 dB
Jim
OK, when unpacking things to laymen, one should be accurate. You mention, P, I and V, but in your formula V turns into E.
Here, you have a typo, P = V^2/R or in your notation P = E^2/R.
Engineers, sigh.... U is voltage and E is the electrical field (U between two points in an electrical field is the line integral of E over the path from point 1 to point 2). V is the unit in which U is measured. I never saw E used for voltage and I think this is very misleading. Maybe a US specific thing?
dB are a bit weird. They refer to the logarithmic scale of power ratios. And that‘s OK. But for voltages, the factor 2 simply comes from the fact that 10*log10(P1/P2) = 10*log10(U1^2/U2^2) = 10*log10(U1/U2)^2 = 10*2*log(U1/U2) = 20*log(U1/U2).So 1 Bel is a factor of ten in power (log10(10) = 1), and a factor of 3.162 in voltage (2*log10(3.162) = 1.
A decibel is one tenth of a Bel, so, if we have a power ratio of x, it's
10 * log10(x) decibels
If we have a voltage ratio of y, it's
20 * log10
If we raise the voltage to 3.162 times what it was before, the power goes up by:
20*log10(3.162) = 10 dB
If we raise the power to 10 times what it was before, the relationship is:
10*log10(10) = 10 dB
Jim
So, dB has a different meaning for voltages and power. The nice thing is that e.g. 12dB more power also means 12dB more voltage (in a linear system). But it is not the same ratio as Jim correctly wrote.
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You're right. I was trying to go with the variable name that Iliah used, but old habits die hard, and I slipped back into the way I learned it.
You are correct, again. Sorry.
Engineers, sigh.... U is voltage and E is the electrical field (U between two points in an electrical field is the line integral of E over the path from point 1 to point 2). V is the unit in which U is measured. I never saw E used for voltage and I think this is very misleading. Maybe a US specific thing?
dB are a bit weird. They refer to the logarithmic scale of power ratios. And that‘s OK. But for voltages, the factor 2 simply comes from the fact that 10*log10(P1/P2) = 10*log10(U1^2/U2^2) = 10*log10(U1/U2)^2 = 10*2*log(U1/U2) = 20*log(U1/U2).So 1 Bel is a factor of ten in power (log10(10) = 1), and a factor of 3.162 in voltage (2*log10(3.162) = 1.
A decibel is one tenth of a Bel, so, if we have a power ratio of x, it's
10 * log10(x) decibels
If we have a voltage ratio of y, it's
20 * log10
If we raise the voltage to 3.162 times what it was before, the power goes up by:
20*log10(3.162) = 10 dB
If we raise the power to 10 times what it was before, the relationship is:
10*log10(10) = 10 dB
Jim
So, dB has a different meaning for voltages and power. The nice thing is that e.g. 12dB more power also means 12dB more voltage (in a linear system). But it is not the same ratio as Jim correctly wrote.
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but, to be fair, it was explained further down
I googled my way to this
dB are a bit weird. They refer to the logarithmic scale of power ratios. And that‘s OK. But for voltages, the factor 2 simply comes from the fact that 10*log10(P1/P2) = 10*log10(U1^2/U2^2) = 10*log10(U1/U2)^2 = 10*2*log(U1/U2) = 20*log(U1/U2).So 1 Bel is a factor of ten in power (log10(10) = 1), and a factor of 3.162 in voltage (2*log10(3.162) = 1.
A decibel is one tenth of a Bel, so, if we have a power ratio of x, it's
10 * log10(x) decibels
If we have a voltage ratio of y, it's
20 * log10
If we raise the voltage to 3.162 times what it was before, the power goes up by:
20*log10(3.162) = 10 dB
If we raise the power to 10 times what it was before, the relationship is:
10*log10(10) = 10 dB
Jim
So, dB has a different meaning for voltages and power. The nice thing is that e.g. 12dB more power also means 12dB more voltage (in a linear system). But it is not the same ratio as Jim correctly wrote.
TN Args
Forum Pro
Further thanks to Jim Kasson, F Decker, D Cox, John Sheehy, dosdan, beatbox and jonas ar. You have all been very helpful.
I would like to question the assertion that dynamic range is dimensionless and is a ratio of two quantities. Wouldn't such a thing be called dynamic ratio?
I would have thought that a range is a difference between two absolute values. And as such, has dimension and unit.
Which brings me to a second question. The use of electrical units is directly relevant to the last 3 dot points in my original post reproduced above, but what about the one above them, the live scene? And would its dynamic range be measured (as a difference) in objective power units, or photopic luminosity units?
cheers
"Range" = dark to light
"Dynamic" = ratio (ie. "relative," as opposed to absolutes)
In the live scene, I'd say luminosity, though this would need to be measured, which could get us into this loop of the other bullet points.
Not sure about irrational bits . But please enlighten me.
I am even less sure about rational ones. Once you start talking about Shannons, the probability that you will have a rational number is zero.
Information theory - Wikipedia
It could be, I suppose, but that's not the standard terminology
With photographic sensors, subtracting the lower bound (however you define that) from the upper bound (presumably full scale) would leave you with a number very close to the upper bound. Of what use is that?
Jim
Yes, but for a certain type of random variables - those with continuous pdfs, and in Lebesgue measure sense then. Otherwise in general one can come up with random variables that have non-zero value with rational output. For e.g. recall technically there is nothing random about a random variable in strict math sense - it is just a function from a collection of sets (sigma algebra) to another domain. That function is not random. So, lets define a binary random variable (i.e. a function) that takes anything in [0, 0.8) to a rational number, say 1/4, and in [0.8, 1] to 1/8. So it has a 0.8 probability of being 1/4, and 0.2 probability of being 1/8. This is just a variation of a Bernoulli random variable.
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You certainly can build exotic examples.
Rational numbers form a tiny set (measure zero) and have a lot of "holes". If we stick to them only, we would have to scratch most of the math and math sciences, including most of the models used in physics. Every course in real analysis, BTW, starts with real numbers.
One doesn't need to be building exotic examples. If you consider 0 and 1 as rational numbers then a standard Bernoulli random variable is an example of a random variable that takes rational output values.
And, Poisson random variable is also an example of random variable that generates rational output, as noted below.
Well, Bernoulli random variables are everywhere in math, physics, and engineering. Many physical processes are modeled through them. As you know, even our friend Poisson random variable internally is related to a Bernoulli random variable.
EDIT: And, if you take integers as rational numbers, then even Poisson random variable is an example of a random variable that has rational output. And, as we know Poisson random variable is deeply embedded in many physical processes including photography.
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Or just take a variable taking zero values and start wondering why we need any numbers different than zero in the first place. Even in your case, the parameter p is most likely to be irrational, loosely speaking, so despite that variable taking 0 and 1 values, its mean may very well be π. How is all that related to Shannons and fractional bits, BTW?
Yet, its mean and st.dev. are most likely to be irrational, roughly speaking. Again, where are the Shannons?
First, "most" of those variables have irrational means and second, even if they did not (but they do), this would not invalidate my "most" statement.
Even the simplest not absolutely trivial diff. equation of exp growth y'=y would be unsolvable without irrational numbers. Then Schrodinger, Maxwell, Einstein, heat, etc., PDEs would be unsolvable. All this just because some people object real numbers. Real numbers do not pose more problems, they make things simpler.
Well, they are.
Yet the probability of, say, value=5 is most likely irrational, roughly speaking.
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Symbol E is used for electric field intensity. EMF (electromotive force), even when denoted by E, in power systems is another term for induced voltage to represent that component of voltage due to a time-varying flux linkage.
Yes, range would be the difference between two extremal values, usually as a continuous range. However, the so called 'dynamic range', which is frequently mixed up with range on these forums, is the number of steps (usually of fixed step size) that one would need to cover the range between these two extremal points. And, as a number, it is usually treated dimensionless.
IMHO, 12 EV is dynamic range, not range. (See here ). 12 EV just says there are 2^12 = 4096 steps between the two extrema of a continuous range. Unless the step size is specified you can't figure out the actual continuous / analog range.
Thanks! And I hereby think I have proven sufficiently that I am not an electrical engineer
alanr0
Senior Member
Jim,
This is certainly how photographic sensors are typically specified, but it is worth bearing in mind that this convention is not adopted in other fields.
In optical telecommunications, optical powers are measured in watts, or in dBm, i.e. decibel power ratio with respect to a 1 mW reference.
Detector dynamic range would be expressed as the ratio of maximum input optical power to minimum optical power input.
For example this detector https://www.hamamatsu.com/resources/pdf/ssd/g9821_series_kird1085e.pdf can cope with optical input powers between 0.004 mW and 1.26 mW, or -24 to +1 dBm, for an input dynamic range of 25 dB (10 x log10(Pmax/Pmin)
The corresponding electrical output range is from 0.006 V to 1.9 V, which the photographic sensor convention would report as a dynamic range of 50 dB (20 x log10(Vmax/Vmin))
I don't know which convention is applied to monitor dynamic range. Most material I recall uses linear contrast ratios, e.g. as here. There is an argument for describing 5000:1 contrast ratio as 37 dB, but I do not recall ever seeing this.
Safer to stick to EV or a linear intensity ratio unless one is confident that one's audience is familiar with your choice of dB convention.
Cheers.
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