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Why do oscilloscopes have bandwidth limits?

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glarsson:

--- Quote from: TimFox on November 02, 2022, 03:55:37 pm ---If you had an infinite (or much too high for the application) analog bandwidth, the amplified thermal noise added to your MHz-bandwidth signal would be huge.

--- End quote ---
I don't have anything infinite at hand to test with, but wouldn't infinite bandwidth result in infinite thermal noise?

TimFox:

--- Quote from: glarsson on November 03, 2022, 08:51:51 am ---
--- Quote from: TimFox on November 02, 2022, 03:55:37 pm ---If you had an infinite (or much too high for the application) analog bandwidth, the amplified thermal noise added to your MHz-bandwidth signal would be huge.

--- End quote ---
I don't have anything infinite at hand to test with, but wouldn't infinite bandwidth result in infinite thermal noise?

--- End quote ---
Yes.  That was my point.
In practice, where there is no such thing as infinite bandwidth, increasing the bandwidth increases the thermal noise voltage proportional to the square root of the bandwidth (all other things being equal).
This is clearly visible on a good analog CRO, looking at the trace width at high sensitivity, when changing the bandwidth.

glarsson:

--- Quote from: TimFox on November 03, 2022, 01:49:43 pm ---
--- Quote from: glarsson on November 03, 2022, 08:51:51 am ---
--- Quote from: TimFox on November 02, 2022, 03:55:37 pm ---If you had an infinite (or much too high for the application) analog bandwidth, the amplified thermal noise added to your MHz-bandwidth signal would be huge.

--- End quote ---
I don't have anything infinite at hand to test with, but wouldn't infinite bandwidth result in infinite thermal noise?

--- End quote ---
Yes.  That was my point.
In practice, where there is no such thing as infinite bandwidth, increasing the bandwidth increases the thermal noise voltage proportional to the square root of the bandwidth (all other things being equal).
This is clearly visible on a good analog CRO, looking at the trace width at high sensitivity, when changing the bandwidth.

--- End quote ---
Yes, but huge is not infinite. You can't use an analog cro to prove what happens at infinite bw.

TimFox:

--- Quote from: glarsson on November 03, 2022, 03:30:09 pm ---
--- Quote from: TimFox on November 03, 2022, 01:49:43 pm ---
--- Quote from: glarsson on November 03, 2022, 08:51:51 am ---
--- Quote from: TimFox on November 02, 2022, 03:55:37 pm ---If you had an infinite (or much too high for the application) analog bandwidth, the amplified thermal noise added to your MHz-bandwidth signal would be huge.

--- End quote ---
I don't have anything infinite at hand to test with, but wouldn't infinite bandwidth result in infinite thermal noise?

--- End quote ---
Yes.  That was my point.
In practice, where there is no such thing as infinite bandwidth, increasing the bandwidth increases the thermal noise voltage proportional to the square root of the bandwidth (all other things being equal).
This is clearly visible on a good analog CRO, looking at the trace width at high sensitivity, when changing the bandwidth.

--- End quote ---
Yes, but huge is not infinite. You can't use an analog cro to prove what happens at infinite bw.

--- End quote ---

Yes, huge is not infinite.  I wrote "infinite (or much too high for the application".
Infinity only makes sense mathematically in "the limit as the variable goes to infinity".
If you take an analog CRO with a very wide inherent bandwidth and look at the trace width as you vary the bandwidth of the vertical amplifier, you see the trace width increase in such a fashion that, using mathematical language, the width increases without bound as the bandwidth increases.
Were an infinite bandwidth possible, that would give infinite energy in the output, which is obviously non-physical.
In one of the simple derivations of thermal noise, the calculation is done for a resistor and capacitor connected together, in thermal equilibrium;  the bandwidth for the noise voltage calculation is determined by that time constant.
Your quest to measure something with infinite bandwidth will be fruitless.

A related problem (the "ultraviolet catastrophe", q.v.) led to the introduction of Planck's constant in thermodynamics:  see https://web.mst.edu/~kosbar/ee3430/ff/Wireless/noise2/index.html

glarsson:

--- Quote from: TimFox on November 03, 2022, 03:36:34 pm ---Your quest to measure something with infinite bandwidth will be fruitless.

--- End quote ---
I have not expressed any intention to measure with infinite bandwidth.

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