From: bill.sloman@ieee.org
On 15/11/2025 8:23 pm, Liz Tuddenham wrote:
> Bill Sloman wrote:
>
>> On 15/11/2025 4:46 am, Liz Tuddenham wrote:
>
>
> [...]
>>>
>>> The Johnson noise of a 50-ohm resistor at 20 C with 5 Kc/s bandwidth is
>>> -130 dBm. If we take the rail-to-rail output voltage of an op-amp to be
>>> about +20 dBm, that gives 150 dB difference. Claims that a device is
>>> capable of achieving this sort of figure in any practical situation is
>>> stretching the limits of credibility.
>>>
>>> If the signal is lower than +20 dBm, you either have to start cooling
>>> the device or reducing the measurement bandwidth, otherwise 150 dB S/N
>>> ratio is impossible to achieve.
>>
>> Johnson noise is broadband. The harmonic of interest in evaluating a low
>> distortion sine wave oscillator are rather narrow band.
>
> When you get down to signals as low as -150 dBm there will be Johnson
> noise and intermodulation products contributed by the components within
> the oscillator. Selecting individual harmonics with a narrow-band
> filter will give an unrealistic number that doesn't represent the total
> unwanted output.
>
>> You are comparing apples and pears as your "5 Kc.s bandwidth" makes
>> clear. if you have been cribbing from a more modern source it would have
>> been a 5kHz bandwidth.
>
> You have no idea what I did, so stop posting offensive nonsense.
I'm pretty confident that you don't have much of an idea what you did
either. That's probably offensive, but sadly it isn't nonsense.
> I have written a calculator based on a spreadsheet which gives the RMS
> noise as a voltage and as dBm from user inputs of resistance, bandwidth
> and temperature. I chose 5 Kc/s as a tolerably low figure for audio
> work; it would be a suitable measurement bandwidth for a 1 Kc/s signal
> if you wanted to include the third harmonic. I chose 50 ohms as it is
> the lowest output impedance in common use - for audio work 600 ohms
> might have been more appropriate but the figures would have been even
> worse.
But if you are looking for distortion in a sine wave, what you need to
know is the harmonic content generated by the distortions.
The harmonics apear at very specific frequencies, and and if the
oscillator generating the sine wave is operating at a stable frequency,
these harmonic will appear at very specific multiples of the base frequency
If you frequency meter says the sine wave is at 1kHz, and keeps on
saying that for more than a second at a time, the bandwidth of the sine
wave is going to be narrower than 1Hz, not 5kHz, and the fifth harmonic
is is going to less than 5Hz wide, not 5kHz wide even if it is at 5KHz.
> I have always written "Kc/s" and "Mc/s" because I regard them as more
> intuitive than having to remember who the units have been named after.
> I presume you didn't notice this in all my previous posts.
I don't have any trouble translating them into the currently accepted
units, and hadn't actually noticed.
I've got a science degree, and even back in the 1960's we got
indoctrinated about using the standard units, and keeping up with the
internationally agreed standard units. "Cycles" is no less arbitrary
than "Herz". For an English speaker it may be more intuitive, but for me
a cycle has two wheels - my wife gave me a unicycle once, and I managed
to learn how to ride it, but it didn't reshape my vocabulary.
> If someone wants to claim distortion products at or below the Johnson
> noise, they need to justify those claims. Selecting a narrow-enough
> bandwidth for the measurement could give any figure you like.
And selecting 5kHz as the bandwidth you like is giving you an amplitude
that fits your argument. It's nonsense, but superficially plausible
nonsense. For a very generous level of superficiality.
--
Bill Sloman, Sydney
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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