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Low frequencies Vector Network Analyzer, arduino based.
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ogden:
Thermal noise formula:



If you type in bandwidth (delta F) 1KHz, you get −144 dBm. If you type in 1000 times smaller bandwidth 1Hz you get −174 dBm which is exactly 30dB lower value. Yes, FFT so to say splits spectrum into smaller bands and in result noise power for individual band decreases. As already said - it happens disregarding what type of "filtering" used.

[edit] Unless someone quote me, OP will not see what I am telling here about noise. Just saying
Kleinstein:

--- Quote from: MasterT on September 22, 2018, 05:59:56 pm ---
--- Quote from: Kleinstein on September 22, 2018, 05:49:15 pm ---The same SNR gain as with the FFT also applies to calculating the Fourier components in an other way. So there is the gain from the reduced bandwidth, but this is not exclusive to an FFT.

--- End quote ---
No, it's not. Reducing bandwidth is usually done by RF preselectors. To do it in software, there is no alternative to FFT in efficiency. Difference is enormous, compare for example with BP FIR, I 'd estimate for fft-2048 fft is x10^6 times more efficient.

--- End quote ---

The FFT is more efficient, if all bins are needed - but not that much. It depends on how the sin/cos values are provided. With FFT2048 the gain is more around 200 times  (around 2028 / log 2048) if sin / cos values are from a table. However, if only 2 bins are needed (and the others are ignored) it is no more efficient - its more like the direct way is more efficient by maybe a factor of 10. In addition the direct way can use much less memory and thus possibly longer time windows if needed. The FFT would normally be limited by the memory.
MasterT:

--- Quote from: Kleinstein on September 22, 2018, 07:01:34 pm ---
--- Quote from: MasterT on September 22, 2018, 05:59:56 pm ---
--- Quote from: Kleinstein on September 22, 2018, 05:49:15 pm ---The same SNR gain as with the FFT also applies to calculating the Fourier components in an other way. So there is the gain from the reduced bandwidth, but this is not exclusive to an FFT.

--- End quote ---
No, it's not. Reducing bandwidth is usually done by RF preselectors. To do it in software, there is no alternative to FFT in efficiency. Difference is enormous, compare for example with BP FIR, I 'd estimate for fft-2048 fft is x10^6 times more efficient.

--- End quote ---

The FFT is more efficient, if all bins are needed - but not that much. It depends on how the sin/cos values are provided. With FFT2048 the gain is more around 200 times  (around 2028 / log 2048) if sin / cos values are from a table. However, if only 2 bins are needed (and the others are ignored) it is no more efficient - its more like the direct way is more efficient by maybe a factor of 10. In addition the direct way can use much less memory and thus possibly longer time windows if needed. The FFT would normally be limited by the memory.

--- End quote ---
I will try to explain one more time. I also gonna to put it into first initial message, to help others with the same doubts why is fft?

Lets put 4 dots.

Phase error - > SNR - > Bandwidth - > FFT.

Is it so hard to connect those 4 dots? It's clear, that in order to get minimum phase error, bandwidth must be shrinked as much as possible. FFT here is the most efficient BPF, that allows to cut 244 Hz out of 250 kHz . Now, I 'd repeat last time, there is NO alternative to fft, stop crying about bins that goes to garbage can, fft is doing one specific function: it's sharply cut 244 Hz out of 250 kHz.  Anything else, single bin DFT, Goertzel, FIR etc - don't do this simple task. Easy they are not able to shrink bandwidth, or they are extremely inefficient on a clock cycle scale.


--- Quote from: Bud on September 22, 2018, 06:38:13 pm ---This device is limited to series passive DUTs, correct?  It can only work with 2 wire circuits that can be inserted between the source and receiver terminals, so no ground referenced and/or active circuits can be measured - is my understanding correct?

--- End quote ---


Good question. Initially, I was thinking to do just capacitor tester, C-V, C-F, ESR, quality etc. That's why 400V capacitor in drawings. To apply high voltage and trace capacitance lost. Than I changed my mind, and decided to complete AD5933 alternative, simple network-impedance analyzer.
 I came to conclusion, that better to leave capacitors in place, to keep DC blocking, doing so any active components could be tested. For example, gain/ phase chart for OPA.  And there is also diodes/ series resistors - for safety, to prevent circuitry from careless operator, since test pad is exposed and anything could goes wrong, external DC , static discharge, high inductance creates huge EMF sparks etc.

 To test active component (amplifier) just connect reference channel - 220 OHm resistor to input, and output goes to 22k resistor. Variable cap shown on a drawings is an example of DUT cap.
22k would creates slight load for amplifier output but it's negligible to any amp I know. And common ground should be connected of course. External DC power for amp (OPA) not limited to -+15 , can be higher up to +400V.

 There are two test connectors,  x100 scale.   DUT is plugged ether between 22k & ground or between 220 & ground. Ground referenced in both cases.   Someone ask me a "theory of operation" , it's  simplest voltage divider. One leg is a resistor, another leg - DUT.  Things that voltage divider is under AC, does not change anything, it's still divider. I would not call it "half bridge" -  do not want to generate more confusion.
 
 
ogden:

--- Quote from: MasterT on September 22, 2018, 10:04:40 pm ---Is it so hard to connect those 4 dots? It's clear, that in order to get minimum phase error, bandwidth must be shrinked as much as possible. FFT here is the most efficient BPF, that allows to cut 244 Hz out of 250 kHz . Now, I 'd repeat last time, there is NO alternative to fft, stop crying about bins that goes to garbage can, fft is doing one specific function: it's sharply cut 244 Hz out of 250 kHz.
--- End quote ---


OMG  :palm:

FFT is not a filter. FFT does not sharply cut it's bins. "Sharp cut" happens only when signal precisely "hits" bin frequency. If incoming signal frequency stand between two bins then both receive power, thus both have nonzero real/imag values after transform. Funny that "FFT vs DFT" topic is written in the chapter "FFT Basics" of the document OP is referring to:


--- Quote from: MasterT on September 22, 2018, 05:43:07 pm ---Link to doc: http://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter5.pdf

--- End quote ---
Dave:
FFT is just a more efficient way to calculate DFT. It exploits the complex conjugate symmetry and periodicity of exp(-j*2*pi*k*n/N) and produces the same result with far fewer computational steps. You get the same benefits from DFT that you get from FFT, because FFT IS DFT.

It makes no sense whatsoever to use FFT when you're only interested in the results of just 1 or 2 bins. It's faster and less wasteful (in terms of RAM) to use DFT in this case.


--- Quote from: MasterT on September 22, 2018, 10:04:40 pm ---FFT here is the most efficient BPF, that allows to cut 244 Hz out of 250 kHz . Now, I 'd repeat last time, there is NO alternative to fft, stop crying about bins that goes to garbage can, fft is doing one specific function: it's sharply cut 244 Hz out of 250 kHz.  Anything else, single bin DFT, Goertzel, FIR etc - don't do this simple task. Easy they are not able to shrink bandwidth, or they are extremely inefficient on a clock cycle scale.
--- End quote ---
You seem to lack the very basic understanding of what FFT is and how it works. Perhaps this video can clear up some of your misconceptions.
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