Measuring the frequency response of a 1 Hz (or lower) filter?

[tec5c]

Traditional methods of measuring the frequency response of a filter are made quite difficult once the cut off frequencies drop below the limits of typical analysers. Without purchasing a low frequency network analyser like the OMNICRON Bode 100 how can one measure a filter which has a cut off frequency that is in the single digit Hz (or even sub Hz) range?

[Unsure of where to post this so please move if necessary.]

[babysitter]

Slowly. Fortunately, for computer-controlled logging the samplerate requirements go somewhat down, allowing you to measure the filter response with no-more-so-expensive remote-controllable DMM.
A Oscilloscope with either memory or a long-exposure picture can be used, too.
Excitation can be done several ways, get a fungen with a low range, you might build a nice slow oscillator for example, use a programmable power supply, something like a HP59501A for computer control.

Also, you could hookup a I2C DAC/RDAC and ADC to arduino, should still be fast enough.

[jeroen79]

A multimeter set to record the peak DC voltage?
Or record a few periods with a DC datalogger and then do the analysis on your PC.
Maybe make some script to speed up the logged signal to a frequency that your equipment can process better.

[David Hess]

A DSO which supports roll or scan mode can substitute for a strip chart recorder.

If your DSO can differentiate and then take the FFT, then the step response can be converted into magnitude and phase.  Unfortunately DSOs which can do this are rare and most throw away the FFT phase results.

If the filter only encompasses the electronic response, then temporarily reducing the value of all of the capacitors or resistors by a decade or decades will allow analysis at a more convenient frequency.

[danadak]

Use sound card for generator ( will do sub Hz sine generation, swept). Set up for
very slow sweep to allow filter to settle.


http://www.radio.imradioha.org/pc_based_test_gear.htm


Then use Arduino to digitize, and upscale timebase for scope to get a flicker free
display. Can even use Arduino to do log scale.

Or use OpAmp rectifier to gen vertical response, and use second channel of generator to gen ramp
for scope sweep.

Note PSOC has both A/D to 20 bits, and OpAmps to build OpAmp rectifier.


http://ww1.microchip.com/downloads/en/AppNotes/01353A.pdf


https://1drv.ms/f/s!Al2JgiX7_qf0iyDXnGfeprN62OJP


Regards, Dana.

[Kalvin]

You could use Arduino to generate the low frequency sine wave using PWM and filtering. Sample the sinusoidal output and filter output, thus you can compute relative phase of the signals and get filter amplitude response. The Ardino has only 10 bit ADC, so you will have less than 60dB dynamic range but if you can live with that dynamic range you should be just fine. Manual or Arduino-controlled range switching is one option to increase dynamic range. As others have suggested, using PC sound card is one option if you can get the sound card to work at low frequencies.

[Tomorokoshi]

A couple options which break the requirement of buying new equipment (but who can pass up an opportunity to buy new equipment?) are:

1. HP 3310A / 3310B Function Generators can go down to 0.1 mHz. They have a VCO input that makes it go to up to 50x the base range. This could be controlled by the output of something which then measures the response of the filter. Perhaps $100 USD on ebay.

2. HP 35665A Dynamic Signal Analyzer (and other similar models) can do swept sine down to 122 uHz depending on options. I haven't tried to run it this low. With some large capacitors and resistors I could try it out and see how well it matches with calculations. Perhaps $500 to $1000 on ebay.

[danadak]

You can also use PSOC WAVEDAC component to generate both sweep and sub
1 hz sine, ramp, whatever.








Regards, Dana.

[Tomorokoshi]

With a 1 Hz cutoff I decided on an RC time constant of 0.2 s. With a 26,000 uF capacitor the resistor is 192 ohms.

For that capacitor for an impedance of 192 ohms the frequency is 31.8 mHz.

The -3 dB point on the analyzer is at around 26 mHz. Perhaps my capacitor is closer to 32,000 uF in these conditions.

Here are a couple scans, one from 15 mHz to 1 Hz, and then at 15 mHz to 100 mHz to try to zoom in. Notice that I am reaching the resolution step limit of the sweeper.

[tec5c]

I imagine that would've taken a fair amount of time to complete with such a slow sweep time.

I have access to a SR780 which I think will be the way to go for my needs. Maybe I just need some more patience... 

[Tomorokoshi]

The sweep times are listed: 7 kiloseconds for the first one, and 3 kiloseconds for the second one. And that was just the sweep time. It took at least as much again for ranging and settling.

As I understand it the SR780 is roughly equivalent, and should do just fine.

[precaud]

Yeah, sweeps are painfully slow at that low freq. To compute the transfer function, a DSA with DC-coupled inputs is the way to go, with a chirp waveform as stimulus, or a haversine pulse. An alternative with a single-channel FFT would be random noise and averaging (64 and up, which takes time...). The 2-channel DSA approach is probably the best.

[Alex Nikitin]

With a 1 Hz cutoff I decided on an RC time constant of 0.2 s. With a 26,000 uF capacitor the resistor is 192 ohms.

For that capacitor for an impedance of 192 ohms the frequency is 31.8 mHz.

The -3 dB point on the analyzer is at around 26 mHz. Perhaps my capacitor is closer to 32,000 uF in these conditions.

Your capacitor is accurate, however the output impedance of the generator is most likely 50 Ohm , which makes for 242 Ohm in total and the calculated frequency of 25.3mHz  .

Cheers

Alex

[Tomorokoshi]

With a 1 Hz cutoff I decided on an RC time constant of 0.2 s. With a 26,000 uF capacitor the resistor is 192 ohms.

For that capacitor for an impedance of 192 ohms the frequency is 31.8 mHz.

The -3 dB point on the analyzer is at around 26 mHz. Perhaps my capacitor is closer to 32,000 uF in these conditions.

Your capacitor is accurate, however the output impedance of the generator is most likely 50 Ohm , which makes for 242 Ohm in total and the calculated frequency of 25.3mHz  .

Cheers

Alex

Of course! An expensive oversight on my part.

[Berni]

I think this could also be possible to do on my HP 89410A (Vector signal analyzer DC-10MHz)

I need to give it a try when i get home.

[chris_leyson]

Measure the filters step response, differentiate the step response to get the impulse response and then calculate the FFT of the impulse response to get the frequency response. Might have to do a bit of averaging to get impulse response.

[David Hess]

Measure the filters step response, differentiate the step response to get the impulse response and then calculate the FFT of the impulse response to get the frequency response. Might have to do a bit of averaging to get impulse response.

That is what I recommended but oscilloscopes which support it are either old and rare or new and expensive.  This EDN article discusses the three methods and this article discusses the DSO FFT calibration problem.

[Alex Nikitin]

I've tried to measure a 1M and 470nF LPF from 50mHz to 10Hz using the HP3563A. Here is the result.

Cheers

Alex

[chris_leyson]

Thanks for the link to the EDN article. To be honest I thought about trying it out on an HP54610 but then remembered how bad the built in math functions are on 8-bit data, Analog Discovery might do better.