Bode plot ( 1Hz to 10 MHz)

[Sariel]

Hello,

I've built a preamplifier (10Hz - 1MHz) designed for low-noise, low-frequency measurements, serving as a pre-gain stage before connecting to an oscilloscope or signal analyzer.

Now, I want to evaluate its performance and obtain a gain vs. frequency plot.

However, many oscilloscopes with Bode plot functionality are limited to a minimum frequency of 10Hz, and VNAs don't operate at such low frequencies.

What would be the best approach to measure it?
[ Specified attachment is not available ]

[AnalogTodd]

I used an older HP4195A to do these measurements (I know what circuit you built based on seeing it on LinkedIn, hello from the writer of that App Note!). While that piece of equipment says it only does 10Hz, it can actually go down to 3Hz with reasonable fidelity.

If you're wanting to just get stuff in the 1Hz to 10Hz range, you can also just take a few discrete points and add them to your data, I would not expect anything to be nonlinear down there.

[mawyatt]

Believe the Siglent DSOs (SDS800XHD and 2000X+ do) Bode Function goes down to 10Hz and up to 120MHz (with capable external AWG). As Todd said you can extrapolate below 10Hz if needed.

Best

[CatalinaWOW]

There are two approaches I would recommend.  The faster and easiest is to collect data points.  Use a signal generator that covers the frequency range.  At the very least you can use Audacity to generate the tones and play them with whatever. Note that to do the high end the Audacity approach is going to be pushed at or beyond its limits, but you can use your scope internal capability to do that end of the job.   Measure the output of your generator with a dvm or your scope and use the same instrument to measure your devices output.  You only need two or three points per decade if your preamp is reasonably well behaved.  You can add samples if you find evidence of resonances or other peculiarities.  Plot using your preferred plotting software (Excel, Libre Office Calc, Octave or others).

The second method is a bit harder.  Get a white noise source.  Audacity is an option.  Use your scope to collect a sample long enough to get your low frequencies (a second is plenty) at a sampling rate high enough to overlap your scopes internal Bode capability.  Export this data and do a Fourier transform on it to verify whiteness.  Feed that to your preamp and take a similar sample of the output.  If your input was white the magnitude of the Fourier transform is the Bode plot.  While there are ways to do Fourier transforms in Excel and Calc, it will be easier to use Octave or similar.

[Sariel]

I used an older HP4195A to do these measurements (I know what circuit you built based on seeing it on LinkedIn, hello from the writer of that App Note!). While that piece of equipment says it only does 10Hz, it can actually go down to 3Hz with reasonable fidelity.

If you're wanting to just get stuff in the 1Hz to 10Hz range, you can also just take a few discrete points and add them to your data, I would not expect anything to be nonlinear down there.

Thank you, Todd! Nice to meet you here as well

I have access to SDS2000X plus, SDG6022 to perform the Bode plot.
I don't yet have access to the SDS2000X plus internal AWG ( need to open this option).
I must say that the manual for these devices lacks enough depth on how to connect the devices and perform well the sweep.

I also have access to Magnova scope. But its AWG/Bode plotter will be available in July.

I do want to try the white noise option. It looks very fun. The SDG6022 has Gaussian noise output which can be frequency-limited.

[mawyatt]

The SDG6022X works well with the SDS2000X+, we know as we have both and have used them together for Bode Plotting on a number of occasions.

If the DSO and AWG are networked together you just need to set the AWG address in the Bode Config menu. If they are not networked, then you can connect the AWG to the DSO with USB and setup in the Bode config menu.

The DSO Bode function is quite good and has many useful features, we've used it to plot Open Loop/Close Loop system responses, Non-Linear Oscillator Injection Locking Characteristics, various Filter responses, mixer frequency translation Bode plots, and so on.

Here's a few links that folks might find interesting/useful.

https://www.eevblog.com/forum/testgear/injection-transformers-bode-plots-application/

https://www.eevblog.com/forum/testgear/diy-transformer-for-use-with-bode-plots/

https://www.eevblog.com/forum/projects/injection-locked-peltz-oscillator-with-bode-analysis/msg4424434/#msg4424434

https://www.eevblog.com/forum/projects/injection-locked-frequency-divider/msg5555107/#msg5555107

https://www.eevblog.com/forum/projects/when-a-precision-pot-is-not!!/

https://www.eevblog.com/forum/testgear/capacitive-impedance-plots-with-sds2104x-plus-bode-function/msg4335745/#msg4335745

https://www.eevblog.com/forum/testgear/admittance-measurements-with-dso-awg-with-bode-function/msg4491952/#msg4491952

https://www.eevblog.com/forum/projects/ceramic-capacitor-behavior/msg5535855/#msg5535855

https://www.eevblog.com/forum/testgear/bode-plot-torture-test/msg4509301/#msg4509301







Best

[Sariel]

The SDG6022X works well with the SDS2000X+, we know as we have both and have used them together for Bode Plotting on a number of occasions.

If the DSO and AWG are networked together you just need to set the AWG address in the Bode Config menu. If they are not networked, then you can connect the AWG to the DSO with USB and setup in the Bode config menu.

The DSO Bode function is quite good and has many useful features, we've used it to plot Open Loop/Close Loop system responses, Non-Linear Oscillator Injection Locking Characteristics, various Filter responses, mixer frequency translation Bode plots, and so on.

Best

How should I connect them using a USB cable?

From the DSO device output (on the back) to the DSG front USB connector? I get an error when I connect as this. Testing config tell me there is no connection.

[mawyatt]

How should I connect them using a USB cable?

From the DSO device output (on the back) to the DSG front USB connector? I get an error when I connect as this. Testing config tell me there is no connection.

Connect USB cable to AWG back and to DSO USB front. Set DSO Bode Config Menu Interface to USB and press Test. Just did so and our DSO/AWG (SDS2000X+/SDG6000X) connected.

BTW one of the nice benefits of having Siglent gear is the depth of on-line real time help you get here from folks like tautech, 2N3055, Performa01, rf-loop and a few others. These folks have extensive knowledge of various test equipment and general electronics, and provide help for all sorts of issues, even non-Siglent equipment on many occasions.

We know, they've helped us a few times

Best

[2N3055]

I used an older HP4195A to do these measurements (I know what circuit you built based on seeing it on LinkedIn, hello from the writer of that App Note!). While that piece of equipment says it only does 10Hz, it can actually go down to 3Hz with reasonable fidelity.

If you're wanting to just get stuff in the 1Hz to 10Hz range, you can also just take a few discrete points and add them to your data, I would not expect anything to be nonlinear down there.

Thank you, Todd! Nice to meet you here as well

I have access to SDS2000X plus, SDG6022 to perform the Bode plot.
I don't yet have access to the SDS2000X plus internal AWG ( need to open this option).
I must say that the manual for these devices lacks enough depth on how to connect the devices and perform well the sweep.

I also have access to Magnova scope. But its AWG/Bode plotter will be available in July.

I do want to try the white noise option. It looks very fun. The SDG6022 has Gaussian noise output which can be frequency-limited.

You can perform Bode plot with internal AWG even without AWG license.
But if you have SDG6000X that use it, it is better.

Mike already said everything about Bode plot. Nothing to add.

As for frequencies lower than 10 Hz....
You keep wiring as for Bode plot.

In measurements, you have both amplitude related measurements and phase too.
You set measurements to measure P-P and Stdev on input(CH1) and output (CH2) and Phase between CH1 and CH2. Enable statistics. Even histicons. Mini histograms will be useful to judge quality of data.

Decide how many points per decade you need between 0.1Hz and 10Hz.

Set SDG6000X to 0.1Hz, set timebase to 100ms/div and let it run so it gathers measurements and stats.
Stop scope. Write down data. Or do screen shot.
Set next frequency on AWG. Adjust timebase on scope. Run scope again.
Wait.. Rinse and repeat.

Enter data in spreadsheet, calculate amplitude ratios and plot.
For calculations, use Mean value of the measurement from stats, that is averaged value.

It is half manual method but all results are in same place so easy to collect.
It is pretty quick as it is, for one time measurement.

If you need to repeat measurement often then some SCPI/Python scripting might save time long term.
With both scope and AWB on Ethernet, it can be scripted to be fully automatic.

Normally, expect this process to be slow. Like minutes per point at lowest end. Capturing only 12 periods at 0.1 Hz is already two minutes. You want to capture at least 10-20 for averaging to do its thing.

[2N3055]

Thank you Mike for your kind words.
Means a world coming from you!

All the best

Siniša

[mawyatt]

Thank you Mike for your kind words.
Means a world coming from you!

All the best

Siniša

Well you deserve this, as you provide considerable help while a few "others" continue to create chaos with no value added!!

BTW the new released firmware for the SDG6000X has a Frequency Sweep Mode which is Stepped rather than Linear or Log, which might prove useful in creating the lower under 10Hz results. We haven't used this Mode just yet so can't comment.

Best

[Jay_Diddy_B]

Hi,

I assume that LNA is similar to the one described in Linear Technology AN-159.
I have built a behavioral model based on the schematic and block diagram.



The simulation can be used to check that the intermediate stages are not being overloaded.

The gain of the circuit is 80dB in the passband. At 1Hz the expected gain is 12dB.

I have attached the model.

Regards,
Jay_Diddy_B
  an159 behavioral.asc (2.85 kB - downloaded 37 times.)

[mawyatt]

That's a considerable range of 160dB between 0.1Hz and ~10Hz, which might prove difficult to measure. Likely requiring an attenuator (or variable attenuator) on the input, as the AWG might not be able to supply a low enough input at 10Hz and above.

Best

[Sariel]

Attached are my full schematic and the simulated frequency response of the preamplifier.
What input levels would you recommend?
Looking again at the frequency response, I think that measuring down to 1Hz will be enough. And perhaps up to 5MHz (?)

 Low_frequency_LNA.pdf (521.95 kB - downloaded 124 times.)

[mawyatt]

Looks like you have +-5V supplies, maybe stay under 5V with signal peak by 1V on each end, so limit output of each stage to 8VPP (+-4Vp) or less. Then work your way from the output to the input with that limit in mind.

You will likely need to increase the input signal amplitude as you move down below 10Hz as the overall gain drops. You will need sufficient output amplitude to get a good SNR at the output at all frequencies, and this will drop considerably below 10Hz as the overall gain decreases.

So adapt your input signal level below 10Hz to keep a good level signal at the output.

Did you get the DSO talking to the AWG for the Bode Function?

BTW make sure your DSO inputs are DC coupled. They are fixed as AC Coupled.

Best

[AnalogTodd]

When I calibrated the original circuit, I used a 60dB attenuator for the input signal. That was actually created using a 1kOhm:1Ohm resistor divider. With 1% resistors, the worst case you can get for variation in the 60dB attenuation is +/-0.2dB. It's not a great idea for doing something that would be RF but works fine for frequencies up to several MHz.

Jay_Diddy_B knows about that LNA as well, he would come to the factory a couple times a year and we would showcase the latest and greatest low noise parts using it. We would take and switch between an older middle ground LDO that ran about 20uV of noise and our new stuff. Ran the output of the LNA to both an oscilloscope and into a guitar amp at the same time. Big difference when you could not only see the change in noise on the scope but hear the difference as well!

[Sariel]

Looks like you have +-5V supplies, maybe stay under 5V with signal peak by 1V on each end, so limit output of each stage to 8VPP (+-4Vp) or less. Then work your way from the output to the input with that limit in mind.

You will likely need to increase the input signal amplitude as you move down below 10Hz as the overall gain drops. You will need sufficient output amplitude to get a good SNR at the output at all frequencies, and this will drop considerably below 10Hz as the overall gain decreases.

So adapt your input signal level below 10Hz to keep a good level signal at the output.

Did you get the DSO talking to the AWG for the Bode Function?

BTW make sure your DSO inputs are DC coupled.

Best

Do I need to configure the DSO inputs (impedance, BW, coupling, voltage level), before initiating the Bode analysis feature of the DSO? Or does the Bode analysis overwrite this configuration when initiated?

[CatalinaWOW]

If your Bode matches the simulation down to 1 Hz, particularly the phase response, it is pretty safe to bet that the next decade down will be fine.  No need to try to achieve 120dB dynamic range in your measurements.

[mawyatt]

When I calibrated the original circuit, I used a 60dB attenuator for the input signal. That was actually created using a 1kOhm:1Ohm resistor divider. With 1% resistors, the worst case you can get for variation in the 60dB attenuation is +/-0.2dB. It's not a great idea for doing something that would be RF but works fine for frequencies up to several MHz.

Jay_Diddy_B knows about that LNA as well, he would come to the factory a couple times a year and we would showcase the latest and greatest low noise parts using it. We would take and switch between an older middle ground LDO that ran about 20uV of noise and our new stuff. Ran the output of the LNA to both an oscilloscope and into a guitar amp at the same time. Big difference when you could not only see the change in noise on the scope but hear the difference as well!

60dB attenuation seems about right for above 10Hz since the OP schematic shows mid-band gain of 60dB. So 1VPP AWG input signal level should keep all the stages well below clipping and provide an acceptable signal level at the output with good SNR for the Bode Plotting.

Recall standard 1% 1/8 watt leaded resistors have ~ 0.4pF shunt capacitance so should be good well above 10MHz for use with the attenuator. If the OP wants better precision then 0.1% resistors could be used, but probably overkill IMO.

At 1Hz the AWG probably could be increased to 10VPP with 60dB attenuator without any stage clipping and the max AWG level (20VPP) at 0.1Hz.

Overall would expect a nice Bode Plot throughout the range from 0.1Hz to 10MHz.

Best 

[Sariel]

When I calibrated the original circuit, I used a 60dB attenuator for the input signal. That was actually created using a 1kOhm:1Ohm resistor divider. With 1% resistors, the worst case you can get for variation in the 60dB attenuation is +/-0.2dB. It's not a great idea for doing something that would be RF but works fine for frequencies up to several MHz.

Jay_Diddy_B knows about that LNA as well, he would come to the factory a couple times a year and we would showcase the latest and greatest low noise parts using it. We would take and switch between an older middle ground LDO that ran about 20uV of noise and our new stuff. Ran the output of the LNA to both an oscilloscope and into a guitar amp at the same time. Big difference when you could not only see the change in noise on the scope but hear the difference as well!

I see. that the lowest signal the DSO can source in Bode mode is 5mVpp. Probably good enough for testing the filter behavior in the range of 0dB to 60 dB.
The input impedance of the preamplifier is 250 ohm. So there is already some attenuation with the 50ohm output of the internal AWG of the DSO.

There are several low frequencies HPF stages inside the preamplifier, so a long stabilizing time has to wait. I hope the bode analysis awaits enough time from point to point in its sweep.
Otherwise, I will do it manually. I just need to verify it once.

[mawyatt]

Looks like you have +-5V supplies, maybe stay under 5V with signal peak by 1V on each end, so limit output of each stage to 8VPP (+-4Vp) or less. Then work your way from the output to the input with that limit in mind.

You will likely need to increase the input signal amplitude as you move down below 10Hz as the overall gain drops. You will need sufficient output amplitude to get a good SNR at the output at all frequencies, and this will drop considerably below 10Hz as the overall gain decreases.

So adapt your input signal level below 10Hz to keep a good level signal at the output.

Did you get the DSO talking to the AWG for the Bode Function?

BTW make sure your DSO inputs are DC coupled.

Best

Do I need to configure the DSO inputs (impedance, BW, coupling, voltage level), before initiating the Bode analysis feature of the DSO? Or does the Bode analysis overwrite this configuration when initiated?

You set things up in the DSO Bode Config Menu. Things like Impedance, Voltage Level,  Start/Stop Freq, Sweep Type Lin/Log, Number of Points, Sweep Keyed Variable Amplitude, Display/Plot Parameters and so on. Can even use all 4 DSO channels simultaneously for 3 independent plots, handy for plotting the gain/phase of a cascaded system each stage like your amplifier  

Plan on spending some time with the Bode Function, it's quite useful/powerfull in capable hands and you will be rewarded for your efforts

Best

[mawyatt]

When I calibrated the original circuit, I used a 60dB attenuator for the input signal. That was actually created using a 1kOhm:1Ohm resistor divider. With 1% resistors, the worst case you can get for variation in the 60dB attenuation is +/-0.2dB. It's not a great idea for doing something that would be RF but works fine for frequencies up to several MHz.

Jay_Diddy_B knows about that LNA as well, he would come to the factory a couple times a year and we would showcase the latest and greatest low noise parts using it. We would take and switch between an older middle ground LDO that ran about 20uV of noise and our new stuff. Ran the output of the LNA to both an oscilloscope and into a guitar amp at the same time. Big difference when you could not only see the change in noise on the scope but hear the difference as well!

I see. that the lowest signal the DSO can source in Bode mode is 5mVpp. Probably good enough for testing the filter behavior in the range of 0dB to 60 dB.
The input impedance of the preamplifier is 250 ohm. So there is already some attenuation with the 50ohm output of the internal AWG of the DSO.

There are several low frequencies HPF stages inside the preamplifier, so a long stabilizing time has to wait. I hope the bode analysis awaits enough time from point to point in its sweep.
Otherwise, I will do it manually. I just need to verify it once.

The Siglent Bode Function utilizes a Frequency Selective measurement capability which is quite good at rejecting unwanted and out of band signals. The function stops at 10Hz and has sufficient time to allow accurate measurements at that frequency with the Frequency Selective feature, you'll have to manually access the lower frequencies and allocate enough settling time for acceptable measurements below 10Hz.

Best

[mawyatt]

If your Bode matches the simulation down to 1 Hz, particularly the phase response, it is pretty safe to bet that the next decade down will be fine.  No need to try to achieve 120dB dynamic range in your measurements.

Altho the design looks like it has a couple three 1st Order High Passes and a cascaded Sallen-Key 2nd Order High Pass, the simulation does look like it's following  ~80dB/Dec High Pass from 0.1Hz and seems "straight line" amplitude to above 1Hz but below 10Hz, so one could measure a couple points below 10Hz and 1Hz and likely be "good enough". If the OP utilizes the Siglent Bode function for 10Hz to 10MHz then that range is covered and no additional effort/time required.

Best

[AnalogTodd]

If your Bode matches the simulation down to 1 Hz, particularly the phase response, it is pretty safe to bet that the next decade down will be fine.  No need to try to achieve 120dB dynamic range in your measurements.

Altho the design looks like it has a couple three 1st Order High Passes and a cascaded Sallen-Key 2nd Order High Pass, the simulation does look like it's following  ~80dB/Dec High Pass from 0.1Hz and seems "straight line" amplitude to above 1Hz but below 10Hz, so one could measure a couple points below 10Hz and 1Hz and likely be "good enough". If the OP utilizes the Siglent Bode function for 10Hz to 10MHz then that range is covered and no additional effort/time required.

Best

Yeah, the design was originally done with one very low frequency (0.5Hz) high pass to do DC blocking from what was being measured (ultra-low noise LDOs) and then one internal high pass (~10Hz) to block DC before a gain stage, the internal 2nd order Sallen-Key High Pass and a final high pass (~10Hz again) to block DC to center the output signal around zero. The internal Sallen-Key tweaked the Q a bit in order to try and make the two 10Hz filters and the Sallen-Key all together be as equivalent as possible to a 4th order Butterworth response.

Nice thing about creating that cheap and cheesy 60dB attenautor was that I could drop a measurable signal on it and put the attenuated version into the LNA and know that I was within the operating range of the LNA and have measurable signal levels at input and output. You can even calibrate the attenuator by putting a signal larger than the LNA might be able to handle but is within the capabilities of your Bode analyzer.

If you want, I can point you to the Application Note I wrote for all of it.

[Jay_Diddy_B]

Hi,
I would set the signal amplitude at Vin to be 0.1mV at 10Hz. You can increase the signal amplitude at a rate of 40dB per decade below 10Hz. Most network analyzer allow for the amplitude to be adjusted during the sweep.

I have implement that here with a lop sweep generator and a low pass filter.
The signal amplitudes at different stages in the signal chain can be observed.





I have attached the model.

Regards,
Jay_Diddy_B

 an159 behavioral.asc (3.61 kB - downloaded 26 times.)