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In the beginning I was using the circuit (at the bottom) to separate the AC from the DC ( the second order filter ) which in fact is just a second order high pass filter and the DC is a zero Hz component, it performed as expected as its cut- off freqency is 11 Hz and the output follows the frequency response

enter image description here

and here is the output

enter image description here

however today I came across another circuit which uses just a capacitor for AC coupling

enter image description here

what concerns me is the part of the coupling which I simulated it in my previous schematic in circuit at the top (with 20 uF capacitor),

at the end I suppose they are both high pass filters, and the (20 uF capacitor ) is supposed to be connected to a load to form the filter, in this case my load is supposed to be the impedence of the the analog pin ( I guess) to which I am connecting my signal ( I am using Arduino Mega )

but still I couldn't figure out which one will perform better in my case ? do I just need 1 capacitor and that is it ? or do I have to implement a complete filter as I did first with this second order filter

Thanks

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at the end I suppose they are both high pass filters, and the (20 uF capacitor ) is supposed to be connected to a load to form the filter, in this case my load is supposed to be the impedence of the the analog pin ( I guess) to which I am connecting my signal

Yes, that's right.

but still I couldn't figure out which one will perform better in my case ?

Without using the extra external resistor you probably improve the efficiency (because the resistor converts some power to heat).

On the other hand if you just use the Arduino input pin as the load, you probably don't get as good of control of the cut-off frequency.

If you just need to eliminate the dc offset and don't really care exactly what the cut-off frequency is, you can probably eliminate the external resistor.

One more thing you should consider is that the input range of the Arduino pin is probably something like 0 to 3.3 V or 0 to 5 V. If you don't re-bias the dc level, you will probably get a signal in a range like -1 to +1 V or -2 to +2 V, which will not interact well with the Arduino. You should probably add something like a resistor divider to re-bias the signal. And then that divider (or it's Thevenin equivalent) can also provide the "load" resistor to set the high-pass cut-off frequency.

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After prototyping the same circuit for an ICP/ IEPE sensor and testing it in the lab, I would like to emphasize that this circuit could potentially be terrible in DC blocking. What happens if the load of this circuit is for example an opamp -which is quite often the case- implementing an anti-aliasing filter, etc?

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Without determining a resistor from the decoupling capacitor to the Ground, two problems may arise:

  1. It is possible that no return path for the DC current exists. This is explained in the following article, "Missing DC Bias Current Return Path When AC-Coupled": https://www.analog.com/en/analog-dialogue/articles/common-problems-when-designing-amplifier-circuits.html

"What actually happens is that the input bias currents will flow through the coupling capacitor, charging it, until the common-mode voltage rating of the amplifier’s input circuit is exceeded or the output is driven into limits. Depending on the polarity of the input bias current, the capacitor will charge up toward the positive supply voltage or down toward the negative supply. The bias voltage is amplified by the closed-loop dc gain of the amplifier. This process can take a long time, thus, a casual lab test (using an ac-coupled scope) might not detect this problem, and the circuit will not fail until hours later."

A malfunctional ac-coupled op-amp circuit. A malfunctional ac-coupled op-amp circuit.

In my case, I observed that the DC part of the signal wasn't blocked at all. However, when I used an oscilloscope, after the AC-coupling-capacitor, the DC part of the signal started slowly to decrease, which brings us to point 2:

  1. If there is a path for the DC current, the impedance of the load should obviously be taken into account, since together with the AC-coupling-capacitor they form a high-pass filter. When dealing with filters, most of us usually focus on the frequency domain. However in this case, the response of the filter in the time domain should also be carefully examined. In the scenario described above, the 20uF AC-coupling-capacitor formed a high-pass filter with the internal resistance of the oscilloscope that I used, which was 1M Ohm. As a simulation for the sensor, I used a sine wave with DC offset. The result is that the DC part of the signal was eventually blocked -only when the probe was attached to the circuit- but that happened after about 2 minutes, which could possibly be more than enough to fry the opamps. Using an online, high-pass filter calculator, the step response of the filter can be observed: (R=1MΩ C=20uF). This result is in line with the behaviour of the circuit that I empirically observed in the lab. R=1MΩ, C=20uF, high-pass filter

Concluding, it seems wise to determine and place a resistor and deliberately form the high-pass filter. Care should be taken when choosing the value of the components, in both the frequency and the time domain. Avoid too high values for the resistance, due to the noise it introduces in the signal (resistor noise model).

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