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Operationally Amplifying Signals

November 03, 2025
LCR Meter electronics embedded tools
"WIP"

Warning

This is a WIP article! I have other priorities right now but I will keep continuing here as I find the time.

We have a clean enough sine wave now , but if you have sharp eyes (or read the previous details section) you may have realized that we only have 200mV of signal left! The reason is because the RC low pass attenuates by literally burning off the undesired components of the signal as heat through the resistor. And since our cutoff is 159Hz, even our 1kHz main frequency is an "undesired component". This is advantageous for us because the harmonics are even more undesired and attenuated, so they are pretty much reduced to unthreatening electrical noise levels.

But we cannot directly push this sine through a capacitor and measure it because it isn't really stable.

It is "high impedance" (there it comes once again). A real AC voltage source like ours can be modeled by an ideal voltage source $V_s$ and a source impedance $Z_s$. Our source impedance corresponds to that of the RC filter plus whatever is in the way of the digital pin. Since we have 10kOhm resistors, they introduce high impedance. When the RC is connected in series with the device under test, it essentially forms a voltage divider with the RC on one and the DUT on the other side.

$$ V_{DUT} = V_s \cdot \frac{Z_{DUT}}{Z_s + Z_{DUT}} $$

We are going to be measuring the voltage drop across the DUT to find out its impedance ($Z_{DUT}$). If $Z_s << Z_{DUT}$ then we can pretty much assume that the voltage drop is solely caused by the DUT alone. However if $Z_s$ is significant (high impedance) then it distorts the voltage reading. I can use a smaller resistor and capacitor, but to get relatively small readings like 10 $\Omega$ without significant error, you need resistors in the milliohms [I don't have those ]. Also that might go a little into the glowing components territory.

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