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I have the following Sallen & Key lowpass filter:

$$T(s)=\frac{\frac{1}{R_1R_2C_1C_2}}{s^2+(\frac{1}{C_1R_1}+\frac{1}{C_1R_2})s+\frac{1}{R_1R_2C_1C_2}}$$

The parameters values are $$R_1=10 k\Omega$$ $$R_2=10 k\Omega$$ $$C_1=150 nF$$ $$C_2=1.65 nF$$

This allowed me to calculate the quality factor, the low-frequency gain, and the poles frequency.

$$T_0=1$$ $$Q_p=4.77$$ $$f_p=1011.66 Hz$$

My question now is: how can I experimentally determine this values using the oscilloscope? Is there any way to do it?

Granger Obliviate
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  • Use a step response and find the [overshoot](https://en.wikipedia.org/wiki/Overshoot_(signal)) and the [settling time](https://en.wikipedia.org/wiki/Settling_time). It's approximate, though. Also see [this](https://electronics.stackexchange.com/q/117124/95619), looks like a duplicate. – a concerned citizen Nov 12 '20 at 17:52
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    Use a sine wave input and look at the output with your scope. With low frequency inputs, you can find the gain (=1). As the frequency gets higher, you will see the output get bigger, and then get really small. Look up in your textbook the frequency response of a second order low pass filter, and it will tell you how to calculate the Q and w0 from the peak gain and gain=0.707 frequency. – user69795 Nov 12 '20 at 19:01
  • @GrangerObliviate are you finished with this question / answer and can it be accepted or, do you need to ask for clarification? – Andy aka Nov 18 '20 at 20:39
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    @Andyaka yes the explanation was very clear, thank you! I forgot to accept your answer, it's done now! – Granger Obliviate Nov 18 '20 at 20:45

1 Answers1

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It's a second order low pass filter so use a signal generator and oscilloscope and look for the magnitude peak and frequency where it occurs: -

enter image description here

The peak amplitude can be converted to zeta (\$\zeta\$) and zeta (aka the damping ratio) relates to Q-factor as follows: -

$$Q = \dfrac{1}{2\zeta}$$

And you can plug \$\zeta\$ into the peaking frequency formula to find the natural resonant frequency (\$\omega_n\$). Then if you wanted, you could double check that at the natural resonant frequency, the amplitude of the sinewave is Q times bigger than it is at very low frequencies.

Andy aka
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