In this lab, we are going to prove that the output signal is the derivative of the input signal. We do some derivation, and get Vo = A*R*2*Pi*f*sin (omega*t). We can see that the output voltage is related to the frequency.
When calculating the theoretical output voltage, there is one trick there. At first, we take f as omega. Then, we figure out that omega=2*pi*f.
We calculate the Vout at frequency of 1k Hz, 2k Hz, and 500 Hz.
This is the circuit we build. We use 470 ohm resistor, and 470 nF capacitor.
We measure our real resistance to be 461 ohm, and real capacitance to be 415 nF.
This is the output when it is at 1K Hz. We get our experimental value to be 1.1544V. Compared to our theoretical value 1.388 V, we have a 16.8% percent difference.
This is the output when it is at 2K Hz. We get our experimental value to be 2.217 V. Compared to our theoretical value 2.776 V, we have a 20.1% percent difference.
This is the output when it is at 1K Hz. We get our experimental value to be 0.603V. Compared to our theoretical value 0.649 V, we have a 7.1% percent difference.
This is a summary table of our measured value and our calculation of % difference. The error could be caused by the inaccuracy of the value we use for capacity.
Summary:
Today, we talk about how op-amp can act as an integrator and differentiator. We talk more about 1st order linear circuit. We talk about the singularity functions. We do a lab on inverting differentiator. We get a max % difference of 20.1% and a minimum of 7.1%. I guess it is due to the capacitance we use is 415 nF instead of 470 nF which is its theoretical value.
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