4-21: Inverting Differentiator

Inverting Differentiator

In this lab, we use an op amp (OP 27) and a capacitor to create an inverting differentiator. This means that the output voltage V_o is (a multiple of) the negative derivative of the input voltage V_in, or V_o = -RC*(dv_i/dt), where R is the feedback resistance, C is the capacitor capacitance, and v_i is the input voltage. If the input voltage v_i = Acos(ωt), where A is the input amplitude and ω is the angular frequency, then its derivative is (dv_i/dt) = -Aωcos(ωt). Thus the output voltage is V_o = RCAωsin(ωt).

 Here are the formulas related to the change of the voltage and current with time for capacitors, and inductors

Pre-Lab: We determine the Vo, V1, V3 ,use the data under.

When f=1kHz, A=1V, offset=0V, The display the waveforms for Vo A= 1.144V and Vin A=1V.

When f=500Hz, A=1V, offset=0V, The display the waveforms for Vo A= 0.586V and Vin A=1V.

When f=2kHz, A=1V, offset=0V, The display the waveforms for Vo A= 2.204V and Vin A=1V.

Theoretical value for the Vout  is much clossed to the experiment value. The min % different is 2.3% the max %different is 8.3%. 

 it has a  amplitude = 2.204V and the same pi/4 phase shit.

Summary: In this lab, we learned  the output voltage has a derivate with respect to the time of the input to the circuit relationship. With a higher frequency the the op amp will have a higher gain for the output, and with a lower frequency the op amp will have a lower gain for the input.