Set up the circuit in Figure 1 below. Adjust the function generator to provide a 200 Hz square wave, with zero DC offset, and 6 volts peak- to-peak. After these adjustments you can visualize the generator as the switching circuit shown illustrated below the circuit.
Figure 1.
Connect the scope to display VC(t) on CH1 and VS(t) on CH2. Ground both displays (with the GND selection) to set the traces at the center of the display; then select the DC presentation, and display VC(t) and VS(t) simultaneously and with the same vertical sensitivity (VOLTS/DIV) for each channel. Record the input and output time functions. Measure the time constant by the method discussed in the notes, and compare it with the value calculated from the values of R and C. In order to measure the time constant accurately, you may have to alter the function generator's frequency. Record and comment upon your observations. Repeat the experiment with all values of C provided by your instructor.
Notice that VS(t) at the output terminals of the function generator is not a perfect square wave. Why? Record the waveforms accurately, especially the "imperfection" in VS(t).
Using the same circuit from part I, if VC(t) is much less than then VR(t) is almost equal to VS(t) and therefore iC(t) is almost equal to Vs(t)/R. Under this condition, VC(t) = 1/RC times the integral of VS(t), and thus the system with can be viewed as an integrator.
Use a square wave of frequency 200 Hz and amplitude 4 V peak-to-peak, and use C = 1 uF. Are the approximations mentioned above valid under these conditions? Display VS(t) and VC(t) simultaneously on the scope as in part 1, except that since VC(t) is much smaller than VC(t) you will have to use different vertical sensitivities (VOLTS/DIV) for the two channels. Try the sinusoidal and triangle waveforms. Record your observations.
Comment on the quality of this circuit as an integrator.
What is the integral of a square wave? Of a sinusoidal wave? Of a triangle wave? (Hints: the square wave is a succession of constants; what function g(t) is the integral of the constant function f(t) = +3? f(t) = -3? The sinusoid is easy, from a basic calculus course. The triangle wave resembles the function f(t) = K1*t + K2; what function g(t) is the integral of that?)