Two Differentiators Circuit Experiment 17 Two Differentiators Circuit

Analog Computing Analog computers Analog controllers First were mechanical systems. Electrical analog computers were developed in the early 1940’s and used extensively. Maximum speed of response was limited to less than 10 MHz. Analog controllers PID (proportional-integral-derivative) controllers Thermostats

Capacitors

If Vin = 0.5V sin(wt), then Vo =[ -R1C1 w cos(wt)] x 0.5V iR iR + iC + i =0 where i = 0mA iC =C1 dVin/dt iR = [0V – Vo]/R1 Vo = -R1C1 dVin/dt iC i = 0 If Vin = 0.5V sin(wt), then Vo =[ -R1C1 w cos(wt)] x 0.5V where -R1C1 w is the maximum gain of the differentiator.

Conversions for Sinusoids A sin(wt +f) A cos(wt + f - 90o) - A sin(wt +f) A sin(wt + f + 180o ) Or A sin(wt + f - 180o ) - A cos(wt +f) A cos(wt + f + 180o ) A cos(wt + f - 180o ) A sin (wt + f - 360o) A sin (wt + f + 360o) A cos(wt +f) A cos (wt + f - 360o) A cos (wt + f + 360o)

Sine – Cosine Conversion Vin = sin(wt) Vo = -R1C1 w cos(wt) Vo = R1C1 w cos(wt – 180o) Vo = R1C1 w sin(wt – 180o + 90o) Vo = R1C1 w sin(wt – 90o) When the input voltage is sinusoidal, the output voltage has a phase shift of 90o with respect to the input voltage.

Limitation of Ideal Differentiator If the input contains electronic noise with high frequency components, the magnitude of the high frequency components will be amplified significantly over the signal of interest and the system could become unstable. It is necessary to modify the circuit to reduce or eliminate such effects (see Practical Differentiator circuit in Experiment 16 of the lab manual).

Circuit to be constructed Function Generator

Circuit Construction Position of the two switches changes the maximum gain of the differentiator. R1 is determined by setting w R1 C1 = 1 when f is 7.23 kHz. Use 0.1 µF for C1. R2 is determined by setting w R2 C1 = 1 when f is 723 Hz. Use two of the three slide switches in the parts kit Three pin black rectangle with knob Middle pin should be connected to the circuit Either one of the outer two pins should be connected to the other portion of the circuit Sliding the knob from right to left changes which outer pin is shorted to the middle pin

Phase Shift --Dt --

Caution: PSpice Transient Analysis Issue Information in first half cycle is incorrect because the initial charge on the capacitor is zero.

Measurement of Phase Angle There are two sets of instructions in the Module. Phase Delay.pdf, which explains how to make a phase angle calculation using the information displayed when the Oscilloscope function of the oscilloscope is used. You should become familiar with this technique. Magnitude and Phase.pdf, which explains how to use the automated measurement tools on the scope to obtain the magnitude and phase of a signal at a single frequency and over a range of frequencies.

Component Measurements To determine where some of the variation of your circuit’s performance compared to the predicted performance, you should measure the values of R1, R2, and C1. WARNING: Do not measure the value of any capacitor using your DMM unless you sure that there is no charge stored on the capacitor or you may damage your DMM. Do not place a wire directly across a capacitor to discharge it. The instantaneous current will be very high. Please a resistor across the terminals of a capacitor to limit the peak inrush current.

dB dB is an abbreviation for decibels