Determine the output voltage waveform for the RC differentiator in Figure 20-26 with the rheostat set so that the total resistance of R1 and R2 is 2 kΩ.

Question

Determine the output voltage waveform for the RC differentiator in Figure 20-26 with the rheostat set so that the total resistance of [latex]R_{1}[/latex] and [latex]R_{2}[/latex] is 2 kΩ.

Accepted Answer

First, calculate the time constant.

[latex] au =R_{tot}C= (2 \ k\Omega )(1 \ \mu F)= 2 \ m s[/latex]

On the rising edge, the resistor voltage immediately jumps to +25 V. Because the pulse width is 5 ms, the capacitor charges for 2.5 time constants and therefore does not reach full charge. Thus, you must use the formula for a decreasing exponential in order to calculate to what voltage the output decreases by the end of the pulse,

[latex]v_{out}=V_{i}e^{-t/RC}= 25e^{-5ms/2ms} = 25 (0.082) = 2.05 \ V[/latex]

where [latex]V_{i}[/latex]= 25 V and t= 5 ms. This calculation gives the resistor voltage ( [latex]V_{out}[/latex] ) at the end of the 5 ms pulse width interval. On the falling edge, the resistor voltage immediately jumps from +2.05 V down to —22.95 V (a 25 V transition). The resulting waveform of the output voltage is shown in Figure 20-27.

Question 20.5: Determine the output voltage waveform for the RC differentia...

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