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The given figure shows an RC circuit with input voltage x (t) and output voltage y(t). The RC circuit is to be used as a low-pass filter.
Now consider the input signal x(t) = ∑∞k→∞ x1 (t-10-6 k), where x1(t) = 20u (t + 0.25 x10-6) -20u(t - 0.25 x10-6). This represents a square wave with a fundamental frequency f0 = 1MHz and 50% duty cycle. This input signal results in the output signal y (t) which has both DC and AC voltage. It is desired the AC voltage present in the output y (t) be negligible so that y(t) is practically DC voltage.
Design Requirements:
Use the circuit shown in the figure and design it in order to satisfy the following requirements:
1- All AC components of the output signal y (t) should be negligible compared to the DC component of y (t). Specifically, the magnitude of all AC components should be at least 100 times less than the DC component. In other words, the following condition must be satisfied:
|Ck ≠ 0, y|/C0,y ≤ 0.01
2- You are given a number of resistors and capacitors to use in your design. Their values are given in table 1. You are allowed to use only one resistor and only one capacitor from the list.
3- The value of the capacitor used in the design should be as small as possible.
Table 1: Available Values of Resistors and Capacitors.
R
0.1Ω
0.5Ω
1Ω
5Ω
10Ω
50Ω
100Ω
1kΩ
5kΩ
20kΩ
C
10 pF
30 pF
300 pF
3nF
300 nF
1μF
15μF
250μF
3μF
10μF
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