Shows an rc circuit with input voltage x t and output

Question

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

Answer 1

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