For an RC low-pass filter with R = 100 k$Omega$ and C = 1 µF a. What is the bandwidth of the filter? b. If the input is a 2 V, peak-to-peak, square wave of period 1 sec, what will the filter output be? Use the square wave Fourier series representation given in Equation 4.15 or 4.16 for $V_{in}(t)$. c. What is cut-off frequency of the filter and the corresponding closest value of $n$ d. Tabulate the frequencies, amplitude components of input signal, amplitude ratio of the filter, and amplitude components of the output signal for the first three values of $n$, and for $n$ near cut-off frequency. e. Draw the frequency spectrum of the input signal and the output signal
Added by Anthony F.
Close
Step 1
The bandwidth of the filter is given by b. If the input is a 2 V, peak-to-peak, square wave of period 1 sec, the output will be 0.707 V at 1 kHz. The amplitude components of Vin(t) are given by c. The cut-off frequency of the filter is n = 1.414 and the Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 63 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
What is a low-pass filter and sketch its gain in frequency domain? What is the cut-off frequency of a normalized Butterworth filter? Next we need design a Butterworth filter with the following specification Gp,db=-4; wp=10; Gs,db=-25; ws=60; Given that Gp,db=-10 log10[1+(wp/wc)2n] and Gs,db=-10 log10[1+(ws/wc)2n] Find the order of the filter order and the cut-off frequency of the filter. Find the transfer function of the filter H(s)
Madhur L.
An $R C$ filter is shown. The filter resistance $R$ is variable between $180 \Omega$ and $2200 \Omega$ and the filter capacitance is $C=0.086 \mu \mathrm{F}$. At what frequency is the output amplitude equal to $1 / \sqrt{2}$ times the input amplitude if $R=$ (a) $180 \Omega$ ? (b) $2200 \Omega$ ? (c) Is this a low-pass or highpass filter? Explain.
Consider the filter circuit shown in Figure P33.56. (a) Show that the ratio of the amplitude of the output voltage to that of the input voltage is $$\frac{\Delta V_{\mathrm{out}}}{\Delta V_{\mathrm{in}}}=\frac{1 / \omega C}{\sqrt{R^{2}+\left(\frac{1}{\omega C^{2}}\right)}}$$ (b) What value does this ratio approach as the frequency decreases toward zero? (c) What value does this ratio approach as the frequency increases without limit? (d) At what frequency is the ratio equal to one-half?
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD