Nilsson & Riedel 9e, p. 349, Problem 9.13. A 80 kHz sinusoidal voltage has zero phase angle and a maximum amplitude of 25 mV. When this voltage is applied across the terminals of a capacitor, the resulting steady-state current has a maximum amplitude of 628.32 A. Numerical answer is [d] 50.0 nF. a) What is the frequency of the current in radians per second? b) What is the phase angle of the current? c) What is the capacitive reactance of the capacitor? d) What is the capacitance of the capacitor in microfarads? e) What is the impedance of the capacitor?
Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!
ELEC153 Circuit Theory II M2A1 Textbook Assignment: Problem Set A: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC series circuit as seen from the two open-ended terminals. Show your answer in rectangular and polar form. The AC signal frequency is 1 KHz. 2. Repeat your analysis of Question 1 for a frequency of 200 Hz. 3. Consider the following AC series circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 20 volts rms at 0 degrees. c. Find the voltage across each component, in polar form. d. Find the real power supplied to the circuit, in Watts. ELEC153 Circuit Theory II M2A2 Textbook Assignment: Problem Set B: Chapter 15 Instructions Save this document and place your answers into it so you can submit it to the appropriate homework dropbox. Handwritten solutions should be scanned and saved as a BMP, GIF, or JPG image, or scanned and pasted into this document. Questions 1. Find the impedance of this AC parallel circuit between the two open-ended terminals, in rectangular and polar forms: 2. Consider the following AC parallel circuit: a. Find the total impedance across the voltage source in polar form. b. Find the source current, in polar form. Note: the source voltage is 12 volts rms at 0 degrees. c. Find the current through each component, in polar form. d. Find the real power supplied to the circuit, in Watts.