ECET 303 HW1 - Carson Hunter (1)

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Purdue University, Fort Wayne *

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303

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Electrical Engineering

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Feb 20, 2024

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ECET 303 - Communications-1 Homework Assignment #1 Due Date: 09/25/2022, before 11:59 pm Note: Please upload your work! Please either type your answers, or write very neat and readable, then scan (no cell-phone-based picture!). Please include the detail of your answers, for each problem. Problem 1. What is the gain of an amplifier with an output of 1.5 V and an input of 30 μV? A v = output/input A v = 1.5V/ 30 μV A v = 50,000 Problem 2. What value of capacitance is required to produce 50 Ω of reactance at 450 MHz? C = 1/(2*pi*f*X c ) C=1/(2*pi*450 MHz*50) C = 7.07 pF Problem 3. What is the value of inductance that will resonate with an 80-pF capacitor at 18 MHz? F = 1/(2*pi*sqrt(L*C)) L = 1/(4pi 2 *C*F 2 ) L = 1/(4*pi 2 * 80pF * 18MHz 2 ) L = 9.772 x 10 -7 H Problem 4. What circuit Q is required to give a bandwidth of 36 MHz at a frequency of 4 GHz? Q = F/BW Q = 4GHz/36MHz Q = 111.11 (Q>100) The circuit required is a series resonant circuit.

Problem 5. Given a three-stage system comprised of two amplifiers and one filter with an input power of P in = 0.1 μW and absolute power gains of A p1 = 75, A p2 = 0.1 and A P3 = 250. Determine: a. The input power in dBm Pin = 0.1 uW = -40dBm b. The dB gain of each of the three stages Stage 1: Ap1= 75 = 18.751 dB Stage 2: Ap2 = 0.1 = -10 dB Stage 3: Ap3 = 250 = 23.979 dB c. The overall gain in dB Pout = 75*0.1*250* 0.1uW = 187.5 uW Ap(db) = 10log 10 (187.5uW/0.1uW) = 32.73 dB d. Output power (P out ) in Watts and dBm Pout = 187.5 uW = 0.0001875W = -7.269 dBm Problem 6. For the square wave as shown below, A A P1 = 75 A P3 2 = 50 A P2 = 0.1 Amplifier Amplifier Filter P in P out +5 V -5 V 1 ms 1 ms

a. Determine fundamental frequency F= 1/T F=1/2ms F= 0.5kHz b. Determine the amplitude of the first four frequency elements: A 1 , A 3 , A 5 , A 7 . Using Fourier series for a square wave A1= 4/pi A3= 4/(3*pi) A5= 4/(5*pi) A7= 4(/7*pi) c. Draw the spectrum of this waveform and specify each and every frequency element’s frequency and amplitude. Problem 7. Convert the following absolute ratios to dB: i) A P = 2500

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Log(2500) * 10 = 33.98 dB ii) A v = 5.75 log(5.75) * 10 = 7.59 dB Problem 8. Convert the following decibel value to absolute ratios: i) A P = 3 dB 3dB/10 = 0.3 10^0.3 = 1.995 ii) ii) A V = 15 dB 15/10 = 1.5 10^1.5 = 31.623 iii) A I = 0 dB 0/10 = 0 10^0 = 1 Problem 9. Convert the following power to dBm. Noe that P dBm = 10 Log 10 (P mW / 1 mW) i) P = 10 μW = -20 dBm ii) P = 1 mW = 0 dBm iii) P = 0.2 mW = -6.98 dBm iv) P = 1000 mW = 30 dBm

Problem 10. Compare Butterworth, Chebychev-1, Chebychev-2, and Elliptic filters for their properties in: pass-band, transition band, and stop-band. Then, draw the frequency response of a low-pass filter for each of these four filter types. A Butterworth filter is designed to have a flat frequency response both the passband and the stopband, it also has a wider transition band than most of the other filters mentioned. The Chebychev-1 instead of being flat in the passband has a ripple, the stopband is flat like the Butterworth filter, and the transition band has a sharper cutoff than the Butterworth filter. The Chebychev-2 is the inverse of the Chebychev-1, where the passband is flat, and the stopband has ripples, with the same characteristics for the transition band. Finally, the Elliptic filter has a equalized ripple in both the passband and the stopband, with the steepest transition band in comparison to the other 3 filters. Problem 11. Use Multisim and design filters with the following specifications. Include the Multisim generated circuit diagrams, as well as their amplitude and phase frequency responses. a. A low-pass Butterworth filter with the following specifications. i. Pass frequency: 10 kHz ii. Stop frequency: 20 kHz iii. Passband gain: -0.5 dB iv. Stopband gain: -50 dB v. Filter load: 50 Ω

b. A passive high-pass Chebyshev filter with the following specifications. This filter is used to eliminate strong power frequency noise from speech. i. Pass frequency: 300 Hz ii. Stop frequency: 100 Hz iii. Passband gain: -0.05 dB iv. Stopband gain: -80 dB v. Filter load: 75 Ω

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