Decibels. Engineers often measure the ratio of two power measurements in decibels, or \(\mathrm{dB}\). The equation for the ratio of two power measurements in decibels is $$ \mathrm{dB}=10 \log _{10} \frac{P_{2}}{P_{1}} $$ where \(P_{2}\) is the power level being measured, and \(P_{1}\) is some reference power level. a. Assume that the reference power level \(P_{1}\) is I milliwatt, and write a program that accepts an input power \(P_{2}\) and converts it into \(\mathrm{dB}\) with respect to the \(1 \mathrm{~mW}\) reference level. (Engineers have a special unit for dB power levels with respect to a \(1 \mathrm{~mW}\) reference: \(\mathrm{dBm}\).) Use good programming practices in your program. b. Write a program that creates a plot of power in watts versus power in \(\mathrm{dBm}\) with respect to a \(1 \mathrm{~mW}\) reference level. Create both a linear \(x y\) plot and a log-linear \(x y\) plot.

To calculate the power ratio in decibels (dB) with reference level P1 as 1 milliwatt, use the formula \( dBm = 10 * \log_{10}(P_2/1\,\text{mW}) \). Write a Python program to accept an input power P2, calculate the dBm, and create a linear xy plot and a log-linear xy plot of power in watts versus power in dBm. ```python import math import numpy as np import matplotlib.pyplot as plt def calculate_dBm(P2_mW): dBm = 10 * math.log10(P2_mW / 1) return dBm def create_plots(): P2_W = np.linspace(0.001, 10, 1000) P2_mW = P2_W * 1000 dBm = 10 * np.log10(P2_mW) plt.figure() plt.plot(P2_W, dBm) plt.xlabel("Power (W)") plt.ylabel("Power (dBm)") plt.title("Linear xy Plot: Power (W) vs Power (dBm)") plt.grid() plt.figure() plt.semilogx(P2_W, dBm) plt.xlabel("Power (W)") plt.ylabel("Power (dBm)") plt.title("Log-linear xy Plot: Power (W) vs Power (dBm)") plt.grid() plt.show() P2_mW = float(input("Enter the P2 power in mW: ")) dBm = calculate_dBm(P2_mW) print("The dBm value is:", dBm) create_plots() ```