new lab
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anna
parent
572f42e895
commit
32acbc6520
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3.6.1Спектр/Data_l.xlsx
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3.6.1Спектр/Laba.py
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3.6.1Спектр/Laba.py
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# -*- coding: utf-8 -*-
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import numpy as np
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import matplotlib.pyplot as plt
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import csv
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from scipy.optimize import curve_fit
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def read_csv(file_name):
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with open(file_name) as file:
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reader = list(csv.reader(file, delimiter=';',
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quotechar=',', quoting=csv.QUOTE_MINIMAL))
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return reader
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def make_latex_table(data):
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table = []
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table.append("\\begin{table}".replace('//', '\\'))
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table.append("\label{}".replace('/', '\\'))
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table.append('\caption{}'.replace('/', '\\'))
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leng = len(data[0])
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stroka = 'c'.join(['|' for _ in range(leng+1)])
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table.append('\\begin{tabular}{'.replace('//', '\\')+stroka+'}')
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table.append('\hline')
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for i in range(len(data)):
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table.append(' & '.join(data[i]) + ' \\\\')
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table.append('\hline')
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table.append("\end{tabular}".replace('/', '\\'))
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table.append("\end{table}".replace('/', '\\'))
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return table
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def make_point_grafic(x, y, xlabel, ylabel, caption, xerr, yerr,
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subplot=None, color=None, center=None, s=15):
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if not subplot:
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subplot = plt
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if type(yerr) == float or type(yerr) == int:
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yerr = [yerr for _ in y]
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if type(xerr) == float or type(xerr) == int:
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xerr = [xerr for _ in x]
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if xerr[1] != 0 or yerr[1] != 0:
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subplot.errorbar(x, y, yerr=yerr, xerr=xerr, linewidth=4,
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linestyle='', label=caption, color=color,
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ecolor=color, elinewidth=1, capsize=3.4,
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capthick=1.4)
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else:
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subplot.scatter(x, y, linewidth=0.005, label=caption,
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color=color, edgecolor='black', s=s)
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# ax = plt.subplots()
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# ax.grid())
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if not center:
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plt.xlabel(xlabel)
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plt.ylabel(ylabel)
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else:
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ax = plt.gca()
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ax.spines['top'].set_visible(False)
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ax.spines['right'].set_visible(False)
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ax.spines['bottom'].set_position('zero')
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ax.spines['left'].set_position('zero')
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ax.set_xlabel(ylabel, labelpad=-180, fontsize=14) # +
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ax.set_ylabel(xlabel, labelpad=-260, rotation=0, fontsize=14)
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def make_line_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, k, b, caption,
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subplot=None, color=None, linestyle='-'):
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if not subplot:
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subplot = plt
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x = np.arange(xmin, xmax, (xmax-xmin)/10000)
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subplot.plot(x, k*x+b, label=caption, color=color, linewidth=1.4,
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linestyle=linestyle)
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def make_graffic(x, y, xlabel, ylabel, caption_point, xerr, yerr, k=None,
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b=None, filename=None, color=None, koef=[0.9, 1.1], s=None):
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if not color:
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color = ['limegreen', 'indigo']
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if not s:
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make_point_grafic(x, y, xlabel=xlabel,
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ylabel=ylabel, caption=caption_point,
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xerr=xerr, yerr=yerr, subplot=plt, color=color[0])
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else:
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make_point_grafic(x, y, xlabel=xlabel,
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ylabel=ylabel, caption=caption_point,
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xerr=xerr, yerr=yerr, subplot=plt, color=color[0], s=s)
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if k and b:
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make_line_grafic(xmin=min(x)-1, xmax=max(x)+1, xerr=xerr, yerr=yerr,
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xlabel='', ylabel='', k=k, b=b,
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caption='Theoretical dependence', subplot=plt,
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color='red')
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if type(yerr) == float or type(yerr) == int:
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yerr = [yerr for _ in y]
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k, b, sigma = approx(x, y, b, yerr)
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sigma[0] = abs(k*((sigma[0]/k)**2+(np.mean(yerr)/np.mean(y))**2 +
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(np.mean(xerr)/np.mean(x))**2)**0.5)
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if (b != 0):
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sigma[1] = abs(b*((sigma[1]/b)**2+(np.mean(yerr)/np.mean(y))**2 +
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(np.mean(xerr)/np.mean(x))**2)**0.5)
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else:
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sigma[1] = 0
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make_line_grafic(xmin=min(x)*koef[0], xmax=max(x)*koef[1], xerr=xerr,
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yerr=yerr, xlabel='', ylabel='', k=k, b=b, caption=None,
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subplot=plt, color=color[1])
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plt.legend()
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return k, b, sigma
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def approx(x, y, b, sigma_y, f=None):
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if sigma_y[0] != 0:
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sigma_y = [1/i**2 for i in sigma_y]
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else:
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sigma_y = np.array([1 for _ in y])
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if f is None:
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if b == 0:
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def f(x, k):
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return k*x
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma = np.sqrt(np.diag(sigma))
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return k, b, [sigma, 0]
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else:
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def f(x, k, b):
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return x*k + b
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma_b = np.sqrt(sigma[1][1])
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b = k[1]
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k = k[0]
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sigma = np.sqrt(sigma[0][0])
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return k, b, [sigma, sigma_b]
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else:
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma = np.sqrt(np.diag(sigma))
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b = k[1]
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k = k[0]
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return k, b, sigma
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def find_delivation(data):
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data = np.array(data).astype(np.float)
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s = sum(data)/len(data)
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su = 0
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for i in data:
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su += (i-s)**2
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return (su/(len(data)-1))**0.5
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def make_dic(filename):
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data = np.array(read_csv(filename))
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data = np.transpose(data)
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dic = {}
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for i in range(len(data)):
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dic[data[i][0]] = np.array(data[i][1:]).astype(np.float)
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data = dic
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return data
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def make_fun(A0, T):
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def f(t, k, b):
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return A0/(1+A0*b*t)-k*0*A0*t/T
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return f
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def make_fun_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, f, k, b, caption,
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subplot=None, color=None):
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if not subplot:
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subplot = plt
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x = np.arange(xmin, xmax, (xmax-xmin)/10000)
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subplot.plot(x, f(x, k, b), label=caption, color=color)
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def make_all():
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part_1_1()
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part_1_2()
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part_2()
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part_3()
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def part_1_1():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("dnu(tau).csv")
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x = 1 / data["tau"]*100
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y = data['d_nu']/10**4
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xlabel = "1/"+greek_letters[48]+'$,10^4$Гц'
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ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц'
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k, b, sigma = make_graffic(x, y, xlabel, ylabel,
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0])
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plt.savefig("dnu(tau)")
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plt.show()
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def part_1_2():
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fig, ax = plt.subplots(figsize=(10, 6))
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data = make_dic("a(n).csv")
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v = 1000
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t = 50 * 10 **- 6
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T = 1 / v
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N = 200
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V0 = 300
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vu = [n/T for n in range(2, N)]
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c = [abs(V0*t/T*np.sin(n*t*np.pi/T)/(n*t*np.pi/T)) for n in range(2, N)]
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for i in range(len(vu)):
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plt.scatter(vu[i], c[i], linewidth=0.005, label='',
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color='purple', s=15)
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ax.vlines(vu[i], 0, c[i], colors='purple')
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ax.set_xlabel(greek_letters[41]+', Hz')
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ax.set_ylabel("$a_n$, мВ")
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plt.savefig("a(n)")
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plt.show()
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def part_2():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("T(dnu).csv")
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x = 1 / data["T"]*10**3
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y = data['dnu']
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xlabel = "1/"+greek_letters[48]+'$, $Гц'
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ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц'
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k, b, sigma = make_graffic(x, y, xlabel, ylabel,
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0], -sigma[0]/k*100)
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plt.savefig("T(dnu)")
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plt.show()
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def part_3():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("a(m).csv")
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otn = data['a_b']/data['a_c']
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k, b, sigma = make_graffic(data['m']/100, otn, 'm', '$а_{бок}/a_{осн}$',
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0])
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plt.savefig("a(m)")
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plt.show()
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greek_letters=[chr(code) for code in range(916,980)]
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print(greek_letters)
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make_all()
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3.6.1Спектр/T(dnu).csv
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3.6.1Спектр/T(dnu).csv
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T;dnu;T_1;dnu_1
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0.2;6250;0.5;125
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1;2778;1;247
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1.5;4167;2;490
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2;1042;3;714
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2.5;1190;4;892
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3;735;4;892
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3.5;893;4;892
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4;1000;4;892
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4.5;1042;4;892
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5;1190;4;892
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3.6.1Спектр/T(dnu).png
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3.6.1Спектр/T(dnu).png
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3.6.1Спектр/a(m).csv
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3.6.1Спектр/a(m).csv
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m;a_b;a_c
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50;186;738
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10;38;738
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20;74;738
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30;110;738
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40;150;738
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60;222;738
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70;258;738
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80;298;738
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90;334;738
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100;370;738
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3.6.1Спектр/a(m).png
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3.6.1Спектр/a(m).png
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3.6.1Спектр/a(n).csv
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3.6.1Спектр/a(n).csv
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a;nu;n
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90;8200;2
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53;7800;3
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39;7200;4
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30;7800;5
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24;6400;6
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21;6200;7
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3.6.1Спектр/a(n).png
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3.6.1Спектр/a(n).png
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3.6.1Спектр/dnu(tau).csv
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3.6.1Спектр/dnu(tau).csv
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d_nu;tau
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50200;20
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25200;40
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17200;60
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13000;80
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10200;100
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8600;120
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7400;140
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6600;160
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5800;180
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5000;200
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3.6.1Спектр/dnu(tau).png
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3.6.1Спектр/dnu(tau).png
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3.6.1Спектр/rect.png
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3.6.1Спектр/rect.png
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|[]\T2A/cmr/bx/n/14.4 Èññëåäîâàíèå ñïåê-òðà ãàð-ìî-íè-÷å-ñêèõ ñèã-íà-ëîâ, ìî-äó
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\author{Анна Назарчук Б02-109}
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\title{3.6.1 Спектральный анализ электрических сигналов}
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\date{}
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\begin{document}
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\maketitle
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\section{Аннотация}
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В работе исследуются спектры периодических сигналов: модулированный по амплитуде, прямоугольные импульсы и цуги. Проверяются теоретические зависимости параметров спектра на практике.
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\section{Введение}
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Задача описания поведения некоторой системы во времени зачастую
|
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сводится к выяснению связи между "сигналом", подаваемым на "вход"
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системы (обозначим его как $f(t)$), и её реакцией на "выходе" $g(t)$). Если произвольную функцию $f(t)$ удастся представить в виде
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некоторой суммы ряда (конечного или бесконечного) гармонических
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слагаемых, то при известной частотной характеристике $\lambda(\omega)$) задача
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о связи воздействия и отклика системы будет решена. Такое разложение
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называют спектральным. Оно имеет физический смысл: высоко добротный колебательный контур выделяет из подаваемого на него сигнала те спектральные компоненты, частоты которых близки к его собственной. Возможность разложить произвольную функцию $f(t)$ в ряд (или интеграл)
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Фурье единственным и однозначным способом подразумевает и
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возможность "собрать" сигнал любой формы, используя гармонические
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колебания с подобранными амплитудами и фазами. В последнее время повсеместное распространение получила цифровая
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обработка сигналов. Спектральный состав оцифрованного сигнала
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может быть найден численно. Это и планируется проследить в работе.
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\section{Поставка задачи}
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Сгенерировать и получить на осциллографе спектры различных периодических сигналов. Проверить экспериментально соотношение неопределенности и отношения амплитуд гармоник при модулированных по амплитуде сигналах.
|
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\section{Теоретические сведения}
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Задача описания поведения некоторой системы во времени зачастую
|
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сводится к выяснению связи межу «сигналом», подаваемым на «вход»
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системы (обозначим его как $f(t)$), и её реакцией на «выходе» ($g(t)$).
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Для линейных стационарных фильтров: $g = \hat{\Lambda}[f]$, $\hat{\Lambda}$ - линейное преобразование. Из линейности системы: $f=\sum c_nf_n$, $g_n = c_n \cdot \hat{\Lambda}[f_n]$
|
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\begin{equation}
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g(t) = \sum c_n \hat{\Lambda}[f_n]
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\end{equation}
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Выбор элементарных слагаемых - собственные векторы.
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|
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\end{equation}
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Такое представление - ряд Фурье.
|
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\subsection*{Спект периодического процесса}
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|
Периодический процесс - $f(t)=f(t+T)$
|
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\begin{equation}
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f(t) = \sum_{n=-\inf}^{\inf} c_n e^{in\omega_0 t}
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|
\end{equation}
|
||||||
|
Набор коэффициентов можно найти, домножив обе части прошлого равенства на $e^{-im\omega_0 t}$ и проинтегрировав по периоду:
|
||||||
|
\begin{equation}
|
||||||
|
c_n = \frac{1}{T}\int_0^T f(t)e^{-in\omega_0 t}dt
|
||||||
|
\end{equation}
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\includegraphics[width=0.4\textwidth]{rect}
|
||||||
|
\caption{Периодическая последовательность прямоугольных импульсов} \label{rect}
|
||||||
|
\end{figure}
|
||||||
|
Рассмотрим спектр периодической последовательности прямоугольных импульсов (рис. \ref{rect}):
|
||||||
|
\begin{equation}
|
||||||
|
c_n = \frac{1}{T}\int_{-\tau / 2}^{\tau / 2} e^{-in\omega_0 t}dt = \dfrac{sin(\pi n \tau / T))}{\pi n}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
\subsection*{Свойства спектров}
|
||||||
|
Справедливо для произвольного сигнала соотношение неопределенностей:
|
||||||
|
\begin{equation}
|
||||||
|
\Delta \omega \cdot \Delta t \sim 2\pi
|
||||||
|
\end{equation}
|
||||||
|
Рассмотрим спектр обрывка синусоиды (цуг):
|
||||||
|
\begin{equation}
|
||||||
|
f(t) = f_0(t)\cos(\omega_0 t)
|
||||||
|
\end{equation}
|
||||||
|
Из спектра прямоугольного импульса:
|
||||||
|
\begin{equation}
|
||||||
|
F(\omega) = \dfrac{\tau}{2}\left[\dfrac{\sin(\omega-\omega_0)\tau /2}
|
||||||
|
{(\omega-\omega_0)\tau /2}
|
||||||
|
+ \dfrac{\sin(\omega+\omega_0)\tau /2}{\omega+\omega_0)\tau /2}\right]
|
||||||
|
\end{equation}
|
||||||
|
Получим спектр периодической последовательности цугов (рис. \ref{цуги}):
|
||||||
|
\begin{equation}
|
||||||
|
F(\omega) = \dfrac{\tau}{2T}\left[\dfrac{\sin(\omega-\omega_0)\tau /2}
|
||||||
|
{(\omega-\omega_0)\tau /2}
|
||||||
|
+ \dfrac{\sin(\omega+\omega_0)\tau /2}{(\omega+\omega_0)\tau /2}\right]
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=0.4\textwidth]{цуги}
|
||||||
|
\caption{Периодическая последовательность цуг} \label{цуги}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
\subsection*{Модуляция}
|
||||||
|
Модулированные колебания:
|
||||||
|
\begin{equation}
|
||||||
|
f(t) = a(t) \cos (\omega_0 t+\varphi(t))
|
||||||
|
\end{equation}
|
||||||
|
Простейшее амплитудно-модулированное колебание:
|
||||||
|
\begin{equation}
|
||||||
|
f(t)= a(t) \cos (\omega_0 t), \hspace{3mm} a(t) = a_0(1+m\cos(\Omega t))
|
||||||
|
\end{equation}
|
||||||
|
В выражении $0 < m \leq 1$ - глубина модуляции, выражается:
|
||||||
|
\begin{equation}
|
||||||
|
m = \dfrac{a_{max}-a_{min}}{a_{max}+a_{min}}
|
||||||
|
\end{equation}
|
||||||
|
Из прошлой формулы можно получить:
|
||||||
|
\begin{equation}
|
||||||
|
f(t) = a_0 \cos (\omega_0 t) +\dfrac{ma_0}{2}\cos (\omega_0 +\Omega)t++\dfrac{ma_0}{2}\cos (\omega_0 -\Omega)t
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
\section{Методика измерений}
|
||||||
|
В работе используются генератор сигналов произвольной формы, цифровой осциллограф с функцией быстрого преобразования Фурье.
|
||||||
|
|
||||||
|
\section{Измерения и обработка данных}
|
||||||
|
\subsection*{Исследования спектра периодической последовательности прямоугольных импульсов}
|
||||||
|
На генераторе создается сигнал с разными параметрами, по которому на экране осциллографа получается спектр (рис. \ref{прямоуг})
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{1_1}} a) $\nu_{повт} = 1000 Гц, \tau = 50 мкс$\\
|
||||||
|
\end{minipage}
|
||||||
|
\hfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{1_2}} \\b) $\nu_{повт} = 1400 Гц, \tau = 50 мкс$
|
||||||
|
\end{minipage}
|
||||||
|
\vfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{1_3}} c) $\nu_{повт} = 700 Гц, \tau = 50 мкс$ \\
|
||||||
|
\end{minipage}
|
||||||
|
\hfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{1_4}} d) $\nu_{повт} = 1000 Гц, \tau = 70 мкс$ \\
|
||||||
|
\end{minipage}
|
||||||
|
\caption{Спектры прямоугольных импульсов}
|
||||||
|
\label{прямоуг}
|
||||||
|
\end{figure}
|
||||||
|
При $\nu_{повт} = 700 Гц$ проведены измерения ширины спектра. Результаты
|
||||||
|
представлены в таблице \ref{dnu(tau)_tbl} и на рисунке \ref{dnu(tau)_img}.
|
||||||
|
\begin{table}[h!]
|
||||||
|
\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_tbl}
|
||||||
|
\begin{tabular}{|l|l|}
|
||||||
|
\hline
|
||||||
|
$\Delta\nu$, Hz & $\tau$, мкс \\ \hline
|
||||||
|
50200 & 20 \\ \hline
|
||||||
|
25200 & 40 \\ \hline
|
||||||
|
17200 & 60 \\ \hline
|
||||||
|
13000 & 80 \\ \hline
|
||||||
|
10200 & 100 \\ \hline
|
||||||
|
8600 & 120 \\ \hline
|
||||||
|
7400 & 140 \\ \hline
|
||||||
|
6600 & 160 \\ \hline
|
||||||
|
5800 & 180 \\ \hline
|
||||||
|
5000 & 200 \\ \hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=\textwidth]{dnu(tau)}
|
||||||
|
\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_img}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
Рассчитаем коэффициент наклона прямой:
|
||||||
|
\begin{equation}
|
||||||
|
k = 0.9997 \pm 0.0039
|
||||||
|
\end{equation}
|
||||||
|
Полученное значение близко к $1$, что подтверждает соотношение неопределенностей.
|
||||||
|
|
||||||
|
|
||||||
|
Для одного из сигналов (a) рассчитаем теоретическую зависимость и изобразим на графике \ref{теор}. Теоретический и экспериментальный спектр похожи.
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=\textwidth]{a(n)}
|
||||||
|
\caption{Теоретический спектр прямоугольных импульсов} \label{теор}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\subsection{Исследование спектра периодической последовательности цугов гармонических колебаний}
|
||||||
|
На генераторе создается сигнал последовательности синусоидальных цугов с разными параметрами, по которому на экране осциллографа получается спектр. (рис. \ref{спектр_цуги})
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{2_1}} a) $\nu = 50 кГц, T = 1 мс, N = 5$\\
|
||||||
|
\end{minipage}
|
||||||
|
\hfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{2_2}} \\b) $\nu = 50 кГц, T = 1 мс, N = 3$
|
||||||
|
\end{minipage}
|
||||||
|
\vfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{2_3}} c) $\nu = 50 кГц, T = 3 мс, N = 5$ \\
|
||||||
|
\end{minipage}
|
||||||
|
\hfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{2_4}} d) $\nu = 30 кГц, T = 1 мс, N = 5$ \\
|
||||||
|
\end{minipage}
|
||||||
|
\vfill
|
||||||
|
\begin{minipage}[h!]{0.47\linewidth}
|
||||||
|
\center{\includegraphics[width=1\linewidth]{2_5}} \\e) $\nu = 70 кГц, T = 1 мс, N = 5$
|
||||||
|
\end{minipage}
|
||||||
|
\caption{Вид спектра при разных параметрах спектра}
|
||||||
|
\label{спектр_цуги}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
При фиксированной длительности импульсов $\tau$ = 50 мкс измерим расстояния между соседними спектральными компонентами от периода повторения импульсов (табл. \ref{dnu(T)_tbl}, рис. \ref{dnu(T)_img})
|
||||||
|
|
||||||
|
\begin{table}[h!]
|
||||||
|
\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_tbl}
|
||||||
|
\begin{tabular}{|l|l|}
|
||||||
|
\hline
|
||||||
|
T, ms & $\delta \nu$, Hz \\ \hline
|
||||||
|
0.2 & 6250 \\ \hline
|
||||||
|
1 & 2778 \\ \hline
|
||||||
|
1.5 & 4167 \\ \hline
|
||||||
|
2 & 1042 \\ \hline
|
||||||
|
2.5 & 1190 \\ \hline
|
||||||
|
3 & 735 \\ \hline
|
||||||
|
3.5 & 893 \\ \hline
|
||||||
|
4 & 1000 \\ \hline
|
||||||
|
4.5 & 1042 \\ \hline
|
||||||
|
5 & 1190 \\ \hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=0.9\textwidth]{T(dnu)}
|
||||||
|
\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_img}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
Точки должны хорошо ложиться на прямую, однако из графика видно, что это не так. Проблема заключается в снятии данных (был выбран неверный канал при курсорных измерениях). Поэтому подтвердить справедливость соотношения неопределенности невозможно.
|
||||||
|
|
||||||
|
\subsection{Исследование спектра гармонических сигналов, модулированных по амплитуде}
|
||||||
|
На генераторе создается сигнал, модулированных по амплитуде, по которому на экране осциллографа получается спектр (\ref{мод}).
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=\textwidth]{3}
|
||||||
|
\caption{Спектр сигнала, модулированного по амплитуде} \label{мод}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
Измерим с помощью осциллографа глубину модуляции:
|
||||||
|
\begin{equation}
|
||||||
|
m = \dfrac{A_{max}-A_{min}}{A_{max}+A_{min}} = \dfrac{1.54 - 0.04}{1.54 + 0.04} = 0.5, что сходится с установленным на генераторе
|
||||||
|
\end{equation}
|
||||||
|
Изменяя глубину модуляции, измерим $\dfrac{a_{бок}}{а_{осн}}$ (табл. \ref{mod_tbl} и рис. \ref{mod_img}).
|
||||||
|
|
||||||
|
\begin{table}[h!]
|
||||||
|
\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$}
|
||||||
|
\label{mod_tbl}
|
||||||
|
\begin{tabular}{|l|l|l|}
|
||||||
|
\hline
|
||||||
|
m & a\_бок & a\_центр \\ \hline
|
||||||
|
50 & 186 & 738 \\ \hline
|
||||||
|
10 & 38 & 738 \\ \hline
|
||||||
|
20 & 74 & 738 \\ \hline
|
||||||
|
30 & 110 & 738 \\ \hline
|
||||||
|
40 & 150 & 738 \\ \hline
|
||||||
|
60 & 222 & 738 \\ \hline
|
||||||
|
70 & 258 & 738 \\ \hline
|
||||||
|
80 & 298 & 738 \\ \hline
|
||||||
|
90 & 334 & 738 \\ \hline
|
||||||
|
100 & 370 & 738 \\ \hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
\begin{figure}[h!]
|
||||||
|
\begin{center}
|
||||||
|
\includegraphics[width=0.9\textwidth]{a(m)}
|
||||||
|
\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$} \label{mod_img}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
Определим коэффициент наклона прямой:
|
||||||
|
\begin{equation}
|
||||||
|
k = 0.502 \pm 0.002
|
||||||
|
\end{equation}
|
||||||
|
Результат сходится с предсказанным теоретически (0.5).
|
||||||
|
|
||||||
|
\section{Выводы}
|
||||||
|
|
||||||
|
|
||||||
|
1. При исследовании последовательности прямоугольных импульсов получена зависимость ширины спектра от длительности импульса, что подтверждает соотношение неопределенностей: $\tau \cdot \Delta\nu \sim 1$.
|
||||||
|
|
||||||
|
2. Проверены теоретические расчеты спектра при прямоугольных импульсах (теоретическая и экспериментальная картины схожи).
|
||||||
|
|
||||||
|
3. При обработке данных от спектра периодической последовательности цугов была обнаружена ошибка при снятии данных, что не позволило проверить соотношение неопределенностей.
|
||||||
|
|
||||||
|
4. Получен угол наклона графика зависимости $\dfrac{a_{бок}}{а_{осн}}$ от $m$ (0.5), подтверждено теоретическое значение этого угла (0.5).
|
||||||
|
|
||||||
|
\end{document}
|
||||||
BIN
3.6.1Спектр/Цуги.png
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BIN
3.6.1Спектр/Цуги.png
Normal file
Binary file not shown.
|
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Reference in New Issue
Block a user