自制LORA平板定向天线

4个月28天前修改于 4个月28天前 IP:上海

操作

今天做了个简单测试 (之前仪器的校正堵头被猫叼不知道哪里去了今天才在冰箱下面找到这个理由不错吧) 然后发现与前面计算的误差较大检查程序发现程序中k0_h式子错了然后重新推导修改

import scipy.integrate
import numpy
from matplotlib import pyplot

z0=50 
wa=367
epsilon_eff=1.2
compress=0.2 # h/l
ratio_from=0
ratio_to=0.5
ratio_show=(ratio_from+ratio_to)/2
match=None

if False:
	def match(z):
		#@outport: C/parallel, @antenna: L/series, L=5.71213169610197e-09, C=2.113795485039202e-11
		L=5.71213169610197e-09
		C=2.113795485039202e-11
		f=434.e6
		w=2.j*numpy.pi*f
		z=z+w*L
		z=1/(w*C+1/z)
		return z

#############################################

ratio=numpy.linspace(ratio_from+0.001, ratio_to-0.001, 1001)
k1_l=ratio*2*numpy.pi 
# k1*l=k0*sqrt(epsilon_eff)*l -> k0*h=k1*l/sqrt(epsilon_eff)/l*h=k1_l/sqrt(epsilon_eff)*compress
k0_h=k1_l/numpy.sqrt(epsilon_eff)*compress
f=lambda theta, k1l, k0h:	(((numpy.cos(k0h*numpy.cos(theta))-numpy.cos(k1l))/(((k0h*numpy.cos(theta))**2)-(k1l**2)))**2)*(numpy.sin(theta)**3)
r_sigma=numpy.vectorize(
	lambda k1l, k0h: 60*((k1l*k0h)**2)*scipy.integrate.quad(f, 0, numpy.pi, args=(k1l, k0h))[0], 
	otypes=[float]
)(k1_l, k0_h)
r1_l=4*k1_l*r_sigma/(2*k1_l-numpy.sin(2*k1_l))
beta_a_l=r1_l/2/wa
t=wa/(numpy.cosh(2*beta_a_l)-numpy.cos(2*k1_l))
z=((numpy.sinh(2*beta_a_l)-beta_a_l/k1_l*numpy.sin(2*k1_l))-1j*(numpy.sin(2*k1_l)+beta_a_l/k1_l*numpy.sinh(2*beta_a_l)))*t

# with matching network
if match:
	z=match(z)

print('At {}λ, RΣ={}, Z={}'.format(
	ratio_show, 
	numpy.interp(ratio_show, ratio, r_sigma),
	numpy.interp(ratio_show, ratio, z)))

fig, ax1=pyplot.subplots()
fig.subplots_adjust(right=0.6)
ax1.set_title('Input impedance of antenna')
ax1.set_xlabel('l/λ')
ax1.set_ylabel('Impedance (Ω)', color='black')
ax1.set_xlim(ratio_from, ratio_to)
ax1.set_xticks(numpy.linspace(ratio_from, ratio_to, 5))
ax1.grid()
plt1a=ax1.plot(ratio, numpy.real(z), linewidth=1, color='blue', label='Real')
plt1b=ax1.plot(ratio, numpy.imag(z), linewidth=1, color='red', label='Imag')

ax2=ax1.twinx()
ax2.set_ylabel('Phase (°)', color='orange')
ax2.set_ylim(-90, 90)
ax2.grid()
plt2=ax2.plot(ratio, numpy.degrees(numpy.angle(z)), linewidth=1, color='orange', label='Phase')

gamma=(z-z0)/(z+z0)
vswr=(1.+numpy.abs(gamma))/(1.-numpy.abs(gamma))

ax3=ax1.twinx()
ax3.spines['right'].set_position(('outward', 60))
ax3.set_ylabel('VSWR', color='black')
ax3.set_ylim(1, 5)
ax3.grid()
plt3=ax3.plot(ratio, vswr, linewidth=1, color='black', label='VSWR')

ax4=ax1.twinx()
ax4.spines['right'].set_position(('outward', 120))
ax4.set_ylabel('RΣ', color='cyan')
plt4=ax4.plot(ratio, r_sigma, linewidth=1, color='cyan', label='RΣ')

plts = plt1a+plt1b+plt2+plt3+plt4
ax3.legend(plts, [t.get_label() for t in plts], loc='upper right')

pyplot.show()

使用背板远离的参数然后结果居然吻合得不错