微带贴片天线-微带线馈电

模型如下：

设计参数同http://www.cnblogs.com/hiramlee0534/p/6283543.html基板参数er = 2.55, H = 1.59mm, 导体为PEC，厚度为0，频率为3GHz, 使用公式计算得到辐射边W=37.503mm。长度与谐振频率有关，使用微带线馈电，连接在辐射一端。计算好天线阻抗，输入端为50 欧姆微带线，中间是1/4波长阻抗变换微带线。计算设计初值 如下

 1 def msa_coax_synthesis(self):
 2         #er =  float(self.lineEdit_ms_er.text()) # relative dielectric constant
 3         h = float(self.lineEdit_ms_H.text())/1.0e3 # substrate thickness
 4         #w = float(self.lineEdit_ms_W.text())/1.0e3 # conductor width
 5         #l = float(self.lineEdit_ms_L.text())/1.0e3 # conductor length
 6         er =  float(self.lineEdit_ms_er.text()) # relative dielectric constant
 7         mur =  float(self.lineEdit_ms_mur.text()) # relative permeability
 8         fc =  float(self.lineEdit_msa_coax_fc.text())*1e6 # frequency in Hz
 9         rough = float(self.lineEdit_ms_rough.text())/1.0e3
10         tand = float(self.lineEdit_ms_loss_tangent.text()) # loss tangent of the dielectric
11         cond = float(self.lineEdit_ms_conductivity.text())
12         mu = mur*4*math.pi*1.0e-7
13         Rc = float(self.lineEdit_msa_coax_Rin.text())
14         t = float(self.lineEdit_ms_T.text())/1.0e3
15         lambda0= self.c/fc #m
16         msa_w = self.c/2.0/fc*math.sqrt(2.0/(er+1.0)) # patch width  m
17         U = msa_w/h # ratio of trace width to substrate thickness
18         if t > 0:
19             T = t/h #ratio of conductor thickness to substrate thickness
20         #(T/PI)*log(1.0 + 4.0*exp(1.0)/(T*pow(coth(sqrt(6.517*u)),2.0)))
21             U1 = U +(T*math.log(1.0+4.0*math.e/T/math.pow(1.0/math.tanh(math.sqrt(6.517*U)),2.0)))/math.pi # from Hammerstad and Jensen
22         #   0.5*(1.0 + 1.0/cosh(sqrt(er-1.0)))*deltau1
23             Ur = U +(U1-U)*(1.0+1.0/(math.cosh(math.sqrt(er-1))))/2.0 # from Hammerstad and Jensen
24         else:
25             U1 = U
26             Ur = U
27 #        Y = self.ee_HandJ(Ur,er)
28 #        Z0 =self.z0_HandJ(Ur)/math.sqrt(Y)
29 #        #ereff0 = Y*math.pow(Z01_U1/Z01_Ur,2)
30 #        ereff0 = Y*math.pow(self.z0_HandJ(U1)/self.z0_HandJ(Ur),2.0)
31         if t > 0:
32             W1 = msa_w +(t/math.pi)*(1+math.log(4.0/math.sqrt(math.pow(t/h,2)+math.pow(1.0/math.pi,2)/math.pow(msa_w/t+1.1,2))))
33         else:
34             W1 = msa_w
35         F = 6.0 + (2.0*math.pi-6.0)*math.exp(-4*math.pow(math.pi,2)/3.0*math.pow(h/W1,0.75))
36         We = 2*math.pi*h/math.log(h*F/W1+math.sqrt(1+math.pow(2*h/W1,2)))
37         A = 1.0 + (1.0/49.0)*math.log((math.pow(U,4.0) + math.pow((U/52.0),2.0))/(math.pow(U,4.0) + 0.432))38             + (1.0/18.7)*math.log(1.0 + math.pow((U/18.1),3.0))
39         #Ber = 0.564*math.pow((er-0.9)/(er+3),0.053)
40         B = 0.564*math.exp(-0.2/(er+0.3))
41         #Y = (er+1.0)/2.0+(er-1.0)/2.0*math.pow(1+10.0/Ur,-(A*B))
42         G= math.pow((1.0 + 10.0/U),(-A*B))-math.log(4)*t/math.pi/math.sqrt(msa_w*h)
43         ereff0 = 0.5*(er+1.0+(er-1.0)*G)
44         fn = fc/1e9*h*1e3
45         u = (msa_w+(W1-msa_w))/h
46         P1 = 0.27488 + (0.6315 + (0.525 / (math.pow((1 + 0.0157*fn),20))) )*u - 0.65683*math.exp(-8.7513*u)
47         P2 = 0.33622*(1 - math.exp(-0.03442*er))
48         P3 = 0.0363*math.exp(-4.6*u)*(1 - math.exp(-math.pow((fn / 38.7),4.97)))
49         P4 = 1 + 2.751*( 1 -  math.exp(-math.pow((er/15.916),8)))
50         P = P1*P2*math.pow(((0.1844 + P3*P4)*fn),1.5763)
51         ereff = (er*P+ereff0)/(1+P) # equavlent ralative dielectric constant
52         #ereff = (er+1.0)/2.0+(er-1.0)/2.0*math.pow(1+12/U,-0.5)
53         A1 = 0.434907*(math.pow(ereff,0.81)+0.26)/(math.pow(ereff,0.81)-0.189)54            *(math.pow(U,0.8544)+0.236)/(math.pow(U,0.8544)+0.87)
55         A2 = 1+ math.pow(U,0.371)/(2.358*er+1)
56         A3 = 1 + 0.5274*math.atan(0.084*math.pow(U,1.9413/A2))/math.pow(ereff,0.9236)
57         A4 = 1 + 0.0377*math.atan(0.067*math.pow(U,1.456))*(6-5*math.exp(0.036*(1-er)))
58         A5 = 1 - 0.218*math.exp(-7.5*U)
59         deltaL = h*A1*A3*A5/A4
60         #deltaL = h*0.412*(ereff+0.3)*(U+0.264)/(ereff-0.258)/(U+0.8)#mm
61         lambda_eff = self.c/fc/math.sqrt(ereff)#mm
62         msa_l = lambda_eff/2-2*deltaL #patch length mm
63         k0 = 2.0*math.pi/(lambda0)
64         keff = k0*math.sqrt(ereff)
65
66         Sw = math.pow(self.c,2)/(4*math.pow(fc,2)*(ereff-1))
67         Pw =math.pow(msa_w/3.0,3)+(Sw/2.0)*(We-msa_w/3.0)
68         Qw = Sw/3.0 -math.pow(msa_w/3.0,2)
69         Rw = math.sqrt(math.pow(Pw,2)+math.pow(Qw,2))
70         W2 = We
71         We = msa_w/3.0+math.pow(Rw+Pw,1.0/3.0)-math.pow(Rw-Pw,1.0/3.0)
72         Rr = math.pow(k0*We,2)/6.0/(60+math.pow(k0*We,2))
73         Gr = 1.0/Rr
74
75         l = keff*(msa_l+deltaL)
76         p = keff*deltaL
77         Fg = special.j0(l)+math.pow(p,2)/(24-math.pow(p,2))*special.jn(2,l)
78         Gm = Gr*Fg
79         Re = 1.0/(2*(Gr))
80         G1 = msa_w/120.0/lambda0*(1-math.pow(k0*h,2)/24)
81         G12 = integrate.quad(lambda x: 1.0/120.0/math.pow(math.pi,2)*math.pow(math.sin(k0*msa_w/2.0*math.cos(x))/math.cos(x),2)*special.j0(math.sin(x)*msa_l*k0)*math.pow(math.sin(x),3), 0, math.pi)
82         #Re = 1.0/2.0/(G1)
83         Re = 1.0/2.0/(G1-G12[0])
84 #        shift = msa_l/math.pi*math.asin(math.sqrt(Rc/Re))
85         self.lineEdit_msa_coax_w.setText(str(msa_w*1.0e3))
86         self.lineEdit_msa_coax_l.setText(str(msa_l*1e3))
87         self.label.setText(str(‘ lambda_eff = ‘)+str(lambda_eff*1.0e3))
88         self.label_test.setText(str(‘ Re = ‘)+str(Re))
89         self.label_test_2.setText(str(‘ ereff = ‘)+str(ereff))
90         self.label_test_3.setText(str(‘ deltaL = ‘)+str(deltaL*1.0e3))
91         self.label_test_4.setText(str(‘ We = ‘)+str(We*1.0e3))
92         self.label_2.setText(str(‘ W1 = ‘)+str(W1))

优化后参数如下

得到仿真结果：

S11

VSWR

输入阻抗

三维方向图

E面和H面方向图