p3_ap_s3

円錐ホーンのユニバーサルパターン

モジュールのインポート

import numpy as np
import scipy as sp
from scipy.integrate import quad
from scipy.special import jv, yv# ベッセル関数
from scipy.special import jn_zeros, jnp_zeros, jnjnp_zeros, jnyn_zeros# ベッセル関数の零点
import matplotlib.pyplot as plt

import scienceplots
#Warning : As of version 2.0.0, you need to add import scienceplots before setting the style (plt.style.use('science')).
plt.style.use(['science', 'notebook'])

ユーザ関数

可変長引数**kwargsより，複数のキーワード引数を辞書として受け取って積分変数以外の変数を引数とし，可変長引数*argsより，複数の引数をタプルとして受け取るように改良した被積分関数が複素数の場合の数値積分の関数を，

def complex_quadrature2(func, a, b, *args, **kwargs):
    def real_func(x, *args):
        return np.real(func(x, *args))
    def imag_func(x, *args):
        return np.imag(func(x, *args))
    real_integral = quad(real_func, a, b, *args, **kwargs)
    imag_integral = quad(imag_func, a, b, *args, **kwargs)
    return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])

電磁界の複素係数から絶対値，デジベル[dB]，偏角[deg]の計算は，

def dbdeg(z):
    q = 180.0/np.pi
    amp = np.abs(z)
    db = 20.0*np.log10(amp)
    rad = np.angle(z)
    rad = np.unwrap(rad)
    deg = rad*q
    return amp,db,deg

モード関数の正規化係数は，

def func_Amn(imode,m, kai):
    if m==0:
        em = 1
    else:
        em = 2
    if imode==1:
        A = np.abs(jv(m,kai))
        A = A*np.sqrt(kai**2-m**2)
    else:
        A = np.abs(jv(m+1,kai))*kai
    return np.sqrt(em/np.pi)/A

ユニバーサルパターンを求めるための積分項の被積分関数は，

def func_Ii(r, t, u, mpm1, kai):
    return jv(mpm1, kai*r)*jv(mpm1, u*r) * np.exp(-1j*2*np.pi*t*r**2) * r

ユニバーサルパターンは，

def func_N(t, u, phi, imode, kai):
    f0 = complex_quadrature2(func_Ii, 0, 1, args=(t, u, 0, kai))
    f2 = complex_quadrature2(func_Ii, 0, 1, args=(t, u, 2, kai))
    return -imode*f2[0]*np.sin(2*phi), f0[0]+imode*f2[0]*np.cos(2*phi)

遮断特性の計算

TE$_{1n}$モードに対する計算を行い，基本TE$_{11}$モードのみ出力すると，

m=1
kai_TE = jnp_zeros(m ,1) # J_m'(x)=0 for TEmn-mode
kai_TE[0]

1.8411837813406593

同様にして，TM$_{1n}$モードに対する計算を行い，TM$_{11}$モードのみ出力すると，

kai_TM = jn_zeros(m ,1 )# J_m(x)=0 for TMmn-mode
kai_TM[0]

3.8317059702075125

数値積分を実行して，

complex_quadrature2(func_Ii, 0, 1, args=(0, 0, 0, kai_TE[0]))

((0.3160277807019953+0j), (3.5086131855654486e-15,), (0.0,))

tパラメータを，

ttt = np.linspace(0.0, 0.7, 15)
ttt

array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,
       0.55, 0.6 , 0.65, 0.7 ])

基本TE$_{11}$モードの開口面振幅分布による利得低下量を数値積分より求めると，

tmp, eta_0 = func_N(0, 0, 0.0, 1, kai[0])
Amn = func_Amn(1,1, kai)
eta = np.abs(Amn*kai*eta_0)**2*np.pi
10*np.log10(eta) # 開口面振幅分布（TE11モード）によ利得低下量

array([-0.77360222])

あるいは，解析的に求めた式より求め，上の計算値との一致を確認しよう．

10*np.log10(2/(kai**2-1)) # 開口面振幅分布（TE11モード）によ利得低下量

array([-0.77360222])

基本TE$_{11}$モードの開口面振幅分布のもとで，位相分布による利得低下量を求めると，

eta_db = np.empty(len(ttt))
print(f"{'t':>8s} {'eta(t)':>10s}")
for j,t in enumerate(ttt):
    tmp, eta = func_N(t, 0, 0.0, 1, kai[0])
    eta_db[j] = 20*np.log10(np.abs(eta/eta_0))
    print(f"{t:8.2f} {eta_db[j]:10.5f}")

t     eta(t)
0.00    0.00000
0.05   -0.03286
0.10   -0.13167
0.15   -0.29718
0.20   -0.53064
0.25   -0.83388
0.30   -1.20930
0.35   -1.66000
0.40   -2.18984
0.45   -2.80353
0.50   -3.50674
0.55   -4.30616
0.60   -5.20945
0.65   -6.22495
0.70   -7.36062

プロットして，

fig = plt.figure() # グラフ領域の作成
plt.grid(color = "gray", linestyle="--")
plt.plot(ttt, eta_db)
plt.xlim(0.0, 0.7) # x軸範囲の設定
plt.ylim(-10.0, 0.0) # y軸範囲の設定
plt.xlabel(r"$t$") # y軸のラベル設定
plt.ylabel("Gain loss [dB]") # x軸のラベル設定
fig.savefig('p3_ap_s3_1.pdf')

ユニバーサルパターンの変数 $t$，$u$ パラメータは，

tt = np.linspace(0.001, 1.0, 6)
uu = np.linspace(0.0, 20.0, 401)

E面パターンを求めて，

q = 180.0/np.pi
phi = 90.0/q # E面
ff_E = np.empty((len(tt),len(uu)), dtype=complex)
for j,t in enumerate(tt):
    tmp, f0 = func_N(t, 0, phi, 1, kai[0])
    for i,u in enumerate(uu):
        tmp, ff_E[j,i] = func_N(t, u, phi, 1, kai[0])
        ff_E[j,i] = ff_E[j,i]/f0
amp_E, db_E, deg_E = dbdeg(ff_E)

E面のユニバーサルパターンをプロットすると，

fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 4)) # グラフ領域の作成，nrows=縦に並べる数，ncols=横に並べる数

for j,t in enumerate(tt):
    ax[0].plot(uu/np.pi, db_E[j,:], label=r"$t=$"+f"{t:.1f}")
ax[0].set_ylim(-50.0, 10.0) # y軸範囲の設定
ax[0].set_ylabel("Relative power [dB]") # x軸のラベル設定
ax[0].legend(ncol=1, loc='lower left', fancybox=False, frameon = True, fontsize=10)

for j,t in enumerate(tt):
    ax[1].plot(uu/np.pi, deg_E[j,:], label=r"$t=$"+f"{t:.1f}")
ax[1].set_ylim(0.0, 900.0) # y軸範囲の設定
ax[1].set_ylabel("Relative phase [deg]") # x軸のラベル設定
ax[1].set_yticks(np.arange(0, 900, step=180))
ax[1].legend(ncol=1, loc='lower right', fancybox=False, frameon = True, fontsize=10)

[i.grid(color = "gray", linestyle="--") for i in ax]
[i.set_xlim([0, 5.0]) for i in ax] # 横軸の範囲指定
[i.set_xlabel(r"$u/\pi$ with $u = \frac{\pi D}{\lambda} \sin \theta$") for i in ax] # 横軸のラベル設定

fig.tight_layout()
fig.savefig('p3_ap_s3_2.pdf')
plt.show()

同様にして，H面パターンを求めて，

phi = 0.0/q # H面
ff_H = np.empty((len(tt),len(uu)), dtype=complex)
for j,t in enumerate(tt):
    tmp, f0 = func_N(t, 0, phi, 1, kai[0])
    for i,u in enumerate(uu):
        tmp, ff_H[j,i] = func_N(t, u, phi, 1, kai[0])
        ff_H[j,i] = ff_H[j,i]/f0
amp_H, db_H, deg_H = dbdeg(ff_H)

H面のユニバーサルパターンをプロットすると，

fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 4)) # グラフ領域の作成，nrows=縦に並べる数，ncols=横に並べる数

for j,t in enumerate(tt):
    ax[0].plot(uu/np.pi, db_H[j,:], label=r"$t=$"+f"{t:.1f}")
ax[0].set_ylim(-50.0, 10.0) # y軸範囲の設定
ax[0].set_ylabel("Relative power [dB]") # x軸のラベル設定
ax[0].legend(ncol=1, loc='lower left', fancybox=False, frameon = True, fontsize=10)

for j,t in enumerate(tt):
    ax[1].plot(uu/np.pi, deg_H[j,:], label=r"$t=$"+f"{t:.1f}")
ax[1].set_ylim(0.0, 900.0) # y軸範囲の設定
ax[1].set_ylabel("Relative phase [deg]") # x軸のラベル設定
ax[1].set_yticks(np.arange(0, 900, step=180))
ax[1].legend(ncol=1, loc='lower right', fancybox=False, frameon = True, fontsize=10)

[i.grid(color = "gray", linestyle="--") for i in ax]
[i.set_xlim([0, 5.0]) for i in ax] # 横軸の範囲指定
[i.set_xlabel(r"$u/\pi$ with $u = \frac{\pi D}{\lambda} \sin \theta$") for i in ax] # 横軸のラベル設定

fig.tight_layout()
fig.savefig('p3_ap_s3_3.pdf')
plt.show()

また，45$^\circ$ 面パターンを求めて，

phi = 45.0/q # X-pol.
ff_C = np.empty((len(tt),len(uu)), dtype=complex)
ff_X = np.empty((len(tt),len(uu)), dtype=complex)
for j,t in enumerate(tt):
    tmp, f0 = func_N(t, 0, phi, 1, kai[0])
    for i,u in enumerate(uu):
        ff_X[j,i], ff_C[j,i] = func_N(t, u, phi, 1, kai[0])
        ff_X[j,i], ff_C[j,i] = ff_X[j,i]/f0, ff_C[j,i]/f0
amp_C, db_C, deg_C = dbdeg(ff_C)
amp_X, db_X, deg_X = dbdeg(ff_X)
deg_X[2:5,:] = deg_X[2:5,:]+360.0

45$^\circ$ 面の交差偏波成分のユニバーサルパターンをプロットして，

fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 4)) # グラフ領域の作成，nrows=縦に並べる数，ncols=横に並べる数

for j,t in enumerate(tt):
    ax[0].plot(uu/np.pi, db_X[j,:], label=r"$t=$"+f"{t:.1f}")
ax[0].set_ylim(-50.0, 5.0) # y軸範囲の設定
ax[0].set_ylabel("Relative power [dB]") # x軸のラベル設定
ax[0].legend(ncol=1, loc='lower left', fancybox=False, frameon = True, fontsize=10)

for j,t in enumerate(tt):
    ax[1].plot(uu/np.pi, deg_X[j,:], label=r"$t=$"+f"{t:.1f}")
ax[1].set_ylim(-180.0, 720.0) # y軸範囲の設定
ax[1].set_ylabel("Relative phase [deg]") # x軸のラベル設定
ax[1].set_yticks(np.arange(-180, 720, step=180))
ax[1].legend(ncol=1, loc='lower right', fancybox=False, frameon = True, fontsize=10)

[i.grid(color = "gray", linestyle="--") for i in ax]
[i.set_xlim([0, 5.0]) for i in ax] # 横軸の範囲指定
[i.set_xlabel(r"$u/\pi$ with $u = \frac{\pi D}{\lambda} \sin \theta$") for i in ax] # 横軸のラベル設定

fig.tight_layout()
fig.savefig('p3_ap_s3_4.pdf')
plt.show()

計算値を出力すると，

for j,t in enumerate(tt):
    print(f"{'u':>8s} {'ampE[dB]':>8s} {'phE[deg]':>8s} {'ampH[dB]':>8s} {'phH[deg]':>8s} {'ampX[dB]':>8s} {'phX[deg]':>8s} {'t':>8s}") 
    for i in range(0,len(uu),10):
        print(f"{uu[i]:8.2f} {db_E[j,i]:8.3f} {deg_E[j,i]:8.3f} {db_H[j,i]:8.3f} {deg_H[j,i]:8.3f} {db_X[j,i]:8.3f} {deg_X[j,i]:8.3f} {tt[j]:8.2f}")

    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000    0.000    0.000    0.000     -inf  180.000     0.00
 0.50   -0.273    0.002   -0.174    0.001  -45.134  179.882     0.00
 1.00   -1.109    0.010   -0.702    0.004  -33.496  179.883     0.00
 1.50   -2.570    0.025   -1.599    0.010  -27.135  179.884     0.00
 2.00   -4.781    0.051   -2.895    0.019  -23.110  179.887     0.00
 2.50   -8.009    0.101   -4.641    0.033  -20.520  179.890     0.00
 3.00  -12.916    0.211   -6.919    0.053  -18.984  179.895     0.00
 3.50  -22.102    0.656   -9.872    0.086  -18.329  179.901     0.00
 4.00  -29.621  178.472  -13.780    0.142  -18.501  179.910     0.00
 4.50  -19.769  179.564  -19.311    0.266  -19.537  179.924     0.00
 5.00  -17.652  179.731  -29.077    0.752  -21.608  179.947     0.00
 5.50  -18.120  179.811  -37.110  178.385  -25.176  179.992     0.00
 6.00  -20.703  179.882  -27.764  179.573  -31.815  180.128     0.00
 6.50  -26.496  180.010  -26.106  179.758  -59.240  354.300     0.00
 7.00  -57.406  186.849  -26.993  179.853  -33.277  359.636     0.00
 7.50  -28.858  359.600  -29.938  179.939  -29.381  359.759     0.00
 8.00  -24.633  359.730  -35.961  180.102  -28.568  359.809     0.00
 8.50  -23.841  359.784  -60.281  184.010  -29.732  359.847     0.00
 9.00  -25.270  359.828  -39.766  359.532  -33.104  359.896     0.00
 9.50  -29.383  359.891  -35.670  359.720  -41.166  360.051     0.00
10.00  -41.215  360.217  -35.107  359.797  -47.062  539.385     0.00
10.50  -36.467  539.582  -36.750  359.857  -36.607  539.717     0.00
11.00  -29.858  539.729  -40.971  359.943  -33.747  539.775     0.00
11.50  -28.020  539.774  -51.990  360.332  -33.508  539.807     0.00
12.00  -28.580  539.806  -49.904  539.457  -35.380  539.839     0.00
12.50  -31.542  539.845  -42.972  539.704  -40.276  539.896     0.00
13.00  -39.317  539.958  -41.217  539.774  -59.471  540.714     0.00
13.50  -44.979  719.485  -41.892  539.821  -43.299  719.682     0.00
14.00  -34.400  719.724  -44.903  539.876  -38.153  719.759     0.00
14.50  -31.476  719.768  -52.280  540.025  -36.739  719.790     0.00
15.00  -31.262  719.794  -61.375  719.192  -37.558  719.814     0.00
15.50  -33.321  719.821  -49.280  719.688  -40.848  719.847     0.00
16.00  -38.939  719.879  -46.293  719.760  -49.824  719.968     0.00
16.50  -63.111  898.285  -46.120  719.801  -50.992  899.613     0.00
17.00  -38.793  899.716  -48.188  719.841  -42.278  899.747     0.00
17.50  -34.574  899.764  -53.559  719.921  -39.669  899.780     0.00
18.00  -33.602  899.787  -84.186  724.230  -39.597  899.800     0.00
18.50  -34.888  899.808  -55.269  899.667  -41.782  899.823     0.00
19.00  -39.073  899.843  -50.796  899.751  -47.701  899.875     0.00
19.50  -53.387  900.109  -49.797  899.788  -65.226 1079.161     0.00
20.00  -43.500 1079.699  -51.063  899.820  -46.483 1079.735     0.00
    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000    0.000    0.000    0.000     -inf  180.000     0.20
 0.50   -0.266    0.496   -0.173    0.220  -44.871  156.030     0.20
 1.00   -1.077    2.080   -0.698    0.899  -33.237  156.213     0.20
 1.50   -2.472    5.087   -1.587    2.108  -26.880  156.530     0.20
 2.00   -4.520   10.281   -2.866    3.978  -22.863  157.005     0.20
 2.50   -7.294   19.343   -4.573    6.755  -20.281  157.675     0.20
 3.00  -10.713   35.910   -6.762   10.880  -18.756  158.603     0.20
 3.50  -13.819   64.863   -9.503   17.202  -18.115  159.895     0.20
 4.00  -14.732   99.043  -12.850   27.429  -18.300  161.745     0.20
 4.50  -14.348  122.823  -16.667   44.887  -19.343  164.536     0.20
 5.00  -14.512  137.397  -20.039   73.079  -21.388  169.153     0.20
 5.50  -15.828  148.322  -21.516  105.168  -24.756  178.100     0.20
 6.00  -18.600  160.052  -21.871  128.741  -29.873  200.806     0.20
 6.50  -23.309  180.682  -22.640  144.417  -33.047  259.246     0.20
 7.00  -28.046  235.270  -24.404  157.033  -29.764  300.408     0.20
 7.50  -25.267  288.361  -27.414  171.112  -27.623  315.448     0.20
 8.00  -22.791  307.643  -31.800  194.358  -27.332  323.581     0.20
 8.50  -22.438  317.661  -35.543  240.916  -28.692  330.439     0.20
 9.00  -23.981  326.032  -34.505  286.365  -32.007  339.881     0.20
 9.50  -27.833  338.019  -33.081  308.393  -38.430  365.247     0.20
10.00  -35.207  376.391  -33.234  321.201  -40.650  451.006     0.20
10.50  -33.360  462.972  -35.043  332.309  -34.984  485.101     0.20
11.00  -28.563  485.983  -38.794  347.770  -32.669  495.456     0.20
11.50  -27.006  494.786  -44.544  385.699  -32.595  501.643     0.20
12.00  -27.636  501.082  -44.406  453.994  -34.500  507.804     0.20
12.50  -30.520  508.738  -40.963  482.783  -39.138  518.954     0.20
13.00  -37.236  528.712  -39.808  495.275  -48.316  575.915     0.20
13.50  -40.716  631.551  -40.634  504.314  -41.630  658.066     0.20
14.00  -33.307  664.872  -43.498  514.991  -37.203  671.854     0.20
14.50  -30.629  673.422  -49.243  538.699  -35.935  677.825     0.20
15.00  -30.471  678.612  -52.828  617.198  -36.794  682.586     0.20
15.50  -32.507  684.043  -47.506  659.194  -40.022  689.135     0.20
16.00  -37.810  695.068  -45.127  672.206  -47.900  710.574     0.20
16.50  -47.754  779.096  -45.095  680.062  -48.628  826.966     0.20
17.00  -37.753  843.150  -47.125  688.022  -41.388  849.386     0.20
17.50  -33.809  852.465  -51.933  702.626  -38.931  855.688     0.20
18.00  -32.890  857.109  -59.524  766.707  -38.898  859.775     0.20
18.50  -34.173  861.309  -53.482  835.140  -41.070  864.336     0.20
19.00  -38.245  868.180  -49.759  850.090  -46.741  874.477     0.20
19.50  -49.210  906.038  -48.904  857.409  -56.756  973.958     0.20
20.00  -42.388 1019.981  -50.173  863.791  -45.591 1026.821     0.20
    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000   -0.000    0.000   -0.000     -inf  180.000     0.40
 0.50   -0.241    1.043   -0.170    0.474  -44.023  130.363     0.40
 1.00   -0.960    4.335   -0.681    1.941  -32.398  130.727     0.40
 1.50   -2.136   10.388   -1.539    4.536  -26.055  131.361     0.40
 2.00   -3.685   20.078   -2.748    8.518  -22.060  132.313     0.40
 2.50   -5.387   34.366   -4.308   14.305  -19.507  133.661     0.40
 3.00   -6.835   53.055   -6.190   22.527  -18.019  135.537     0.40
 3.50   -7.707   73.304   -8.302   33.984  -17.421  138.169     0.40
 4.00   -8.187   91.492  -10.433   49.273  -17.651  141.966     0.40
 4.50   -8.772  106.598  -12.274   67.809  -18.720  147.735     0.40
 5.00   -9.845  119.902  -13.651   87.236  -20.681  157.224     0.40
 5.50  -11.623  133.669  -14.749  105.106  -23.475  174.426     0.40
 6.00  -14.169  151.259  -15.936  120.869  -26.071  205.591     0.40
 6.50  -17.064  177.813  -17.500  135.642  -26.140  243.003     0.40
 7.00  -18.689  214.117  -19.575  151.404  -24.764  267.979     0.40
 7.50  -18.366  245.850  -22.102  170.821  -24.024  282.911     0.40
 8.00  -17.935  266.710  -24.614  196.510  -24.409  294.063     0.40
 8.50  -18.462  281.850  -26.218  226.798  -26.041  305.526     0.40
 9.00  -20.258  296.450  -26.790  254.137  -29.077  322.426     0.40
 9.50  -23.496  316.900  -27.276  275.253  -32.969  356.685     0.40
10.00  -27.235  356.396  -28.391  292.712  -33.298  408.446     0.40
10.50  -26.891  407.552  -30.405  310.472  -30.844  439.011     0.40
11.00  -24.678  435.728  -33.271  333.742  -29.583  454.386     0.40
11.50  -23.868  451.018  -35.976  368.663  -29.908  465.284     0.40
12.00  -24.721  462.993  -36.486  408.239  -31.883  476.903     0.40
12.50  -27.409  477.489  -35.767  436.358  -35.867  496.922     0.40
13.00  -32.208  507.377  -35.722  455.117  -40.246  549.104     0.40
13.50  -33.885  573.356  -36.894  470.954  -37.343  604.305     0.40
14.00  -30.011  611.439  -39.424  489.611  -34.354  625.148     0.40
14.50  -27.997  626.862  -42.986  520.488  -33.479  636.100     0.40
15.00  -28.016  636.984  -44.530  569.358  -34.453  645.317     0.40
15.50  -29.995  647.629  -42.820  606.336  -37.510  657.943     0.40
16.00  -34.527  667.306  -41.647  626.532  -43.330  690.659     0.40
16.50  -39.563  731.909  -41.976  640.857  -43.538  768.667     0.40
17.00  -34.668  787.770  -43.914  655.692  -38.699  799.516     0.40
17.50  -31.441  804.533  -47.589  679.339  -36.655  811.197     0.40
18.00  -30.682  813.636  -50.969  729.121  -36.743  819.189     0.40
18.50  -31.963  821.961  -48.926  778.500  -38.876  828.170     0.40
19.00  -35.723  835.080  -46.646  801.353  -43.906  846.765     0.40
19.50  -42.870  881.160  -46.165  814.878  -49.264  922.003     0.40
20.00  -39.201  962.346  -47.451  827.104  -42.920  974.407     0.40
    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000   -0.000    0.000   -0.000     -inf  180.000     0.60
 0.50   -0.177    1.706   -0.156    0.825  -42.350   99.974     0.60
 1.00   -0.672    6.932   -0.621    3.363  -30.741  100.515     0.60
 1.50   -1.368   15.858   -1.376    7.790  -24.427  101.459     0.60
 2.00   -2.068   28.284   -2.382   14.385  -20.473  102.884     0.60
 2.50   -2.569   43.048   -3.565   23.440  -17.977  104.918     0.60
 3.00   -2.834   58.213   -4.803   35.063  -16.562  107.780     0.60
 3.50   -3.033   72.312   -5.953   48.860  -16.054  111.850     0.60
 4.00   -3.413   85.136   -6.924   63.811  -16.380  117.822     0.60
 4.50   -4.157   97.451   -7.752   78.719  -17.508  127.034     0.60
 5.00   -5.361  110.571   -8.577   92.910  -19.317  142.059     0.60
 5.50   -7.006  126.248   -9.558  106.495  -21.193  166.416     0.60
 6.00   -8.859  146.431  -10.802  120.167  -21.756  197.769     0.60
 6.50  -10.362  171.516  -12.340  134.950  -20.880  224.287     0.60
 7.00  -11.050  197.635  -14.097  151.971  -19.981  242.392     0.60
 7.50  -11.267  220.000  -15.861  171.962  -19.811  255.866     0.60
 8.00  -11.704  238.194  -17.342  194.275  -20.562  268.356     0.60
 8.50  -12.781  254.646  -18.429  216.667  -22.274  283.266     0.60
 9.00  -14.652  272.740  -19.345  237.218  -24.749  305.509     0.60
 9.50  -17.124  297.132  -20.432  255.931  -26.724  339.940     0.60
10.00  -19.072  331.411  -21.917  274.321  -26.422  376.251     0.60
10.50  -19.146  366.719  -23.825  294.664  -25.250  400.807     0.60
11.00  -18.491  392.132  -25.888  319.315  -24.827  417.139     0.60
11.50  -18.516  410.222  -27.476  348.338  -25.555  430.924     0.60
12.00  -19.675  426.334  -28.210  377.046  -27.554  446.909     0.60
12.50  -22.100  446.018  -28.609  401.185  -30.694  472.641     0.60
13.00  -25.297  478.534  -29.367  421.461  -32.797  517.060     0.60
13.50  -26.207  525.915  -30.821  441.017  -31.290  557.628     0.60
14.00  -24.425  560.236  -32.967  463.906  -29.573  579.883     0.60
14.50  -23.288  579.733  -35.212  494.447  -29.211  594.194     0.60
15.00  -23.606  594.095  -36.226  530.569  -30.352  607.251     0.60
15.50  -25.520  609.449  -35.970  561.210  -33.151  625.089     0.60
16.00  -29.133  634.721  -35.845  583.631  -37.138  661.563     0.60
16.50  -31.943  686.656  -36.601  602.252  -37.071  718.346     0.60
17.00  -29.471  733.202  -38.428  622.097  -34.080  749.628     0.60
17.50  -27.183  754.690  -41.083  649.582  -32.612  765.178     0.60
18.00  -26.696  767.850  -42.941  689.672  -32.891  776.702     0.60
18.50  -27.986  780.144  -42.359  728.119  -34.969  789.835     0.60
19.00  -31.308  798.515  -41.344  753.361  -39.167  814.531     0.60
19.50  -35.982  843.707  -41.349  771.369  -42.164  875.262     0.60
20.00  -34.042  905.958  -42.667  788.456  -38.362  921.633     0.60
    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000    0.000    0.000    0.000     -inf  180.000     0.80
 0.50    0.008    2.380   -0.097    1.360  -39.396   57.559     0.80
 1.00    0.085    9.116   -0.368    5.436  -27.814   58.250     0.80
 1.50    0.324   18.968   -0.750   12.163  -21.548   59.465     0.80
 2.00    0.740   30.160   -1.155   21.265  -17.664   61.312     0.80
 2.50    1.207   41.239   -1.497   32.123  -15.267   63.984     0.80
 3.00    1.541   51.674   -1.748   43.861  -13.983   67.815     0.80
 3.50    1.592   61.727   -1.954   55.678  -13.644   73.405     0.80
 4.00    1.274   72.100   -2.212   67.173  -14.170   81.893     0.80
 4.50    0.566   83.725   -2.619   78.398  -15.445   95.453     0.80
 5.00   -0.469   97.683   -3.243   89.730  -17.009  117.405     0.80
 5.50   -1.644  114.892   -4.110  101.726  -17.635  147.606     0.80
 6.00   -2.647  135.226   -5.195  114.999  -16.718  175.877     0.80
 6.50   -3.244  156.677   -6.419  130.064  -15.450  195.987     0.80
 7.00   -3.554  176.676   -7.649  147.052  -14.740  210.672     0.80
 7.50   -3.930  194.382   -8.755  165.426  -14.831  223.538     0.80
 8.00   -4.668  210.785   -9.703  184.119  -15.737  237.496     0.80
 8.50   -5.899  227.787  -10.589  202.248  -17.325  255.701     0.80
 9.00   -7.556  247.777  -11.573  219.711  -19.025  281.475     0.80
 9.50   -9.240  272.834  -12.774  237.171  -19.680  313.046     0.80
10.00  -10.254  301.654  -14.215  255.726  -19.115  340.813     0.80
10.50  -10.454  328.529  -15.785  276.460  -18.498  361.141     0.80
11.00  -10.535  350.375  -17.239  299.648  -18.573  377.204     0.80
11.50  -11.127  368.883  -18.353  323.939  -19.563  392.837     0.80
12.00  -12.490  387.399  -19.180  347.170  -21.457  412.215     0.80
12.50  -14.575  410.194  -20.017  368.432  -23.709  440.817     0.80
13.00  -16.641  441.801  -21.140  388.612  -24.593  478.364     0.80
13.50  -17.196  478.425  -22.651  409.635  -23.681  510.080     0.80
14.00  -16.534  507.681  -24.405  433.695  -22.821  531.291     0.80
14.50  -16.202  528.449  -25.941  461.704  -22.934  547.412     0.80
15.00  -16.871  545.797  -26.806  490.906  -24.229  563.496     0.80
15.50  -18.713  564.915  -27.203  517.046  -26.694  585.384     0.80
16.00  -21.473  593.077  -27.742  539.382  -29.293  621.877     0.80
16.50  -23.129  636.020  -28.820  560.206  -29.084  666.000     0.80
17.00  -21.941  674.678  -30.511  582.892  -27.309  694.899     0.80
17.50  -20.593  698.171  -32.450  611.038  -26.444  712.656     0.80
18.00  -20.469  714.614  -33.687  644.737  -26.960  727.112     0.80
18.50  -21.792  730.512  -33.779  676.555  -28.963  743.939     0.80
19.00  -24.627  752.929  -33.642  701.618  -32.306  772.479     0.80
19.50  -27.716  794.933  -34.109  722.298  -33.990  823.011     0.80
20.00  -26.715  844.767  -35.462  742.899  -31.651  863.158     0.80
    u ampE[dB] phE[deg] ampH[dB] phH[deg] ampX[dB] phX[deg]        t
 0.00    0.000   -0.000    0.000   -0.000     -inf -180.000     1.00
 0.50    0.358    0.599    0.113    1.157  -36.301  -18.195     1.00
 1.00    1.285    2.264    0.434    4.389  -24.759  -17.433     1.00
 1.50    2.458    4.778    0.904    9.123  -18.562  -16.085     1.00
 2.00    3.574    8.075    1.432   14.751  -14.784  -14.011     1.00
 2.50    4.438   12.281    1.918   20.870  -12.541  -10.959     1.00
 3.00    4.947   17.681    2.273   27.348  -11.479   -6.458     1.00
 3.50    5.069   24.699    2.434   34.265  -11.457    0.415     1.00
 4.00    4.830   33.891    2.367   41.843  -12.414   11.601     1.00
 4.50    4.323   45.850    2.061   50.385  -14.108   31.118     1.00
 5.00    3.732   60.879    1.537   60.221  -15.302   63.167     1.00
 5.50    3.284   78.376    0.846   71.644  -14.267   97.884     1.00
 6.00    3.095   96.654    0.066   84.777  -12.247  121.784     1.00
 6.50    3.056  114.021   -0.712   99.433  -10.773  137.664     1.00
 7.00    2.927  129.966   -1.425  115.066  -10.169  150.566     1.00
 7.50    2.511  145.140   -2.080  130.997  -10.406  163.718     1.00
 8.00    1.722  160.799   -2.747  146.787  -11.347  179.816     1.00
 8.50    0.603  178.437   -3.514  162.448  -12.615  201.559     1.00
 9.00   -0.626  199.281   -4.445  178.396  -13.400  229.265     1.00
 9.50   -1.594  223.068   -5.542  195.255  -13.142  257.100     1.00
10.00   -2.083  247.213   -6.738  213.579  -12.445  279.504     1.00
10.50   -2.322  269.040   -7.906  233.490  -12.100  297.150     1.00
11.00   -2.731  288.301   -8.931  254.386  -12.448  313.024     1.00
11.50   -3.591  306.641   -9.806  275.222  -13.542  330.264     1.00
12.00   -4.966  326.520  -10.655  295.310  -15.174  352.363     1.00
12.50   -6.621  350.638  -11.631  314.817  -16.571  381.755     1.00
13.00   -7.904  379.821  -12.825  334.623  -16.745  413.679     1.00
13.50   -8.271  409.556  -14.202  355.880  -16.118  439.705     1.00
14.00   -8.179  434.556  -15.583  379.346  -15.778  459.388     1.00
14.50   -8.407  455.012  -16.720  404.470  -16.236  476.427     1.00
15.00   -9.354  474.070  -17.535  429.352  -17.608  494.849     1.00
15.50  -11.076  495.740  -18.235  452.492  -19.666  519.565     1.00
16.00  -13.117  524.725  -19.112  474.111  -21.248  554.339     1.00
16.50  -14.128  561.035  -20.332  495.755  -20.957  590.249     1.00
17.00  -13.635  593.492  -21.839  519.463  -19.937  616.208     1.00
17.50  -13.056  616.971  -23.304  546.602  -19.593  634.860     1.00
18.00  -13.322  635.602  -24.272  575.817  -20.339  651.547     1.00
18.50  -14.688  654.445  -24.717  603.337  -22.236  671.449     1.00
19.00  -17.048  679.621  -25.124  627.355  -24.790  701.988     1.00
19.50  -19.104  718.000  -25.930  649.272  -25.694  744.965     1.00
20.00  -18.626  759.140  -27.285  671.944  -24.232  779.713     1.00