12. Blindagem
Compatibilidade Eletromagnética
12. Blindagem
Blindagem é a redução do acoplamento eletromagnético por uma barreira. Seu desempenho depende do campo incidente, material, espessura, frequência, geometria e, sobretudo, de aberturas e junções. Uma caixa metálica não corrige automaticamente uma fonte ou caminho de retorno mal projetado.
12.1 Eficácia de blindagem
12.1.1 Os três mecanismos de blindagem
A eficácia pode ser expressa por campo elétrico, magnético ou potência:
$$
SE_E=20\log_{10}\frac{|E_i|}{|E_t|},\qquad
SE_H=20\log_{10}\frac{|H_i|}{|H_t|},
$$
$$
SE_P=10\log_{10}\frac{P_i}{P_t}.
$$
É essencial declarar a grandeza, posição e configuração. Em uma parede plana ideal, costuma-se decompor
$$
SE\approx R+A+B,
$$
onde $R$ é perda por reflexão, $A$ por absorção e $B$ corrige múltiplas reflexões internas.
Insight para Estudantes: A reflexão ($R$) domina para campos elétricos e ondas de campo distante porque há grande descasamento de impedância entre o ar ($377\ \Omega$) e o metal ($\approx0\ \Omega$). A absorção ($A$) domina para campos magnéticos de baixa frequência e materiais de alta permeabilidade. As aberturas e fendas frequentemente tornam $SE$ muito menor que $R+A+B$.
12.2 Fontes de campo distante
No campo distante, a onda apresenta impedância aproximadamente igual à do meio. A reflexão resulta do grande descasamento entre ar e material condutor. A absorção cresce com a espessura $t$ em relação à profundidade pelicular:
$$
\delta=\sqrt{\frac{2}{\omega\mu\sigma}},\qquad
A_{dB}=8{,}686\frac{t}{\delta}.
$$
Boa condutividade favorece reflexão; alta permeabilidade e espessura favorecem absorção magnética. Quando $A$ é grande, múltiplas reflexões internas tornam-se desprezíveis.
12.2.1 Prova da perda por absorção
$$
|E(z)|=|E(0)|e^{-z/\delta}.
$$
Portanto, a perda por absorção de uma espessura $t$ é
$$
A_{dB}=20\log_{10}(e^{t/\delta})=8{,}686\frac{t}{\delta}.
$$
12.3 Campo próximo elétrico e magnético
No campo próximo, a impedância da onda depende da fonte. Uma fonte predominantemente elétrica tem alta $|E/H|$ e costuma ser bem atenuada por materiais condutores finos. Uma fonte magnética de baixa frequência tem baixa $|E/H|$; reflexão é menor e a profundidade pelicular é grande, tornando a blindagem mais difícil.
A primeira mitigação para campo magnético próximo é reduzir área de laço, aproximar ida e retorno e aumentar distância. Se uma blindagem for necessária, materiais de alta permeabilidade desviam fluxo em baixa frequência; materiais condutores espessos produzem correntes opostas quando a frequência permite.
12.4 Aberturas e descontinuidades
O desempenho real geralmente é limitado por fendas, ventilação, displays, portas, parafusos e penetrações de cabos. A maior dimensão da abertura importa mais que sua área total. Uma fenda longa pode irradiar como antena mesmo sendo estreita.
Medidas práticas:
- usar muitas aberturas pequenas em vez de uma longa;
- reduzir espaçamento entre pontos de contato;
- manter continuidade elétrica em juntas, removendo tinta isolante onde apropriado;
- usar gaxetas compatíveis com material, ambiente e corrosão;
- empregar estruturas abaixo do corte, como colmeias ou guias, quando necessário;
- filtrar condutores ao atravessar a fronteira da blindagem.
12.5 Cabos e conectores
A blindagem do cabo deve ser tratada como continuação da envolvente. Uma terminação circunferencial de 360° apresenta baixa indutância. Pigtails acrescentam aproximadamente $j\omega L$ e podem anular o benefício em alta frequência. Filtros e protetores devem ficar na penetração, evitando que corrente externa circule no interior antes de ser desviada.
12.6 Ressonâncias de cavidade
Uma envolvente condutora pode sustentar modos ressonantes. Fontes internas e aberturas posicionadas em máximos de campo podem produzir acoplamento intenso. Absorvedores, mudanças geométricas, amortecimento, reposicionamento da fonte e redução da energia excitada podem ser mais eficazes que simplesmente aumentar a espessura da parede.
12.7 Blindagem como problema de sistema
Uma estratégia consistente define uma fronteira EMC:
- onde correntes externas devem circular;
- onde cabos cruzam a fronteira;
- como suas blindagens são terminadas;
- onde filtros e supressores desviam corrente;
- como portas, juntas e ventilação mantêm continuidade;
- quais fontes internas ainda precisam ser reduzidas.
12.8 Exemplo resolvido — Absorção
Para $t=100$ µm e $\delta=20$ µm:
$$
A=8{,}686\frac{100}{20}=43{,}43\ \text{dB}.
$$
Esse resultado é da parede contínua ideal. Uma fenda pode limitar o gabinete a valor muito inferior.
12.9 Exemplo resolvido — Indutância de pigtail
Um pigtail apresenta 30 nH. A 100 MHz,
$$
|Z|=2\pi fL=2\pi(10^8)(30\times10^{-9})=18{,}85\ \Omega.
$$
Uma conexão circunferencial curta pode reduzir essa impedância em ordens de grandeza, evitando que tensão de modo comum se desenvolva entre blindagem e chassi.
12.10 Insight: o ponto fraco domina
Se a parede oferece 80 dB, mas a penetração de cabo oferece 25 dB, o sistema não oferece 105 dB nem uma média próxima de 52 dB. O caminho de menor atenuação tende a dominar. A eficácia total deve ser avaliada como rede de caminhos paralelos de acoplamento.
12.11 Baixa frequência magnética
Para campos quase estáticos, reflexão em metal comum pode ser pequena. Há três estratégias distintas:
- reduzir o campo na fonte diminuindo área de laço e $di/dt$;
- aumentar distância;
- desviar fluxo com material de alta permeabilidade sem saturá-lo.
Dobras, folgas e saturação local degradam materiais de alta permeabilidade. Propriedades após conformação podem diferir das propriedades de catálogo.
12.12 Lista de Exercícios Propostos
E.1 Um material tem profundidade pelicular de 20 µm na frequência de interesse e espessura de 100 µm. Estime a perda por absorção.
E.2 Explique por que uma fenda longa é problemática mesmo com pequena área.
E.3 Compare blindagem de campo elétrico próximo e campo magnético próximo em baixa frequência.
E.4 Por que um pigtail degrada a terminação de um cabo em RF?
E.5 Defina uma fronteira EMC para um equipamento com alimentação, Ethernet e ventilação.
E.6 Calcule a reatância de uma conexão de 10 nH a 30 MHz e 300 MHz.
E.7 Uma parede ideal oferece 60 dB. Uma alteração dobra sua espessura em unidades de $\delta$. Quantos dB de absorção são acrescentados?
E.8 Explique por que tinta, oxidação e poucos parafusos podem transformar uma junta curta em fenda eletricamente longa.
12.13 Gabarito
E.1 Perda por absorção para material com profundidade pelicular de 20 µm e espessura de 100 µm.
Equação: $A=8{,}686\times(t/\delta)$.
Com $t=100$ µm e $\delta=20$ µm: $t/\delta=100/20=5$.
$A=8{,}686\times5=43{,}43$ dB.
Resposta: $A=43{,}43$ dB.
E.6 Reatância de conexão de 10 nH a 30 MHz e 300 MHz.
Equação: $X_L=2\pi f L$.
Para $f=30$ MHz: $X_{30\text{MHz}}=2\pi(3\times10^7)(10\times10^{-9})=2\pi\times0{,}3=1{,}88\ \Omega$.
Para $f=300$ MHz: $X_{300\text{MHz}}=2\pi(3\times10^8)(10\times10^{-9})=2\pi\times3=18{,}85\ \Omega$.
Resposta: $X_{30\text{MHz}}=1{,}88\ \Omega$; $X_{300\text{MHz}}=18{,}85\ \Omega$.
E.7 Acréscimo de absorção quando espessura dobra em unidades de $\delta$.
Cada profundidade pelicular adicional acrescenta 8,686 dB de absorção.
Se a espessura dobra em unidades de $\delta$ (ou seja, aumenta de $n\delta$ para $(n+1)\delta$), o acréscimo é 8,686 dB.
Resposta: O acréscimo de uma profundidade pelicular adicional acrescenta 8,686 dB de absorção.
12.14 Exemplo numérico adicional — Eficácia de blindagem vs. espessura
Material: cobre, $\sigma=5.8\times10^7$ S/m, $\mu_r=1$.
Frequência: $f=100$ MHz.
Profundidade pelicular: $\delta=\sqrt{2/(\omega\mu\sigma)}$
$\omega=2\pi\cdot10^8$, $\mu=4\pi\times10^{-7}$.
$\delta=\sqrt{2/(2\pi\cdot10^8\cdot4\pi\times10^{-7}\cdot5.8\times10^7)}$
$=\sqrt{2/(4.58\times10^9)}=\sqrt{4.37\times10^{-10}}=2.09\times10^{-5}$ m $=20.9$ µm.
Para $t=100$ µm: $t/\delta=4.78$.
$A_{dB}=8.686\cdot4.78=41.5$ dB.
12.15 Código Python — Eficácia de blindagem por absorção vs. frequência
PYTHON
import numpy as np
import matplotlib.pyplot as plt
# Parâmetros do material (cobre)
sigma = 5.8e7 # Condutividade (S/m)
mu_r = 1.0
mu_0 = 4 * np.pi * 1e-7
# Faixa de frequência
f = np.logspace(6, 9, 100) # 1 MHz a 1 GHz
w = 2 * np.pi * f
# Profundidade pelicular
delta = np.sqrt(2 / (w * mu_0 * mu_r * sigma))
# Espessura da blindagem
t = 100e-6 # 100 µm
# Eficácia de absorção (dB)
# A_dB = 8.686 * t / delta
A_dB = 8.686 * t / delta
plt.figure(figsize=(8, 5))
plt.semilogx(f, A_dB, 'b-', linewidth=2)
plt.xlabel('Frequência (Hz)')
plt.ylabel('Eficácia de Absorção (dB)')
plt.title('Eficácia de Blindagem por Absorção vs Frequência (Cobre, t=100µm)')
plt.grid(True, which='both', linestyle='--')
plt.show()
12.16 Exemplo numérico adicional — Eficácia total de blindagem com aberturas
Problema: Uma parede oferece $SE=80$ dB, mas uma penetração de cabo oferece $SE=25$ dB. Qual é a eficácia total aproximada do sistema?
Solução:
A eficácia total não é a média nem a soma. O caminho de menor atenuação domina. Neste caso, a penetração de cabo com $SE=25$ dB torna-se o ponto fraco.
Eficácia total aproximada: $SE_{total}\approx25$ dB (do caminho mais fraco).
Insight para Estudantes: Em blindagem, o sistema é tão forte quanto seu ponto mais fraco. Uma fenda de 1 cm pode reduzir uma blindagem de 80 dB para 20 dB. Sempre identifique e trate aberturas, penetrções de cabos, e juntas antes de otimizar a espessura da parede.
12.17 Ressonâncias de cavidade retangular
Para uma cavidade ideal de dimensões $a$, $b$ e $d$, as frequências modais são
$$
f_{mnp}=\frac{c}{2}\sqrt{\left(\frac ma\right)^2+
\left(\frac nb\right)^2+\left(\frac pd\right)^2},
$$
com combinações permitidas conforme o modo TE ou TM. Uma caixa de $30\times20\times10$ cm possui escala modal mais baixa próxima de $c/(2a)\approx500$ MHz. Perdas, conteúdo interno e aberturas deslocam e amortecem os picos.
12.17.1 Código Python — mapa dos modos inferiores
PYTHON
import itertools
import numpy as np
c = 299_792_458.0
a, b, d = 0.30, 0.20, 0.10
modes = []
for m, n, p in itertools.product(range(4), repeat=3):
if (m, n, p) == (0, 0, 0):
continue
f = c/2*np.sqrt((m/a)**2 + (n/b)**2 + (p/d)**2)
modes.append((f, m, n, p))
for f, m, n, p in sorted(modes)[:10]:
print(f'({m}{n}{p}): {f/1e6:7.1f} MHz')
Output:
(100): 499.7 MHz (010): 749.5 MHz (110): 900.8 MHz (200): 999.3 MHz (210): 1249.1 MHz (001): 1499.0 MHz (020): 1499.0 MHz (300): 1499.0 MHz (101): 1580.0 MHz (120): 1580.0 MHz
12.18 Aberturas: limite dominante
Uma abertura estreita de maior dimensão $l\ll\lambda$ pode ser triada por uma atenuação que cresce quando $\lambda/l$ cresce. Equações empíricas como $SE\approx20\log_{10}(\lambda/2l)$ dependem de geometria, incidência e regime; não devem ser usadas como prova de conformidade.
12.18.1 Exemplo numérico — material excelente, abertura dominante
Uma folha de cobre pode oferecer absorção ideal superior a 100 dB em alta frequência, enquanto uma fenda de 10 cm em 1 GHz tem $l/\lambda\approx0{,}33$ e já não é eletricamente pequena. Somar “100 dB do material” a uma expressão de abertura é incorreto: os caminhos estão em paralelo e o vazamento dominante limita o conjunto.
12.19 Código Python — absorção, abertura e limite do conjunto
PYTHON
import numpy as np
import matplotlib.pyplot as plt
mu0 = 4*np.pi*1e-7
sigma = 5.8e7
t = 0.5e-3
l = 20e-3
f = np.logspace(4, 10, 800)
delta = np.sqrt(2/(2*np.pi*f*mu0*sigma))
A = 8.686*t/delta
lam = 299_792_458/f
SE_ap = 20*np.log10(np.maximum(lam/(2*l), 1.0))
# Caminhos de vazamento em paralelo: somar transmissões de potência
T_material = 10**(-A/10)
T_aperture = 10**(-SE_ap/10)
SE_total = -10*np.log10(T_material + T_aperture)
plt.semilogx(f, A, label='absorção da folha')
plt.semilogx(f, SE_ap, label='triagem da abertura')
plt.semilogx(f, SE_total, lw=2.5, label='limite combinado')
plt.ylim(-3, 180); plt.xlabel('Frequência (Hz)'); plt.ylabel('SE (dB)')
plt.grid(True, which='both', alpha=.3); plt.legend(); plt.tight_layout()
12.20 Campo magnético de baixa frequência
Para campos magnéticos próximos, alta condutividade e pequena espessura podem ser insuficientes porque a absorção é pequena e a impedância da onda é baixa. Materiais de alta permeabilidade desviam fluxo, mas saturação, juntas e degradação por conformação devem entrar no modelo. Compare sempre densidade de fluxo máxima com a curva $B$–$H$ do material.
12.21 Laboratório SPICE — ressonâncias de cavidade
Uma cavidade retangular pode ser modelada como um circuito RLC ressonante para cada modo. Para o modo fundamental, a impedância de entrada perto da ressonância é
$$
Z_{in}=R+ j\omega L + \frac{1}{j\omega C},
$$
onde $R$ modela as perdas por condução nas paredes e por cargas internas.
SPICE
* Modelagem de cavidade ressonante como circuito RLC
Lcav 1 2 10n
Ccav 2 0 100p
Rloss 2 0 50
Vin 1 0 AC 1
.ac dec 200 10k 1G
.meas ac f_res MAX vm(2)
.print ac vm(2) vp(2)
.end
Output:
Note: vin: has no value, DC 0 assumed
Warning: can't parse 'vm': ignored
Circuit: generated from textbook spice code block
Doing analysis at TEMP = 27.000000 and TNOM = 27.000000
Using SPARSE 1.3 as Direct Linear Solver
No. of Data Rows : 1001
Measurements for AC Analysis
f_res = 5.01764e+00 at= 1.56675e+08
generated from textbook spice code block
AC Analysis Tue Aug 11 11:11:03 2026
--------------------------------------------------------------------------------Ver mais (1054 linhas)
Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 0 1.000000e+04 1.000000e+00 -1.25664e-05 1 1.011579e+04 1.000000e+00 -1.27119e-05 2 1.023293e+04 1.000000e+00 -1.28591e-05 3 1.035142e+04 1.000000e+00 -1.30080e-05 4 1.047129e+04 1.000000e+00 -1.31586e-05 5 1.059254e+04 1.000000e+00 -1.33110e-05 6 1.071519e+04 1.000000e+00 -1.34651e-05 7 1.083927e+04 1.000000e+00 -1.36210e-05 8 1.096478e+04 1.000000e+00 -1.37788e-05 9 1.109175e+04 1.000000e+00 -1.39383e-05 10 1.122018e+04 1.000000e+00 -1.40997e-05 11 1.135011e+04 1.000000e+00 -1.42630e-05 12 1.148154e+04 1.000000e+00 -1.44281e-05 13 1.161449e+04 1.000000e+00 -1.45952e-05 14 1.174898e+04 1.000000e+00 -1.47642e-05 15 1.188502e+04 1.000000e+00 -1.49352e-05 16 1.202264e+04 1.000000e+00 -1.51081e-05 17 1.216186e+04 1.000000e+00 -1.52830e-05 18 1.230269e+04 1.000000e+00 -1.54600e-05 19 1.244515e+04 1.000000e+00 -1.56390e-05 20 1.258925e+04 1.000000e+00 -1.58201e-05 21 1.273503e+04 1.000000e+00 -1.60033e-05 22 1.288250e+04 1.000000e+00 -1.61886e-05 23 1.303167e+04 1.000000e+00 -1.63761e-05 24 1.318257e+04 1.000000e+00 -1.65657e-05 25 1.333521e+04 1.000000e+00 -1.67575e-05 26 1.348963e+04 1.000000e+00 -1.69516e-05 27 1.364583e+04 1.000000e+00 -1.71479e-05 28 1.380384e+04 1.000000e+00 -1.73464e-05 29 1.396368e+04 1.000000e+00 -1.75473e-05 30 1.412538e+04 1.000000e+00 -1.77505e-05 31 1.428894e+04 1.000000e+00 -1.79560e-05 32 1.445440e+04 1.000000e+00 -1.81639e-05 33 1.462177e+04 1.000000e+00 -1.83743e-05 34 1.479108e+04 1.000000e+00 -1.85870e-05 35 1.496236e+04 1.000000e+00 -1.88023e-05 36 1.513561e+04 1.000000e+00 -1.90200e-05 37 1.531087e+04 1.000000e+00 -1.92402e-05 38 1.548817e+04 1.000000e+00 -1.94630e-05 39 1.566751e+04 1.000000e+00 -1.96884e-05 40 1.584893e+04 1.000000e+00 -1.99164e-05 41 1.603245e+04 1.000000e+00 -2.01470e-05 42 1.621810e+04 1.000000e+00 -2.03803e-05 43 1.640590e+04 1.000000e+00 -2.06163e-05 44 1.659587e+04 1.000000e+00 -2.08550e-05 45 1.678804e+04 1.000000e+00 -2.10965e-05 46 1.698244e+04 1.000000e+00 -2.13408e-05 47 1.717908e+04 1.000000e+00 -2.15879e-05 48 1.737801e+04 1.000000e+00 -2.18378e-05 49 1.757924e+04 1.000000e+00 -2.20907e-05 50 1.778279e+04 1.000000e+00 -2.23465e-05 51 1.798871e+04 1.000000e+00 -2.26053e-05 52 1.819701e+04 1.000000e+00 -2.28670e-05 53 1.840772e+04 1.000000e+00 -2.31318e-05 54 1.862087e+04 1.000000e+00 -2.33997e-05 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 55 1.883649e+04 1.000000e+00 -2.36706e-05 56 1.905461e+04 1.000000e+00 -2.39447e-05 57 1.927525e+04 1.000000e+00 -2.42220e-05 58 1.949845e+04 1.000000e+00 -2.45025e-05 59 1.972423e+04 1.000000e+00 -2.47862e-05 60 1.995262e+04 1.000000e+00 -2.50732e-05 61 2.018366e+04 1.000000e+00 -2.53635e-05 62 2.041738e+04 1.000000e+00 -2.56572e-05 63 2.065380e+04 1.000000e+00 -2.59543e-05 64 2.089296e+04 1.000000e+00 -2.62549e-05 65 2.113489e+04 1.000000e+00 -2.65589e-05 66 2.137962e+04 1.000000e+00 -2.68664e-05 67 2.162719e+04 1.000000e+00 -2.71775e-05 68 2.187762e+04 1.000000e+00 -2.74922e-05 69 2.213095e+04 1.000000e+00 -2.78106e-05 70 2.238721e+04 1.000000e+00 -2.81326e-05 71 2.264644e+04 1.000000e+00 -2.84584e-05 72 2.290868e+04 1.000000e+00 -2.87879e-05 73 2.317395e+04 1.000000e+00 -2.91212e-05 74 2.344229e+04 1.000000e+00 -2.94584e-05 75 2.371374e+04 1.000000e+00 -2.97996e-05 76 2.398833e+04 1.000000e+00 -3.01446e-05 77 2.426610e+04 1.000000e+00 -3.04937e-05 78 2.454709e+04 1.000000e+00 -3.08468e-05 79 2.483133e+04 1.000000e+00 -3.12040e-05 80 2.511886e+04 1.000000e+00 -3.15653e-05 81 2.540973e+04 1.000000e+00 -3.19308e-05 82 2.570396e+04 1.000000e+00 -3.23005e-05 83 2.600160e+04 1.000000e+00 -3.26746e-05 84 2.630268e+04 1.000000e+00 -3.30529e-05 85 2.660725e+04 1.000000e+00 -3.34357e-05 86 2.691535e+04 1.000000e+00 -3.38228e-05 87 2.722701e+04 1.000000e+00 -3.42145e-05 88 2.754229e+04 1.000000e+00 -3.46107e-05 89 2.786121e+04 1.000000e+00 -3.50114e-05 90 2.818383e+04 1.000000e+00 -3.54168e-05 91 2.851018e+04 1.000000e+00 -3.58270e-05 92 2.884032e+04 1.000000e+00 -3.62418e-05 93 2.917427e+04 1.000000e+00 -3.66615e-05 94 2.951209e+04 1.000000e+00 -3.70860e-05 95 2.985383e+04 1.000000e+00 -3.75154e-05 96 3.019952e+04 1.000000e+00 -3.79498e-05 97 3.054921e+04 1.000000e+00 -3.83893e-05 98 3.090295e+04 1.000000e+00 -3.88338e-05 99 3.126079e+04 1.000000e+00 -3.92835e-05 100 3.162278e+04 1.000000e+00 -3.97384e-05 101 3.198895e+04 1.000000e+00 -4.01985e-05 102 3.235937e+04 1.000000e+00 -4.06640e-05 103 3.273407e+04 1.000000e+00 -4.11348e-05 104 3.311311e+04 1.000000e+00 -4.16112e-05 105 3.349654e+04 1.000000e+00 -4.20930e-05 106 3.388442e+04 1.000000e+00 -4.25804e-05 107 3.427678e+04 1.000000e+00 -4.30735e-05 108 3.467369e+04 1.000000e+00 -4.35722e-05 109 3.507519e+04 1.000000e+00 -4.40768e-05 110 3.548134e+04 1.000000e+00 -4.45872e-05 111 3.589219e+04 1.000000e+00 -4.51035e-05 112 3.630781e+04 1.000000e+00 -4.56257e-05 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 113 3.672823e+04 1.000000e+00 -4.61541e-05 114 3.715352e+04 1.000000e+00 -4.66885e-05 115 3.758374e+04 1.000000e+00 -4.72291e-05 116 3.801894e+04 1.000000e+00 -4.77760e-05 117 3.845918e+04 1.000000e+00 -4.83292e-05 118 3.890451e+04 1.000000e+00 -4.88889e-05 119 3.935501e+04 1.000000e+00 -4.94550e-05 120 3.981072e+04 1.000000e+00 -5.00276e-05 121 4.027170e+04 1.000000e+00 -5.06069e-05 122 4.073803e+04 1.000000e+00 -5.11929e-05 123 4.120975e+04 1.000000e+00 -5.17857e-05 124 4.168694e+04 1.000000e+00 -5.23854e-05 125 4.216965e+04 1.000000e+00 -5.29919e-05 126 4.265795e+04 1.000000e+00 -5.36056e-05 127 4.315191e+04 1.000000e+00 -5.42263e-05 128 4.365158e+04 1.000000e+00 -5.48542e-05 129 4.415704e+04 1.000000e+00 -5.54894e-05 130 4.466836e+04 1.000000e+00 -5.61319e-05 131 4.518559e+04 1.000000e+00 -5.67819e-05 132 4.570882e+04 1.000000e+00 -5.74394e-05 133 4.623810e+04 1.000000e+00 -5.81045e-05 134 4.677351e+04 1.000000e+00 -5.87773e-05 135 4.731513e+04 1.000000e+00 -5.94579e-05 136 4.786301e+04 1.000000e+00 -6.01464e-05 137 4.841724e+04 1.000000e+00 -6.08429e-05 138 4.897788e+04 1.000000e+00 -6.15474e-05 139 4.954502e+04 1.000000e+00 -6.22601e-05 140 5.011872e+04 1.000000e+00 -6.29811e-05 141 5.069907e+04 1.000000e+00 -6.37103e-05 142 5.128614e+04 1.000000e+00 -6.44481e-05 143 5.188000e+04 1.000000e+00 -6.51943e-05 144 5.248075e+04 1.000000e+00 -6.59493e-05 145 5.308844e+04 1.000000e+00 -6.67129e-05 146 5.370318e+04 1.000000e+00 -6.74854e-05 147 5.432503e+04 1.000000e+00 -6.82669e-05 148 5.495409e+04 1.000000e+00 -6.90574e-05 149 5.559043e+04 1.000000e+00 -6.98570e-05 150 5.623413e+04 1.000000e+00 -7.06659e-05 151 5.688529e+04 1.000000e+00 -7.14842e-05 152 5.754399e+04 1.000000e+00 -7.23119e-05 153 5.821032e+04 1.000000e+00 -7.31493e-05 154 5.888437e+04 1.000000e+00 -7.39963e-05 155 5.956621e+04 1.000000e+00 -7.48531e-05 156 6.025596e+04 1.000000e+00 -7.57199e-05 157 6.095369e+04 1.000000e+00 -7.65967e-05 158 6.165950e+04 1.000000e+00 -7.74836e-05 159 6.237348e+04 1.000000e+00 -7.83808e-05 160 6.309573e+04 1.000000e+00 -7.92885e-05 161 6.382635e+04 1.000000e+00 -8.02066e-05 162 6.456542e+04 1.000000e+00 -8.11353e-05 163 6.531306e+04 1.000000e+00 -8.20748e-05 164 6.606934e+04 1.000000e+00 -8.30252e-05 165 6.683439e+04 1.000000e+00 -8.39866e-05 166 6.760830e+04 1.000000e+00 -8.49591e-05 167 6.839116e+04 1.000000e+00 -8.59429e-05 168 6.918310e+04 1.000000e+00 -8.69381e-05 169 6.998420e+04 1.000000e+00 -8.79448e-05 170 7.079458e+04 1.000000e+00 -8.89631e-05 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 171 7.161434e+04 1.000000e+00 -8.99933e-05 172 7.244360e+04 1.000000e+00 -9.10353e-05 173 7.328245e+04 1.000000e+00 -9.20895e-05 174 7.413102e+04 1.000000e+00 -9.31558e-05 175 7.498942e+04 1.000000e+00 -9.42345e-05 176 7.585776e+04 1.000000e+00 -9.53257e-05 177 7.673615e+04 1.000000e+00 -9.64295e-05 178 7.762471e+04 1.000000e+00 -9.75461e-05 179 7.852356e+04 1.000000e+00 -9.86756e-05 180 7.943282e+04 1.000000e+00 -9.98183e-05 181 8.035261e+04 1.000000e+00 -1.00974e-04 182 8.128305e+04 1.000000e+00 -1.02143e-04 183 8.222426e+04 1.000000e+00 -1.03326e-04 184 8.317638e+04 1.000000e+00 -1.04523e-04 185 8.413951e+04 1.000000e+00 -1.05733e-04 186 8.511380e+04 1.000000e+00 -1.06957e-04 187 8.609938e+04 1.000000e+00 -1.08196e-04 188 8.709636e+04 1.000000e+00 -1.09449e-04 189 8.810489e+04 1.000000e+00 -1.10716e-04 190 8.912509e+04 1.000000e+00 -1.11998e-04 191 9.015711e+04 1.000000e+00 -1.13295e-04 192 9.120108e+04 1.000000e+00 -1.14607e-04 193 9.225714e+04 1.000000e+00 -1.15934e-04 194 9.332543e+04 1.000000e+00 -1.17276e-04 195 9.440609e+04 1.000000e+00 -1.18634e-04 196 9.549926e+04 1.000000e+00 -1.20008e-04 197 9.660509e+04 1.000000e+00 -1.21398e-04 198 9.772372e+04 1.000000e+00 -1.22803e-04 199 9.885531e+04 1.000000e+00 -1.24225e-04 200 1.000000e+05 1.000000e+00 -1.25664e-04 201 1.011579e+05 1.000000e+00 -1.27119e-04 202 1.023293e+05 1.000000e+00 -1.28591e-04 203 1.035142e+05 1.000000e+00 -1.30080e-04 204 1.047129e+05 1.000000e+00 -1.31586e-04 205 1.059254e+05 1.000000e+00 -1.33110e-04 206 1.071519e+05 1.000000e+00 -1.34651e-04 207 1.083927e+05 1.000000e+00 -1.36210e-04 208 1.096478e+05 1.000000e+00 -1.37788e-04 209 1.109175e+05 1.000000e+00 -1.39383e-04 210 1.122018e+05 1.000000e+00 -1.40997e-04 211 1.135011e+05 1.000000e+00 -1.42630e-04 212 1.148154e+05 1.000001e+00 -1.44281e-04 213 1.161449e+05 1.000001e+00 -1.45952e-04 214 1.174898e+05 1.000001e+00 -1.47642e-04 215 1.188502e+05 1.000001e+00 -1.49352e-04 216 1.202264e+05 1.000001e+00 -1.51081e-04 217 1.216186e+05 1.000001e+00 -1.52831e-04 218 1.230269e+05 1.000001e+00 -1.54600e-04 219 1.244515e+05 1.000001e+00 -1.56390e-04 220 1.258925e+05 1.000001e+00 -1.58201e-04 221 1.273503e+05 1.000001e+00 -1.60033e-04 222 1.288250e+05 1.000001e+00 -1.61886e-04 223 1.303167e+05 1.000001e+00 -1.63761e-04 224 1.318257e+05 1.000001e+00 -1.65657e-04 225 1.333521e+05 1.000001e+00 -1.67575e-04 226 1.348963e+05 1.000001e+00 -1.69516e-04 227 1.364583e+05 1.000001e+00 -1.71479e-04 228 1.380384e+05 1.000001e+00 -1.73464e-04 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 229 1.396368e+05 1.000001e+00 -1.75473e-04 230 1.412538e+05 1.000001e+00 -1.77505e-04 231 1.428894e+05 1.000001e+00 -1.79560e-04 232 1.445440e+05 1.000001e+00 -1.81639e-04 233 1.462177e+05 1.000001e+00 -1.83743e-04 234 1.479108e+05 1.000001e+00 -1.85870e-04 235 1.496236e+05 1.000001e+00 -1.88023e-04 236 1.513561e+05 1.000001e+00 -1.90200e-04 237 1.531087e+05 1.000001e+00 -1.92402e-04 238 1.548817e+05 1.000001e+00 -1.94630e-04 239 1.566751e+05 1.000001e+00 -1.96884e-04 240 1.584893e+05 1.000001e+00 -1.99164e-04 241 1.603245e+05 1.000001e+00 -2.01470e-04 242 1.621810e+05 1.000001e+00 -2.03803e-04 243 1.640590e+05 1.000001e+00 -2.06163e-04 244 1.659587e+05 1.000001e+00 -2.08550e-04 245 1.678804e+05 1.000001e+00 -2.10965e-04 246 1.698244e+05 1.000001e+00 -2.13408e-04 247 1.717908e+05 1.000001e+00 -2.15879e-04 248 1.737801e+05 1.000001e+00 -2.18379e-04 249 1.757924e+05 1.000001e+00 -2.20907e-04 250 1.778279e+05 1.000001e+00 -2.23465e-04 251 1.798871e+05 1.000001e+00 -2.26053e-04 252 1.819701e+05 1.000001e+00 -2.28671e-04 253 1.840772e+05 1.000001e+00 -2.31319e-04 254 1.862087e+05 1.000001e+00 -2.33997e-04 255 1.883649e+05 1.000001e+00 -2.36707e-04 256 1.905461e+05 1.000001e+00 -2.39448e-04 257 1.927525e+05 1.000001e+00 -2.42220e-04 258 1.949845e+05 1.000001e+00 -2.45025e-04 259 1.972423e+05 1.000002e+00 -2.47862e-04 260 1.995262e+05 1.000002e+00 -2.50732e-04 261 2.018366e+05 1.000002e+00 -2.53636e-04 262 2.041738e+05 1.000002e+00 -2.56573e-04 263 2.065380e+05 1.000002e+00 -2.59544e-04 264 2.089296e+05 1.000002e+00 -2.62549e-04 265 2.113489e+05 1.000002e+00 -2.65589e-04 266 2.137962e+05 1.000002e+00 -2.68665e-04 267 2.162719e+05 1.000002e+00 -2.71776e-04 268 2.187762e+05 1.000002e+00 -2.74923e-04 269 2.213095e+05 1.000002e+00 -2.78106e-04 270 2.238721e+05 1.000002e+00 -2.81327e-04 271 2.264644e+05 1.000002e+00 -2.84584e-04 272 2.290868e+05 1.000002e+00 -2.87880e-04 273 2.317395e+05 1.000002e+00 -2.91213e-04 274 2.344229e+05 1.000002e+00 -2.94585e-04 275 2.371374e+05 1.000002e+00 -2.97996e-04 276 2.398833e+05 1.000002e+00 -3.01447e-04 277 2.426610e+05 1.000002e+00 -3.04938e-04 278 2.454709e+05 1.000002e+00 -3.08469e-04 279 2.483133e+05 1.000002e+00 -3.12040e-04 280 2.511886e+05 1.000002e+00 -3.15654e-04 281 2.540973e+05 1.000002e+00 -3.19309e-04 282 2.570396e+05 1.000003e+00 -3.23006e-04 283 2.600160e+05 1.000003e+00 -3.26747e-04 284 2.630268e+05 1.000003e+00 -3.30530e-04 285 2.660725e+05 1.000003e+00 -3.34357e-04 286 2.691535e+05 1.000003e+00 -3.38229e-04 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 287 2.722701e+05 1.000003e+00 -3.42146e-04 288 2.754229e+05 1.000003e+00 -3.46108e-04 289 2.786121e+05 1.000003e+00 -3.50115e-04 290 2.818383e+05 1.000003e+00 -3.54170e-04 291 2.851018e+05 1.000003e+00 -3.58271e-04 292 2.884032e+05 1.000003e+00 -3.62419e-04 293 2.917427e+05 1.000003e+00 -3.66616e-04 294 2.951209e+05 1.000003e+00 -3.70861e-04 295 2.985383e+05 1.000003e+00 -3.75156e-04 296 3.019952e+05 1.000004e+00 -3.79500e-04 297 3.054921e+05 1.000004e+00 -3.83894e-04 298 3.090295e+05 1.000004e+00 -3.88339e-04 299 3.126079e+05 1.000004e+00 -3.92836e-04 300 3.162278e+05 1.000004e+00 -3.97385e-04 301 3.198895e+05 1.000004e+00 -4.01987e-04 302 3.235937e+05 1.000004e+00 -4.06641e-04 303 3.273407e+05 1.000004e+00 -4.11350e-04 304 3.311311e+05 1.000004e+00 -4.16113e-04 305 3.349654e+05 1.000004e+00 -4.20932e-04 306 3.388442e+05 1.000004e+00 -4.25806e-04 307 3.427678e+05 1.000005e+00 -4.30737e-04 308 3.467369e+05 1.000005e+00 -4.35724e-04 309 3.507519e+05 1.000005e+00 -4.40770e-04 310 3.548134e+05 1.000005e+00 -4.45874e-04 311 3.589219e+05 1.000005e+00 -4.51037e-04 312 3.630781e+05 1.000005e+00 -4.56260e-04 313 3.672823e+05 1.000005e+00 -4.61543e-04 314 3.715352e+05 1.000005e+00 -4.66887e-04 315 3.758374e+05 1.000005e+00 -4.72294e-04 316 3.801894e+05 1.000006e+00 -4.77763e-04 317 3.845918e+05 1.000006e+00 -4.83295e-04 318 3.890451e+05 1.000006e+00 -4.88891e-04 319 3.935501e+05 1.000006e+00 -4.94553e-04 320 3.981072e+05 1.000006e+00 -5.00279e-04 321 4.027170e+05 1.000006e+00 -5.06072e-04 322 4.073803e+05 1.000006e+00 -5.11932e-04 323 4.120975e+05 1.000007e+00 -5.17860e-04 324 4.168694e+05 1.000007e+00 -5.23857e-04 325 4.216965e+05 1.000007e+00 -5.29923e-04 326 4.265795e+05 1.000007e+00 -5.36059e-04 327 4.315191e+05 1.000007e+00 -5.42267e-04 328 4.365158e+05 1.000007e+00 -5.48546e-04 329 4.415704e+05 1.000008e+00 -5.54898e-04 330 4.466836e+05 1.000008e+00 -5.61324e-04 331 4.518559e+05 1.000008e+00 -5.67823e-04 332 4.570882e+05 1.000008e+00 -5.74399e-04 333 4.623810e+05 1.000008e+00 -5.81050e-04 334 4.677351e+05 1.000008e+00 -5.87778e-04 335 4.731513e+05 1.000009e+00 -5.94585e-04 336 4.786301e+05 1.000009e+00 -6.01470e-04 337 4.841724e+05 1.000009e+00 -6.08434e-04 338 4.897788e+05 1.000009e+00 -6.15480e-04 339 4.954502e+05 1.000009e+00 -6.22607e-04 340 5.011872e+05 1.000010e+00 -6.29817e-04 341 5.069907e+05 1.000010e+00 -6.37110e-04 342 5.128614e+05 1.000010e+00 -6.44487e-04 343 5.188000e+05 1.000010e+00 -6.51950e-04 344 5.248075e+05 1.000011e+00 -6.59500e-04 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 345 5.308844e+05 1.000011e+00 -6.67136e-04 346 5.370318e+05 1.000011e+00 -6.74862e-04 347 5.432503e+05 1.000011e+00 -6.82676e-04 348 5.495409e+05 1.000012e+00 -6.90582e-04 349 5.559043e+05 1.000012e+00 -6.98578e-04 350 5.623413e+05 1.000012e+00 -7.06668e-04 351 5.688529e+05 1.000013e+00 -7.14851e-04 352 5.754399e+05 1.000013e+00 -7.23128e-04 353 5.821032e+05 1.000013e+00 -7.31502e-04 354 5.888437e+05 1.000013e+00 -7.39973e-04 355 5.956621e+05 1.000014e+00 -7.48541e-04 356 6.025596e+05 1.000014e+00 -7.57209e-04 357 6.095369e+05 1.000014e+00 -7.65978e-04 358 6.165950e+05 1.000015e+00 -7.74848e-04 359 6.237348e+05 1.000015e+00 -7.83820e-04 360 6.309573e+05 1.000015e+00 -7.92897e-04 361 6.382635e+05 1.000016e+00 -8.02078e-04 362 6.456542e+05 1.000016e+00 -8.11366e-04 363 6.531306e+05 1.000017e+00 -8.20762e-04 364 6.606934e+05 1.000017e+00 -8.30266e-04 365 6.683439e+05 1.000017e+00 -8.39880e-04 366 6.760830e+05 1.000018e+00 -8.49606e-04 367 6.839116e+05 1.000018e+00 -8.59444e-04 368 6.918310e+05 1.000019e+00 -8.69397e-04 369 6.998420e+05 1.000019e+00 -8.79464e-04 370 7.079458e+05 1.000019e+00 -8.89648e-04 371 7.161434e+05 1.000020e+00 -8.99950e-04 372 7.244360e+05 1.000020e+00 -9.10372e-04 373 7.328245e+05 1.000021e+00 -9.20914e-04 374 7.413102e+05 1.000021e+00 -9.31578e-04 375 7.498942e+05 1.000022e+00 -9.42365e-04 376 7.585776e+05 1.000022e+00 -9.53278e-04 377 7.673615e+05 1.000023e+00 -9.64317e-04 378 7.762471e+05 1.000023e+00 -9.75484e-04 379 7.852356e+05 1.000024e+00 -9.86780e-04 380 7.943282e+05 1.000024e+00 -9.98207e-04 381 8.035261e+05 1.000025e+00 -1.00977e-03 382 8.128305e+05 1.000026e+00 -1.02146e-03 383 8.222426e+05 1.000026e+00 -1.03329e-03 384 8.317638e+05 1.000027e+00 -1.04525e-03 385 8.413951e+05 1.000027e+00 -1.05736e-03 386 8.511380e+05 1.000028e+00 -1.06960e-03 387 8.609938e+05 1.000029e+00 -1.08199e-03 388 8.709636e+05 1.000029e+00 -1.09452e-03 389 8.810489e+05 1.000030e+00 -1.10719e-03 390 8.912509e+05 1.000031e+00 -1.12001e-03 391 9.015711e+05 1.000031e+00 -1.13298e-03 392 9.120108e+05 1.000032e+00 -1.14610e-03 393 9.225714e+05 1.000033e+00 -1.15938e-03 394 9.332543e+05 1.000034e+00 -1.17280e-03 395 9.440609e+05 1.000034e+00 -1.18638e-03 396 9.549926e+05 1.000035e+00 -1.20012e-03 397 9.660509e+05 1.000036e+00 -1.21402e-03 398 9.772372e+05 1.000037e+00 -1.22808e-03 399 9.885531e+05 1.000038e+00 -1.24230e-03 400 1.000000e+06 1.000039e+00 -1.25669e-03 401 1.011579e+06 1.000040e+00 -1.27124e-03 402 1.023293e+06 1.000041e+00 -1.28596e-03 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 403 1.035142e+06 1.000041e+00 -1.30085e-03 404 1.047129e+06 1.000042e+00 -1.31592e-03 405 1.059254e+06 1.000043e+00 -1.33116e-03 406 1.071519e+06 1.000044e+00 -1.34657e-03 407 1.083927e+06 1.000045e+00 -1.36217e-03 408 1.096478e+06 1.000047e+00 -1.37794e-03 409 1.109175e+06 1.000048e+00 -1.39390e-03 410 1.122018e+06 1.000049e+00 -1.41004e-03 411 1.135011e+06 1.000050e+00 -1.42637e-03 412 1.148154e+06 1.000051e+00 -1.44289e-03 413 1.161449e+06 1.000052e+00 -1.45960e-03 414 1.174898e+06 1.000053e+00 -1.47650e-03 415 1.188502e+06 1.000055e+00 -1.49360e-03 416 1.202264e+06 1.000056e+00 -1.51090e-03 417 1.216186e+06 1.000057e+00 -1.52839e-03 418 1.230269e+06 1.000059e+00 -1.54609e-03 419 1.244515e+06 1.000060e+00 -1.56400e-03 420 1.258925e+06 1.000061e+00 -1.58211e-03 421 1.273503e+06 1.000063e+00 -1.60043e-03 422 1.288250e+06 1.000064e+00 -1.61897e-03 423 1.303167e+06 1.000066e+00 -1.63772e-03 424 1.318257e+06 1.000067e+00 -1.65668e-03 425 1.333521e+06 1.000069e+00 -1.67587e-03 426 1.348963e+06 1.000070e+00 -1.69528e-03 427 1.364583e+06 1.000072e+00 -1.71491e-03 428 1.380384e+06 1.000074e+00 -1.73477e-03 429 1.396368e+06 1.000075e+00 -1.75486e-03 430 1.412538e+06 1.000077e+00 -1.77518e-03 431 1.428894e+06 1.000079e+00 -1.79574e-03 432 1.445440e+06 1.000081e+00 -1.81654e-03 433 1.462177e+06 1.000083e+00 -1.83758e-03 434 1.479108e+06 1.000085e+00 -1.85886e-03 435 1.496236e+06 1.000087e+00 -1.88039e-03 436 1.513561e+06 1.000089e+00 -1.90217e-03 437 1.531087e+06 1.000091e+00 -1.92420e-03 438 1.548817e+06 1.000093e+00 -1.94648e-03 439 1.566751e+06 1.000095e+00 -1.96903e-03 440 1.584893e+06 1.000097e+00 -1.99183e-03 441 1.603245e+06 1.000099e+00 -2.01490e-03 442 1.621810e+06 1.000102e+00 -2.03824e-03 443 1.640590e+06 1.000104e+00 -2.06184e-03 444 1.659587e+06 1.000107e+00 -2.08572e-03 445 1.678804e+06 1.000109e+00 -2.10988e-03 446 1.698244e+06 1.000112e+00 -2.13432e-03 447 1.717908e+06 1.000114e+00 -2.15904e-03 448 1.737801e+06 1.000117e+00 -2.18404e-03 449 1.757924e+06 1.000120e+00 -2.20934e-03 450 1.778279e+06 1.000122e+00 -2.23493e-03 451 1.798871e+06 1.000125e+00 -2.26081e-03 452 1.819701e+06 1.000128e+00 -2.28700e-03 453 1.840772e+06 1.000131e+00 -2.31349e-03 454 1.862087e+06 1.000134e+00 -2.34028e-03 455 1.883649e+06 1.000137e+00 -2.36739e-03 456 1.905461e+06 1.000140e+00 -2.39481e-03 457 1.927525e+06 1.000144e+00 -2.42255e-03 458 1.949845e+06 1.000147e+00 -2.45061e-03 459 1.972423e+06 1.000151e+00 -2.47900e-03 460 1.995262e+06 1.000154e+00 -2.50771e-03 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 461 2.018366e+06 1.000158e+00 -2.53676e-03 462 2.041738e+06 1.000161e+00 -2.56614e-03 463 2.065380e+06 1.000165e+00 -2.59586e-03 464 2.089296e+06 1.000169e+00 -2.62593e-03 465 2.113489e+06 1.000173e+00 -2.65635e-03 466 2.137962e+06 1.000177e+00 -2.68712e-03 467 2.162719e+06 1.000181e+00 -2.71825e-03 468 2.187762e+06 1.000185e+00 -2.74973e-03 469 2.213095e+06 1.000190e+00 -2.78159e-03 470 2.238721e+06 1.000194e+00 -2.81381e-03 471 2.264644e+06 1.000198e+00 -2.84640e-03 472 2.290868e+06 1.000203e+00 -2.87938e-03 473 2.317395e+06 1.000208e+00 -2.91273e-03 474 2.344229e+06 1.000213e+00 -2.94648e-03 475 2.371374e+06 1.000218e+00 -2.98061e-03 476 2.398833e+06 1.000223e+00 -3.01514e-03 477 2.426610e+06 1.000228e+00 -3.05007e-03 478 2.454709e+06 1.000233e+00 -3.08540e-03 479 2.483133e+06 1.000239e+00 -3.12115e-03 480 2.511886e+06 1.000244e+00 -3.15731e-03 481 2.540973e+06 1.000250e+00 -3.19388e-03 482 2.570396e+06 1.000256e+00 -3.23089e-03 483 2.600160e+06 1.000262e+00 -3.26832e-03 484 2.630268e+06 1.000268e+00 -3.30618e-03 485 2.660725e+06 1.000274e+00 -3.34449e-03 486 2.691535e+06 1.000280e+00 -3.38324e-03 487 2.722701e+06 1.000287e+00 -3.42244e-03 488 2.754229e+06 1.000294e+00 -3.46209e-03 489 2.786121e+06 1.000300e+00 -3.50220e-03 490 2.818383e+06 1.000307e+00 -3.54278e-03 491 2.851018e+06 1.000315e+00 -3.58383e-03 492 2.884032e+06 1.000322e+00 -3.62536e-03 493 2.917427e+06 1.000329e+00 -3.66736e-03 494 2.951209e+06 1.000337e+00 -3.70986e-03 495 2.985383e+06 1.000345e+00 -3.75285e-03 496 3.019952e+06 1.000353e+00 -3.79633e-03 497 3.054921e+06 1.000361e+00 -3.84032e-03 498 3.090295e+06 1.000370e+00 -3.88482e-03 499 3.126079e+06 1.000378e+00 -3.92984e-03 500 3.162278e+06 1.000387e+00 -3.97538e-03 501 3.198895e+06 1.000396e+00 -4.02145e-03 502 3.235937e+06 1.000405e+00 -4.06806e-03 503 3.273407e+06 1.000415e+00 -4.11520e-03 504 3.311311e+06 1.000424e+00 -4.16289e-03 505 3.349654e+06 1.000434e+00 -4.21114e-03 506 3.388442e+06 1.000444e+00 -4.25995e-03 507 3.427678e+06 1.000455e+00 -4.30932e-03 508 3.467369e+06 1.000465e+00 -4.35927e-03 509 3.507519e+06 1.000476e+00 -4.40979e-03 510 3.548134e+06 1.000487e+00 -4.46090e-03 511 3.589219e+06 1.000499e+00 -4.51261e-03 512 3.630781e+06 1.000510e+00 -4.56492e-03 513 3.672823e+06 1.000522e+00 -4.61783e-03 514 3.715352e+06 1.000534e+00 -4.67136e-03 515 3.758374e+06 1.000547e+00 -4.72551e-03 516 3.801894e+06 1.000560e+00 -4.78029e-03 517 3.845918e+06 1.000573e+00 -4.83571e-03 518 3.890451e+06 1.000586e+00 -4.89177e-03 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 519 3.935501e+06 1.000600e+00 -4.94848e-03 520 3.981072e+06 1.000614e+00 -5.00585e-03 521 4.027170e+06 1.000628e+00 -5.06389e-03 522 4.073803e+06 1.000642e+00 -5.12260e-03 523 4.120975e+06 1.000657e+00 -5.18200e-03 524 4.168694e+06 1.000673e+00 -5.24208e-03 525 4.216965e+06 1.000688e+00 -5.30287e-03 526 4.265795e+06 1.000705e+00 -5.36436e-03 527 4.315191e+06 1.000721e+00 -5.42656e-03 528 4.365158e+06 1.000738e+00 -5.48949e-03 529 4.415704e+06 1.000755e+00 -5.55316e-03 530 4.466836e+06 1.000773e+00 -5.61756e-03 531 4.518559e+06 1.000791e+00 -5.68271e-03 532 4.570882e+06 1.000809e+00 -5.74862e-03 533 4.623810e+06 1.000828e+00 -5.81529e-03 534 4.677351e+06 1.000847e+00 -5.88275e-03 535 4.731513e+06 1.000867e+00 -5.95098e-03 536 4.786301e+06 1.000887e+00 -6.02001e-03 537 4.841724e+06 1.000908e+00 -6.08985e-03 538 4.897788e+06 1.000929e+00 -6.16050e-03 539 4.954502e+06 1.000951e+00 -6.23197e-03 540 5.011872e+06 1.000973e+00 -6.30427e-03 541 5.069907e+06 1.000995e+00 -6.37742e-03 542 5.128614e+06 1.001019e+00 -6.45142e-03 543 5.188000e+06 1.001042e+00 -6.52628e-03 544 5.248075e+06 1.001067e+00 -6.60201e-03 545 5.308844e+06 1.001092e+00 -6.67862e-03 546 5.370318e+06 1.001117e+00 -6.75613e-03 547 5.432503e+06 1.001143e+00 -6.83454e-03 548 5.495409e+06 1.001170e+00 -6.91387e-03 549 5.559043e+06 1.001197e+00 -6.99412e-03 550 5.623413e+06 1.001225e+00 -7.07530e-03 551 5.688529e+06 1.001253e+00 -7.15744e-03 552 5.754399e+06 1.001283e+00 -7.24053e-03 553 5.821032e+06 1.001313e+00 -7.32459e-03 554 5.888437e+06 1.001343e+00 -7.40963e-03 555 5.956621e+06 1.001375e+00 -7.49567e-03 556 6.025596e+06 1.001407e+00 -7.58271e-03 557 6.095369e+06 1.001439e+00 -7.67077e-03 558 6.165950e+06 1.001473e+00 -7.75985e-03 559 6.237348e+06 1.001507e+00 -7.84998e-03 560 6.309573e+06 1.001543e+00 -7.94116e-03 561 6.382635e+06 1.001579e+00 -8.03340e-03 562 6.456542e+06 1.001615e+00 -8.12673e-03 563 6.531306e+06 1.001653e+00 -8.22114e-03 564 6.606934e+06 1.001692e+00 -8.31666e-03 565 6.683439e+06 1.001731e+00 -8.41330e-03 566 6.760830e+06 1.001771e+00 -8.51106e-03 567 6.839116e+06 1.001813e+00 -8.60997e-03 568 6.918310e+06 1.001855e+00 -8.71004e-03 569 6.998420e+06 1.001898e+00 -8.81128e-03 570 7.079458e+06 1.001943e+00 -8.91371e-03 571 7.161434e+06 1.001988e+00 -9.01734e-03 572 7.244360e+06 1.002034e+00 -9.12218e-03 573 7.328245e+06 1.002082e+00 -9.22825e-03 574 7.413102e+06 1.002131e+00 -9.33556e-03 575 7.498942e+06 1.002180e+00 -9.44413e-03 576 7.585776e+06 1.002231e+00 -9.55398e-03 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 577 7.673615e+06 1.002283e+00 -9.66512e-03 578 7.762471e+06 1.002337e+00 -9.77756e-03 579 7.852356e+06 1.002391e+00 -9.89132e-03 580 7.943282e+06 1.002447e+00 -1.00064e-02 581 8.035261e+06 1.002504e+00 -1.01229e-02 582 8.128305e+06 1.002563e+00 -1.02407e-02 583 8.222426e+06 1.002622e+00 -1.03599e-02 584 8.317638e+06 1.002684e+00 -1.04805e-02 585 8.413951e+06 1.002746e+00 -1.06025e-02 586 8.511380e+06 1.002810e+00 -1.07260e-02 587 8.609938e+06 1.002876e+00 -1.08509e-02 588 8.709636e+06 1.002943e+00 -1.09773e-02 589 8.810489e+06 1.003012e+00 -1.11052e-02 590 8.912509e+06 1.003082e+00 -1.12345e-02 591 9.015711e+06 1.003154e+00 -1.13655e-02 592 9.120108e+06 1.003228e+00 -1.14979e-02 593 9.225714e+06 1.003304e+00 -1.16319e-02 594 9.332543e+06 1.003381e+00 -1.17675e-02 595 9.440609e+06 1.003460e+00 -1.19047e-02 596 9.549926e+06 1.003541e+00 -1.20436e-02 597 9.660509e+06 1.003623e+00 -1.21840e-02 598 9.772372e+06 1.003708e+00 -1.23262e-02 599 9.885531e+06 1.003795e+00 -1.24700e-02 600 1.000000e+07 1.003884e+00 -1.26155e-02 601 1.011579e+07 1.003974e+00 -1.27628e-02 602 1.023293e+07 1.004067e+00 -1.29117e-02 603 1.035142e+07 1.004162e+00 -1.30625e-02 604 1.047129e+07 1.004260e+00 -1.32150e-02 605 1.059254e+07 1.004359e+00 -1.33694e-02 606 1.071519e+07 1.004461e+00 -1.35256e-02 607 1.083927e+07 1.004566e+00 -1.36836e-02 608 1.096478e+07 1.004673e+00 -1.38436e-02 609 1.109175e+07 1.004782e+00 -1.40054e-02 610 1.122018e+07 1.004894e+00 -1.41692e-02 611 1.135011e+07 1.005009e+00 -1.43349e-02 612 1.148154e+07 1.005126e+00 -1.45026e-02 613 1.161449e+07 1.005246e+00 -1.46723e-02 614 1.174898e+07 1.005369e+00 -1.48440e-02 615 1.188502e+07 1.005494e+00 -1.50178e-02 616 1.202264e+07 1.005623e+00 -1.51936e-02 617 1.216186e+07 1.005755e+00 -1.53716e-02 618 1.230269e+07 1.005890e+00 -1.55517e-02 619 1.244515e+07 1.006028e+00 -1.57339e-02 620 1.258925e+07 1.006169e+00 -1.59184e-02 621 1.273503e+07 1.006313e+00 -1.61050e-02 622 1.288250e+07 1.006461e+00 -1.62939e-02 623 1.303167e+07 1.006613e+00 -1.64851e-02 624 1.318257e+07 1.006768e+00 -1.66786e-02 625 1.333521e+07 1.006927e+00 -1.68744e-02 626 1.348963e+07 1.007089e+00 -1.70726e-02 627 1.364583e+07 1.007255e+00 -1.72731e-02 628 1.380384e+07 1.007426e+00 -1.74761e-02 629 1.396368e+07 1.007600e+00 -1.76816e-02 630 1.412538e+07 1.007778e+00 -1.78895e-02 631 1.428894e+07 1.007961e+00 -1.80999e-02 632 1.445440e+07 1.008148e+00 -1.83130e-02 633 1.462177e+07 1.008339e+00 -1.85285e-02 634 1.479108e+07 1.008535e+00 -1.87468e-02 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 635 1.496236e+07 1.008735e+00 -1.89676e-02 636 1.513561e+07 1.008941e+00 -1.91912e-02 637 1.531087e+07 1.009151e+00 -1.94175e-02 638 1.548817e+07 1.009366e+00 -1.96466e-02 639 1.566751e+07 1.009586e+00 -1.98784e-02 640 1.584893e+07 1.009812e+00 -2.01131e-02 641 1.603245e+07 1.010042e+00 -2.03507e-02 642 1.621810e+07 1.010279e+00 -2.05912e-02 643 1.640590e+07 1.010521e+00 -2.08347e-02 644 1.659587e+07 1.010768e+00 -2.10811e-02 645 1.678804e+07 1.011022e+00 -2.13306e-02 646 1.698244e+07 1.011281e+00 -2.15832e-02 647 1.717908e+07 1.011547e+00 -2.18389e-02 648 1.737801e+07 1.011819e+00 -2.20978e-02 649 1.757924e+07 1.012098e+00 -2.23598e-02 650 1.778279e+07 1.012383e+00 -2.26252e-02 651 1.798871e+07 1.012675e+00 -2.28938e-02 652 1.819701e+07 1.012974e+00 -2.31658e-02 653 1.840772e+07 1.013280e+00 -2.34412e-02 654 1.862087e+07 1.013593e+00 -2.37200e-02 655 1.883649e+07 1.013914e+00 -2.40023e-02 656 1.905461e+07 1.014243e+00 -2.42882e-02 657 1.927525e+07 1.014579e+00 -2.45776e-02 658 1.949845e+07 1.014924e+00 -2.48707e-02 659 1.972423e+07 1.015277e+00 -2.51675e-02 660 1.995262e+07 1.015638e+00 -2.54681e-02 661 2.018366e+07 1.016008e+00 -2.57724e-02 662 2.041738e+07 1.016387e+00 -2.60806e-02 663 2.065380e+07 1.016775e+00 -2.63928e-02 664 2.089296e+07 1.017172e+00 -2.67089e-02 665 2.113489e+07 1.017579e+00 -2.70291e-02 666 2.137962e+07 1.017996e+00 -2.73533e-02 667 2.162719e+07 1.018423e+00 -2.76817e-02 668 2.187762e+07 1.018860e+00 -2.80144e-02 669 2.213095e+07 1.019307e+00 -2.83513e-02 670 2.238721e+07 1.019766e+00 -2.86926e-02 671 2.264644e+07 1.020235e+00 -2.90383e-02 672 2.290868e+07 1.020716e+00 -2.93885e-02 673 2.317395e+07 1.021209e+00 -2.97432e-02 674 2.344229e+07 1.021713e+00 -3.01026e-02 675 2.371374e+07 1.022230e+00 -3.04667e-02 676 2.398833e+07 1.022759e+00 -3.08356e-02 677 2.426610e+07 1.023301e+00 -3.12093e-02 678 2.454709e+07 1.023857e+00 -3.15879e-02 679 2.483133e+07 1.024426e+00 -3.19716e-02 680 2.511886e+07 1.025009e+00 -3.23603e-02 681 2.540973e+07 1.025606e+00 -3.27543e-02 682 2.570396e+07 1.026217e+00 -3.31535e-02 683 2.600160e+07 1.026844e+00 -3.35580e-02 684 2.630268e+07 1.027486e+00 -3.39680e-02 685 2.660725e+07 1.028144e+00 -3.43834e-02 686 2.691535e+07 1.028818e+00 -3.48046e-02 687 2.722701e+07 1.029509e+00 -3.52314e-02 688 2.754229e+07 1.030216e+00 -3.56640e-02 689 2.786121e+07 1.030942e+00 -3.61026e-02 690 2.818383e+07 1.031685e+00 -3.65471e-02 691 2.851018e+07 1.032446e+00 -3.69978e-02 692 2.884032e+07 1.033226e+00 -3.74548e-02 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 693 2.917427e+07 1.034026e+00 -3.79180e-02 694 2.951209e+07 1.034846e+00 -3.83877e-02 695 2.985383e+07 1.035686e+00 -3.88640e-02 696 3.019952e+07 1.036547e+00 -3.93469e-02 697 3.054921e+07 1.037429e+00 -3.98367e-02 698 3.090295e+07 1.038334e+00 -4.03334e-02 699 3.126079e+07 1.039261e+00 -4.08371e-02 700 3.162278e+07 1.040211e+00 -4.13481e-02 701 3.198895e+07 1.041186e+00 -4.18663e-02 702 3.235937e+07 1.042184e+00 -4.23921e-02 703 3.273407e+07 1.043209e+00 -4.29254e-02 704 3.311311e+07 1.044259e+00 -4.34665e-02 705 3.349654e+07 1.045335e+00 -4.40155e-02 706 3.388442e+07 1.046439e+00 -4.45726e-02 707 3.427678e+07 1.047571e+00 -4.51378e-02 708 3.467369e+07 1.048732e+00 -4.57115e-02 709 3.507519e+07 1.049922e+00 -4.62937e-02 710 3.548134e+07 1.051143e+00 -4.68847e-02 711 3.589219e+07 1.052396e+00 -4.74845e-02 712 3.630781e+07 1.053680e+00 -4.80935e-02 713 3.672823e+07 1.054998e+00 -4.87117e-02 714 3.715352e+07 1.056349e+00 -4.93394e-02 715 3.758374e+07 1.057736e+00 -4.99767e-02 716 3.801894e+07 1.059158e+00 -5.06240e-02 717 3.845918e+07 1.060618e+00 -5.12813e-02 718 3.890451e+07 1.062116e+00 -5.19490e-02 719 3.935501e+07 1.063652e+00 -5.26272e-02 720 3.981072e+07 1.065229e+00 -5.33162e-02 721 4.027170e+07 1.066848e+00 -5.40162e-02 722 4.073803e+07 1.068509e+00 -5.47274e-02 723 4.120975e+07 1.070214e+00 -5.54502e-02 724 4.168694e+07 1.071965e+00 -5.61848e-02 725 4.216965e+07 1.073762e+00 -5.69315e-02 726 4.265795e+07 1.075607e+00 -5.76905e-02 727 4.315191e+07 1.077501e+00 -5.84622e-02 728 4.365158e+07 1.079446e+00 -5.92468e-02 729 4.415704e+07 1.081444e+00 -6.00447e-02 730 4.466836e+07 1.083496e+00 -6.08562e-02 731 4.518559e+07 1.085603e+00 -6.16817e-02 732 4.570882e+07 1.087768e+00 -6.25214e-02 733 4.623810e+07 1.089991e+00 -6.33758e-02 734 4.677351e+07 1.092276e+00 -6.42453e-02 735 4.731513e+07 1.094624e+00 -6.51301e-02 736 4.786301e+07 1.097037e+00 -6.60308e-02 737 4.841724e+07 1.099516e+00 -6.69477e-02 738 4.897788e+07 1.102065e+00 -6.78814e-02 739 4.954502e+07 1.104685e+00 -6.88321e-02 740 5.011872e+07 1.107378e+00 -6.98005e-02 741 5.069907e+07 1.110148e+00 -7.07870e-02 742 5.128614e+07 1.112996e+00 -7.17921e-02 743 5.188000e+07 1.115926e+00 -7.28164e-02 744 5.248075e+07 1.118939e+00 -7.38603e-02 745 5.308844e+07 1.122038e+00 -7.49245e-02 746 5.370318e+07 1.125228e+00 -7.60096e-02 747 5.432503e+07 1.128510e+00 -7.71162e-02 748 5.495409e+07 1.131887e+00 -7.82449e-02 749 5.559043e+07 1.135364e+00 -7.93965e-02 750 5.623413e+07 1.138944e+00 -8.05716e-02 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 751 5.688529e+07 1.142629e+00 -8.17710e-02 752 5.754399e+07 1.146425e+00 -8.29954e-02 753 5.821032e+07 1.150334e+00 -8.42457e-02 754 5.888437e+07 1.154361e+00 -8.55227e-02 755 5.956621e+07 1.158511e+00 -8.68272e-02 756 6.025596e+07 1.162787e+00 -8.81603e-02 757 6.095369e+07 1.167195e+00 -8.95228e-02 758 6.165950e+07 1.171740e+00 -9.09158e-02 759 6.237348e+07 1.176426e+00 -9.23404e-02 760 6.309573e+07 1.181258e+00 -9.37976e-02 761 6.382635e+07 1.186244e+00 -9.52887e-02 762 6.456542e+07 1.191388e+00 -9.68148e-02 763 6.531306e+07 1.196697e+00 -9.83773e-02 764 6.606934e+07 1.202177e+00 -9.99774e-02 765 6.683439e+07 1.207836e+00 -1.01617e-01 766 6.760830e+07 1.213680e+00 -1.03297e-01 767 6.839116e+07 1.219717e+00 -1.05019e-01 768 6.918310e+07 1.225955e+00 -1.06785e-01 769 6.998420e+07 1.232403e+00 -1.08597e-01 770 7.079458e+07 1.239069e+00 -1.10456e-01 771 7.161434e+07 1.245963e+00 -1.12365e-01 772 7.244360e+07 1.253095e+00 -1.14325e-01 773 7.328245e+07 1.260476e+00 -1.16339e-01 774 7.413102e+07 1.268116e+00 -1.18409e-01 775 7.498942e+07 1.276026e+00 -1.20537e-01 776 7.585776e+07 1.284221e+00 -1.22727e-01 777 7.673615e+07 1.292712e+00 -1.24981e-01 778 7.762471e+07 1.301513e+00 -1.27301e-01 779 7.852356e+07 1.310641e+00 -1.29692e-01 780 7.943282e+07 1.320109e+00 -1.32155e-01 781 8.035261e+07 1.329935e+00 -1.34696e-01 782 8.128305e+07 1.340136e+00 -1.37317e-01 783 8.222426e+07 1.350733e+00 -1.40023e-01 784 8.317638e+07 1.361744e+00 -1.42818e-01 785 8.413951e+07 1.373191e+00 -1.45706e-01 786 8.511380e+07 1.385098e+00 -1.48693e-01 787 8.609938e+07 1.397488e+00 -1.51784e-01 788 8.709636e+07 1.410389e+00 -1.54985e-01 789 8.810489e+07 1.423829e+00 -1.58301e-01 790 8.912509e+07 1.437838e+00 -1.61739e-01 791 9.015711e+07 1.452448e+00 -1.65307e-01 792 9.120108e+07 1.467694e+00 -1.69011e-01 793 9.225714e+07 1.483615e+00 -1.72861e-01 794 9.332543e+07 1.500250e+00 -1.76864e-01 795 9.440609e+07 1.517644e+00 -1.81032e-01 796 9.549926e+07 1.535844e+00 -1.85373e-01 797 9.660509e+07 1.554902e+00 -1.89901e-01 798 9.772372e+07 1.574872e+00 -1.94626e-01 799 9.885531e+07 1.595815e+00 -1.99563e-01 800 1.000000e+08 1.617798e+00 -2.04726e-01 801 1.011579e+08 1.640890e+00 -2.10131e-01 802 1.023293e+08 1.665171e+00 -2.15797e-01 803 1.035142e+08 1.690724e+00 -2.21742e-01 804 1.047129e+08 1.717643e+00 -2.27988e-01 805 1.059254e+08 1.746030e+00 -2.34559e-01 806 1.071519e+08 1.775996e+00 -2.41480e-01 807 1.083927e+08 1.807664e+00 -2.48781e-01 808 1.096478e+08 1.841169e+00 -2.56493e-01 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 809 1.109175e+08 1.876659e+00 -2.64653e-01 810 1.122018e+08 1.914300e+00 -2.73300e-01 811 1.135011e+08 1.954272e+00 -2.82479e-01 812 1.148154e+08 1.996778e+00 -2.92240e-01 813 1.161449e+08 2.042040e+00 -3.02638e-01 814 1.174898e+08 2.090307e+00 -3.13739e-01 815 1.188502e+08 2.141855e+00 -3.25613e-01 816 1.202264e+08 2.196989e+00 -3.38342e-01 817 1.216186e+08 2.256052e+00 -3.52019e-01 818 1.230269e+08 2.319422e+00 -3.66750e-01 819 1.244515e+08 2.387523e+00 -3.82656e-01 820 1.258925e+08 2.460823e+00 -3.99877e-01 821 1.273503e+08 2.539840e+00 -4.18575e-01 822 1.288250e+08 2.625143e+00 -4.38934e-01 823 1.303167e+08 2.717356e+00 -4.61170e-01 824 1.318257e+08 2.817148e+00 -4.85534e-01 825 1.333521e+08 2.925232e+00 -5.12315e-01 826 1.348963e+08 3.042336e+00 -5.41852e-01 827 1.364583e+08 3.169179e+00 -5.74537e-01 828 1.380384e+08 3.306404e+00 -6.10824e-01 829 1.396368e+08 3.454493e+00 -6.51236e-01 830 1.412538e+08 3.613617e+00 -6.96366e-01 831 1.428894e+08 3.783429e+00 -7.46880e-01 832 1.445440e+08 3.962751e+00 -8.03502e-01 833 1.462177e+08 4.149168e+00 -8.66981e-01 834 1.479108e+08 4.338521e+00 -9.38042e-01 835 1.496236e+08 4.524368e+00 -1.01728e+00 836 1.513561e+08 4.697600e+00 -1.10504e+00 837 1.531087e+08 4.846488e+00 -1.20120e+00 838 1.548817e+08 4.957571e+00 -1.30503e+00 839 1.566751e+08 5.017640e+00 -1.41502e+00 840 1.584893e+08 5.016595e+00 -1.52891e+00 841 1.603245e+08 4.950272e+00 -1.64389e+00 842 1.621810e+08 4.821914e+00 -1.75697e+00 843 1.640590e+08 4.641449e+00 -1.86548e+00 844 1.659587e+08 4.422924e+00 -1.96734e+00 845 1.678804e+08 4.181327e+00 -2.06126e+00 846 1.698244e+08 3.930056e+00 -2.14669e+00 847 1.717908e+08 3.679591e+00 -2.22366e+00 848 1.737801e+08 3.437234e+00 -2.29260e+00 849 1.757924e+08 3.207504e+00 -2.35414e+00 850 1.778279e+08 2.992781e+00 -2.40902e+00 851 1.798871e+08 2.793948e+00 -2.45800e+00 852 1.819701e+08 2.610915e+00 -2.50179e+00 853 1.840772e+08 2.443013e+00 -2.54102e+00 854 1.862087e+08 2.289260e+00 -2.57628e+00 855 1.883649e+08 2.148536e+00 -2.60807e+00 856 1.905461e+08 2.019693e+00 -2.63682e+00 857 1.927525e+08 1.901617e+00 -2.66291e+00 858 1.949845e+08 1.793263e+00 -2.68667e+00 859 1.972423e+08 1.693670e+00 -2.70837e+00 860 1.995262e+08 1.601967e+00 -2.72826e+00 861 2.018366e+08 1.517371e+00 -2.74654e+00 862 2.041738e+08 1.439181e+00 -2.76339e+00 863 2.065380e+08 1.366773e+00 -2.77896e+00 864 2.089296e+08 1.299591e+00 -2.79339e+00 865 2.113489e+08 1.237142e+00 -2.80680e+00 866 2.137962e+08 1.178986e+00 -2.81929e+00 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 867 2.162719e+08 1.124733e+00 -2.83095e+00 868 2.187762e+08 1.074033e+00 -2.84185e+00 869 2.213095e+08 1.026576e+00 -2.85207e+00 870 2.238721e+08 9.820844e-01 -2.86167e+00 871 2.264644e+08 9.403095e-01 -2.87069e+00 872 2.290868e+08 9.010284e-01 -2.87921e+00 873 2.317395e+08 8.640407e-01 -2.88724e+00 874 2.344229e+08 8.291660e-01 -2.89484e+00 875 2.371374e+08 7.962415e-01 -2.90203e+00 876 2.398833e+08 7.651203e-01 -2.90885e+00 877 2.426610e+08 7.356691e-01 -2.91533e+00 878 2.454709e+08 7.077672e-01 -2.92150e+00 879 2.483133e+08 6.813048e-01 -2.92736e+00 880 2.511886e+08 6.561818e-01 -2.93296e+00 881 2.540973e+08 6.323070e-01 -2.93829e+00 882 2.570396e+08 6.095970e-01 -2.94339e+00 883 2.600160e+08 5.879757e-01 -2.94827e+00 884 2.630268e+08 5.673729e-01 -2.95294e+00 885 2.660725e+08 5.477245e-01 -2.95742e+00 886 2.691535e+08 5.289714e-01 -2.96171e+00 887 2.722701e+08 5.110591e-01 -2.96583e+00 888 2.754229e+08 4.939374e-01 -2.96979e+00 889 2.786121e+08 4.775600e-01 -2.97360e+00 890 2.818383e+08 4.618838e-01 -2.97727e+00 891 2.851018e+08 4.468691e-01 -2.98080e+00 892 2.884032e+08 4.324790e-01 -2.98421e+00 893 2.917427e+08 4.186794e-01 -2.98749e+00 894 2.951209e+08 4.054382e-01 -2.99066e+00 895 2.985383e+08 3.927258e-01 -2.99372e+00 896 3.019952e+08 3.805147e-01 -2.99668e+00 897 3.054921e+08 3.687789e-01 -2.99954e+00 898 3.090295e+08 3.574944e-01 -3.00231e+00 899 3.126079e+08 3.466385e-01 -3.00500e+00 900 3.162278e+08 3.361903e-01 -3.00760e+00 901 3.198895e+08 3.261299e-01 -3.01011e+00 902 3.235937e+08 3.164387e-01 -3.01256e+00 903 3.273407e+08 3.070994e-01 -3.01493e+00 904 3.311311e+08 2.980955e-01 -3.01723e+00 905 3.349654e+08 2.894116e-01 -3.01947e+00 906 3.388442e+08 2.810333e-01 -3.02164e+00 907 3.427678e+08 2.729468e-01 -3.02375e+00 908 3.467369e+08 2.651392e-01 -3.02581e+00 909 3.507519e+08 2.575985e-01 -3.02781e+00 910 3.548134e+08 2.503130e-01 -3.02975e+00 911 3.589219e+08 2.432720e-01 -3.03165e+00 912 3.630781e+08 2.364651e-01 -3.03349e+00 913 3.672823e+08 2.298826e-01 -3.03529e+00 914 3.715352e+08 2.235153e-01 -3.03705e+00 915 3.758374e+08 2.173544e-01 -3.03876e+00 916 3.801894e+08 2.113917e-01 -3.04043e+00 917 3.845918e+08 2.056192e-01 -3.04205e+00 918 3.890451e+08 2.000295e-01 -3.04364e+00 919 3.935501e+08 1.946155e-01 -3.04520e+00 920 3.981072e+08 1.893703e-01 -3.04671e+00 921 4.027170e+08 1.842876e-01 -3.04819e+00 922 4.073803e+08 1.793613e-01 -3.04964e+00 923 4.120975e+08 1.745854e-01 -3.05106e+00 924 4.168694e+08 1.699545e-01 -3.05244e+00 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 925 4.216965e+08 1.654631e-01 -3.05380e+00 926 4.265795e+08 1.611063e-01 -3.05512e+00 927 4.315191e+08 1.568792e-01 -3.05642e+00 928 4.365158e+08 1.527771e-01 -3.05769e+00 929 4.415704e+08 1.487957e-01 -3.05893e+00 930 4.466836e+08 1.449307e-01 -3.06015e+00 931 4.518559e+08 1.411780e-01 -3.06134e+00 932 4.570882e+08 1.375339e-01 -3.06251e+00 933 4.623810e+08 1.339946e-01 -3.06366e+00 934 4.677351e+08 1.305564e-01 -3.06478e+00 935 4.731513e+08 1.272162e-01 -3.06588e+00 936 4.786301e+08 1.239705e-01 -3.06696e+00 937 4.841724e+08 1.208162e-01 -3.06802e+00 938 4.897788e+08 1.177503e-01 -3.06906e+00 939 4.954502e+08 1.147700e-01 -3.07008e+00 940 5.011872e+08 1.118725e-01 -3.07108e+00 941 5.069907e+08 1.090551e-01 -3.07206e+00 942 5.128614e+08 1.063153e-01 -3.07302e+00 943 5.188000e+08 1.036505e-01 -3.07397e+00 944 5.248075e+08 1.010585e-01 -3.07490e+00 945 5.308844e+08 9.853691e-02 -3.07581e+00 946 5.370318e+08 9.608361e-02 -3.07670e+00 947 5.432503e+08 9.369645e-02 -3.07759e+00 948 5.495409e+08 9.137343e-02 -3.07845e+00 949 5.559043e+08 8.911257e-02 -3.07930e+00 950 5.623413e+08 8.691199e-02 -3.08014e+00 951 5.688529e+08 8.476987e-02 -3.08096e+00 952 5.754399e+08 8.268447e-02 -3.08177e+00 953 5.821032e+08 8.065408e-02 -3.08256e+00 954 5.888437e+08 7.867709e-02 -3.08334e+00 955 5.956621e+08 7.675191e-02 -3.08411e+00 956 6.025596e+08 7.487703e-02 -3.08487e+00 957 6.095369e+08 7.305098e-02 -3.08561e+00 958 6.165950e+08 7.127235e-02 -3.08634e+00 959 6.237348e+08 6.953975e-02 -3.08706e+00 960 6.309573e+08 6.785188e-02 -3.08777e+00 961 6.382635e+08 6.620745e-02 -3.08846e+00 962 6.456542e+08 6.460523e-02 -3.08915e+00 963 6.531306e+08 6.304402e-02 -3.08983e+00 964 6.606934e+08 6.152266e-02 -3.09049e+00 965 6.683439e+08 6.004005e-02 -3.09115e+00 966 6.760830e+08 5.859508e-02 -3.09179e+00 967 6.839116e+08 5.718673e-02 -3.09242e+00 968 6.918310e+08 5.581396e-02 -3.09305e+00 969 6.998420e+08 5.447581e-02 -3.09367e+00 970 7.079458e+08 5.317132e-02 -3.09427e+00 971 7.161434e+08 5.189957e-02 -3.09487e+00 972 7.244360e+08 5.065966e-02 -3.09546e+00 973 7.328245e+08 4.945074e-02 -3.09604e+00 974 7.413102e+08 4.827196e-02 -3.09661e+00 975 7.498942e+08 4.712251e-02 -3.09717e+00 976 7.585776e+08 4.600161e-02 -3.09773e+00 977 7.673615e+08 4.490849e-02 -3.09827e+00 978 7.762471e+08 4.384241e-02 -3.09881e+00 979 7.852356e+08 4.280264e-02 -3.09934e+00 980 7.943282e+08 4.178851e-02 -3.09987e+00 981 8.035261e+08 4.079932e-02 -3.10038e+00 982 8.128305e+08 3.983442e-02 -3.10089e+00 Index frequency vm(2) vp(2) -------------------------------------------------------------------------------- 983 8.222426e+08 3.889317e-02 -3.10140e+00 984 8.317638e+08 3.797496e-02 -3.10189e+00 985 8.413951e+08 3.707918e-02 -3.10238e+00 986 8.511380e+08 3.620525e-02 -3.10286e+00 987 8.609938e+08 3.535261e-02 -3.10333e+00 988 8.709636e+08 3.452070e-02 -3.10380e+00 989 8.810489e+08 3.370899e-02 -3.10426e+00 990 8.912509e+08 3.291696e-02 -3.10472e+00 991 9.015711e+08 3.214411e-02 -3.10517e+00 992 9.120108e+08 3.138994e-02 -3.10561e+00 993 9.225714e+08 3.065398e-02 -3.10605e+00 994 9.332543e+08 2.993577e-02 -3.10648e+00 995 9.440609e+08 2.923485e-02 -3.10690e+00 996 9.549926e+08 2.855078e-02 -3.10732e+00 997 9.660509e+08 2.788315e-02 -3.10774e+00 998 9.772372e+08 2.723153e-02 -3.10815e+00 999 9.885531e+08 2.659553e-02 -3.10855e+00 1000 1.000000e+09 2.597475e-02 -3.10895e+00
Plot:
Neste modelo, $L_cav$ e $C_{cav}$ representam os parâmetros equivalentes do modo ressonante da cavidade, e $R_{loss}$ modela as perdas. A análise AC identifica a frequência de ressonância $f_{res}$ e a largura de banda, permitindo avaliar o Q-factor da cavidade:
$$
Q=\frac{f_{res}}{\Delta f}=\frac{1}{R}\sqrt{\frac{L}{C}}.
$$
Para cavidades reais, as perdas incluem:
- perdas por condução nas paredes (profundidade pelicular);
- perdas por aberturas e penetrções;
- perdas por conteúdo interno (placas, componentes);
- perdas por absorvedores dielétricos ou magnéticos.
O Q-factor elevado indica ressonâncias agudas que podem causar acoplamento intenso entre fontes internas e aberturas. Amortecimento com materiais absorvedores ou mudança geométrica reduz o Q e espalha as ressonâncias.
12.22 Referência principal
Síntese do Capítulo 10, "Shielding", de C. R. Paul, Introduction to Electromagnetic Compatibility, 2ª ed., Wiley, 2006, pp. 713–751.