19. Projeto e simulação com KiCad
Compatibilidade Eletromagnética
19. Projeto e simulação com KiCad
Pré-requisito recomendado: Introdução ao SPICE para EMC. Este capítulo aplica a sintaxe e os critérios de validação ao fluxo KiCad/ngspice e ao layout de PCB.
O KiCad é uma suite de EDA (Electronic Design Automation) open-source amplamente utilizada para projeto de esquemáticos e PCBs. Para EMC e integridade de sinal, o KiCad oferece capacidades de simulação SPICE integradas (baseadas em Ngspice) que permitem analisar reflexões, ringing, impedância da PDN e espectro de sinais antes da fabricação.
19.1 Introdução ao KiCad para EMC
O fluxo de trabalho do KiCad para projetos EMC inclui:
- Eeschema: Captura esquemática com modelagem de componentes não ideais.
- PCBNew: Layout de PCB com regras de EMC (planos de referência, roteamento diferenciado, etc.).
- Simulador SPICE: Análise transiente, AC e Fourier para validação de integridade de sinal e emissões.
Insight para Estudantes: O KiCad não é um simulador de campos eletromagnéticos 3D como CST ou HFSS. Ele é um simulador de circuitos (SPICE). Para EMC de baixa e média frequência (integridade de sinal, acoplamento por impedância comum, reflexões em linhas), o SPICE é suficiente e muito mais rápido. Para radiação direta e acoplamento por campo próximo complexo, ferramentas 3D são necessárias.
19.2 Configuração do simulador SPICE no KiCad
No KiCad 8+, o simulador SPICE é integrado e baseado em Ngspice. Para configurar:
- Abra o Eeschema e vá em
Simulação > Configuração do Simulador SPICE. - Selecione o tipo de simulação: Transiente, AC, DC Sweep, ou Fourier.
- Configure os parâmetros:
- Transiente: tempo inicial, tempo final, passo de máxima.
- AC: tipo de varredura (dec, lin, log), número de pontos por década, frequência inicial e final.
- Fourier: frequência fundamental, número de harmônicos.
Dica Pedagógica: Sempre valide se os modelos SPICE dos componentes estão corretos. Componentes padrão do KiCad podem não incluir ESL/ESR. Use modelos personalizados ou subcircuitos para precisão EMC.
19.3 Modelagem de componentes não ideais no esquemático
Para simulações realistas de EMC, é crucial incluir parasitas:
- Capacitores: Inclua ESL e ESR nos modelos SPICE. No KiCad, isso é feito usando modelos SPICE personalizados ou subcircuitos.
- Indutores: Inclua capacitância parasita e resistência série.
- Trilhas como linhas de transmissão: Use modelos T-line ou delay lines no SPICE.
19.3.1 Modelo SPICE de capacitor real
Um capacitor real pode ser modelado como:
.subckt REAL_CAP C_node E_node
R_esr C_node e1 {ESR}
L_esl e1 e2 {ESL}
C_main e2 E_node {C_val}
.ends REAL_CAPNo esquemático do KiCad, você pode usar um componente "SPICE: subcircuit" e vincular este modelo.
19.4 Regras de layout para EMC no PCB Editor
19.4.1 Planos de referência
- Mantenha um plano de terra contínuo sob trilhas de alta velocidade.
- Evite splits no plano sob trilhas críticas.
19.4.2 Roteamento de sinais diferenciais
- Mantenha o espaçamento constante entre os pares.
- Roteie o par sobre o mesmo plano de referência.
19.4.3 Desacoplamento e PDN
- Coloque capacitores de desacoplamento o mais próximo possível dos pinos de alimentação do CI.
- Use vias múltiplas para conectar capacitores aos planos.
19.5 Simulação SPICE integrada no KiCad
O KiCad 8+ inclui um simulador SPICE integrado baseado em Ngspice. Para configurar:
- No Eeschema, adicione as diretivas SPICE:
SPICE: transient,SPICE: ac,SPICE: fourier. - Use o menu
Simulação > Simulador SPICE.
19.5.1 Simulação transiente para integridade de sinal
Para analisar reflexões e ringing em uma linha de transmissão, modele a linha como uma rede L-C pi ou use linhas de transmissão distribuídas.
Netlist SPICE de exemplo para linha com reflexões:
* Linha de transmissão modelada como rede L-C
Vsrc src 0 PULSE(0 3.3 0 50p 50p 1n 2n)
Rs src n1 50
* Modelo de linha: L=10nH, C=5pF
L1 n1 n2 10nH
C1 n2 n3 5pF
L2 n3 n4 10nH
C2 n4 0 5pF
Rload n4 0 50
.tran 0.05n 5n
.probe tran V(n4)
.endNo KiCad, você pode criar este esquemático usando componentes R, L, C e uma fonte PULSE. Execute a simulação transiente e observe a tensão em n4: para carga casada ($R_{load}=50\ \Omega$), não deve haver reflexões; para carga aberta, espera-se overshoot.
19.5.2 Simulação AC para impedância da PDN
Para calcular a impedância da Power Distribution Network (PDN):
- Crie um esquemático com a fonte de alimentação e os capacitores de desacoplamento.
- Adicione uma fonte de corrente AC de 1 A entre VCC e GND no ponto de interesse.
- Configure análise AC:
.ac dec 100 10k 100M - Meça a tensão no nodo VCC:
Z_pdN = V(VCC)/I(Vsrc)
Netlist SPICE de exemplo para PDN:
* PDN com capacitores de desacoplamento
Vcc vcc 0 DC 3.3
* Fonte de corrente AC para medição de impedância
Iac vcc 0 AC 1
* Capacitores: 10uF, 100nF, 10nF
C1 vcc gnd 10uF ESL=5nH ESR=50m
C2 vcc gnd 100nF ESL=1nH ESR=30m
C3 vcc gnd 10nF ESL=0.5nH ESR=20m
.ac dec 100 10k 100M
.probe ac V(vcc)
.endInsight para Estudantes: Na simulação AC do KiCad, a impedância é medida como $Z = V/I$. Como $I=1$ A AC, $Z$ em volts é numericamente igual a $Z$ em ohms. Plotando
V(vcc)em escala logarítmica, você obtém diretamente a magnitude da impedância da PDN.
19.5.3 Análise de Fourier para emissões espectrais
Para estimar as emissões conduzidas/radiadas a partir de sinais digitais:
- Execute simulação transiente por vários ciclos em regime estacionário.
- Adicione diretiva
.four N f0 V(nodo), ondeNé o número de harmônicos ef0é a frequência fundamental.
.four 100MHz V(clock_node)Isso gera os coeficientes de Fourier no arquivo de saída, permitindo estimar o espectro de emissões.
19.6 Exemplos práticos de simulação no KiCad
19.6.1 Exemplo: reflexão em linha aberta
Esquemático SPICE:
Vsrc src 0 PULSE(0 3.3 0 50p 50p 1n 2n)
Rs src n1 50
L1 n1 n2 10nH
C1 n2 0 5pF
Rload n2 0 open
.tran 0.1n 5nNo KiCad, use componentes R, L, C e configure a fonte PULSE. Execute a simulação transiente e observe a tensão em n2: para carga aberta, espera-se overshoot de 2x (6.6 V) após o atraso de propagação.
19.6.2 Exemplo: impedância da PDN com múltiplos capacitores
Configuração:
- Fonte VCC = 3.3 V.
- Capacitores: 10 µF, 100 nF, 10 nF com ESL e ESR modelados.
- Fonte de corrente AC 1 A entre VCC e GND.
19.7 Fluxo de trabalho recomendado para EMC no KiCad
- Esquemático: Inclua modelagem SPICE para componentes críticos.
- Simulação pré-layout: Valide integridade de sinal e PDN com modelos simplificados.
- Layout PCB: Aplique regras de EMC (planos, roteamento, decap).
- Extração parasita: Após o layout, extraia L, C, R parasitas (se o KiCad ou ferramenta externa suportar).
- Simulação pós-layout: Revalide com modelos realistas.
19.8 Limitações das simulações no KiCad
O KiCad SPICE é limitado a modelos de circuito concentrado e linhas de transmissão distribuídas simples. Para:
- Acoplamento capacitivo/indutivo detalhado entre trilhas: use ferramentas de extrator de parasitas (como Q3D Extractor, que se integra ao KiCad).
- Simulação de radiação e antenas: use CST Studio, HFSS ou FEKO.
- Análise de campo próximo 3D: use ferramentas especializadas.
Insight para Estudantes: O KiCad é excelente para a fase inicial de validação de conceitos e para simulações de integridade de sinal e PDN. Para problemas de EMC radiada e acoplamento complexo por campo, o fluxo típico é: KiCad para layout e extração de parasitas, depois ferramenta 3D para análise de campos.
19.9 Código Python — Gerador de netlist SPICE para KiCad
Para facilitar a criação de modelos complexos, um script Python pode gerar netlists SPICE prontas para uso no KiCad:
PYTHON
# generate_spice_netlist.py
def generate_transmission_line_netlist(length_m, z0_ohm, vp_m_s, pulse_amplitude, pulse_tr_ns, file_out='tl_line.sp'):
"""Gera netlist SPICE para linha de transmissão modelada como rede L-C pi."""
# Parâmetros da linha
# Z0 = sqrt(L/C), vp = 1/sqrt(LC)
# L = Z0 / vp, C = 1 / (Z0 * vp)
L_per_section = z0_ohm / vp_m_s # H
C_per_section = 1.0 / (z0_ohm * vp_m_s) # F
# Número de seções pi (regra prática: >= 5 para precisão)
n_sections = 5
L_sec = L_per_section * length_m / n_sections
C_sec = C_per_section * length_m / n_sections
with open(file_out, 'w') as f:
f.write(f"* Linha de transmissão: L={length_m}m, Z0={z0_ohm}Ohm, vp={vp_m_s}m/s\n")
f.write(f"Vsrc src 0 PULSE(0 {pulse_amplitude} 0 {pulse_tr_ns*1e-9} {pulse_tr_ns*1e-9} {2*pulse_tr_ns*1e-9} {10*pulse_tr_ns*1e-9})\n")
f.write(f"Rs src n1 {z0_ohm}\n")
# Rede L-C pi
for i in range(n_sections):
n_in = f"n{i+1}"
n_mid = f"n{i+2}"
f.write(f"L{i+1} {n_in} {n_mid} {L_sec*1e9}nH\n")
if i == 0:
f.write(f"C{i+1} {n_mid} 0 {C_sec*1e12}pF\n")
else:
f.write(f"C{i+1} {n_mid} 0 {C_sec*1e12}pF\n")
f.write(f"Rload n{n_sections+1} 0 {z0_ohm}\n")
f.write(f".tran 0.01n {10*pulse_tr_ns*1e-9}\n")
f.write(f".probe tran V(n{n_sections+1})\n")
f.write(".end\n")
print(f"Netlist gerada: {file_out}")
# Exemplo de uso:
# generate_transmission_line_netlist(length_m=0.3, z0_ohm=50, vp_m_s=2e8, pulse_amplitude=3.3, pulse_tr_ns=0.1)
19.10 Interpretação de resultados no simulador do KiCad
Após executar uma simulação no KiCad:
- Gráficos Transientes: Use o visualizador para plotar tensões e correntes. Identifique ringing, overshoot, e tempo de estabilização.
- Gráficos AC: Para impedância da PDN, plotee
V(vcc)em escala logarítmica. A linha horizontal deZ_target(ex: 50 mΩ) deve ser respeitada. - Saída Fourier: O arquivo de texto gerado contém os coeficientes. Converta dBmV para estimar emissões.
Insight para Estudantes: O simulador do KiCad é baseado em Ngspice, que usa métodos numéricos de integração. Para sinais com bordas muito rápidas (< 10 ps), reduza o passo de simulação máxima e verifique a convergência. Instabilidades numéricas podem gerar oscilações falsas.
19.11 Exercícios práticos com KiCad
E.1 Monte um esquemático no KiCad com uma fonte PULSE e linha de transmissão modelada como rede L-C. Execute simulação transiente e observe reflexões.
E.2 Projete uma PDN com 3 capacitores e simule a impedância AC. Verifique se atinge < 50 mΩ na banda desejada.
E.3 Simule um sinal clock com análise de Fourier e extraia os níveis dos harmônicos para estimar emissões.
E.4 Use o script Python acima para gerar uma netlist de linha de transmissão e importe no KiCad para simulação.
19.12 Validação cruzada KiCad–Python
Um experimento reproduzível deve usar os mesmos parâmetros em ambos os ambientes. Para um capacitor real,
SPICE
* capacitor real: 100 nF, ESR 30 mΩ, ESL 1 nH
V1 in 0 DC 0 AC 1
L_esl in n1 1n
R_esr n1 n2 30m
C_main n2 0 100n
.ac dec 100 1k 1G
.print ac vm(in) mag(v1#branch)
.end
Output:
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 : 601
generated from textbook spice code block
AC Analysis Tue Aug 11 11:11:03 2026
--------------------------------------------------------------------------------
Index frequency vm(in) mag(v1#branch)
--------------------------------------------------------------------------------
0 1.000000e+03 1.000000e+00 6.283185e-04
1 1.023293e+03 1.000000e+00 6.429540e-04
2 1.047129e+03 1.000000e+00 6.579303e-04
3 1.071519e+03 1.000000e+00 6.732554e-04
4 1.096478e+03 1.000000e+00 6.889376e-04
5 1.122018e+03 1.000000e+00 7.049850e-04Ver mais (625 linhas)
6 1.148154e+03 1.000000e+00 7.214062e-04 7 1.174898e+03 1.000000e+00 7.382099e-04 8 1.202264e+03 1.000000e+00 7.554050e-04 9 1.230269e+03 1.000000e+00 7.730007e-04 10 1.258925e+03 1.000000e+00 7.910062e-04 11 1.288250e+03 1.000000e+00 8.094311e-04 12 1.318257e+03 1.000000e+00 8.282851e-04 13 1.348963e+03 1.000000e+00 8.475784e-04 14 1.380384e+03 1.000000e+00 8.673210e-04 15 1.412538e+03 1.000000e+00 8.875235e-04 16 1.445440e+03 1.000000e+00 9.081966e-04 17 1.479108e+03 1.000000e+00 9.293512e-04 18 1.513561e+03 1.000000e+00 9.509986e-04 19 1.548817e+03 1.000000e+00 9.731502e-04 20 1.584893e+03 1.000000e+00 9.958178e-04 21 1.621810e+03 1.000000e+00 1.019013e-03 22 1.659587e+03 1.000000e+00 1.042749e-03 23 1.698244e+03 1.000000e+00 1.067038e-03 24 1.737801e+03 1.000000e+00 1.091892e-03 25 1.778279e+03 1.000000e+00 1.117326e-03 26 1.819701e+03 1.000000e+00 1.143352e-03 27 1.862087e+03 1.000000e+00 1.169984e-03 28 1.905461e+03 1.000000e+00 1.197236e-03 29 1.949845e+03 1.000000e+00 1.225124e-03 30 1.995262e+03 1.000000e+00 1.253660e-03 31 2.041738e+03 1.000000e+00 1.282862e-03 32 2.089296e+03 1.000000e+00 1.312743e-03 33 2.137962e+03 1.000000e+00 1.343321e-03 34 2.187762e+03 1.000000e+00 1.374611e-03 35 2.238721e+03 1.000000e+00 1.406630e-03 36 2.290868e+03 1.000000e+00 1.439395e-03 37 2.344229e+03 1.000000e+00 1.472922e-03 38 2.398833e+03 1.000000e+00 1.507231e-03 39 2.454709e+03 1.000000e+00 1.542339e-03 40 2.511886e+03 1.000000e+00 1.578265e-03 41 2.570396e+03 1.000000e+00 1.615027e-03 42 2.630268e+03 1.000000e+00 1.652646e-03 43 2.691535e+03 1.000000e+00 1.691141e-03 44 2.754229e+03 1.000000e+00 1.730533e-03 45 2.818383e+03 1.000000e+00 1.770842e-03 46 2.884032e+03 1.000000e+00 1.812090e-03 47 2.951209e+03 1.000000e+00 1.854300e-03 48 3.019952e+03 1.000000e+00 1.897492e-03 49 3.090295e+03 1.000000e+00 1.941690e-03 50 3.162278e+03 1.000000e+00 1.986918e-03 51 3.235937e+03 1.000000e+00 2.033199e-03 52 3.311311e+03 1.000000e+00 2.080558e-03 53 3.388442e+03 1.000000e+00 2.129021e-03 54 3.467369e+03 1.000000e+00 2.178612e-03 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 55 3.548134e+03 1.000000e+00 2.229358e-03 56 3.630781e+03 1.000000e+00 2.281287e-03 57 3.715352e+03 1.000000e+00 2.334425e-03 58 3.801894e+03 1.000000e+00 2.388801e-03 59 3.890451e+03 1.000000e+00 2.444443e-03 60 3.981072e+03 1.000000e+00 2.501381e-03 61 4.073803e+03 1.000000e+00 2.559646e-03 62 4.168694e+03 1.000000e+00 2.619268e-03 63 4.265795e+03 1.000000e+00 2.680278e-03 64 4.365158e+03 1.000000e+00 2.742710e-03 65 4.466836e+03 1.000000e+00 2.806596e-03 66 4.570882e+03 1.000000e+00 2.871970e-03 67 4.677351e+03 1.000000e+00 2.938867e-03 68 4.786301e+03 1.000000e+00 3.007322e-03 69 4.897788e+03 1.000000e+00 3.077371e-03 70 5.011872e+03 1.000000e+00 3.149053e-03 71 5.128614e+03 1.000000e+00 3.222403e-03 72 5.248075e+03 1.000000e+00 3.297463e-03 73 5.370318e+03 1.000000e+00 3.374271e-03 74 5.495409e+03 1.000000e+00 3.452868e-03 75 5.623413e+03 1.000000e+00 3.533295e-03 76 5.754399e+03 1.000000e+00 3.615596e-03 77 5.888437e+03 1.000000e+00 3.699814e-03 78 6.025596e+03 1.000000e+00 3.785994e-03 79 6.165950e+03 1.000000e+00 3.874181e-03 80 6.309573e+03 1.000000e+00 3.964423e-03 81 6.456542e+03 1.000000e+00 4.056766e-03 82 6.606934e+03 1.000000e+00 4.151260e-03 83 6.760830e+03 1.000000e+00 4.247955e-03 84 6.918310e+03 1.000000e+00 4.346903e-03 85 7.079458e+03 1.000000e+00 4.448155e-03 86 7.244360e+03 1.000000e+00 4.551766e-03 87 7.413102e+03 1.000000e+00 4.657791e-03 88 7.585776e+03 1.000000e+00 4.766285e-03 89 7.762471e+03 1.000000e+00 4.877306e-03 90 7.943282e+03 1.000000e+00 4.990913e-03 91 8.128305e+03 1.000000e+00 5.107166e-03 92 8.317638e+03 1.000000e+00 5.226127e-03 93 8.511380e+03 1.000000e+00 5.347859e-03 94 8.709636e+03 1.000000e+00 5.472427e-03 95 8.912509e+03 1.000000e+00 5.599896e-03 96 9.120108e+03 1.000000e+00 5.730335e-03 97 9.332543e+03 1.000000e+00 5.863812e-03 98 9.549926e+03 1.000000e+00 6.000397e-03 99 9.772372e+03 1.000000e+00 6.140165e-03 100 1.000000e+04 1.000000e+00 6.283188e-03 101 1.023293e+04 1.000000e+00 6.429542e-03 102 1.047129e+04 1.000000e+00 6.579305e-03 103 1.071519e+04 1.000000e+00 6.732557e-03 104 1.096478e+04 1.000000e+00 6.889379e-03 105 1.122018e+04 1.000000e+00 7.049853e-03 106 1.148154e+04 1.000000e+00 7.214066e-03 107 1.174898e+04 1.000000e+00 7.382103e-03 108 1.202264e+04 1.000000e+00 7.554054e-03 109 1.230269e+04 1.000000e+00 7.730011e-03 110 1.258925e+04 1.000000e+00 7.910066e-03 111 1.288250e+04 1.000000e+00 8.094316e-03 112 1.318257e+04 1.000000e+00 8.282857e-03 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 113 1.348963e+04 1.000000e+00 8.475790e-03 114 1.380384e+04 1.000000e+00 8.673216e-03 115 1.412538e+04 1.000000e+00 8.875242e-03 116 1.445440e+04 1.000000e+00 9.081973e-03 117 1.479108e+04 1.000000e+00 9.293520e-03 118 1.513561e+04 1.000000e+00 9.509994e-03 119 1.548817e+04 1.000000e+00 9.731511e-03 120 1.584893e+04 1.000000e+00 9.958187e-03 121 1.621810e+04 1.000000e+00 1.019014e-02 122 1.659587e+04 1.000000e+00 1.042750e-02 123 1.698244e+04 1.000000e+00 1.067039e-02 124 1.737801e+04 1.000000e+00 1.091894e-02 125 1.778279e+04 1.000000e+00 1.117327e-02 126 1.819701e+04 1.000000e+00 1.143353e-02 127 1.862087e+04 1.000000e+00 1.169985e-02 128 1.905461e+04 1.000000e+00 1.197238e-02 129 1.949845e+04 1.000000e+00 1.225125e-02 130 1.995262e+04 1.000000e+00 1.253662e-02 131 2.041738e+04 1.000000e+00 1.282864e-02 132 2.089296e+04 1.000000e+00 1.312746e-02 133 2.137962e+04 1.000000e+00 1.343324e-02 134 2.187762e+04 1.000000e+00 1.374614e-02 135 2.238721e+04 1.000000e+00 1.406633e-02 136 2.290868e+04 1.000000e+00 1.439397e-02 137 2.344229e+04 1.000000e+00 1.472925e-02 138 2.398833e+04 1.000000e+00 1.507234e-02 139 2.454709e+04 1.000000e+00 1.542343e-02 140 2.511886e+04 1.000000e+00 1.578269e-02 141 2.570396e+04 1.000000e+00 1.615031e-02 142 2.630268e+04 1.000000e+00 1.652650e-02 143 2.691535e+04 1.000000e+00 1.691146e-02 144 2.754229e+04 1.000000e+00 1.730538e-02 145 2.818383e+04 1.000000e+00 1.770848e-02 146 2.884032e+04 1.000000e+00 1.812096e-02 147 2.951209e+04 1.000000e+00 1.854306e-02 148 3.019952e+04 1.000000e+00 1.897498e-02 149 3.090295e+04 1.000000e+00 1.941697e-02 150 3.162278e+04 1.000000e+00 1.986925e-02 151 3.235937e+04 1.000000e+00 2.033207e-02 152 3.311311e+04 1.000000e+00 2.080567e-02 153 3.388442e+04 1.000000e+00 2.129030e-02 154 3.467369e+04 1.000000e+00 2.178622e-02 155 3.548134e+04 1.000000e+00 2.229369e-02 156 3.630781e+04 1.000000e+00 2.281298e-02 157 3.715352e+04 1.000000e+00 2.334437e-02 158 3.801894e+04 1.000000e+00 2.388813e-02 159 3.890451e+04 1.000000e+00 2.444457e-02 160 3.981072e+04 1.000000e+00 2.501396e-02 161 4.073803e+04 1.000000e+00 2.559662e-02 162 4.168694e+04 1.000000e+00 2.619285e-02 163 4.265795e+04 1.000000e+00 2.680297e-02 164 4.365158e+04 1.000000e+00 2.742730e-02 165 4.466836e+04 1.000000e+00 2.806617e-02 166 4.570882e+04 1.000000e+00 2.871992e-02 167 4.677351e+04 1.000000e+00 2.938891e-02 168 4.786301e+04 1.000000e+00 3.007348e-02 169 4.897788e+04 1.000000e+00 3.077399e-02 170 5.011872e+04 1.000000e+00 3.149082e-02 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 171 5.128614e+04 1.000000e+00 3.222435e-02 172 5.248075e+04 1.000000e+00 3.297497e-02 173 5.370318e+04 1.000000e+00 3.374307e-02 174 5.495409e+04 1.000000e+00 3.452906e-02 175 5.623413e+04 1.000000e+00 3.533337e-02 176 5.754399e+04 1.000000e+00 3.615641e-02 177 5.888437e+04 1.000000e+00 3.699862e-02 178 6.025596e+04 1.000000e+00 3.786045e-02 179 6.165950e+04 1.000000e+00 3.874236e-02 180 6.309573e+04 1.000000e+00 3.964481e-02 181 6.456542e+04 1.000000e+00 4.056829e-02 182 6.606934e+04 1.000000e+00 4.151328e-02 183 6.760830e+04 1.000000e+00 4.248028e-02 184 6.918310e+04 1.000000e+00 4.346981e-02 185 7.079458e+04 1.000000e+00 4.448239e-02 186 7.244360e+04 1.000000e+00 4.551855e-02 187 7.413102e+04 1.000000e+00 4.657886e-02 188 7.585776e+04 1.000000e+00 4.766387e-02 189 7.762471e+04 1.000000e+00 4.877415e-02 190 7.943282e+04 1.000000e+00 4.991030e-02 191 8.128305e+04 1.000000e+00 5.107292e-02 192 8.317638e+04 1.000000e+00 5.226262e-02 193 8.511380e+04 1.000000e+00 5.348004e-02 194 8.709636e+04 1.000000e+00 5.472582e-02 195 8.912509e+04 1.000000e+00 5.600063e-02 196 9.120108e+04 1.000000e+00 5.730513e-02 197 9.332543e+04 1.000000e+00 5.864002e-02 198 9.549926e+04 1.000000e+00 6.000602e-02 199 9.772372e+04 1.000000e+00 6.140384e-02 200 1.000000e+05 1.000000e+00 6.283422e-02 201 1.023293e+05 1.000000e+00 6.429793e-02 202 1.047129e+05 1.000000e+00 6.579575e-02 203 1.071519e+05 1.000000e+00 6.732846e-02 204 1.096478e+05 1.000000e+00 6.889688e-02 205 1.122018e+05 1.000000e+00 7.050184e-02 206 1.148154e+05 1.000000e+00 7.214421e-02 207 1.174898e+05 1.000000e+00 7.382483e-02 208 1.202264e+05 1.000000e+00 7.554462e-02 209 1.230269e+05 1.000000e+00 7.730448e-02 210 1.258925e+05 1.000000e+00 7.910534e-02 211 1.288250e+05 1.000000e+00 8.094817e-02 212 1.318257e+05 1.000000e+00 8.283394e-02 213 1.348963e+05 1.000000e+00 8.476365e-02 214 1.380384e+05 1.000000e+00 8.673833e-02 215 1.412538e+05 1.000000e+00 8.875903e-02 216 1.445440e+05 1.000000e+00 9.082681e-02 217 1.479108e+05 1.000000e+00 9.294279e-02 218 1.513561e+05 1.000000e+00 9.510807e-02 219 1.548817e+05 1.000000e+00 9.732382e-02 220 1.584893e+05 1.000000e+00 9.959121e-02 221 1.621810e+05 1.000000e+00 1.019114e-01 222 1.659587e+05 1.000000e+00 1.042857e-01 223 1.698244e+05 1.000000e+00 1.067154e-01 224 1.737801e+05 1.000000e+00 1.092017e-01 225 1.778279e+05 1.000000e+00 1.117459e-01 226 1.819701e+05 1.000000e+00 1.143495e-01 227 1.862087e+05 1.000000e+00 1.170137e-01 228 1.905461e+05 1.000000e+00 1.197400e-01 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 229 1.949845e+05 1.000000e+00 1.225299e-01 230 1.995262e+05 1.000000e+00 1.253848e-01 231 2.041738e+05 1.000000e+00 1.283063e-01 232 2.089296e+05 1.000000e+00 1.312960e-01 233 2.137962e+05 1.000000e+00 1.343553e-01 234 2.187762e+05 1.000000e+00 1.374859e-01 235 2.238721e+05 1.000000e+00 1.406896e-01 236 2.290868e+05 1.000000e+00 1.439679e-01 237 2.344229e+05 1.000000e+00 1.473228e-01 238 2.398833e+05 1.000000e+00 1.507558e-01 239 2.454709e+05 1.000000e+00 1.542690e-01 240 2.511886e+05 1.000000e+00 1.578640e-01 241 2.570396e+05 1.000000e+00 1.615430e-01 242 2.630268e+05 1.000000e+00 1.653077e-01 243 2.691535e+05 1.000000e+00 1.691603e-01 244 2.754229e+05 1.000000e+00 1.731028e-01 245 2.818383e+05 1.000000e+00 1.771373e-01 246 2.884032e+05 1.000000e+00 1.812659e-01 247 2.951209e+05 1.000000e+00 1.854909e-01 248 3.019952e+05 1.000000e+00 1.898144e-01 249 3.090295e+05 1.000000e+00 1.942389e-01 250 3.162278e+05 1.000000e+00 1.987667e-01 251 3.235937e+05 1.000000e+00 2.034002e-01 252 3.311311e+05 1.000000e+00 2.081419e-01 253 3.388442e+05 1.000000e+00 2.129943e-01 254 3.467369e+05 1.000000e+00 2.179600e-01 255 3.548134e+05 1.000000e+00 2.230417e-01 256 3.630781e+05 1.000000e+00 2.282421e-01 257 3.715352e+05 1.000000e+00 2.335640e-01 258 3.801894e+05 1.000000e+00 2.390103e-01 259 3.890451e+05 1.000000e+00 2.445838e-01 260 3.981072e+05 1.000000e+00 2.502877e-01 261 4.073803e+05 1.000000e+00 2.561248e-01 262 4.168694e+05 1.000000e+00 2.620985e-01 263 4.265795e+05 1.000000e+00 2.682118e-01 264 4.365158e+05 1.000000e+00 2.744682e-01 265 4.466836e+05 1.000000e+00 2.808709e-01 266 4.570882e+05 1.000000e+00 2.874234e-01 267 4.677351e+05 1.000000e+00 2.941293e-01 268 4.786301e+05 1.000000e+00 3.009921e-01 269 4.897788e+05 1.000000e+00 3.080157e-01 270 5.011872e+05 1.000000e+00 3.152037e-01 271 5.128614e+05 1.000000e+00 3.225602e-01 272 5.248075e+05 1.000000e+00 3.300890e-01 273 5.370318e+05 1.000000e+00 3.377943e-01 274 5.495409e+05 1.000000e+00 3.456803e-01 275 5.623413e+05 1.000000e+00 3.537512e-01 276 5.754399e+05 1.000000e+00 3.620115e-01 277 5.888437e+05 1.000000e+00 3.704656e-01 278 6.025596e+05 1.000000e+00 3.791183e-01 279 6.165950e+05 1.000000e+00 3.879741e-01 280 6.309573e+05 1.000000e+00 3.970381e-01 281 6.456542e+05 1.000000e+00 4.063151e-01 282 6.606934e+05 1.000000e+00 4.158102e-01 283 6.760830e+05 1.000000e+00 4.255287e-01 284 6.918310e+05 1.000000e+00 4.354760e-01 285 7.079458e+05 1.000000e+00 4.456575e-01 286 7.244360e+05 1.000000e+00 4.560789e-01 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 287 7.413102e+05 1.000000e+00 4.667459e-01 288 7.585776e+05 1.000000e+00 4.776645e-01 289 7.762471e+05 1.000000e+00 4.888409e-01 290 7.943282e+05 1.000000e+00 5.002811e-01 291 8.128305e+05 1.000000e+00 5.119917e-01 292 8.317638e+05 1.000000e+00 5.239791e-01 293 8.511380e+05 1.000000e+00 5.362502e-01 294 8.709636e+05 1.000000e+00 5.488119e-01 295 8.912509e+05 1.000000e+00 5.616713e-01 296 9.120108e+05 1.000000e+00 5.748357e-01 297 9.332543e+05 1.000000e+00 5.883125e-01 298 9.549926e+05 1.000000e+00 6.021095e-01 299 9.772372e+05 1.000000e+00 6.162346e-01 300 1.000000e+06 1.000000e+00 6.306959e-01 301 1.023293e+06 1.000000e+00 6.455018e-01 302 1.047129e+06 1.000000e+00 6.606608e-01 303 1.071519e+06 1.000000e+00 6.761818e-01 304 1.096478e+06 1.000000e+00 6.920739e-01 305 1.122018e+06 1.000000e+00 7.083463e-01 306 1.148154e+06 1.000000e+00 7.250087e-01 307 1.174898e+06 1.000000e+00 7.420709e-01 308 1.202264e+06 1.000000e+00 7.595431e-01 309 1.230269e+06 1.000000e+00 7.774358e-01 310 1.258925e+06 1.000000e+00 7.957597e-01 311 1.288250e+06 1.000000e+00 8.145260e-01 312 1.318257e+06 1.000000e+00 8.337460e-01 313 1.348963e+06 1.000000e+00 8.534315e-01 314 1.380384e+06 1.000000e+00 8.735947e-01 315 1.412538e+06 1.000000e+00 8.942481e-01 316 1.445440e+06 1.000000e+00 9.154045e-01 317 1.479108e+06 1.000000e+00 9.370774e-01 318 1.513561e+06 1.000000e+00 9.592804e-01 319 1.548817e+06 1.000000e+00 9.820278e-01 320 1.584893e+06 1.000000e+00 1.005334e+00 321 1.621810e+06 1.000000e+00 1.029215e+00 322 1.659587e+06 1.000000e+00 1.053685e+00 323 1.698244e+06 1.000000e+00 1.078761e+00 324 1.737801e+06 1.000000e+00 1.104461e+00 325 1.778279e+06 1.000000e+00 1.130800e+00 326 1.819701e+06 1.000000e+00 1.157797e+00 327 1.862087e+06 1.000000e+00 1.185471e+00 328 1.905461e+06 1.000000e+00 1.213841e+00 329 1.949845e+06 1.000000e+00 1.242927e+00 330 1.995262e+06 1.000000e+00 1.272749e+00 331 2.041738e+06 1.000000e+00 1.303330e+00 332 2.089296e+06 1.000000e+00 1.334691e+00 333 2.137962e+06 1.000000e+00 1.366856e+00 334 2.187762e+06 1.000000e+00 1.399849e+00 335 2.238721e+06 1.000000e+00 1.433695e+00 336 2.290868e+06 1.000000e+00 1.468421e+00 337 2.344229e+06 1.000000e+00 1.504053e+00 338 2.398833e+06 1.000000e+00 1.540619e+00 339 2.454709e+06 1.000000e+00 1.578151e+00 340 2.511886e+06 1.000000e+00 1.616678e+00 341 2.570396e+06 1.000000e+00 1.656232e+00 342 2.630268e+06 1.000000e+00 1.696848e+00 343 2.691535e+06 1.000000e+00 1.738562e+00 344 2.754229e+06 1.000000e+00 1.781409e+00 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 345 2.818383e+06 1.000000e+00 1.825428e+00 346 2.884032e+06 1.000000e+00 1.870661e+00 347 2.951209e+06 1.000000e+00 1.917150e+00 348 3.019952e+06 1.000000e+00 1.964939e+00 349 3.090295e+06 1.000000e+00 2.014076e+00 350 3.162278e+06 1.000000e+00 2.064610e+00 351 3.235937e+06 1.000000e+00 2.116594e+00 352 3.311311e+06 1.000000e+00 2.170081e+00 353 3.388442e+06 1.000000e+00 2.225131e+00 354 3.467369e+06 1.000000e+00 2.281804e+00 355 3.548134e+06 1.000000e+00 2.340165e+00 356 3.630781e+06 1.000000e+00 2.400282e+00 357 3.715352e+06 1.000000e+00 2.462227e+00 358 3.801894e+06 1.000000e+00 2.526078e+00 359 3.890451e+06 1.000000e+00 2.591917e+00 360 3.981072e+06 1.000000e+00 2.659828e+00 361 4.073803e+06 1.000000e+00 2.729905e+00 362 4.168694e+06 1.000000e+00 2.802245e+00 363 4.265795e+06 1.000000e+00 2.876954e+00 364 4.365158e+06 1.000000e+00 2.954142e+00 365 4.466836e+06 1.000000e+00 3.033928e+00 366 4.570882e+06 1.000000e+00 3.116441e+00 367 4.677351e+06 1.000000e+00 3.201816e+00 368 4.786301e+06 1.000000e+00 3.290201e+00 369 4.897788e+06 1.000000e+00 3.381752e+00 370 5.011872e+06 1.000000e+00 3.476639e+00 371 5.128614e+06 1.000000e+00 3.575044e+00 372 5.248075e+06 1.000000e+00 3.677165e+00 373 5.370318e+06 1.000000e+00 3.783212e+00 374 5.495409e+06 1.000000e+00 3.893417e+00 375 5.623413e+06 1.000000e+00 4.008029e+00 376 5.754399e+06 1.000000e+00 4.127318e+00 377 5.888437e+06 1.000000e+00 4.251578e+00 378 6.025596e+06 1.000000e+00 4.381130e+00 379 6.165950e+06 1.000000e+00 4.516323e+00 380 6.309573e+06 1.000000e+00 4.657541e+00 381 6.456542e+06 1.000000e+00 4.805200e+00 382 6.606934e+06 1.000000e+00 4.959763e+00 383 6.760830e+06 1.000000e+00 5.121733e+00 384 6.918310e+06 1.000000e+00 5.291669e+00 385 7.079458e+06 1.000000e+00 5.470185e+00 386 7.244360e+06 1.000000e+00 5.657964e+00 387 7.413102e+06 1.000000e+00 5.855762e+00 388 7.585776e+06 1.000000e+00 6.064421e+00 389 7.762471e+06 1.000000e+00 6.284880e+00 390 7.943282e+06 1.000000e+00 6.518188e+00 391 8.128305e+06 1.000000e+00 6.765524e+00 392 8.317638e+06 1.000000e+00 7.028211e+00 393 8.511380e+06 1.000000e+00 7.307743e+00 394 8.709636e+06 1.000000e+00 7.605810e+00 395 8.912509e+06 1.000000e+00 7.924329e+00 396 9.120108e+06 1.000000e+00 8.265483e+00 397 9.332543e+06 1.000000e+00 8.631763e+00 398 9.549926e+06 1.000000e+00 9.026024e+00 399 9.772372e+06 1.000000e+00 9.451544e+00 400 1.000000e+07 1.000000e+00 9.912104e+00 401 1.023293e+07 1.000000e+00 1.041207e+01 402 1.047129e+07 1.000000e+00 1.095649e+01 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 403 1.071519e+07 1.000000e+00 1.155125e+01 404 1.096478e+07 1.000000e+00 1.220314e+01 405 1.122018e+07 1.000000e+00 1.292006e+01 406 1.148154e+07 1.000000e+00 1.371116e+01 407 1.174898e+07 1.000000e+00 1.458694e+01 408 1.202264e+07 1.000000e+00 1.555933e+01 409 1.230269e+07 1.000000e+00 1.664158e+01 410 1.258925e+07 1.000000e+00 1.784791e+01 411 1.288250e+07 1.000000e+00 1.919248e+01 412 1.318257e+07 1.000000e+00 2.068737e+01 413 1.348963e+07 1.000000e+00 2.233878e+01 414 1.380384e+07 1.000000e+00 2.414033e+01 415 1.412538e+07 1.000000e+00 2.606252e+01 416 1.445440e+07 1.000000e+00 2.803803e+01 417 1.479108e+07 1.000000e+00 2.994608e+01 418 1.513561e+07 1.000000e+00 3.160606e+01 419 1.548817e+07 1.000000e+00 3.279768e+01 420 1.584893e+07 1.000000e+00 3.332033e+01 421 1.621810e+07 1.000000e+00 3.307359e+01 422 1.659587e+07 1.000000e+00 3.210585e+01 423 1.698244e+07 1.000000e+00 3.059024e+01 424 1.737801e+07 1.000000e+00 2.874868e+01 425 1.778279e+07 1.000000e+00 2.678056e+01 426 1.819701e+07 1.000000e+00 2.482865e+01 427 1.862087e+07 1.000000e+00 2.297813e+01 428 1.905461e+07 1.000000e+00 2.127039e+01 429 1.949845e+07 1.000000e+00 1.971876e+01 430 1.995262e+07 1.000000e+00 1.832066e+01 431 2.041738e+07 1.000000e+00 1.706560e+01 432 2.089296e+07 1.000000e+00 1.593984e+01 433 2.137962e+07 1.000000e+00 1.492906e+01 434 2.187762e+07 1.000000e+00 1.401957e+01 435 2.238721e+07 1.000000e+00 1.319893e+01 436 2.290868e+07 1.000000e+00 1.245613e+01 437 2.344229e+07 1.000000e+00 1.178155e+01 438 2.398833e+07 1.000000e+00 1.116684e+01 439 2.454709e+07 1.000000e+00 1.060482e+01 440 2.511886e+07 1.000000e+00 1.008929e+01 441 2.570396e+07 1.000000e+00 9.614928e+00 442 2.630268e+07 1.000000e+00 9.177119e+00 443 2.691535e+07 1.000000e+00 8.771883e+00 444 2.754229e+07 1.000000e+00 8.395768e+00 445 2.818383e+07 1.000000e+00 8.045774e+00 446 2.884032e+07 1.000000e+00 7.719284e+00 447 2.951209e+07 1.000000e+00 7.414006e+00 448 3.019952e+07 1.000000e+00 7.127934e+00 449 3.090295e+07 1.000000e+00 6.859297e+00 450 3.162278e+07 1.000000e+00 6.606535e+00 451 3.235937e+07 1.000000e+00 6.368264e+00 452 3.311311e+07 1.000000e+00 6.143255e+00 453 3.388442e+07 1.000000e+00 5.930415e+00 454 3.467369e+07 1.000000e+00 5.728766e+00 455 3.548134e+07 1.000000e+00 5.537431e+00 456 3.630781e+07 1.000000e+00 5.355626e+00 457 3.715352e+07 1.000000e+00 5.182641e+00 458 3.801894e+07 1.000000e+00 5.017839e+00 459 3.890451e+07 1.000000e+00 4.860641e+00 460 3.981072e+07 1.000000e+00 4.710524e+00 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 461 4.073803e+07 1.000000e+00 4.567012e+00 462 4.168694e+07 1.000000e+00 4.429671e+00 463 4.265795e+07 1.000000e+00 4.298108e+00 464 4.365158e+07 1.000000e+00 4.171960e+00 465 4.466836e+07 1.000000e+00 4.050897e+00 466 4.570882e+07 1.000000e+00 3.934615e+00 467 4.677351e+07 1.000000e+00 3.822836e+00 468 4.786301e+07 1.000000e+00 3.715303e+00 469 4.897788e+07 1.000000e+00 3.611778e+00 470 5.011872e+07 1.000000e+00 3.512044e+00 471 5.128614e+07 1.000000e+00 3.415898e+00 472 5.248075e+07 1.000000e+00 3.323153e+00 473 5.370318e+07 1.000000e+00 3.233634e+00 474 5.495409e+07 1.000000e+00 3.147181e+00 475 5.623413e+07 1.000000e+00 3.063642e+00 476 5.754399e+07 1.000000e+00 2.982879e+00 477 5.888437e+07 1.000000e+00 2.904759e+00 478 6.025596e+07 1.000000e+00 2.829161e+00 479 6.165950e+07 1.000000e+00 2.755971e+00 480 6.309573e+07 1.000000e+00 2.685082e+00 481 6.456542e+07 1.000000e+00 2.616393e+00 482 6.606934e+07 1.000000e+00 2.549811e+00 483 6.760830e+07 1.000000e+00 2.485246e+00 484 6.918310e+07 1.000000e+00 2.422616e+00 485 7.079458e+07 1.000000e+00 2.361842e+00 486 7.244360e+07 1.000000e+00 2.302850e+00 487 7.413102e+07 1.000000e+00 2.245570e+00 488 7.585776e+07 1.000000e+00 2.189937e+00 489 7.762471e+07 1.000000e+00 2.135887e+00 490 7.943282e+07 1.000000e+00 2.083363e+00 491 8.128305e+07 1.000000e+00 2.032307e+00 492 8.317638e+07 1.000000e+00 1.982668e+00 493 8.511380e+07 1.000000e+00 1.934393e+00 494 8.709636e+07 1.000000e+00 1.887436e+00 495 8.912509e+07 1.000000e+00 1.841751e+00 496 9.120108e+07 1.000000e+00 1.797295e+00 497 9.332543e+07 1.000000e+00 1.754026e+00 498 9.549926e+07 1.000000e+00 1.711904e+00 499 9.772372e+07 1.000000e+00 1.670893e+00 500 1.000000e+08 1.000000e+00 1.630956e+00 501 1.023293e+08 1.000000e+00 1.592059e+00 502 1.047129e+08 1.000000e+00 1.554169e+00 503 1.071519e+08 1.000000e+00 1.517254e+00 504 1.096478e+08 1.000000e+00 1.481285e+00 505 1.122018e+08 1.000000e+00 1.446233e+00 506 1.148154e+08 1.000000e+00 1.412070e+00 507 1.174898e+08 1.000000e+00 1.378770e+00 508 1.202264e+08 1.000000e+00 1.346306e+00 509 1.230269e+08 1.000000e+00 1.314655e+00 510 1.258925e+08 1.000000e+00 1.283793e+00 511 1.288250e+08 1.000000e+00 1.253697e+00 512 1.318257e+08 1.000000e+00 1.224345e+00 513 1.348963e+08 1.000000e+00 1.195717e+00 514 1.380384e+08 1.000000e+00 1.167792e+00 515 1.412538e+08 1.000000e+00 1.140550e+00 516 1.445440e+08 1.000000e+00 1.113974e+00 517 1.479108e+08 1.000000e+00 1.088044e+00 518 1.513561e+08 1.000000e+00 1.062743e+00 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 519 1.548817e+08 1.000000e+00 1.038053e+00 520 1.584893e+08 1.000000e+00 1.013960e+00 521 1.621810e+08 1.000000e+00 9.904464e-01 522 1.659587e+08 1.000000e+00 9.674973e-01 523 1.698244e+08 1.000000e+00 9.450978e-01 524 1.737801e+08 1.000000e+00 9.232335e-01 525 1.778279e+08 1.000000e+00 9.018906e-01 526 1.819701e+08 1.000000e+00 8.810556e-01 527 1.862087e+08 1.000000e+00 8.607155e-01 528 1.905461e+08 1.000000e+00 8.408575e-01 529 1.949845e+08 1.000000e+00 8.214694e-01 530 1.995262e+08 1.000000e+00 8.025393e-01 531 2.041738e+08 1.000000e+00 7.840557e-01 532 2.089296e+08 1.000000e+00 7.660073e-01 533 2.137962e+08 1.000000e+00 7.483832e-01 534 2.187762e+08 1.000000e+00 7.311730e-01 535 2.238721e+08 1.000000e+00 7.143662e-01 536 2.290868e+08 1.000000e+00 6.979529e-01 537 2.344229e+08 1.000000e+00 6.819235e-01 538 2.398833e+08 1.000000e+00 6.662685e-01 539 2.454709e+08 1.000000e+00 6.509788e-01 540 2.511886e+08 1.000000e+00 6.360453e-01 541 2.570396e+08 1.000000e+00 6.214596e-01 542 2.630268e+08 1.000000e+00 6.072130e-01 543 2.691535e+08 1.000000e+00 5.932975e-01 544 2.754229e+08 1.000000e+00 5.797050e-01 545 2.818383e+08 1.000000e+00 5.664278e-01 546 2.884032e+08 1.000000e+00 5.534582e-01 547 2.951209e+08 1.000000e+00 5.407890e-01 548 3.019952e+08 1.000000e+00 5.284129e-01 549 3.090295e+08 1.000000e+00 5.163230e-01 550 3.162278e+08 1.000000e+00 5.045124e-01 551 3.235937e+08 1.000000e+00 4.929745e-01 552 3.311311e+08 1.000000e+00 4.817029e-01 553 3.388442e+08 1.000000e+00 4.706911e-01 554 3.467369e+08 1.000000e+00 4.599332e-01 555 3.548134e+08 1.000000e+00 4.494231e-01 556 3.630781e+08 1.000000e+00 4.391549e-01 557 3.715352e+08 1.000000e+00 4.291230e-01 558 3.801894e+08 1.000000e+00 4.193219e-01 559 3.890451e+08 1.000000e+00 4.097460e-01 560 3.981072e+08 1.000000e+00 4.003902e-01 561 4.073803e+08 1.000000e+00 3.912493e-01 562 4.168694e+08 1.000000e+00 3.823183e-01 563 4.265795e+08 1.000000e+00 3.735922e-01 564 4.365158e+08 1.000000e+00 3.650663e-01 565 4.466836e+08 1.000000e+00 3.567360e-01 566 4.570882e+08 1.000000e+00 3.485967e-01 567 4.677351e+08 1.000000e+00 3.406439e-01 568 4.786301e+08 1.000000e+00 3.328733e-01 569 4.897788e+08 1.000000e+00 3.252807e-01 570 5.011872e+08 1.000000e+00 3.178620e-01 571 5.128614e+08 1.000000e+00 3.106131e-01 572 5.248075e+08 1.000000e+00 3.035301e-01 573 5.370318e+08 1.000000e+00 2.966091e-01 574 5.495409e+08 1.000000e+00 2.898466e-01 575 5.623413e+08 1.000000e+00 2.832386e-01 576 5.754399e+08 1.000000e+00 2.767818e-01 Index frequency vm(in) mag(v1#branch) -------------------------------------------------------------------------------- 577 5.888437e+08 1.000000e+00 2.704726e-01 578 6.025596e+08 1.000000e+00 2.643076e-01 579 6.165950e+08 1.000000e+00 2.582834e-01 580 6.309573e+08 1.000000e+00 2.523969e-01 581 6.456542e+08 1.000000e+00 2.466449e-01 582 6.606934e+08 1.000000e+00 2.410243e-01 583 6.760830e+08 1.000000e+00 2.355321e-01 584 6.918310e+08 1.000000e+00 2.301652e-01 585 7.079458e+08 1.000000e+00 2.249209e-01 586 7.244360e+08 1.000000e+00 2.197963e-01 587 7.413102e+08 1.000000e+00 2.147887e-01 588 7.585776e+08 1.000000e+00 2.098953e-01 589 7.762471e+08 1.000000e+00 2.051136e-01 590 7.943282e+08 1.000000e+00 2.004410e-01 591 8.128305e+08 1.000000e+00 1.958751e-01 592 8.317638e+08 1.000000e+00 1.914133e-01 593 8.511380e+08 1.000000e+00 1.870532e-01 594 8.709636e+08 1.000000e+00 1.827926e-01 595 8.912509e+08 1.000000e+00 1.786292e-01 596 9.120108e+08 1.000000e+00 1.745607e-01 597 9.332543e+08 1.000000e+00 1.705850e-01 598 9.549926e+08 1.000000e+00 1.666999e-01 599 9.772372e+08 1.000000e+00 1.629034e-01 600 1.000000e+09 1.000000e+00 1.591935e-01
Plot:
Compare $|Z|=|V/I|$ com o cálculo Python de Comportamento não ideal de componentes. Critérios mínimos:
- autorressonância dentro de 1% com a mesma discretização;
- assíntotas capacitivas e indutivas com inclinação correta;
- ESR igual ao mínimo de impedância no modelo série;
- análise repetida com passo mais fino.
19.13 Netlist completa — filtro de entrada
SPICE
* fonte, filtro LC real e carga
Vsrc src 0 AC 1
Rsrc src n1 5
L1 n1 n2 4.7u
R_L n2 n3 80m
Cpar n1 n3 8p
L_esl n3 n4 1.2n
R_esr n4 n5 30m
C1 n5 0 220n
Rload n3 0 20
.ac dec 100 1k 1G
.print ac vm(n3)
.end
Output:
Note: vsrc: has no value, DC 0 assumed
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 : 601
generated from textbook spice code block
AC Analysis Tue Aug 11 11:11:03 2026
--------------------------------------------------------------------------------
Index frequency vm(n3)
--------------------------------------------------------------------------------
0 1.000000e+03 7.974556e-01
1 1.023293e+03 7.974560e-01
2 1.047129e+03 7.974563e-01
3 1.071519e+03 7.974567e-01Ver mais (627 linhas)
4 1.096478e+03 7.974571e-01 5 1.122018e+03 7.974576e-01 6 1.148154e+03 7.974580e-01 7 1.174898e+03 7.974585e-01 8 1.202264e+03 7.974589e-01 9 1.230269e+03 7.974595e-01 10 1.258925e+03 7.974600e-01 11 1.288250e+03 7.974605e-01 12 1.318257e+03 7.974611e-01 13 1.348963e+03 7.974617e-01 14 1.380384e+03 7.974624e-01 15 1.412538e+03 7.974630e-01 16 1.445440e+03 7.974638e-01 17 1.479108e+03 7.974645e-01 18 1.513561e+03 7.974653e-01 19 1.548817e+03 7.974661e-01 20 1.584893e+03 7.974669e-01 21 1.621810e+03 7.974678e-01 22 1.659587e+03 7.974687e-01 23 1.698244e+03 7.974697e-01 24 1.737801e+03 7.974707e-01 25 1.778279e+03 7.974718e-01 26 1.819701e+03 7.974729e-01 27 1.862087e+03 7.974740e-01 28 1.905461e+03 7.974752e-01 29 1.949845e+03 7.974765e-01 30 1.995262e+03 7.974779e-01 31 2.041738e+03 7.974793e-01 32 2.089296e+03 7.974807e-01 33 2.137962e+03 7.974823e-01 34 2.187762e+03 7.974839e-01 35 2.238721e+03 7.974855e-01 36 2.290868e+03 7.974873e-01 37 2.344229e+03 7.974892e-01 38 2.398833e+03 7.974911e-01 39 2.454709e+03 7.974931e-01 40 2.511886e+03 7.974952e-01 41 2.570396e+03 7.974974e-01 42 2.630268e+03 7.974998e-01 43 2.691535e+03 7.975022e-01 44 2.754229e+03 7.975047e-01 45 2.818383e+03 7.975074e-01 46 2.884032e+03 7.975102e-01 47 2.951209e+03 7.975131e-01 48 3.019952e+03 7.975162e-01 49 3.090295e+03 7.975194e-01 50 3.162278e+03 7.975227e-01 51 3.235937e+03 7.975262e-01 52 3.311311e+03 7.975299e-01 53 3.388442e+03 7.975338e-01 54 3.467369e+03 7.975378e-01 Index frequency vm(n3) -------------------------------------------------------------------------------- 55 3.548134e+03 7.975420e-01 56 3.630781e+03 7.975465e-01 57 3.715352e+03 7.975511e-01 58 3.801894e+03 7.975559e-01 59 3.890451e+03 7.975610e-01 60 3.981072e+03 7.975663e-01 61 4.073803e+03 7.975719e-01 62 4.168694e+03 7.975777e-01 63 4.265795e+03 7.975838e-01 64 4.365158e+03 7.975902e-01 65 4.466836e+03 7.975969e-01 66 4.570882e+03 7.976039e-01 67 4.677351e+03 7.976112e-01 68 4.786301e+03 7.976189e-01 69 4.897788e+03 7.976269e-01 70 5.011872e+03 7.976353e-01 71 5.128614e+03 7.976442e-01 72 5.248075e+03 7.976534e-01 73 5.370318e+03 7.976630e-01 74 5.495409e+03 7.976732e-01 75 5.623413e+03 7.976838e-01 76 5.754399e+03 7.976948e-01 77 5.888437e+03 7.977064e-01 78 6.025596e+03 7.977186e-01 79 6.165950e+03 7.977313e-01 80 6.309573e+03 7.977446e-01 81 6.456542e+03 7.977586e-01 82 6.606934e+03 7.977732e-01 83 6.760830e+03 7.977885e-01 84 6.918310e+03 7.978045e-01 85 7.079458e+03 7.978212e-01 86 7.244360e+03 7.978388e-01 87 7.413102e+03 7.978572e-01 88 7.585776e+03 7.978764e-01 89 7.762471e+03 7.978965e-01 90 7.943282e+03 7.979176e-01 91 8.128305e+03 7.979396e-01 92 8.317638e+03 7.979627e-01 93 8.511380e+03 7.979869e-01 94 8.709636e+03 7.980122e-01 95 8.912509e+03 7.980387e-01 96 9.120108e+03 7.980664e-01 97 9.332543e+03 7.980955e-01 98 9.549926e+03 7.981259e-01 99 9.772372e+03 7.981577e-01 100 1.000000e+04 7.981910e-01 101 1.023293e+04 7.982258e-01 102 1.047129e+04 7.982623e-01 103 1.071519e+04 7.983005e-01 104 1.096478e+04 7.983404e-01 105 1.122018e+04 7.983822e-01 106 1.148154e+04 7.984260e-01 107 1.174898e+04 7.984718e-01 108 1.202264e+04 7.985198e-01 109 1.230269e+04 7.985699e-01 110 1.258925e+04 7.986224e-01 111 1.288250e+04 7.986774e-01 112 1.318257e+04 7.987349e-01 Index frequency vm(n3) -------------------------------------------------------------------------------- 113 1.348963e+04 7.987950e-01 114 1.380384e+04 7.988580e-01 115 1.412538e+04 7.989238e-01 116 1.445440e+04 7.989927e-01 117 1.479108e+04 7.990648e-01 118 1.513561e+04 7.991403e-01 119 1.548817e+04 7.992192e-01 120 1.584893e+04 7.993017e-01 121 1.621810e+04 7.993881e-01 122 1.659587e+04 7.994784e-01 123 1.698244e+04 7.995729e-01 124 1.737801e+04 7.996716e-01 125 1.778279e+04 7.997750e-01 126 1.819701e+04 7.998830e-01 127 1.862087e+04 7.999960e-01 128 1.905461e+04 8.001142e-01 129 1.949845e+04 8.002377e-01 130 1.995262e+04 8.003668e-01 131 2.041738e+04 8.005018e-01 132 2.089296e+04 8.006429e-01 133 2.137962e+04 8.007904e-01 134 2.187762e+04 8.009445e-01 135 2.238721e+04 8.011056e-01 136 2.290868e+04 8.012738e-01 137 2.344229e+04 8.014496e-01 138 2.398833e+04 8.016333e-01 139 2.454709e+04 8.018251e-01 140 2.511886e+04 8.020255e-01 141 2.570396e+04 8.022347e-01 142 2.630268e+04 8.024531e-01 143 2.691535e+04 8.026811e-01 144 2.754229e+04 8.029190e-01 145 2.818383e+04 8.031673e-01 146 2.884032e+04 8.034264e-01 147 2.951209e+04 8.036967e-01 148 3.019952e+04 8.039786e-01 149 3.090295e+04 8.042724e-01 150 3.162278e+04 8.045788e-01 151 3.235937e+04 8.048981e-01 152 3.311311e+04 8.052308e-01 153 3.388442e+04 8.055773e-01 154 3.467369e+04 8.059381e-01 155 3.548134e+04 8.063137e-01 156 3.630781e+04 8.067045e-01 157 3.715352e+04 8.071110e-01 158 3.801894e+04 8.075337e-01 159 3.890451e+04 8.079731e-01 160 3.981072e+04 8.084295e-01 161 4.073803e+04 8.089035e-01 162 4.168694e+04 8.093954e-01 163 4.265795e+04 8.099056e-01 164 4.365158e+04 8.104344e-01 165 4.466836e+04 8.109823e-01 166 4.570882e+04 8.115495e-01 167 4.677351e+04 8.121362e-01 168 4.786301e+04 8.127426e-01 169 4.897788e+04 8.133688e-01 170 5.011872e+04 8.140148e-01 Index frequency vm(n3) -------------------------------------------------------------------------------- 171 5.128614e+04 8.146805e-01 172 5.248075e+04 8.153657e-01 173 5.370318e+04 8.160701e-01 174 5.495409e+04 8.167932e-01 175 5.623413e+04 8.175344e-01 176 5.754399e+04 8.182927e-01 177 5.888437e+04 8.190673e-01 178 6.025596e+04 8.198566e-01 179 6.165950e+04 8.206591e-01 180 6.309573e+04 8.214729e-01 181 6.456542e+04 8.222956e-01 182 6.606934e+04 8.231246e-01 183 6.760830e+04 8.239567e-01 184 6.918310e+04 8.247881e-01 185 7.079458e+04 8.256146e-01 186 7.244360e+04 8.264313e-01 187 7.413102e+04 8.272324e-01 188 7.585776e+04 8.280116e-01 189 7.762471e+04 8.287614e-01 190 7.943282e+04 8.294735e-01 191 8.128305e+04 8.301384e-01 192 8.317638e+04 8.307455e-01 193 8.511380e+04 8.312829e-01 194 8.709636e+04 8.317370e-01 195 8.912509e+04 8.320929e-01 196 9.120108e+04 8.323339e-01 197 9.332543e+04 8.324416e-01 198 9.549926e+04 8.323955e-01 199 9.772372e+04 8.321731e-01 200 1.000000e+05 8.317498e-01 201 1.023293e+05 8.310987e-01 202 1.047129e+05 8.301906e-01 203 1.071519e+05 8.289941e-01 204 1.096478e+05 8.274753e-01 205 1.122018e+05 8.255983e-01 206 1.148154e+05 8.233250e-01 207 1.174898e+05 8.206155e-01 208 1.202264e+05 8.174285e-01 209 1.230269e+05 8.137216e-01 210 1.258925e+05 8.094519e-01 211 1.288250e+05 8.045764e-01 212 1.318257e+05 7.990535e-01 213 1.348963e+05 7.928431e-01 214 1.380384e+05 7.859081e-01 215 1.412538e+05 7.782153e-01 216 1.445440e+05 7.697366e-01 217 1.479108e+05 7.604503e-01 218 1.513561e+05 7.503418e-01 219 1.548817e+05 7.394051e-01 220 1.584893e+05 7.276434e-01 221 1.621810e+05 7.150696e-01 222 1.659587e+05 7.017071e-01 223 1.698244e+05 6.875895e-01 224 1.737801e+05 6.727605e-01 225 1.778279e+05 6.572732e-01 226 1.819701e+05 6.411894e-01 227 1.862087e+05 6.245781e-01 228 1.905461e+05 6.075142e-01 Index frequency vm(n3) -------------------------------------------------------------------------------- 229 1.949845e+05 5.900770e-01 230 1.995262e+05 5.723484e-01 231 2.041738e+05 5.544112e-01 232 2.089296e+05 5.363476e-01 233 2.137962e+05 5.182374e-01 234 2.187762e+05 5.001571e-01 235 2.238721e+05 4.821785e-01 236 2.290868e+05 4.643679e-01 237 2.344229e+05 4.467858e-01 238 2.398833e+05 4.294857e-01 239 2.454709e+05 4.125150e-01 240 2.511886e+05 3.959140e-01 241 2.570396e+05 3.797166e-01 242 2.630268e+05 3.639507e-01 243 2.691535e+05 3.486381e-01 244 2.754229e+05 3.337953e-01 245 2.818383e+05 3.194339e-01 246 2.884032e+05 3.055611e-01 247 2.951209e+05 2.921801e-01 248 3.019952e+05 2.792908e-01 249 3.090295e+05 2.668901e-01 250 3.162278e+05 2.549724e-01 251 3.235937e+05 2.435300e-01 252 3.311311e+05 2.325535e-01 253 3.388442e+05 2.220321e-01 254 3.467369e+05 2.119538e-01 255 3.548134e+05 2.023058e-01 256 3.630781e+05 1.930749e-01 257 3.715352e+05 1.842471e-01 258 3.801894e+05 1.758084e-01 259 3.890451e+05 1.677446e-01 260 3.981072e+05 1.600415e-01 261 4.073803e+05 1.526851e-01 262 4.168694e+05 1.456615e-01 263 4.265795e+05 1.389569e-01 264 4.365158e+05 1.325581e-01 265 4.466836e+05 1.264520e-01 266 4.570882e+05 1.206261e-01 267 4.677351e+05 1.150679e-01 268 4.786301e+05 1.097658e-01 269 4.897788e+05 1.047082e-01 270 5.011872e+05 9.988421e-02 271 5.128614e+05 9.528320e-02 272 5.248075e+05 9.089501e-02 273 5.370318e+05 8.670991e-02 274 5.495409e+05 8.271854e-02 275 5.623413e+05 7.891197e-02 276 5.754399e+05 7.528165e-02 277 5.888437e+05 7.181939e-02 278 6.025596e+05 6.851738e-02 279 6.165950e+05 6.536816e-02 280 6.309573e+05 6.236461e-02 281 6.456542e+05 5.949992e-02 282 6.606934e+05 5.676762e-02 283 6.760830e+05 5.416151e-02 284 6.918310e+05 5.167570e-02 285 7.079458e+05 4.930458e-02 286 7.244360e+05 4.704277e-02 Index frequency vm(n3) -------------------------------------------------------------------------------- 287 7.413102e+05 4.488518e-02 288 7.585776e+05 4.282694e-02 289 7.762471e+05 4.086341e-02 290 7.943282e+05 3.899018e-02 291 8.128305e+05 3.720304e-02 292 8.317638e+05 3.549797e-02 293 8.511380e+05 3.387115e-02 294 8.709636e+05 3.231896e-02 295 8.912509e+05 3.083791e-02 296 9.120108e+05 2.942471e-02 297 9.332543e+05 2.807621e-02 298 9.549926e+05 2.678940e-02 299 9.772372e+05 2.556144e-02 300 1.000000e+06 2.438959e-02 301 1.023293e+06 2.327127e-02 302 1.047129e+06 2.220400e-02 303 1.071519e+06 2.118542e-02 304 1.096478e+06 2.021329e-02 305 1.122018e+06 1.928547e-02 306 1.148154e+06 1.839992e-02 307 1.174898e+06 1.755470e-02 308 1.202264e+06 1.674794e-02 309 1.230269e+06 1.597789e-02 310 1.258925e+06 1.524286e-02 311 1.288250e+06 1.454125e-02 312 1.318257e+06 1.387151e-02 313 1.348963e+06 1.323220e-02 314 1.380384e+06 1.262191e-02 315 1.412538e+06 1.203933e-02 316 1.445440e+06 1.148318e-02 317 1.479108e+06 1.095226e-02 318 1.513561e+06 1.044542e-02 319 1.548817e+06 9.961557e-03 320 1.584893e+06 9.499623e-03 321 1.621810e+06 9.058621e-03 322 1.659587e+06 8.637596e-03 323 1.698244e+06 8.235639e-03 324 1.737801e+06 7.851884e-03 325 1.778279e+06 7.485501e-03 326 1.819701e+06 7.135701e-03 327 1.862087e+06 6.801732e-03 328 1.905461e+06 6.482874e-03 329 1.949845e+06 6.178441e-03 330 1.995262e+06 5.887778e-03 331 2.041738e+06 5.610262e-03 332 2.089296e+06 5.345296e-03 333 2.137962e+06 5.092311e-03 334 2.187762e+06 4.850766e-03 335 2.238721e+06 4.620141e-03 336 2.290868e+06 4.399943e-03 337 2.344229e+06 4.189700e-03 338 2.398833e+06 3.988962e-03 339 2.454709e+06 3.797299e-03 340 2.511886e+06 3.614301e-03 341 2.570396e+06 3.439577e-03 342 2.630268e+06 3.272753e-03 343 2.691535e+06 3.113473e-03 344 2.754229e+06 2.961396e-03 Index frequency vm(n3) -------------------------------------------------------------------------------- 345 2.818383e+06 2.816199e-03 346 2.884032e+06 2.677570e-03 347 2.951209e+06 2.545214e-03 348 3.019952e+06 2.418849e-03 349 3.090295e+06 2.298205e-03 350 3.162278e+06 2.183025e-03 351 3.235937e+06 2.073063e-03 352 3.311311e+06 1.968085e-03 353 3.388442e+06 1.867868e-03 354 3.467369e+06 1.772199e-03 355 3.548134e+06 1.680872e-03 356 3.630781e+06 1.593695e-03 357 3.715352e+06 1.510483e-03 358 3.801894e+06 1.431057e-03 359 3.890451e+06 1.355249e-03 360 3.981072e+06 1.282898e-03 361 4.073803e+06 1.213852e-03 362 4.168694e+06 1.147962e-03 363 4.265795e+06 1.085090e-03 364 4.365158e+06 1.025103e-03 365 4.466836e+06 9.678732e-04 366 4.570882e+06 9.132800e-04 367 4.677351e+06 8.612083e-04 368 4.786301e+06 8.115485e-04 369 4.897788e+06 7.641960e-04 370 5.011872e+06 7.190515e-04 371 5.128614e+06 6.760208e-04 372 5.248075e+06 6.350141e-04 373 5.370318e+06 5.959463e-04 374 5.495409e+06 5.587368e-04 375 5.623413e+06 5.233093e-04 376 5.754399e+06 4.895919e-04 377 5.888437e+06 4.575165e-04 378 6.025596e+06 4.270195e-04 379 6.165950e+06 3.980412e-04 380 6.309573e+06 3.705263e-04 381 6.456542e+06 3.444234e-04 382 6.606934e+06 3.196856e-04 383 6.760830e+06 2.962705e-04 384 6.918310e+06 2.741404e-04 385 7.079458e+06 2.532627e-04 386 7.244360e+06 2.336102e-04 387 7.413102e+06 2.151617e-04 388 7.585776e+06 1.979024e-04 389 7.762471e+06 1.818247e-04 390 7.943282e+06 1.669289e-04 391 8.128305e+06 1.532233e-04 392 8.317638e+06 1.407245e-04 393 8.511380e+06 1.294568e-04 394 8.709636e+06 1.194500e-04 395 8.912509e+06 1.107359e-04 396 9.120108e+06 1.033414e-04 397 9.332543e+06 9.727982e-05 398 9.549926e+06 9.254073e-05 399 9.772372e+06 8.908017e-05 400 1.000000e+07 8.681549e-05 401 1.023293e+07 8.562680e-05 402 1.047129e+07 8.536545e-05 Index frequency vm(n3) -------------------------------------------------------------------------------- 403 1.071519e+07 8.586712e-05 404 1.096478e+07 8.696560e-05 405 1.122018e+07 8.850400e-05 406 1.148154e+07 9.034183e-05 407 1.174898e+07 9.235813e-05 408 1.202264e+07 9.445165e-05 409 1.230269e+07 9.653929e-05 410 1.258925e+07 9.855367e-05 411 1.288250e+07 1.004406e-04 412 1.318257e+07 1.021565e-04 413 1.348963e+07 1.036665e-04 414 1.380384e+07 1.049423e-04 415 1.412538e+07 1.059611e-04 416 1.445440e+07 1.067041e-04 417 1.479108e+07 1.071556e-04 418 1.513561e+07 1.073024e-04 419 1.548817e+07 1.071331e-04 420 1.584893e+07 1.066374e-04 421 1.621810e+07 1.058060e-04 422 1.659587e+07 1.046305e-04 423 1.698244e+07 1.031023e-04 424 1.737801e+07 1.012134e-04 425 1.778279e+07 9.895560e-05 426 1.819701e+07 9.632047e-05 427 1.862087e+07 9.329939e-05 428 1.905461e+07 8.988332e-05 429 1.949845e+07 8.606275e-05 430 1.995262e+07 8.182760e-05 431 2.041738e+07 7.716720e-05 432 2.089296e+07 7.207017e-05 433 2.137962e+07 6.652441e-05 434 2.187762e+07 6.051704e-05 435 2.238721e+07 5.403430e-05 436 2.290868e+07 4.706159e-05 437 2.344229e+07 3.958333e-05 438 2.398833e+07 3.158300e-05 439 2.454709e+07 2.304300e-05 440 2.511886e+07 1.394470e-05 441 2.570396e+07 4.268339e-06 442 2.630268e+07 6.007218e-06 443 2.691535e+07 1.690387e-05 444 2.754229e+07 2.844523e-05 445 2.818383e+07 4.065609e-05 446 2.884032e+07 5.356264e-05 447 2.951209e+07 6.719251e-05 448 3.019952e+07 8.157487e-05 449 3.090295e+07 9.674044e-05 450 3.162278e+07 1.127216e-04 451 3.235937e+07 1.295525e-04 452 3.311311e+07 1.472690e-04 453 3.388442e+07 1.659088e-04 454 3.467369e+07 1.855117e-04 455 3.548134e+07 2.061194e-04 456 3.630781e+07 2.277759e-04 457 3.715352e+07 2.505272e-04 458 3.801894e+07 2.744218e-04 459 3.890451e+07 2.995105e-04 460 3.981072e+07 3.258468e-04 Index frequency vm(n3) -------------------------------------------------------------------------------- 461 4.073803e+07 3.534867e-04 462 4.168694e+07 3.824890e-04 463 4.265795e+07 4.129155e-04 464 4.365158e+07 4.448310e-04 465 4.466836e+07 4.783033e-04 466 4.570882e+07 5.134038e-04 467 4.677351e+07 5.502071e-04 468 4.786301e+07 5.887917e-04 469 4.897788e+07 6.292398e-04 470 5.011872e+07 6.716374e-04 471 5.128614e+07 7.160749e-04 472 5.248075e+07 7.626469e-04 473 5.370318e+07 8.114528e-04 474 5.495409e+07 8.625965e-04 475 5.623413e+07 9.161871e-04 476 5.754399e+07 9.723388e-04 477 5.888437e+07 1.031171e-03 478 6.025596e+07 1.092810e-03 479 6.165950e+07 1.157387e-03 480 6.309573e+07 1.225040e-03 481 6.456542e+07 1.295913e-03 482 6.606934e+07 1.370157e-03 483 6.760830e+07 1.447931e-03 484 6.918310e+07 1.529402e-03 485 7.079458e+07 1.614743e-03 486 7.244360e+07 1.704137e-03 487 7.413102e+07 1.797775e-03 488 7.585776e+07 1.895858e-03 489 7.762471e+07 1.998596e-03 490 7.943282e+07 2.106208e-03 491 8.128305e+07 2.218925e-03 492 8.317638e+07 2.336989e-03 493 8.511380e+07 2.460653e-03 494 8.709636e+07 2.590182e-03 495 8.912509e+07 2.725855e-03 496 9.120108e+07 2.867962e-03 497 9.332543e+07 3.016811e-03 498 9.549926e+07 3.172719e-03 499 9.772372e+07 3.336024e-03 500 1.000000e+08 3.507077e-03 501 1.023293e+08 3.686246e-03 502 1.047129e+08 3.873919e-03 503 1.071519e+08 4.070499e-03 504 1.096478e+08 4.276412e-03 505 1.122018e+08 4.492103e-03 506 1.148154e+08 4.718038e-03 507 1.174898e+08 4.954708e-03 508 1.202264e+08 5.202624e-03 509 1.230269e+08 5.462326e-03 510 1.258925e+08 5.734377e-03 511 1.288250e+08 6.019370e-03 512 1.318257e+08 6.317924e-03 513 1.348963e+08 6.630691e-03 514 1.380384e+08 6.958353e-03 515 1.412538e+08 7.301626e-03 516 1.445440e+08 7.661262e-03 517 1.479108e+08 8.038050e-03 518 1.513561e+08 8.432815e-03 Index frequency vm(n3) -------------------------------------------------------------------------------- 519 1.548817e+08 8.846427e-03 520 1.584893e+08 9.279796e-03 521 1.621810e+08 9.733878e-03 522 1.659587e+08 1.020968e-02 523 1.698244e+08 1.070825e-02 524 1.737801e+08 1.123069e-02 525 1.778279e+08 1.177817e-02 526 1.819701e+08 1.235191e-02 527 1.862087e+08 1.295319e-02 528 1.905461e+08 1.358335e-02 529 1.949845e+08 1.424380e-02 530 1.995262e+08 1.493604e-02 531 2.041738e+08 1.566162e-02 532 2.089296e+08 1.642219e-02 533 2.137962e+08 1.721946e-02 534 2.187762e+08 1.805525e-02 535 2.238721e+08 1.893146e-02 536 2.290868e+08 1.985011e-02 537 2.344229e+08 2.081330e-02 538 2.398833e+08 2.182324e-02 539 2.454709e+08 2.288227e-02 540 2.511886e+08 2.399286e-02 541 2.570396e+08 2.515758e-02 542 2.630268e+08 2.637916e-02 543 2.691535e+08 2.766047e-02 544 2.754229e+08 2.900453e-02 545 2.818383e+08 3.041453e-02 546 2.884032e+08 3.189382e-02 547 2.951209e+08 3.344594e-02 548 3.019952e+08 3.507461e-02 549 3.090295e+08 3.678378e-02 550 3.162278e+08 3.857760e-02 551 3.235937e+08 4.046044e-02 552 3.311311e+08 4.243693e-02 553 3.388442e+08 4.451196e-02 554 3.467369e+08 4.669067e-02 555 3.548134e+08 4.897851e-02 556 3.630781e+08 5.138125e-02 557 3.715352e+08 5.390497e-02 558 3.801894e+08 5.655610e-02 559 3.890451e+08 5.934145e-02 560 3.981072e+08 6.226822e-02 561 4.073803e+08 6.534402e-02 562 4.168694e+08 6.857693e-02 563 4.265795e+08 7.197547e-02 564 4.365158e+08 7.554870e-02 565 4.466836e+08 7.930619e-02 566 4.570882e+08 8.325809e-02 567 4.677351e+08 8.741515e-02 568 4.786301e+08 9.178877e-02 569 4.897788e+08 9.639103e-02 570 5.011872e+08 1.012347e-01 571 5.128614e+08 1.063334e-01 572 5.248075e+08 1.117015e-01 573 5.370318e+08 1.173543e-01 574 5.495409e+08 1.233078e-01 575 5.623413e+08 1.295792e-01 576 5.754399e+08 1.361866e-01 Index frequency vm(n3) -------------------------------------------------------------------------------- 577 5.888437e+08 1.431492e-01 578 6.025596e+08 1.504872e-01 579 6.165950e+08 1.582220e-01 580 6.309573e+08 1.663762e-01 581 6.456542e+08 1.749735e-01 582 6.606934e+08 1.840391e-01 583 6.760830e+08 1.935991e-01 584 6.918310e+08 2.036810e-01 585 7.079458e+08 2.143135e-01 586 7.244360e+08 2.255263e-01 587 7.413102e+08 2.373504e-01 588 7.585776e+08 2.498174e-01 589 7.762471e+08 2.629597e-01 590 7.943282e+08 2.768101e-01 591 8.128305e+08 2.914015e-01 592 8.317638e+08 3.067663e-01 593 8.511380e+08 3.229359e-01 594 8.709636e+08 3.399400e-01 595 8.912509e+08 3.578057e-01 596 9.120108e+08 3.765564e-01 597 9.332543e+08 3.962104e-01 598 9.549926e+08 4.167795e-01 599 9.772372e+08 4.382675e-01 600 1.000000e+09 4.606676e-01
Plot:
Varra ESR, ESL, $Z_S$ e carga. Compare a perda de inserção com a rede ABCD de Modelagem de problemas EMC; diferenças indicam topologia ou convenções de porta inconsistentes.
19.14 Critérios de convergência e documentação
Em transiente, limite o passo máximo a uma fração do menor tempo de subida ou atraso relevante e repita com metade do passo. Em AC, refine a malha em ressonâncias. Registre versão do KiCad/ngspice, modelos, opções do solver, condições iniciais e mensagens de convergência.
19.15 Referência principal
Documentação do KiCad Simulation (Ngspice), Guias de Layout para EMC, e práticas de integridade de sinal em projetos open-source.