public static Complex InputImpedance(IList<BoreSectionCalculations> boreSections, double freq)
{
FrequencyCalculations freqCalc = new FrequencyCalculations(freq);
ComplexMatrix cascadeMatrix = ComplexMatrix.IdentityMatrix();
foreach (BoreSectionCalculations boreSection in boreSections)
cascadeMatrix = cascadeMatrix * TransmissionMatrix(freqCalc, boreSection);
Complex terminatingImpedance = TerminatingImpedance(freqCalc, boreSections[boreSections.Count - 1]);
Complex inputPressure = terminatingImpedance * cascadeMatrix[0, 0] + cascadeMatrix[0, 1];
Complex inputFlow = terminatingImpedance * cascadeMatrix[1, 0] + cascadeMatrix[1, 1];
return ((inputPressure / inputFlow));
}
public static ComplexMatrix TransmissionMatrix(FrequencyCalculations freq, BoreSectionCalculations boreSection)
{
Complex gamma = Gamma(freq, boreSection);
Complex C, D, characteristicImpedance;
ComplexMathUtils.CoshSinh(gamma * boreSection.SphericalLength, out C, out D);
characteristicImpedance = CharacteristicImpedance(freq, boreSection);
ComplexMatrix transmissionMatrix = new ComplexMatrix();
if (boreSection.IsCylindrical)
{
transmissionMatrix[0, 0] = C;
transmissionMatrix[0, 1] = characteristicImpedance * D;
transmissionMatrix[1, 0] = characteristicImpedance.Reciprocal() * D;
transmissionMatrix[1, 1] = C;
}
else
{
double outputinput = boreSection.OutputXi / boreSection.InputXi;
double inputoutput = 1 / outputinput;
Complex dgammaoutput = D / (gamma * boreSection.OutputXi);
transmissionMatrix[0, 0] = outputinput * (C - dgammaoutput);
transmissionMatrix[1, 1] = ((C * inputoutput) + dgammaoutput);
transmissionMatrix[0, 1] = inputoutput * characteristicImpedance * D;
Complex gammaXi2Inv = 1 / (gamma * gamma * (boreSection.InputXi * boreSection.InputXi));
transmissionMatrix[1, 0] = (1 / characteristicImpedance) *
(
D *
(
outputinput - gammaXi2Inv
) +
(
C * gamma * boreSection.SphericalLength * gammaXi2Inv
)
);
}
if (boreSection.OpeningRadius > boreSection.ClosingRadius)
return transmissionMatrix.Inverse;
return transmissionMatrix;
}
private static Complex Gamma(FrequencyCalculations freq, BoreSectionCalculations boreSection)
{
double temp = freq.gammaT2 / boreSection.AverageRadius;
return new Complex(temp, freq.gammaT1 + temp);
}
private static Complex TerminatingImpedance(FrequencyCalculations freq, BoreSectionCalculations lastSection)
{
return new Complex(freq.terminatingImpedanceT1.Real, freq.terminatingImpedanceT1.Imaginary / (double)lastSection.ClosingRadius);
}
private static Complex CharacteristicImpedance(FrequencyCalculations freq, BoreSectionCalculations boreSection)
{
double temp = freq.characteristicImpedanceT1 / boreSection.SphericalAreaTimesAverageRadius;
return new Complex((airDensity * speedSound) / boreSection.SphericalArea + temp, -1 * temp);
}
