スミスチャートをROOTで描く（２）

もし、あなたがZ(DUT)だけでなく、あなたのアンテナの放射インピーダンスも知りたければ、あなたは、ケーブルの長さと短縮率に応じて、スミスチャート上で負荷の方向へ移動（反時計回りの回転）しなければなりません。

この図では、青色の点がZ(DUT)を、緑色のそれが放射インピーダンスを示しています。

freq1=7.02687 MHz, freq2=7.02978 MHz
amp(v2/v1)=0.778415, phase(v2/v1)=-0.53185 rad
v1=(1,0i), v2=(0.670893,-0.394757i), v3=(1.32911,0.394757i)
z=(0.382788,-0.410701i), z50=(19.1394,-20.535i)
gamma=(-0.329107,-0.394757i), abs=0.51395, arg=-129.818 deg
vswr=3.1148
cable_length=20 m, velocity_factor=0.67, phase_toward_load=143 deg

// file name = mytest46.cc
{
  ifstream finput("owondata.txt");
  Int_t iskip=8;
  std::string s;

  for(Int_t i=0;i<iskip;i++) {
    getline(finput, s);
  }

  const Int_t icount_max=8192;
  Int_t icount=0;
  Double_t dummy, data1[icount_max], data2[icount_max], data3[icount_max];
  while(icount < icount_max) {
    finput >> data1[icount] >> dummy >> data2[icount] >> data3[icount];
    if(finput.eof()) break;
    icount++;
  }

  TCanvas *c1 = new TCanvas("c1","Test",0,0,800,600);
  TGraph *g = new TGraph(icount, data1, data2);
  g->SetMarkerStyle( 20 ); 
  g->SetMarkerSize( 0.5 );
  g->Draw("AP");
  TF1 *f1 = new TF1("f1", "[0]*sin([1]*x+[2])-[3]");
  f1->SetParameter(0, 2000.0);
  f1->SetParameter(1, 0.022);
  f1->SetParameter(2, 0.0);
  f1->SetParameter(3, 0.0);
  f1->SetLineColor(kRed);
  g->Fit(f1);

  TGraph *h = new TGraph(icount, data1, data3);
  h->SetMarkerStyle( 24 ); 
  h->SetMarkerSize( 0.5 );
  h->Draw("P");
  TF1 *f2 = new TF1("f2", "[0]*sin([1]*x+[2])-[3]");
  f2->SetParameter(0, 2000.0);
  f2->SetParameter(1, 0.022);
  f2->SetParameter(2, 0.0);
  f2->SetParameter(3, 0.0);
  f2->SetLineColor(kYellow);
  h->Fit(f2);

  Double_t freq1, freq2;
  const Double_t fsample = 2000.0; // MHz (interpolated)
  freq1 = fsample / ( 2.0*TMath::Pi() / f1->GetParameter(1) );
  freq2 = fsample / ( 2.0*TMath::Pi() / f2->GetParameter(1) );
  std::cout << "freq1=" << freq1 << " MHz, freq2=" << freq2 << " MHz" << std::endl;

  Double_t amp, phase;
  amp   = f2->GetParameter(0) / f1->GetParameter(0);
  phase = f2->GetParameter(2) - f1->GetParameter(2);
  std::cout << "amp(v2/v1)=" << amp << ", phase(v2/v1)=" << phase << " rad" << std::endl;

  TComplex v1, v2, v3, Z, z50;
  v1  = TComplex(1.0, 0.0);
  v2  = TComplex( amp*TMath::Cos(phase), amp*TMath::Sin(phase) );
  v3  = 2.0*v1 - v2;
  z   = v2/v3;
  z50 = 50.0*z;
  std::cout << "v1=" << v1 << ", v2=" << v2 << ", v3=" << v3 << std::endl;
  std::cout << "z=" << z << ", z50=" << z50 << std::endl;

  TComplex gg;
  Double_t gg_rho, gg_theta, vswr;
  gg  = (z-1.0)/(z+1.0);
  vswr = (1.0+TComplex::Abs(gg)) / (1.0-TComplex::Abs(gg));

  std::cout << "gamma=" << gg 
            << ", abs=" << gg.Rho()
            << ", arg=" << gg.Theta()*360.0/(2.0*TMath::Pi()) << " deg" << std::endl;
  std::cout << "vswr=" << vswr << std::endl;

  TCanvas * CPol = new TCanvas("CPol", "Test", 900, 0, 600, 600);
  const Int_t ncircle = 360;

  Double_t radius[ncircle];
  Double_t theta [ncircle];
  for (Int_t i=0; i<ncircle; i++) {
    radius[i] = gg.Rho();
    theta [i] = TMath::Pi()*2.0*(Double_t)i/(Double_t)(ncircle-1);
  }

  Double_t radius_r[ncircle];
  Double_t theta_r [ncircle];
  Double_t r_center = z.Re() / (z.Re()+1.0);
  Double_t r_radius = 1.0    / (z.Re()+1.0);
  for (Int_t i=0; i<ncircle; i++) {
    Double_t th = TMath::Pi()*2.0*(Double_t)i/(Double_t)(ncircle-1);
    Double_t re = r_center + r_radius*TMath::Cos(th);
    Double_t im =            r_radius*TMath::Sin(th);
    TComplex ww = TComplex(re, im);
    radius_r[i] = ww.Rho  ();
    theta_r [i] = ww.Theta();
  }

  Double_t radius_x[ncircle];
  Double_t theta_x [ncircle];
  TComplex x_center = TComplex(1.0, 1.0/z.Im());
  Double_t x_radius = 1.0/ z.Im();
  for (Int_t i=0; i<ncircle; i++) {
    Double_t th = TMath::Pi()*2.0*(Double_t)i/(Double_t)(ncircle-1);
    Double_t re = x_center.Re() + x_radius*TMath::Cos(th);
    Double_t im = x_center.Im() + x_radius*TMath::Sin(th);
    TComplex ww = TComplex(re, im);
    radius_x[i] = ww.Rho  ();
    theta_x [i] = ww.Theta();
  }

  TGraphPolar * grP1 = new TGraphPolar(ncircle, theta, radius);
  grP1->SetTitle("Smith Chart");
  grP1->SetMarkerStyle(20);
  grP1->SetMarkerSize(2.0);
  grP1->SetMarkerColor(4);
  grP1->SetLineColor(2);
  grP1->SetLineWidth(3);
  grP1->Draw("C");
  CPol->Update();

  grP1->GetPolargram()->SetToRadian();
  grP1->GetPolargram()->SetRangeRadial(0,1);

  TGraphPolar * grP2 = new TGraphPolar(ncircle, theta_r, radius_r);
  grP2->SetMarkerStyle(20);
  grP2->SetMarkerSize(2.0);
  grP2->SetMarkerColor(4);
  grP2->SetLineColor(9);
  grP2->SetLineWidth(3);
  grP2->Draw("C");

  TGraphPolar * grP3 = new TGraphPolar(ncircle, theta_x, radius_x);
  grP3->SetMarkerStyle(20);
  grP3->SetMarkerSize(2.0);
  grP3->SetMarkerColor(4);
  grP3->SetLineColor(6);
  grP3->SetLineWidth(3);
  grP3->Draw("C");

  TMarker *m0 = new TMarker(gg.Re(), gg.Im(), 20);
  m0->SetMarkerSize(2.0);
  m0->SetMarkerColor(4);
  m0->Draw();

  Double_t freq = (freq1+freq2)/2.0; // MHz
  Double_t cable_length = 20.0; // meter
  Double_t velocity_factor = 0.67;
  Double_t wave_length = velocity_factor * (300.0 / freq);
  Double_t phase_toward_load = 2.0 * 2.0 * TMath::Pi() * (cable_length / wave_length);
  std::cout << "cable_length=" << cable_length
            << " m, velocity_factor=" << velocity_factor
            << ", phase_toward_load=" << (Int_t) ( phase_toward_load * 360.0 / (2.0*TMath::Pi()) ) % 360
            << " deg" << std::endl;

  TComplex gg_toward_load = gg * TComplex::Exp(TComplex(0.0, phase_toward_load));

  TMarker *m1 = new TMarker(gg_toward_load.Re(), gg_toward_load.Im(), 20);
  m1->SetMarkerSize(2.0);
  m1->SetMarkerColor(8);
  m1->Draw();
}