導波管
をテンプレートにして作成
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開始行:
[[回路学第二]]
- 物質中のMaxwell方程式~
&mimetex(\mathrm{div}D = \rho);~
&mimetex(\mathrm{div}B = 0);~
&mimetex(\mathrm{rot}E = -\dot{B});~
&mimetex(\mathrm{rot}H = j + \dot{D});~
&mimetex(D = \varepsilon E);~
&mimetex(H = \frac{1}{\mu}B);
- 完全導体の境界条件~
&mimetex(E \times n = 0);~
&mimetex(B \cdot n = 0);~
nは境界面の法線ベクトル
- 矩形導波管~
&mimetex(x=0,a);、&mimetex(y=0,b);に完全導体の壁があると...
特定のモードの複素電磁波を考えると、~
境界条件からモードの一般形は~
&mimetex(E_x = A(x)\sin(\kappa_y y)e^{-\omega t + \kappa_...
&mimetex(E_y = B(y)\sin(\kappa_x x)e^{-\omega t + \kappa_...
&mimetex(E_z = C\sin(\kappa_x x)\sin(\kappa_y y)e^{j(-\om...
となり、~
&mimetex(\frac{\kappa_x}{a\pi} \in \mathbb{N});、&mimetex...
&mimetex(A'(x)\sin(\kappa_y y) + B'(y)\sin(\kappa_x x) + ...
&mimetex(\kappa_x^2 + \kappa_y^2 + \kappa_z^2 = \omega^2);
を満たす。
-- TEモード。&mimetex(E_z=0);のモード。~
&mimetex(A'(x)\sin(\kappa_y y) + B'(x)\sin(\kappa_x x) = ...
&mimetex(\frac{A'(x)}{\sin(\kappa_x x)} + \frac{B'(y)}{\s...
&mimetex(A(x) = \kappa_y \cos(\kappa_x x));~
&mimetex(B(y) = -\kappa_x \cos(\kappa_x y));~
なので、
&mimetex(E_x = \kappa_y \cos(\kappa_x x)\sin(\kappa_y y)e...
&mimetex(E_y = -\kappa_x\sin(\kappa_x x)\cos(\kappa_y y)e...
&mimetex(E_z = 0);~
-- TMモード。&mimetex(B_z=0);のモード。~
&mimetex(j\omega B_z = \{\kappa_y B(x)\cos(\kappa_y y) - ...
&mimetex(\frac{\kappa_y A(x)}{\sin(\kappa_x x)} - \frac{\...
&mimetex(A(x) = \kappa_x \sin(\kappa_x x));~
&mimetex(B(y) = \kappa_y \sin(\kappa_y y));~
//&mimetex((\kappa_x^2 + \kappa_y^2)E_{0} \cos(\kappa_x x...
終了行:
[[回路学第二]]
- 物質中のMaxwell方程式~
&mimetex(\mathrm{div}D = \rho);~
&mimetex(\mathrm{div}B = 0);~
&mimetex(\mathrm{rot}E = -\dot{B});~
&mimetex(\mathrm{rot}H = j + \dot{D});~
&mimetex(D = \varepsilon E);~
&mimetex(H = \frac{1}{\mu}B);
- 完全導体の境界条件~
&mimetex(E \times n = 0);~
&mimetex(B \cdot n = 0);~
nは境界面の法線ベクトル
- 矩形導波管~
&mimetex(x=0,a);、&mimetex(y=0,b);に完全導体の壁があると...
特定のモードの複素電磁波を考えると、~
境界条件からモードの一般形は~
&mimetex(E_x = A(x)\sin(\kappa_y y)e^{-\omega t + \kappa_...
&mimetex(E_y = B(y)\sin(\kappa_x x)e^{-\omega t + \kappa_...
&mimetex(E_z = C\sin(\kappa_x x)\sin(\kappa_y y)e^{j(-\om...
となり、~
&mimetex(\frac{\kappa_x}{a\pi} \in \mathbb{N});、&mimetex...
&mimetex(A'(x)\sin(\kappa_y y) + B'(y)\sin(\kappa_x x) + ...
&mimetex(\kappa_x^2 + \kappa_y^2 + \kappa_z^2 = \omega^2);
を満たす。
-- TEモード。&mimetex(E_z=0);のモード。~
&mimetex(A'(x)\sin(\kappa_y y) + B'(x)\sin(\kappa_x x) = ...
&mimetex(\frac{A'(x)}{\sin(\kappa_x x)} + \frac{B'(y)}{\s...
&mimetex(A(x) = \kappa_y \cos(\kappa_x x));~
&mimetex(B(y) = -\kappa_x \cos(\kappa_x y));~
なので、
&mimetex(E_x = \kappa_y \cos(\kappa_x x)\sin(\kappa_y y)e...
&mimetex(E_y = -\kappa_x\sin(\kappa_x x)\cos(\kappa_y y)e...
&mimetex(E_z = 0);~
-- TMモード。&mimetex(B_z=0);のモード。~
&mimetex(j\omega B_z = \{\kappa_y B(x)\cos(\kappa_y y) - ...
&mimetex(\frac{\kappa_y A(x)}{\sin(\kappa_x x)} - \frac{\...
&mimetex(A(x) = \kappa_x \sin(\kappa_x x));~
&mimetex(B(y) = \kappa_y \sin(\kappa_y y));~
//&mimetex((\kappa_x^2 + \kappa_y^2)E_{0} \cos(\kappa_x x...
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