Module 5.5 Reflection Coefficient

Introduction:

    In this module, we discuss the characteristics of the reflection coefficient along a lossless transmission line terminated with a load., Observe the dynamic behavior of the reflection coefficient along the transmission line by adjusting the range sliders.
    Ex.1：When observation distance is prolonged or the frequency( \(f\) ) increases, it can be found from the phase distribution that the period of the reflection coefficient is a half of the wavelength.
    Ex.2：When the load impedance is a pure resistance ( \(R_L\) ), the phase of the load reflection coefficient is always 0 degree if \(R_L > Z_0\); otherwise, the phase of the load reflection coefficient is always 180 degrees if \(R_L < Z_0\).
    Ex.3：When the frequency ( \(f\) ) changes, the magnitude of the source reflection coefficient stays the same and only the phase of the source reflection coefficient changes.

Formula:

1. \(\Gamma(z)\) : Voltage reflection coefficient at z, defined by
  \(\Gamma(z)=\left|\Gamma_{0}\right| \cdot e^{j\theta} \cdot e^{-j2\beta|z|}\)
2. \(SWR\) : Voltage standing wave ratio, defined by
      SWR\(=\frac{V_{\max } }{V_{\min } } =\frac{1+\left|\Gamma (0)\right|}{1-\left|\Gamma (0)\right|} \)

Parameters:

1. \(\left|\Gamma (0)\right|\) : Voltage reflection coefficient at z = 0, defined by
      \(\Gamma (0)=\left|\Gamma (0)\right|\cdot e^{j\theta } =\frac{Z_{L} -Z_{0} }{Z_{L} +Z_{0} } \)
2. \(Z_{L}\) : Load impedance, defined by
      \(Z_{L} =R_{L} +jX_{L} =Z_{0} \cdot \frac{1+\Gamma (0)}{1-\Gamma (0)}   (\Omega) \)
     a. \(R_{L}\) : Real part of \(Z_{L}\),
     b. \(X_{L}\) : Imaginary part of \(Z_{L}\).
3. \(\theta\) : Phase angle of the voltage reflection coefficient, (rad)
4. \(\beta\) : Phase constant, (rad/m)
5. \(f\) : Operating frequency, (GHz)
6. \(d\) : Length of the transmission line, value equal to 10 cm
7. \(Z_{0}\) : Characteristic impedance of the transmission line, \((\Omega)\)