Analysis of impedance matching by microwave technology based on Smith Circle chart---

To analyze a matching network using Smith round charts

① the matching network into several segments, each corresponding to an impedance graph or a point on the admittance map;

② according to the operating frequency, the resistance (resistor) or reactance (capacitor and inductor) of the series element, the conductivity of the shunt element (resistor) or the electrical Na (capacitor and inductor), wherein the reactance of the inductor equals the positive value of inductance, the reactance of the capacitor equals the negative capacitance, the inductor is equal to the inductance negative reciprocal, The capacitance of the capacitor is equal to the positive reciprocal of the tolerance;

③ according to the characteristics of resistance, the corresponding resistors, reactance, conductance, electrical na regularization, in the impedance map for the Z=Z/Z0=R+JX, in the admittance map for Y=Y/Y0=G+JB, wherein Z=R+JX,Y=G+JB;

The ④ is analyzed from the segment farthest from the port, and the corresponding point of the segment is marked on the impedance graph, which is the starting point of the analysis;

⑤ if the components on the paragraph are in series, the impedance diagram should be processed on the following steps:
A. If the previous treatment is carried out in the admittance map, it is necessary to take the previous treatment of the admittance point to the origin of the center of the symmetry point, so that the previous treatment of the corresponding impedance point, if the previous treatment is completed in the impedance diagram, then ignore this step;
B1. To add the normalized reactance corresponding to the resistor circle at the above impedance point, an intermediate point is obtained;
C1. Add the normalized resistor corresponding to the corresponding reactance circle along the middle point;
Or
B2. Adding the normalized resistor corresponding to the reactance circle along the above impedance point, an intermediate point is obtained;
C2. Add the normalized reactance corresponding to the corresponding resistor circle in this middle point;
D. At this point, the corresponding impedance point of the paragraph is obtained;

⑥ if the components on the paragraph are in parallel, they should be processed on the admittance map, with the following steps:
A. If the previous treatment is carried out in the impedance diagram, then the previous processing of the impedance point to the origin of the center of the symmetry point, so that the previous treatment of the corresponding admittance point, if the previous treatment is completed in the admittance map, then ignore this step;
B1. The corresponding conductivity circle along the admittance point is added to the normalized electron na corresponding to the section, and an intermediate point is obtained.
C1. Then add the normalized conductance corresponding to this intermediate point by the corresponding electric Na circle;
Or
B2. By adding the normalized conductance corresponding to the above admittance point, an intermediate point is obtained;
C2. The corresponding conductance circle along the middle point is added to the normalized electron na corresponding to the segment;
D. At this point, the admittance point corresponding to the paragraph is obtained;

⑦ the normalized impedance of the matching network by repeating the processing of ⑤ or ⑥ on a per-segment basis, in the order of departure from the port to the nearest, until all processing has been completed.





The essence of impedance matching is to make the impedance of the load coupled with the impedance of the matching network, equal to the impedance of the signal source conjugate.