Answer 03: why can Smith circle "allow left string and right parallel"?

There are many kinds of impedance requirements for transmission lines , Such as 50Ω、75Ω、90Ω、100Ω、120Ω etc. . Normalized impedance is actually a set of “ General killing ” Impedance method , That is, although the system impedance faced in each case may be different , But when the actual impedance and the system impedance become more and more simultaneous , Then the value after division will be closer to 1.

Reference resources 《 answer 01：Smith Why can a circle “ Feel up and down Left string right parallel ”？》、

《 answer 02：Smith Why can a circle “ Feel up and down Left string right parallel ”？》 We know ——

In the rectangular coordinate diagram of complex plane impedance , There are several special lines ：

The impedance of the black line , There is a characteristic ： The real part is 0;( The resistance is 0) The impedance of the red line , There is a characteristic ： The imaginary part is 0;( inductance 、 The capacitance is 0) The impedance of the blue line , There is a characteristic ： The real part is 1;( The resistance is 50 ohm ) The impedance of the yellow line , There is a characteristic ： The imaginary part is -1; The impedance of the orange line , There is a characteristic ： The imaginary part is 1

When the real part is 0, X The more emotional , Go directly above the black line , X The more tolerant , Go more and more below the negative of the black line , Embodied in the actual circuit , When you connect inductors in series ,X Change in the direction of sensibility , When you connect capacitors in series ,X Change in the direction of inclusiveness .

In transmission line impedance matching , Move the complex impedance point to the desired position by adding components , That is, the position of the system impedance . Therefore, the complex impedance diagram of rectangular coordinates “ Bending ” Become Smith After the picture , Can also show ： Series inductance capacitance Will move the point along the constant resistance circle . The concrete manifestation is ：

The series inductance will move clockwise along the constant resistance circle ,

The series capacitor will move counterclockwise along the constant resistance circle .

stay Smith In the figure , Series inductance and capacitance will move the impedance point along the constant resistance circle , So what if it's in parallel ？ This requires understanding the admittance ——

Admittance is actually the reciprocal of impedance , hold Smith Circular graph 180 The admittance map can be obtained by turning degrees .

In the admittance diagram ,

Parallel inductance , Move counterclockwise along the admittance diagram ;

Parallel capacitance , Move clockwise along the admittance diagram .

The composite type formed by combining reactance diagram and admittance diagram Smith The circle chart is like a chessboard , In the rules of chess ,“ vehicle ” Go straight ,“ Horse ” Go to the opposite corner of the sun ,“ like ” Go to the opposite corner of the field . And in the Smith In a circle , inductance 、 capacitance 、 The resistance also has different ways .

The formula we often say ： Feel up and down , Left string right parallel , The concrete embodiment is ：

Series inductance , Move clockwise along the reactance diagram ;

Series capacitors , Move counterclockwise along the reactance diagram

Parallel inductance , Move counterclockwise along the admittance diagram ;

Parallel capacitance , Move clockwise along the admittance diagram

Through this feature , During our debugging , In fact, it is through the combination of each pure element , Move the complex impedance point to the system impedance position .

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