Impedance circle

Introduction

The impedance circle draws a series of circles and arcs on the reflection coefficient of reflection coefficient according to the relationship between impedance and reflection coefficient, which represents impedance Instead, the size of the residential wave ratio is, so that they can be easily read out in the reflection coefficient unit circle. It is a tool that effectively selects the matching impedance when designing high frequency and microwave circuitry. Through a concise mapping, instead of complex plural calculations, the matching of complex impedance is simple, easy to learn, and is a valid tool for engineers in high frequency. In the field of radio design, the impedance circle map has been widely used.

is shown in

representing a correspondence between the input impedance and the voltage reflection coefficient. The input impedance of any reference surface on the transmission line corresponds to the reflection coefficient of the reflection coefficient, i.e.

Z _{c _{C < / SUB> Relationship between normalization input impedance and reflection coefficients in both sides of the equation}}

Represents normalized resistance,

represents normalized reactance. The reflection coefficient is multiple, which can be expressed as

< P> Let the second equal sign, the imaginary part is equal,

From the above two, you can draw

= constant and

Line, et al.

line. The following is discussed:

1, et al.

line

Plus the equation 1 side at the same time 1 Press

Power order / p>

This formula is represented on

The circular cluster of the parameter, the center is in the

point, and the radius is

. When the value of

is different, different circles will be drawn on the complex plane. As shown in Fig. 2

2, the

line

is arranged in the power sequence of г ', there is

< Section>

formula

This is in

is the round cluster equation of the parameter, center in

, the radius is

, given a

value can be

Go to a circle,

can be negative, positive representative resistance, negative representative resistance. When the value of

is different, different circles will be drawn on the complex plane. The basic impedance circle is obtained as shown in

line and the like

lines. By it can read the impedance of the past on the reflection coefficients.

3, etc. |

| Line, etc.

line, etc.

line

A series of concentric clusters of (0,0) for the center of the complex surface, etc., is equivalent to |

. The size of the

| is determined by the ratio of the radius of the circle and the maximum circle.

Because

Take a one-to-value relationship, etc. |

| is now the

line, etc.

line, but the value is different. The reading of the standing wave factor

is determined by the

value of the orthopedic intersection between the

circle.

4, et al θ line

θ refers to the phase value of the reflection coefficient, and the θ line is through the rapid radial line cluster of the origin, θ = 0 in

_r positive half shaft, counterclockwise is the direction increasing, clockwise is the direction of the angle reduction, and the size of the θ is read by the "angular" number of the large circle, and is often used "electric length" Reading instead of angle reading.

Features

1, there are three special points on the circle, that is, match points - coordinates (0, 0); short road points - coordinates (-1, 0 ); Open line - coordinate is (1, 0).

2, the real part of each point impedance on each of the circumferences, the impedance of the impedance is determined by the reactance value of the circle and the curve intersection, and any of the impedances in the circumference corresponds to the indication of this point. It can be determined as needed.

3, the upper half of the real shaft is the trajectory of the inductive impedance, the lower half of the solid shaft is the trajectory of the capacitive impedance, the left half is parallel, the right semicircle is in series. The unit circle is a pure reactance; the real shaft is a pure resistance; the right half shaft of the real shaft is a voltage band, the left half is a voltage range.

Application

The application main point of the impedance circle is first calculated, followed by mastering the operation of the impedance, the third is the meaning of clear point movement.

1, the impedance is marked on the impedance circle, which can find the curve intersection of the reactance in the circumferential movement according to the circular field.

2, impedance transformation and operation: along the shaft operation, along the circumference operation, alternately and anti-circle and impedance circle to solve impedance transformations.

3, key application is to complete impedance matching, the method of achieving this goal is to increasing series and parallel components on the Smith circling until we want the impedance value, and then translated, You can calculate the parameters of the matching element. From the graphic, you will find a way to connect the point on the Smith circle.

4, calculating the transmission line standby on the transmission line according to the load impedance.

5, based on the input of the input, the input impedance, the input impedance, and the reflection coefficient of the input end according to the load impedance and transmission line length.

6, the load impedance is determined based on the standing wave coefficient of the line and the position of the voltage wave node.