Practical impedance circular Graph Software

The smith plot (impedance circular diagram) is a tool for effectively selecting and calculating the matching impedance during design of the very high frequency and ultra high frequency circuits. The computation of complex numbers is simple, easy to learn, and is an effective tool for engineers in high-frequency fields. Smith diagram has been widely used in overseas radio design fields. This Smith Diagram CAD software is designed with most engineering and technical personnel taking it as a convenient tool for use without having to focus on many projects unrelated to design, therefore, the structure related to the computer environment adopts a method to meet the general file operations, in order to achieve practical and simple purposes, and indeed play the role of a tool. This is the application software developed by the author using VB several years ago. Although it was not pushed to the market at that time, it is still practical as a tool. Here we will introduce it.

Brief description of the Smith Diagram

Smith figure Composition 1

 

A standard Smith diagram can represent both the complex impedance and the complex electric gain. The two concepts are displayed in one graph.
For the complex impedance diagram, the horizontal axis in the diagram represents the resistance R of the real number, the left side of the horizontal axis represents the 0 resistance, and the non-linearity from left to right increases to the right end representing the infinite resistance, A group of constant resistance circles tangent to the right endpoint. the upper half of the arc represents the inductance of the virtual part. The clockwise direction is increased from 0 to infinity (non-linear ), A cluster of constant inductance arcs that are in the upward direction tangent to the right endpoint. the lower half of the arc represents the capacity of the virtual part, which increases from 0 to infinity (non-linear) in the counterclockwise direction ), A cluster of constant capacitance arcs that are tangent to the right endpoint.

The horizontal axis in the diagram represents the conductivity G of the real number, the left side of the horizontal axis represents the 0 conductivity, And the 0 conductivity represents the open circuit in the circuit, from the left to the right nonlinear increase to the right end of the infinite conductivity, the infinite conductivity represents the short-circuit state, in the figure is a cluster of always-conducting circles tangent to the right endpoint; the upper half of the arc represents the capacity of the virtual part. The clockwise direction is increased from 0 to infinity (non-linear), which is composed of a cluster of constant circular edges that are tangent to the right endpoint; the lower half of the arc represents the inductance of the virtual part, which is increased from 0 to infinity (non-linear) in a counter-clockwise direction. It is a constant arc formed in the downward direction of a cluster tangent to the right endpoint.
The scale of the outermost ring of the figure represents the scale value of the 1/2 wavelength transmission line wave distance, and the scale value is complementary in the direction (clockwise direction and clockwise direction for load. The scale of the secondary outer ring represents the angle of the reflection coefficient (and the attenuation angle ). They are used for transmission line matching.

In the figure, the Circle centered on the image center represents the standing wave circle of a certain standing wave ratio. The Standing Wave Ratio of the outermost circle is infinite, and the Standing Wave Ratio of the center is 1.
The Smith diagram consists of the following parts: Diagram, input, conversion output, balance ruler adjustment, auxiliary adjustment, display matching circuit frame, and file operation.
The brief functions of each part are as follows:
Input box: Enter the real and virtual values of the matched object.
Impedance series: the start point of the matched object is in Impedance series.
Electricity and nano-parallel: the starting point of the matching object is in the electric and nano-parallel mode.
R or G: Enter the reference relative value of the actual part.
X or B: Enter the benchmark relative value of the virtual part.
Recovery 1: used when re-selecting the input mode

Conversion output box: Equivalent Transformation of the matching impedance.
Serial to parallel: select the transformation method from the series impedance to the parallel electrode.
And to the string: select the transformation method from the parallel electrode to the series Impedance
G or R: display the converted equivalent resistance or conductivity value
B or X: display the converted equivalent capacitance or impedance value.
Transform: The command button for automatic equivalent transformation of impedance and electricity supply
Restore 2: Make the conversion output box start again
Adjusting frame of the balance ruler: increase or decrease the inductance or power supply, and find the corresponding equivalent conversion point on the constant 1 circle.
Matching Method 1: select this matching method when the starting point is in the right half circle
Matching Method 2: select this matching method when the starting point is in the left semi-circle (no equivalent transformation is required)
Balance ruler Angle Adjustment: adjust the angle of the balance ruler and find the corresponding equivalent conversion point on the constant 1 circle
Recovery 3: Make the balance ruler adjustment process start again
Auxiliary adjustment box: Based on the above conditions, we can draw a matched impedance or electrode, and set the total impedance imaginary part to 0.
Starting point position of arc 1: Adjust the matching starting point of the impedance or electric charge to the transformed point.
Arc 1 endpoint adjustment: adjusts the arc 1 length (its length represents the relative value of a part of the matching impedance or electrode)
ARC 2 endpoint adjustment: Adjust the ARC 2 length (its length represents the relative value of the other part of the matching impedance or electrode)
Auxiliary X1 or B1 adjustment: display adjustment of the middle of the upper half circle or the electric zone for the sake of clarity.
Auxiliary X2 or B2 adjustment: display adjustment of the middle half of the half circle or the electric charge for the sake of drawing clarity
Show matching circuit box: displays the matching impedance network diagram.
Show matching circuit diagram: command button for displaying matching impedance Network Diagram
File Operations: read, write, save, print, and online help operations on the drawn files.
Open File: Open the Smith graph file (with the extension. FRM)
Save file: Save the Smith graph file (with the extension. FRM)
Printing: printed Smith figures
Help: Open the Online Help File
Version: Provide the version information of the software.
End: The command button at the end of the Smith Chart

How to Use the Smith Diagram

Based on the difference between the right half of the graph and the left half of the graph from the start point, there are two ways to use them.
1: when the starting point is in the right half of the graph (matching method 1 ):
It is assumed that the data is in parallel with the conductivity (in this case, the relative value of the data is obtained for the data transfer and the data transfer is measured in B = 1 and G = 3)
Step 1: In the input box, select the power-in parallel mode, and enter the conductivity G = 3 and the Capacity B = 1. In the figure, the circular arc of the conductivity circle of the Red G = 3 and B = 1 is displayed, and its intersection is the input start point.
Step 2: In the transformation output box, select and change the string type, and press the convert command button, automatically represents the equivalent transformation values of R = 0.3 and x =-0.1 after the transformation. At the same time, the blue R = 0.3 resistance circle and x =-0.1 resistance arc are displayed in the figure, the intersection is equivalent to the output point.

Step 3: In the balance ruler adjustment box, select matching method 1. Then adjust the angle of the balance ruler. A black thick line is displayed in the figure, which is symmetric to the center of the image. The balance ruler angle is adjustable, and its left end is always located on the constant resistance circle of R = 0.3 after transformation. Adjust the angle clockwise so that the right side of the balance ruler is just above the constant 1 circle. The adjustment process ends.
Step 4: In the auxiliary adjustment box, adjust the starting point of arc 1 to make the starting point of arc 1 (coarse Black Point) the constant resistance circle along r = 0.3 appears at the intersection after the transformation.
Step 5: In the auxiliary adjustment box, adjust the end point of arc 1 so that the end point of arc 1 of the Black crude line is equal to the left end point of the balancing ruler.
Step 6: In the auxiliary adjustment box, adjust the ARC 2 endpoint to make the end point of the dark green arc 2 (the starting point of the ARC 2 is in the center of the graph and does not need to be adjusted) just until the right endpoint of the balancing ruler on the constant 1 circle.

Step 7: In the auxiliary adjustment box, according to the size of the inverse value corresponding to the left end of the balancing ruler at the position of the r = 0.3 constant resistance circle (which can be read from the impedance scale ), enter the value in the auxiliary X1 or B1 box. A green arc is displayed, and the position of the arc in the outer ring must be the same as the value adjusted by the auxiliary X1 or B1.
Step 8: In the auxiliary adjustment box, according to the size of the electric charge value corresponding to the right side of the balancing ruler at the position of 1 circle (which can be read from the electric charge scale ), enter this value in the auxiliary X2 or B2 box. In this case, another green electric arc appears. The position of the electric arc in the outer ring must be the same as the value adjusted by the auxiliary X2 or B2.
Step 9: press the show matching circuit diagram button in the lower part. The entire matching impedance network diagram and the relative values of each element are displayed automatically in the small box above the button.

So far, the matching method 1 process is complete.

　

 

2:Where the starting point is in the left half of the graph (matching method 2 ):
It is assumed that the resistance and the inductive resistance are in series (in this case, the relative values of the resistance and the inductive resistance are obtained, for example, r = 0.1 and x = 0.2)
Step 1: In the input box, select the impedance connection mode. The input resistor R = 0.1 and the inductance resistance x = 0.2. In the figure, the red r = 0.1 resistance circle and the x = 0.2 inductive Arc are displayed. The intersection is the input start point.
Step 2: In the transformation output box, select the string-to-string and transformation mode, and press the transformation command button to automatically display the equivalent values of G = 2 and B = 0.4 after the transformation; at the same time, the Blue G = 2 conductivity circle and B = 0.4 inductive Arc are shown in the figure, and its intersection is equivalent to the output point.
Step 3: Select matching method 2 in the balance ruler adjustment box. Then adjust the angle of the balance ruler. A black thick line is displayed in the figure, which is symmetric to the center of the image. The balance ruler angle is adjustable, and its left side is always located on the constant resistance circle of R = 0.1 before the transformation. Adjust the angle clockwise so that the right side of the balance ruler is just above the constant 1 circle. The adjustment process ends.

Step 4: In the auxiliary adjustment box, adjust the starting point of arc 1 to make the starting point of arc 1 (coarse Black Point) the constant resistance circle along r = 0.1 appears at the intersection before the transformation.
Step 5: In the auxiliary adjustment box, adjust the end point of arc 1 so that the end point of arc 1 of the Black crude line is equal to the left end point of the balancing ruler.
Step 6: In the auxiliary adjustment box, adjust the ARC 2 endpoint to make the end point of the dark green arc 2 (the starting point of the ARC 2 is in the center of the graph and does not need to be adjusted) just until the right endpoint of the balancing ruler on the constant 1 circle.
Step 7: In the auxiliary adjustment box, according to the size of the inverse value corresponding to the left end of the balancing ruler at the position of the r = 0.1 constant resistance circle (which can be read from the impedance scale ), enter the value in the auxiliary X1 or B1 box. A green arc is displayed, and the position of the arc in the outer ring must be the same as the value adjusted by the auxiliary X1 or B1.

Step 8: In the auxiliary adjustment box, according to the size of the electric charge value corresponding to the right side of the balancing ruler at the position of 1 circle (which can be read from the electric charge scale ), enter this value in the auxiliary X1 or B1 box. In this case, another green electric arc appears. The position of the electric arc in the outer ring must be the same as that of the auxiliary X2 or B2.
Step 9: press the show matching circuit diagram button in the lower part. The entire matching impedance network diagram and the relative values of each element are displayed automatically in the small box above the button.
Now the matching method 2 process is complete.

 

 

Matching of the length and contacts when the transmission line eliminates the standing wave (to be)

 

 

 

Considerations for Smith Diagram

The unit of the series element must use ohm; the unit of the parallel element must use Siemens

Currently, it can be applied to less than 2000 systems.