#Single stub matching smith chart generator
#Single stub matching smith chart series

2.ДЄ Smith chart is divided into an inductive region and an capacitive region: a.ДЇor an вЂњimpedance chartвЂќ or an вЂњimpedance & admittance chartвЂќ: the upper half plane is the inductive region, corresponding to Im( z)>0 and Im( y)0. Moving along such a circle corresponds to changing the real part of admittance. e.ДЄ constant susceptance b circle consists of points that have the same normalized susceptance. Moving along such a circle corresponds to adding a parallel inductor or capacitor. d.ДЄ constant conductance g circle consists of points that have the same normalized conductance. Moving along such a circle corresponds to changing the real part of impedance. c.ДЄ constant reactance x circle consists of points that have the same normalized reactance.

#Single stub matching smith chart series

Moving along such a circle corresponds to adding a series inductor or capacitor. b.ДЄ constant resistance r circle consists of points that have the same normalized resistance. Moving along such a circle corresponds to moving along a lossless transmission line. There are five types of constant-valued circles on the Smith chart: a.ДЄ constant-| О“| circle, also called a constant standing wave ratio (SWR) circle, consists of points that have the same magnitude in reflection coefficient. Comparison of impedance chart, admittance chart, and impedance and admittance chart. The normalized impedance at point B is read as 0.47 в€’ j0.44, which, after denormalization (multiplication by 50), yields (23.5 в€’ j22) О©.ДЇigure 1.13. For convenience, |О“| = 0.45 circle is drawn in Figure 4.13 and allows the determination of the reflection coefficient at any point along the line. Thus, we obtain the input reflection coefficient О“ in = 0.45в€ -123В°. Since |О“| is constant for a lossless transmission line, the reflection coefficient at the input, denoted by point B on the 0.421О» TG radial line, has the same radius as point A (= 0. Thus, the position of the input terminal is at 0.088 + 0.333 = 0.421О» TG. The input terminal is at a distance of 0.333О» TG from the load, located at 0.088О». The angle of О“ L is measured using the corresponding angle of reflection coefficient scale on the periphery of the unit circle as 116.5В°. If the radius of point A is projected onto the reflection coefficient, E orI, scale at the bottom of the chart, the measurement is |О“ L| = 0.45.

#Single stub matching smith chart generator

Thus, point A reads 0.088О» toward generator (TG). The relative position of a point on the transmission line can be determined by extending the radius of the point to intersect one of these two scales and reading its value in О». One complete rotation around the chart amounts to a half wavelength traversal. Two scales on the Smith chart's outer periphery indicate movement in wavelengths either toward the generator (clockwise) or toward the load (counterclockwise). This point can be translated to the input by moving (1/3)О» toward the generator. The load impedance is normalized, and the point (0.5 + j0.5) is plotted and shown as point A in Figure 4.13. The input impedance and reflection coefficient can be determined by using the Smith chart. Suppose that a (1/3)О»-long, 50 О© line is connected to a load impedance of (25 + j25) О©. For better clarity and practice, it is highly recommended to follow this example by repeating the graphical solution taps on a new Smith chart. The basic operations of the chart can be understood by an example to be discussed next. ДЇigure 4.13 displays a typical commercially available Smith chart.

This is useful in oscillator design, where designers routinely have to work with negative resistance values. The use of a compressed Smith Chart therefore allows the designer to visualize device parameters over the complete frequency range, where both positive and negative resistance behavior may be exhibited. From 6 to 10В GHz, the pole lies inside the О“ 3 = 1 boundary of the Smith Chart in Figure 4.10, indicating that negative resistance can be generated in this device using passive shunt feedback. An example of the use of a compressed Smith Chart to plot the negative resistance behavior of an MHG9000 GaAs MESFET, in terms of shunt feedback pole locations (as defined in Chapter 8) on the О“ 3 plane from 2 to 18В GHz is shown in Figure 4.10. In order to represent negative resistances we need to compress the conventional Smith Chart to be a subset of a larger chart, which typically has a radius of |О“| = 3.16, this value being chosen to represent 10 dB return gain. Negative resistance values plotted on a Smith Chart lie outside the |О“| = 1 boundary of the conventional Smith Chart.