The input terminal is at a distance of 0.333λ TG from the load, located at 0.088λ. The angle of Γ L is measured using the corresponding angle of reflection coefficient scale on the periphery of the unit circle as 116.5°. If the radius of point A is projected onto the reflection coefficient, E orI, scale at the bottom of the chart, the measurement is |Γ L| = 0.45.
USING SMITH CHART GENERATOR
Thus, point A reads 0.088λ 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 λ. 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)λ 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)λ-long, 50 Ω line is connected to a load impedance of (25 + j25) Ω. 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. įigure 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 10 GHz, the pole lies inside the Γ 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 Γ 3 plane from 2 to 18 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 |Γ| = 3.16, this value being chosen to represent 10 dB return gain. Negative resistance values plotted on a Smith Chart lie outside the |Γ| = 1 boundary of the conventional Smith Chart.
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