The Smith chart (graphical) procedure goes as follows, refer to Figure 2E.8:Ĭhoose a normalization impedance, Z o, for the problem at hand. ĭistance to the first voltage minimum = From point A to point D, read on the wavelength toward generator scale. The value of the real impedance at the intersection of the constant SWR circle with the real axis is the VSWR = 3.87. Y ′ in = 0.72 + j 1.2 → Y in = Y ′ in Z o = 0.72 + j 1.2 100 = ( 0.0072 + j 0.0012 ) Ω − 1.ĭistance to the first voltage maximum = from point A to point C, read on the WTG scale. Input load admittance is point E, diagonally across from point B on the SWR circle. On the constant SWR circle, move a distance of 0.3 λ toward generator, WTG, to point B, read normalize impedance and multiply by Z o. Γ L = 0.59.Įxtent the line connecting the center of the chart and the normalized impedance point to the Γ angle scale to read the angle of reflection coefficient angle = ∠104°. Project the SWR circle on the Γ scale to find the magnitude of the reflection coefficient at the load. Locate the normalized load impedance on the Smith chart, point A, draw the constant SWR circle, with center at the origin. This is because a λ/2 distance change corresponds to 4 π ⋅ = 2 π which is 360°. Both scales are provided along the perimeter of a circle located outside the phase angle scale with the "TOWARD GENERATOR (WTG)" scale marked on the outer side of the circle and the "TOWARD LOAD (WTL)" scale marked on the inner side of the circle.īoth scales carry tick marks from 0 to 0.5 in a full circle, 360°. One of these scales increases counterclockwise to enable tracking "increasing z" locations as we move toward the load, while the other scale increases clockwise for tracking "decreasing z" locations (increasing d) toward the source (generator). The normalized distance scales provide direct calibration of the quantity. One can use the phase angle scale to enter these rotations on the chart, however, two normalized distance scales are given to facilitate this process without multiplying the 4 π by the. If z 2 > z 1, the change is an increase in the angle and hence a counterclockwise rotation, and for z 2 < z 1, the rotation is clockwise. | Γ ( z 2 ) | = | Γ ( z 1 ) | e + 2 α ( z 2 − z 1 ) and ∠ Γ ( z 2 ) = ∠ Γ ( z 1 ) + 4 π ⋅ Ĭonsequently, moving on the line from z 1 to z 2 implies a change of the angle of the phasor (rotation) by 4 π ⋅. ADDENDUM 13G: METALLIC RECTANGULAR CAVITY RESONATORSĪPPENDIX F: Historical Review of EM Scientists.ADDENDUM 13F: PHYSICAL INSIGHT IN GUIDED WAVE PROPAGATION.ADDENDUM 13E: ACTIVE AND DOMINANT MODE IDENTIFICATION.ADDENDUM 13D: FIELD MAPS FOR THE TE 10 AND TM 11 MODES.ADDENDUM 13C: WAVE EQUATION SOLUTION FOR METALLIC RECTANGULAR WAVEGUIDES: CONTINUATION FOR ALL FIELD COMPONENTS.ADDENDUM 13B: PHASE AND GROUP VELOCITIES. ADDENDUM 13A: WAVE EQUATION SOLUTION FOR METALLIC RECTANGULAR WAVEGUIDES: THE LONGITUDINAL COMPONENT OF THE ELECTRIC FIELD PHASOR.Time-Domain Derivation of the Power Flow Density for the TE 10 ModeĪ Physical View of Wave Propagation and Power Flow in Waveguides Historical review of EM scientists Show more Show less.Wave polarization and propagation in multiple layers.Magnetic materials, magnetic circuits, and inductance.Uniqueness theorem and graphical and numerical solutions.Electric force, field, energy, and potential.Electrostatic fields, electric flux, and Gauss' law.An introduction to electromagnetic fields and waves.You will learn about static and time-varying fields, wave propagation and polarization, transmission lines and waveguides, and more. Electromagnetic Fields and Waves: Fundamentals of Engineering presents detailed explanations of the topic of EM fields in a holistic fashion that integrates the math and the physics of the material with students' realistic preparation in mind. Written by two electrical engineering experts and experienced educators, the book is designed to accommodate both one- and two-semester curricula. This core introductory-level undergraduate textbook offers solid coverage of the fundamentals of electromagnetic fields and waves. Understand electromagnetic field principles, engineering techniques, and applications.
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