Electronic Applications of the Smith Chart: In Waveguide, Circuit, and Component Analysis

Chapter 5: Waveguide Phase Representations

5.1 Phase Relationships

The phase relationship between the reflected and incident traveling voltage waves, and between the reflected and incident traveling current waves, at various positions along a waveguide has been discussed briefly in Chaps. 1 and 3. In Chap. 4 an additional phase relationship, namely, that between the steady-state (standing wave) voltage and the steady-state (standing wave) current at various coincident points along a waveguide was discussed. The two former relationships are, respectively, the phase angle of the voltage reflection coefficient and the phase angle of the current reflection coefficient. The latter is the phase angle of the power factor-the power factor itself being thus defined as the cosine of this angle [35]. All three of the foregoing phase relationships have been shown to be graphically representable as overlays on the impedance coordinates of the SMITH CHART.

It has also been shown that the voltage current phase relationship (phase angle of power factor) overlay (Fig. 4.2) can be applied to a SMITH CHART whose coordinates are labeled to represent either impedances or admittances (such as the SMITH CHART of Fig. 3.3). Directions were indicated therein for properly orienting the overlay on the specific coordinates selected, and for interpreting the sign of the indicated phase angle.

In this chapter some fundamental waveguide phase conventions will first be reviewed. Following this, more generalized uses of the peripheral scale labeled "angle of reflection coefficient" (Fig. 3.3) will be presented. Next, a discussion of the voltage, current, and power...

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