In many cases, the antenna or other load impedance is not known. If it is not matched to the line, the line modifies this impedance so that the transmitter sees a different impedance. One way to find the overall impedance as well as the antenna or other load impedance is to measure the combined

Question

In many cases, the antenna or other load impedance is not known. If it is not matched to the line, the line modifies this impedance so that the transmitter sees a different impedance. One way to find the overall impedance as well as the antenna or other load impedance is to measure the combined impedance of the load and the transmission line at the transmitter end, using an impedance bridge. Then the Smith chart can be used to find the individual impedance values.

A 50-ft RG-11/U foam dielectric coaxial cable with a characteristic impedance of 75 Ω and a velocity factor of 0.8 has an operating frequency of 72 MHz. The load is an antenna whose actual impedance is unknown. A measurement at the transmitter end of the cable gives a complex impedance of 82 + j 43. What is the impedance of the antenna?

Accepted Answer

One wavelength at 72 MHz is 984/72 = 13.67 ft. Taking the velocity factor into account yields

λ = 13.67 × 0.8 = 10.93 ft

The length of the 50-ft cable, in wavelengths, is 50/10.93 = 4.57. As before, it is the 0.57 λ value that is of practical use.

First, the measured impedance is normalized and plotted. The prime center is 75 Ω. In Fig. 13-37 Z = (82 + j 43)/75 = 1.09 + j 0.52 is plotted on the Smith chart. The SWR circle is plotted through this point from the prime center. A tangent line is then drawn from the circle to the linear SWR chart on the bottom. The SWR is 1.67.

Next, a line is drawn from prime center to the normalized impedance point and through the wavelength plots on the perimeter of the graphs. It intersects the “toward load” scale at point X, or 0.346 λ. Refer to the figure.

The plotted impedance is what is seen at the generator end, so it is necessary to move around the graph to the load in the counterclockwise direction to find the load impedance. We move a distance equal to the length of the cable, which is 4.57 λ . Nine full rotations from point X represents 4.5 λ, which brings us back to point X. We then rotate 0.07 λ more, counterclockwise, to complete the length. This puts us at the 0.346 + 0.07 = 0.416 λ point, which is designated point Y in Fig. 13-37. We then draw a line from Y to the prime center. The point at which this line intersects the SWR circle is the actual antenna impedance. The normalized value is 0.72 + j 0.33. Multiplying by 75 gives the actual value of the antenna impedance:

Z = 75(0.72 + j 0.33) = 54 + j 24.75 Ω

Question 13.4.3: In many cases, the antenna or other load impedance is not kn...

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