## Microwave Passive Repeater

which is definitely far field. And, since the other path is even longer, it may also be assumed to be far field.

At this point, it is necessary to determine the gain of the passive repeater. This may be done either by referring to the curves in Fig. 11, or in the case where curves are not available, the gain of the passive reflector may be calculated. To calculate passive repeater gain, the passive repeater which has the smaller effective area (actual area times the cosine of half the larger horizontal included angle) must first be determined. In the case of Fig. 12, both horizontal angles are the same (27 degrees) and both passive repeaters are the same size, so it will make no difference which we select for calculation purposes.

The gain of a 30 x 40 ft passive repeater at 5,787 GHz, with a horizontal included angle of 27 degrees is:

20 log io

where A = actual passive area in square feet, cos a = cosine of half the horizontal included angle, and A2 = wavelength in feet, squared.

- There will be a slight amount of coupling loss between the two passive repeaters. The coupling loss for various spacings and passive orientations may be determined by use of the curves in Fig. 1 and the associated calculations. For example, for the conditions in Fig. 3E and Fig. 12, it would be necessary to check the b/a ratio of the two passive repeaters. This is done by determining the effective area of each of the two passive repeaters:

If there should be a difference in the size of the effective areas, the larger effective area is considered to be b.

Determining the value of 1/K2 to complete the double passive repeater efficiency calculation, we find that:

Ae where X - wavelength in feet, di = the separation between the two passive repeaters, and Ae = the effective area of the smaller of the two passive repeaters. The separation between the two reflectors is not critical. At frequencies above about 2 GHz and with passive repeater sizes larger than about 16 x 20 ft, the spacing may extend to as much as 1000 ft without degrading the gain of the double passive more than 2 dB. Let's assume 500 ft for the example in Fig. 12.

This places the 1 /K2 point of Fig. 1 along the left margin of the graph. Following the — = 1 curve, we find a coupling loss of about 0.9 dB.

30*43 PASS EVE REPEATED 10..O PASSIVE REPEATED

30*43 PASS EVE REPEATED 10..O PASSIVE REPEATED

Losses:

134.2 13.2 miles at 5.787 GHz

136.2 16.7 miles at 5.787 GHz

1,7 dB 40 ft waveguide and connectors 0.9 dB double passive coupling efficiency

273.0 dB

43.9 dBm rf input to receiver; fade margin of 37.1 dB

Totaling system gains and losses: Gains:

+30 dBm transmitter power output

42.5 dB 10 ft parabola at 5.787 GHz

42.5 dB 10 ft parabola at 5.787 GHz

114.1 Passive gain 30 x 40 ft at 5,787 GHz +2291.1 dB

The calculations and path sketches shown on the preceding pages are not just theoretical. Similar configurations have been installed using passive repeaters hundreds of times during the 20 years or so that microwave has been a communications too! and not an experimental toy. A high percentage of the passive repeaters installed, though, have been installed only in the last 5 years or so. This is because of the spread through the communication industry of the knowledge of the techniques of passive repeaters. It is also due in great part to the demise of "rules of thumb" which formerly played a great part in the "engineering" of early-day microwave systems. One favorite rule of thumb that used to be touted and that really has no basis in fact, is the one that said, "If the product of the path lengths exceeds 30, then a passive

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