Final answer:
In the Primary Surveillance Radar (PSR), if one transmitter amplifier module fails or is in standby, the remaining seven amplifier modules will provide a minimum of 14kW peak power. To find out the coverage in nautical miles (nm), we can use the Radio Range equation, which states that the range is directly proportional to the square root of the power. By using the provided information and calculating the range when the transmitter's output power is increased, it is determined that the distance in the same direction that would have the same maximum field strength as the original 100 km distance is 90kW.
Step-by-step explanation:
In the Primary Surveillance Radar (PSR), if one transmitter amplifier module fails or is in standby, the remaining seven amplifier modules will provide a minimum of 14kW peak power. To determine the coverage in nautical miles (nm), we need to use the Radio Range equation, which states that the range is directly proportional to the square root of the power. Assuming the power is divided equally among the eight amplifier modules, each module will provide 14kW/8 = 1.75kW peak power.
Let's assume a certain power-to-range conversion constant, k, such that range = k * sqrt(power). Since we know the range when the power is 1.75kW, we can substitute these values into the equation to find k. Using the given reference information, we can calculate:
For the given 60kW transmitter:
- Range = k * sqrt(60kW) at 100 km
For the increased 90kW transmitter:
- Range = k * sqrt(90kW) at ?? km
By setting the two equations equal to each other, we can solve for the range when the transmitter's output power is increased:
- k * sqrt(60kW) = k * sqrt(90kW)
- sqrt(60kW) = sqrt(90kW)
- sqrt(60kW) = 3 * sqrt(10kW)
- sqrt(10kW) = 3 * sqrt(10kW)
Therefore, for the distance in the same direction to have the same maximum field strength as the original 100 km distance, the transmitter's output power would need to be increased to 90kW.