PULSE-REPETITION FREQUENCY AND POWER CALCULATIONS. - The energy content of a continuous-wave radar transmission may be easily figured because the transmitter operates continuously. However, pulsed radar transmitters are switched on and off to provide range timing information with each pulse. The resulting waveform for a transmitter was shown in figure 1-3. The amount of energy in this waveform is important because maximum range is directly related to transmitter output power. The more energy the radar system transmits, the greater the target detection range will be. The energy content of the pulse is equal to the PEAK (maximum) POWER LEVEL of the pulse multiplied by the pulse width. However, meters used to measure power in a radar system do so over a period of time that is longer than the pulse width. For this reason, pulse-repetition time is included in the power calculations for transmitters. Power measured over such a period of time is referred to as AVERAGE POWER. Figure 1-5 illustrates the way this average power would be shown as the total energy content of the pulse. The shaded area represents the total energy content of the pulse; the crosshatched area represents average power and is equal to peak power spread out over the prt. (Keep in mind, as you look at figure 1-5, that no energy is actually present between pulses in a pulsed radar system. The figure is drawn just to show you how average power is calculated.) Pulse-repetition time is used to help figure average power because it defines the total time from the beginning of one pulse to the beginning of the next pulse. Average power is figured as follows:

Figure 1-5. - Pulse energy content.

Because 1/prt is equal to prf, the formula may be written as follows:

The product of pulse width (pw) and pulse-repetition frequency (prf) in the above formula is called the DUTY CYCLE of a radar system. The duty cycle is a ratio of the time on to the time off of the transmitter, as shown in figure 1-6. The duty cycle is used to calculate both the peak power and average power of a radar system. The formula for duty cycle is shown below:

NOTE: Pulse repetition frequency (prf) and pulse repetition rate (prr) are interchangeable terms.

Figure 1-6. - Duty cycle.

Since the duty cycle of a radar is usually known, the most common formula for average power is expressed as:

Transposing the above formula gives us a common formula for peak power:

Peak power must be calculated more often than average power. This is because, as previously mentioned, most measurement instruments measure average power directly. An example is shown below:

Where:

Before figuring P_pk, you must figure duty cycle as follows:

Now that you have duty cycle, P_pk may be calculated as follows:

ANTENNA HEIGHT AND SPEED. - Another factor affecting radar range is antenna height. The high-frequency energy transmitted by a radar system travels in a straight line and does not normally bend to conform to the curvature of the earth. Because of this, the height of both the antenna and the target are factors in detection range. The distance to the horizon (in nautical miles) for a radar system varies with the height of the antenna according to the following formula:

For example, assume antenna height to be 64 feet in the following calculations:

A target at a range greater than the radar horizon will not be detected unless it is high enough to be above the horizon. An example of the antenna- and target-height relationship is shown in figure 1-7.

Figure 1-7. - Radar horizon.

The antenna-rotation rate also affects maximum detection range. The slower an antenna rotates, the greater the detection range of a radar system. When the antenna is rotated at 10 revolutions per minute (rpm), the beam of energy strikes each target for just one-half the time it would if the rotation were 5 rpm. The number of strikes per antenna revolution is referred to as HITS PER SCAN. During each revolution enough pulses must be transmitted to return a usable echo.

NOTE: The more pulses transmitted to a given area (at slower antenna speeds), the greater the number of hits per scan.

As an example, if the antenna rotates at 20 rpm, it completes a revolution in 3 seconds. During this time, a transmitter with a prf of 200 pulses per second (pps) transmits 600 pulses. Since 360 degrees of azimuth must be covered, the following formula shows the number of pulses for each degree of azimuth:

Such a low number of pulses for any given target area greatly increases the likelihood that some targets will be missed entirely; therefore, prf and antenna speed must be matched for maximum efficiency.

Q.6 Atmospheric interference with the travel of electromagnetic energy increases with what rf energy characteristic?
Q.7 How is prt related to prf?
Q.8 What type of radar transmitter power is measured over a period of time?
Q.9 What term is used to describe the product of pulse width and pulse-repetition frequency?