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**DUTY CYCLE**

Duty cycle (or duty factor) is a measure of the fraction of the time a radar is transmitting. It is important
because it relates to peak and average power in the determination of total energy output. This, in turn,
ultimately effects the strength of the reflected signal as well as the required power supply capacity and cooling
requirements of the transmitter.

Although there are exceptions, most radio frequency (RF) measurements are
either continuous wave (CW) or pulsed RF. CW RF is uninterrupted RF such as from an oscillator. Amplitude
modulated (AM), frequency modulated (FM), and phase modulated (PM) RF are considered CW since the RF is
continuously present. The power may vary with time due to modulation, but RF is always present. Pulsed RF, on the
other hand, is bursts (pulses) of RF with no RF present between bursts. The most general case of pulsed RF
consists of pulses of a fixed pulse width (PW) which come at a fixed time interval, or period, (T). For clarity
and ease of this discussion, it is assumed that all RF pulses in a pulse train have the same amplitude. Pulses at
a fixed interval of time arrive at a rate or frequency referred to as the pulse repetition frequency (PRF) of so
many pulse per second. Pulse repetition interval (PRI) and PRF are reciprocals of each other.

**[1]**
PRF = 1/T = 1/PRI

Power measurements are classified as either peak pulse power, P

_{p}, or average
power, P

_{ave}. The actual power in pulsed RF occurs during the pulses, but most power measurement methods
measure the heating effects of the RF energy to obtain an average value of the power. It is correct to use either
value for reference so long as one or the other is consistently used. Frequently it is necessary to convert from P

_{p}
to P

_{ave}, or vice versa; therefore the relationship between the two must be understood. Figure 1 shows
the comparison between P

_{p} and P

_{ave}.

**Figure 1. RF Pulse Train**

The average value is defined as that level where the pulse area above the average is equal to area below
average between pulses. If the pulses are evened off in such a way as to fill in the area between pulses, the
level obtained is the average value, as shown in Figure 1 where the shaded area of the pulse is used to fill in
the area between pulses. The area of the pulse is the pulse width multiplied by the peak pulse power. The average
area is equal to the average value of power multiplied by the pulse period.

Since the two values are equal:

**[2] **P

_{ave}
x T = P

_{p} x PW

or

**[3]
**P

_{ave}/P

_{p} = PW/T

Using [1]

**[4]
**P

_{ave}/P

_{p} = PW/T = PW x PRF = PW/PRI = duty cycle

(note that the symbol

τ represents pulse width (PW) in most reference books)

The ratio of the average power to the peak pulse power is the duty cycle and represents the percentage of time the
power is present. In the case of a square wave the duty cycle is 0.5 (50%) since the pulses are present 1/2 the
time, the definition of a square wave.

For Figure 1, the pulse width is 1 unit of time and the period is
10 units. In this case the duty cycle is:

PW/T = 1/10 = 0.1 (10%).

A more typical case would be a PRF
of 1,000 and a pulse width of 1.0 microseconds. Using [4], the duty cycle is 0.000001 x 1,000 = 0.001. The RF
power is present one-thousandth of the time and the average power is 0.001 times the peak power. Conversely, if
the power were measured with a power meter which responds to average power, the peak power would be 1,000 time the
average reading.

Besides expressing duty cycle as a ratio as obtained in equation [4], it is commonly expressed as either a
percentage or in decibels (dB). To express the duty cycle of equation [4] as a percentage, multiply the value
obtained by 100 and add the percent symbol. Thus a duty cycle of 0.001 is also 0.1%.

The duty cycle can be
expressed logarithmically (dB) so it can be added to or subtracted from power measured in dBm/dBW rather than
converting to, and using absolute units.

**[5] **Duty cycle (dB) = 10 log(duty cycle
ratio)

For the example of the 0.001 duty cycle, this would be 10 log(0.001) = -30 dB. Thus the average
power would be 30 dB less than the peak power. Conversely, the peak power is 30 dB higher than the average power.

For pulse radars operating in the PRF range of 0.25-10 kHz and PD radars operating in the PRF range of 10-500
kHz, typical duty cycles would be:

Pulse : 0.1 - 3% = 0.001 - .03 = -30 to -15 dB

Pulse Doppler
: 5 - 50% = 0.05 - .5 = -13 to -3 dB

Continuous Wave : 100% =
1 = 0 dB

Intermediate Frequency Bandwidths of typical signals are:

Pulse 1 to 10 MHz

Chirp or Phase coded pulse 0.1 to 10
MHz

CW or PD 0.1 to 5 kHz

PRF is usually subdivided into the following categories: Low 0.25-4 kHz; Medium 8-40 kHz; High 50-300 kHz.

**Table of Contents
for Electronics Warfare and Radar Engineering Handbook**

Introduction |
Abbreviations | Decibel | Duty
Cycle | Doppler Shift | Radar Horizon / Line
of Sight | Propagation Time / Resolution | Modulation
| Transforms / Wavelets | Antenna Introduction
/ Basics | Polarization | Radiation Patterns |
Frequency / Phase Effects of Antennas |
Antenna Near Field | Radiation Hazards |
Power Density | One-Way Radar Equation / RF Propagation
| Two-Way Radar Equation (Monostatic) |
Alternate Two-Way Radar Equation |
Two-Way Radar Equation (Bistatic) |
Jamming to Signal (J/S) Ratio - Constant Power [Saturated] Jamming
| Support Jamming | Radar Cross Section (RCS) |
Emission Control (EMCON) | RF Atmospheric
Absorption / Ducting | Receiver Sensitivity / Noise |
Receiver Types and Characteristics |
General Radar Display Types |
IFF - Identification - Friend or Foe | Receiver
Tests | Signal Sorting Methods and Direction Finding |
Voltage Standing Wave Ratio (VSWR) / Reflection Coefficient / Return
Loss / Mismatch Loss | Microwave Coaxial Connectors |
Power Dividers/Combiner and Directional Couplers |
Attenuators / Filters / DC Blocks |
Terminations / Dummy Loads | Circulators
and Diplexers | Mixers and Frequency Discriminators |
Detectors | Microwave Measurements |
Microwave Waveguides and Coaxial Cable |
Electro-Optics | Laser Safety |
Mach Number and Airspeed vs. Altitude Mach Number |
EMP/ Aircraft Dimensions | Data Busses | RS-232 Interface
| RS-422 Balanced Voltage Interface | RS-485 Interface |
IEEE-488 Interface Bus (HP-IB/GP-IB) | MIL-STD-1553 &
1773 Data Bus |

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