Measurement Pulse repetition frequency

1 measurement

1.1 range ambiguity
1.2 low prf
1.3 medium prf
1.4 high prf
1.5 sonar
1.6 laser

measurement

prf crucial systems , devices measure distance.

radar
laser range finder
sonar

different prf allow systems perform different functions.

a radar system uses radio frequency electromagnetic signal reflected target determine information target.

prf required radar operation. rate @ transmitter pulses sent air or space.

range ambiguity

a real target in 100 km or second-sweep echo in distance of 400 km?

a radar system determines range through time delay between pulse transmission , reception relation:

range

=



c
τ

2




{\displaystyle {\text{range}}={\frac {c\tau }{2}}}

for accurate range determination pulse must transmitted , reflected before next pulse transmitted. gives rise maximum unambiguous range limit:

max range

=



c

τ

prt



2


=


c

2


prf







{




τ

prt


=


1
prf










{\displaystyle {\text{max range}}={\frac {c\tau _{\text{prt}}}{2}}={\frac {c}{2\,{\text{prf}}}}\qquad {\begin{cases}\tau _{\text{prt}}={\frac {1}{\text{prf}}}\end{cases}}}

the maximum range defines range ambiguity detected targets. because of periodic nature of pulsed radar systems, impossible radar system determine difference between targets separated integer multiples of maximum range using single prf. more sophisticated radar systems avoid problem through use of multiple prfs either simultaneously on different frequencies or on single frequency changing prt.

the range ambiguity resolution process used identify true range when prf above limit.

low prf

systems using prf below 3 khz considered low prf because direct range can measured distance of @ least 50 km. radar systems using low prf typically produce unambiguous range.

unambiguous doppler processing becomes increasing challenge due coherency limitations prf falls below 3 khz.

for example, l-band radar 500 hz pulse rate produces ambiguous velocity above 75 m/s (170 mile/hour), while detecting true range 300 km. combination appropriate civilian aircraft radar , weather radar.

300 km range

=


c

2
×
500





{\displaystyle {\text{300 km range}}={\frac {c}{2\times 500}}}









75 m/s velocity

=



500
×
c


2
×

10

9







{\displaystyle {\text{75 m/s velocity}}={\frac {500\times c}{2\times 10^{9}}}}

low prf radar have reduced sensitivity in presence of low-velocity clutter interfere aircraft detection near terrain. moving target indicator required acceptable performance near terrain, introduces radar scalloping issues complicate receiver. low prf radar intended aircraft , spacecraft detection heavily degraded weather phenomenon, cannot compensated using moving target indicator.

medium prf

range , velocity can both identified using medium prf, neither 1 can identified directly. medium prf 3 khz 30 khz, corresponds radar range 5 km 50 km. ambiguous range, smaller maximum range. range ambiguity resolution used determine true range in medium prf radar.

medium prf used pulse-doppler radar, required look-down/shoot-down capability in military systems. doppler radar return not ambiguous until velocity exceeds speed of sound.

a technique called ambiguity resolution required identify true range , speed. doppler signals fall between 1.5 khz, , 15 khz, audible, audio signals medium-prf radar systems can used passive target classification.

for example, l band radar system using prf of 10 khz duty cycle of 3.3% can identify true range distance of 450 km (30 * c / 10,000 km/s). instrumented range. unambiguous velocity 1,500 m/s (3,300 mile/hour).

450 km

=


c

0.033
×
2
×
10
,
000





{\displaystyle {\text{450 km}}={\frac {c}{0.033\times 2\times 10,000}}}







1,500 m/s

=



10
,
000
×
c


2
×

10

9







{\displaystyle {\text{1,500 m/s}}={\frac {10,000\times c}{2\times 10^{9}}}}

the unambiguous velocity of l-band radar using prf of 10 khz 1,500 m/s (3,300 mile/hour) (10,000 x c / (2 x 10^9)). true velocity can found objects moving under 45,000 m/s if band pass filter admits signal (1,500/0.033).

medium prf has unique radar scalloping issues require redundant detection schemes.

high prf

systems using prf above 30 khz function better known interrupted continuous-wave (icw) radar because direct velocity can measured 4.5 km/s @ l band, range resolution becomes problematic.

high prf limited systems require close-in performance, proximity fuses , law enforcement radar.

for example, if 30 samples taken during quiescent phase between transmit pulses using 30 khz prf, true range can determined maximum of 150 km using 1 microsecond samples (30 x c / 30,000 km/s). reflectors beyond range might detectable, true range cannot identified.

150 km

=



30
×
c


2
×
30
,
000





{\displaystyle {\text{150 km}}={\frac {30\times c}{2\times 30,000}}}







4,500 m/s

=



30
,
000
×
c


2
×

10

9







{\displaystyle {\text{4,500 m/s}}={\frac {30,000\times c}{2\times 10^{9}}}}

it becomes increasingly difficult take multiple samples between transmit pulses @ these pulse frequencies, range measurements limited short distances.

sonar

sonar systems operate radar, except medium liquid or air, , frequency of signal either audio or ultra-sonic. radar, lower frequencies propagate relatively higher energies longer distances less resolving ability. higher frequencies, damp out faster, provide increased resolution of nearby objects.

signals propagate @ speed of sound in medium (almost water), , maximum prf depends upon size of object being examined. example, speed of sound in water 1,497 m/s, , human body 0.5 m thick, prf ultrasound images of human body should less 2 khz (1,497/0.5).

as example, ocean depth approximately 2 km, sound takes on second return sea floor. sonar slow technology low prf reason.

laser

light waves can used radar frequencies, in case system known lidar, short light radar .

laser range or other light signal frequency range finders operate radar @ higher frequencies. non-laser light detection utilized extensively in automated machine control systems (e.g. electric eyes controlling garage door, conveyor sorting gates, etc.), , use pulse rate detection , ranging @ heart, same type of system radar—without bells , whistles of human interface.

unlike lower radio signal frequencies, light not bend around curve of earth or reflect off ionosphere c-band search radar signals, , lidar useful in line of sight applications higher frequency radar systems.