1. EEE381B Pulsed radar A pulsed radar is characterized by a high power transmitter that generates an endless sequence of pulses. The rate at which the pulses are repeated is defined as the pulse repetition frequency. Denote: – pulse width, , usually expressed in  sec – pulse repetition frequency, PRF, usually in kHz – pulse period, T p = 1/PRF, usually in  sec

2. EEE381B Pulsed modulation [1]

3. EEE381B Pulsed radar bandwidth In the frequency domain, the transmitted and received signals are composed of spectral components centered on the radar operating frequency, f 0, with a sin(x)/x shape. The practical limits of the frequency response is f 0  1/ , and therefore the bandwidth of the receiver must be at least: BW Rx ≥ 2/ 

4. EEE381B Pulsed radar range resolution The range resolution of a radar is its ability to distinguish two closely spaced targets along the same line of sight (LOS). The range resolution is a function of the pulse length, where pulse length, L p = c . – For example, a 1  sec pulse width yields a pulse length of 0.3 km. Two targets can be resolved in range if: L p < 2(R 2 – R 1 )

5. EEE381B Pulsed radar range ambiguity The PRF is another key radar parameter and is arguably one of the most difficult design decisions. The range of a target becomes ambiguous as a function of half the pulse period; in other words targets that are further than half the pulse period yield ambiguous range results. R amb = c / (2 PRF) = cT p / 2

6. POWER CALCULATIONS P avg = P pk *(pw/prt) where P avg = average power P pk =peak power pw = pulse width prt = pulse repetition time Because 1/prt is equal to prf, the formula may be written as follows: P avg = P pk *(pw*prt)= P pk *Duty cycle

7. Rmin & Rmax Minimum range= ((Pulse width+ Recovery time) /2) *299,9232 where the radiated energy from a radar set travels at approximately 299,9232 meters per microsecond. The maximum (unambiguous )range for a given radar system can be determined by the following formula: Rmax= (Electromagnetic energy speed /2)*prt = (162,000 nautical miles per second /2) *prt

8. THE RADAR EQUATION where P t = power transmitted by the radar (watts) G t = gain of the radar transmit antenna (dimensionless) r = distance from the radar to the target (meters) σ = radar cross section of the target (meters squared) A eff = effective area of the radar receiving antenna (meters squared) P r = power received back from the target by the radar (watts)

9. The Doppler effect The Doppler ferquency is given by: f D = (2*V)/λ where f D = Doppler Frequency [Hz] λ = wavelength [m] v = speed of the wave-source [m/s] This equation is valid, if the speed if the source of a wave is like the radial speed. But the airplane usually flies in another direction than the direction towards to the radar. Only the radial speed is then also measured. However, this is different from the aim speed so that the following equation is valid: f D = (2*V*cos α)/λ v = speed of the aircraft [m/s]. α = angle between the direction of the transmitted/reflected signal and the direction of flight of the target λ. When α=0 the doppler frequency is maximum. The doppler is zero when the trajectory is perpendicular to the radar line of sight (0 = 90°).

10. EEE381B Quick response exercise # 2 Given a 10.5 GHz intercept radar and a transmitter capable of providing a peak power of 44 dBW at a PRF of 2 kHz: – What pulse width yields an average power of 50W? – What is the bandwidth in MHz and in % of this signal?

11. EEE381B Pulsed radar calculations Design the pulse parameters so as to achieve maximum average power for an unspecified Ku band pulsed radar given the following component specifications and system requirements: – the receiver has a bandwidth of at least 0.5% across the band – the required range resolution is 50m – The required range ambiguity is 25 km – For cooling purposes, ensure that the duty cycle of the transmitter does not exceed 0.2%

12. EEE381B Airborne radar bands [1]

13. EEE381B Radar range equation calculation The US Navy AN/SPS-48 Air Search Radar is a medium-range, three-dimensional (height, range, and bearing) air search radar. Published technical specifications include: – Operating frequency 2900-3100 MHz – Transmitter peak power 60-2200 kW – PRF 161-1366 Hz, and pulse widths of 9 / 3 μsec – Phased array antenna with a gain of 38.5 dB 1) For its published maximum range of 250 miles for a nominal target such as the F-18, what is the receiver chain sensitivity in bBm? 2) a plane is flying making 45° with the line of sight of this radar calculate the corresponding Doppler frequency captured if it has a velocity of 800 Km/h.

14. Doppler radar A Doppler radar is controlling vehicles speed at a of frequency F = 24.125 GHz (K band Mesta 208) emits wave trains with a PRF (Pulse Repetition Frequency) F 0 = 30kHz. The Doppler angle α between the axis of the radar beam and the axis of movement of vehicles measured is 25 °. a) What is the wavelength of the signal? b) What is the maximum speed |V Max |measured by radar? c) What is the Doppler frequency ∆F corresponding to a measured vehicle speed of 130km / h? d) The calculation speed is achieved using an FFT algorithm on a number N = 256 points. How accurate dv on measuring the speed?

15. Doppler radar An air Doppler radar control approach emits a EMW with a frequency F = 3GHz. The pulse duration τ emitted is equal to 1 μs and the repetition period T 0 is 100 μs. a) What is the wavelength of the signal? What is the PRF? b) What is the speed |V Max | measurable by this radar? c) What is the maximum range R max of this radar? d) What is the blind zone of the radar? e) Two planes during landing, follow with a spacing of 120m. What does the air traffic controller on the radar screen? Why?

16. Doppler radar A vehicle is traveling in urban area (speed limited to 50km / h) is controlled by a Doppler radar of the gendarmerie type Mesta 208, K-band (F = 24.125 GHz). In passing vehicle wave frequency response is F '= F + 2500Hz. The viewing angle is equal to α = 25 °.This car is it offending?