1. ECEN5633 Radar Theory Lecture #3 20 January 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 2.1 & 2.5 n Problems 1.11, 14, & 16 n Quiz #1 u Live: 29 January u DL < 5 February

2. ECEN5633 Radar Theory Lecture #4 22 January 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 2.8 & 2.9 n Problems 2.1, 3, & 5 n Quiz #1 u Live: 29 January u DL < 5 February

3. Last Time n Doppler Shift u x(at) ↔ X(f/a)/|a| u Transmitting Frequency = f1? Received Frequency = f1(1 + 2v r /c) > f1 if target approaching u Frequency Shift = + 2v r /λ

4. Free Space Equations n RF Link Equation u P r = P t *G t *G r *λ 2 /(4πd) 2 n Radar Equation u P r = σ*P t *G 2 ant *λ 2 /[(4π) 3 d 4 ] n If P t = peak power, P r does also If P t = average power, P r does also

5. Free Space Equations n Provide estimates of the power delivered to the output of receiving antenna… n …provided that Polarization is correct XMTR \ RCVRHorizontalVerticalRight Circular Left Circular Horizontal1.00.0About 1/2 Vertical0.01.0About 1/2 Right CircularAbout 1/2 1.00.0 Left CircularAbout 1/2 0.01.0 Change in P r

6. Antenna RCS n Horizontally Polarized EM → Vertically Polarized Antenna It's all reradiated. n Horizontally Polarized EM → Horizontally Polarized Antenna Some is reradiated. n Antennas can have a high RCS

7. F-22 Raptor

8. Pulse Radar Range Ambiguity & Resolution n Want RTT < T – Tp u T = 1/PRF u Tp = Pulse Width u If RTT > T - Tp, reported range is too small n Two targets distance d apart, where 2d/c < Tp? u Returned echoes will overlap in time u Can't resolve targets

9. Multipath

10. Multipath (20 m antenna height)

11. Radar Radiation Patter source: Communication and Radar Systems, by Nicolaos Tzannes

12. Ludwig Boltzmann n Austrian Physicist n Born 1844 n Died 1906 n Statistical Mechanics u How atomic properties (mass, charge, etc.) affect physical properties n k = 1.381(10 -23 ) watts/(Hz*K) u Relates energy with temperature source: Wikipedia

13. Noise Temp depends on G D n What Main Lobe is pointing at is important! u Side Lobe gains are 16 dB down = 10 1.6 = 39.81 times weaker

14. Miteq LNA n JS3-18002200-15-10P n Gain 26 dB minimum u 10 2.6 = 398.1 n Noise Temp = 122 o K Source: www.miteq.com

15. Free Space Equations n RF Link Equation u P r = P t *G t *G r *λ 2 /[(4πd) 2 L o ] n Radar Equation u P r = σ*P t *G 2 ant *λ 2 /[(4π) 3 d 4 L o ] n L o = All other losses u polarization, impedance mismatches, rain, etc. n Multipath u May cause actual P r to deviate from calculated

16. Thermal Noise n Good Power Spectrum Models u White Noise u Band limited White Noise n Gaussian Distributed voltages u Zero Mean Scope snapshot would look like this.

17. Discrete Time White Noise Waveforms (255 point Gaussian Noise) Thermal Noise is Gaussian Distributed. Time Volts 0

18. 15 bin Histogram (255 points of Gaussian Noise) Volts Bin Count

19. 15 bin Histogram (2500 points of Gaussian Noise) Volts Bin Count 0 400

20. Carl Frederich Gauss n German Mathematician & Physicist n Born 1777 n Died 1855 n Ranks as one of history's greatest Mathematicians n Normal PDF's named after him source: Wikipedia

21. Noise Model for any Device S in & N in GS in & G(N in + N d ) G N d = kT o W n + + G = 1/L Active Device? Get T o off spec sheet. Passive Device? T o = (L-1)T o physical

22. Noise Bandwidth n Low Pass u Given Transfer Function H(f) u Find Power Transfer Function |H(f)| 2 = H(f)H * (f) u Find area under |H(f)| 2 F Call this Area1 u Note |H(0)| 2 u Take an ideal filter… F … with same height |H(0)| 2 as actual filter… F … adjust max frequency 'til ideal filter has area = Area1 F Max frequency value of ideal filter = Wn

23. Noise Bandwidth n Band Pass u Given Transfer Function H(f) u Find Power Transfer Function |H(f)| 2 = H(f)H * (f) u Find area under |H(f)| 2 F Call this Area1 u Note |H(f c )| 2 u Take an ideal band pass filter… F … centered at f c Hz… F … with same height |H(f c )| 2 as actual filter… F … adjust width 'til ideal filter has area = Area1 F Positive frequency width of ideal filter = Wn