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Advanced Microwave Circuits and Systems Part 16

Tham khảo tài liệu 'advanced microwave circuits and systems part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 444 Advanced Microwave Circuits and Systems where a t is the incidental amplitude modulation of the source and s t is the frequency modulating signal which is linear for a linear chirp. The instantaneous frequency f t is given by f t f0 K .s t 12 where f0 is the start frequency. The backscattered signal received at the Reader can be expressed as y t LJT f t - T .a t - T .cos t-T 2f t - t K. Js t dt y f t - t 0 13 where T is the round trip delay and L is the total loss assumed constant over the frequency band between antennas A1 and A2 through the scattering antenna. 90 -90n 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Frequency GHz 400 ------------------ ---------------------- Fig. 7 a -400 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 0.0 0.5 1.0 1.5 2.0 25 3. 0 Fig. 7 b Time microsec Fig. 7. a Phase Ripple of r f Fig. 7. b Time Domain IF Waveform Depicting Phase Modulation The output from the mixer M1 after filtering can be approximated as Ztag t 1 2.L.a2 t .r f t .cos 2 rtfoT KT.s t y f t 14 Remote Characterization of Microwave Networks - Principles and Applications 445 provided the delay T is small compared to the chirp duration. For the special case of a linear chirp 14 becomes Ztag t .L.a2 t .r f t .cos 2 foT KT.t v f t 15 The IF signal in such a case is a nominal sine wave with frequency Kt 2ả B Tr .t 16 where B chirp bandwidth and TR chirp duration The IF is thus a modulated sine wave of carrier frequency B Tr .t together with amplitude and phase modulation according to r f t . In other words a mapping occurs for the complex function r f from the frequency to time domain. Therefore demodulation of the IF signal in 15 should provide information on the reflection coefficient between frequencies f0 and f0 B. Fig.7 b represents ztag t as generated by simulation with the following parameters f0 6.9 GHz B 1 GHz TR 3 ps with a round trip delay T produced by propagation through 2 meters in air i.e.1 meter in each