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Error in synchronous Demodulator

Error in synchronous Demodulator. ระบบวิทยุ (Radio System) 252442 ผู้ช่วยศาสตราจารย์ธราดล โกมลมิศร์ ภาควิชาวิศวกรรมไฟฟ้า คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเชียงใหม่. ก ำหนดให้. Carrier (f c =100,000Hz) Cos2 p f c t = Cos2 p 100,000t Modulating signal (f m =1,000Hz)

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Error in synchronous Demodulator

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  1. Error in synchronous Demodulator ระบบวิทยุ (Radio System) 252442 ผู้ช่วยศาสตราจารย์ธราดล โกมลมิศร์ ภาควิชาวิศวกรรมไฟฟ้า คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเชียงใหม่

  2. กำหนดให้ • Carrier (fc=100,000Hz) Cos2pfct = Cos2p100,000t • Modulating signal (fm=1,000Hz) Cos2pfmt = Cos2p1,000t • DSB-SC Modulated signal Cos2pfctCos2pfmt = Cos2p100,000tCos2p1,000t = 0.5Cos2p101,000t+0.5Cos2p99,000t • SSB Modulated signal (USB) 0.5Cos2p101,000t • SSB Modulated signal (LSB) 0.5Cos2p99,000t Error in Synchronous Demodulator

  3. No error fLO=fC: DSB-SC • Local Oscillator = Cos2p100,000t • Demodulated signal for DSB-SC (before LPF) • (0.5Cos2p101,000t+0.5Cos2p99,000t)Cos2p100,000t • 0.5Cos2p101,000tCos2p100,000t+0.5Cos2p99,000tCos2p100,000t • 0.25Cos2p201,000t + 0.25Cos2p1,000t+0.25Cos2p199,000t + 0.25Cos(-2p1,000t) • Demodulated signal for DSB-SC (After LPF) • 0.25Cos2p1,000t + 0.25Cos2p1,000t= 0.5Cos2p1,000t Error in Synchronous Demodulator

  4. No error fLO=fC : DSB-SC • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f -199,000 201,000 -201,000 1,000 199,000 -1,000 f 1,000 -1,000 1,000 Hz (ok) Error in Synchronous Demodulator

  5. No error fLO=fC: SSB-USB • Local Oscillator = Cos2p100,000t • Demodulated signal for SSB-USB (before LPF) =0.5Cos2p101,000tCos2p100,000t =0.25Cos2p201,000t + 0.25Cos2p1,000t • Demodulated signal for SSB-USB (After LPF) =0.25Cos2p1,000t Error in Synchronous Demodulator

  6. No error fLO=fC : SSB-USB • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f 201,000 -201,000 1,000 -1,000 f 1,000 -1,000 1,000 Hz (ok) Error in Synchronous Demodulator

  7. Frequency error Df= +1 Hz : DSB-SC • Local Oscillator = Cos2p100,001t • Demodulated signal for DSB-SC (before LPF) =(0.5Cos2p101,000t+0.5Cos2p99,000t)Cos2p100,001t = 0.5Cos2p101,000tCos2p100,001t+0.5Cos2p99,000tCos2p100,001t = 0.25Cos2p201,001t + 0.25Cos2p999t+0.25Cos2p199,001t + 0.25Cos2p1,001t • Demodulated signal for DSB-SC (After LPF) =0.25Cos2p999t + 0.25Cos2p1,001t = 0.5Cos2p1,000tCos2p1t Error in Synchronous Demodulator

  8. Frequency error Df= +1 Hz : DSB-SC • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f -199,001 201,001 -201,001 999 1,001 199,001 -1,001 -999 f 999 1,001 -1,001 -999 1,000 Hz 1 Hz Error in Synchronous Demodulator

  9. Frequency error Df= +1 Hz : SSB-USB • Local Oscillator = Cos2p100,001t • Demodulated signal for SSB-USB (before LPF) =0.5Cos2p101,000tCos2p100,001t =0.25Cos2p201,001t + 0.25Cos2p999t • Demodulated signal for SSB-USB (After LPF) = 0.25Cos2p999t Error in Synchronous Demodulator

  10. Frequency error Df= +1 Hz : SSB-USB • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f 201,001 -201,001 999 -999 f 999 -999 999 Hz (frequency change) Error in Synchronous Demodulator

  11. Phase error q= p/4 : DSB-SC • Local Oscillator = Cos(2p100,000t+p/4) • Demodulated signal for DSB-SC (before LPF) =(0.5Cos2p101,000t+0.5Cos2p99,000t)Cos(2p100,000t+p/4) = 0.5Cos2p101,000tCos(2p100,000t+p/4)+0.5Cos2p99,000tCos(2p100,000t+p/4) = 0.25Cos(2p201,000t+p/4) + 0.25Cos(2p1,000t-p/4)+0.25Cos(2p199,000t+p/4) + 0.25Cos(-2p1,000t-p/4) • Demodulated signal for DSB-SC (After LPF) =0.25Cos(2p1,000t-p/4) + 0.25Cos(2p1,000t+p/4) = 0.5Cos2p1,000tCosp/4=0.707x0.5Cos2p1,000t Error in Synchronous Demodulator

  12. Phase error q= p/4 : DSB-SC • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f -199,000 201,000 -201,000 1,000 199,000 -1,000 f 1,000 -1,000 1kHz (amplitude drop) Error in Synchronous Demodulator

  13. Phase error q= p/4 : SSB-USB • Local Oscillator = Cos(2p100,000t+p/4) • Demodulated signal for DSB-SC (before LPF) = 0.5Cos2p101,000tCos(2p100,000t+p/4) = 0.25Cos(2p201,000t+p/4) + 0.25Cos(2p1,000t-p/4) • Demodulated signal for DSB-SC (After LPF) =0.25Cos(2p1,000t-p/4) Error in Synchronous Demodulator

  14. Phase error q= p/4 : SSB-USB • Spectrum (before LPF) • Spectrum (after LPF) • Signal (after LPF) f 201,000 -201,000 1,000 -1,000 f 1,000 -1,000 1kHz(shift phase) Error in Synchronous Demodulator

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