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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

Error in synchronous Demodulator

ระบบวิทยุ (Radio System) 252442

ผู้ช่วยศาสตราจารย์ธราดล โกมลมิศร์

ภาควิชาวิศวกรรมไฟฟ้า

คณะวิศวกรรมศาสตร์ มหาวิทยาลัยเชียงใหม่

slide2
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

no error f lo f c dsb sc
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

no error f lo f c dsb sc1
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

no error f lo f c ssb usb
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

no error f lo f c ssb usb1
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

frequency error d f 1 hz dsb sc
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

frequency error d f 1 hz dsb sc1
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

frequency error d f 1 hz ssb usb
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

frequency error d f 1 hz ssb usb1
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

phase error q p 4 dsb sc
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

phase error q p 4 dsb sc1
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

phase error q p 4 ssb usb
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

phase error q p 4 ssb usb1
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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