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Demodulation of AM Signal

The document discusses two types of AM demodulators: the square law detector and the envelope detector. The square law detector uses a nonlinear device and extraction of the desired signal term from its output equation. The envelope detector consists of a diode and RC filter. It extracts the envelope of the input AM signal and provides an output that exactly follows the message signal.

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Vartika Nanda
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158 views16 pages

Demodulation of AM Signal

The document discusses two types of AM demodulators: the square law detector and the envelope detector. The square law detector uses a nonlinear device and extraction of the desired signal term from its output equation. The envelope detector consists of a diode and RC filter. It extracts the envelope of the input AM signal and provides an output that exactly follows the message signal.

Uploaded by

Vartika Nanda
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Demodulation of AM signal

Types of AM demodulator
• Demodulation- Process of recovering the original message signal
from the modulated signal
AM
Demodulators

Square law Envelope


detector detector
Square law detector

• Square law detector is obtained using square law modulator


Square law detector
• The input-output relation for a nonlinear device is given as
V2 (t )  aV1 (t )  bV1 (t )      (1)
2
Square law detector
• The input-output relation for a nonlinear device is given as
V2 (t )  aV1 (t )  bV1 (t )      (1)
2

• When a nonlinear device is used for AM demodulation, the input


signal is given as
V1 (t )  aVc cos c t  2bVmVc cos mt cos c t      (2)
Square law detector
• The input-output relation for a nonlinear device is given as
V2 (t )  aV1 (t )  bV1 (t )      (1)
2

• When a nonlinear device is used for AM demodulation, the input


signal is given as
V1 (t )  aVc cos c t  2bVmVc cos mt cos c t      (2)
2b
V1 (t )  aVc cos c t[1  m(t )]      (3)
a
2b
Amplitude Sensitivity k
a
V1 (t )  Vc cos c t[1  km(t )]      (4)
Square law detector
• Sub Eq.(4) in Eq.(1),
V2 (t )  aVc cos c t[1  km(t )]  b{Vc cos c t[1  km(t )]}2      (5)
Square law detector
• Sub Eq.(4) in Eq.(1),
V2 (t )  aVc cos c t[1  km(t )]  b{Vc cos c t[1  km(t )]}2      (5)

V2 (t )  aVc cos c t[1  km(t )]  bV 2 c cos 2 c t[1  k 2 m 2 (t )  2km(t )]      (6)


Square law detector
• Sub Eq.(4) in Eq.(1),
V2 (t )  aVc cos c t[1  km(t )]  b{Vc cos c t[1  km(t )]}2      (5)

V2 (t )  aVc cos c t[1  km(t )]  bV 2 c cos 2 c t[1  k 2 m 2 (t )  2km(t )]      (6)

V2 (t )  aVc cos c t[1  km(t )] 


1
bV 2
c [1  cos 2c t ][1  k 2 m 2 (t )  2km(t )]      (7)
2
Square law detector
• Sub Eq.(4) in Eq.(1),
V2 (t )  aVc cos c t[1  km(t )]  b{Vc cos c t[1  km(t )]}2      (5)

V2 (t )  aVc cos c t[1  km(t )]  bV 2 c cos 2 c t[1  k 2 m 2 (t )  2km(t )]      (6)


V2 (t )  aVc cos c t[1  km(t )] 
1
bV c [1  cos 2c t ][1  k 2 m 2 (t )  2km(t )]      (7)
2

2
bVc2 bVc2
V2 (t )  aVc cos c t  aVc km(t ) cos c t   cos 2c t
2 2
bVc2 k 2 m 2 (t ) bVc2 k 2 m 2 (t )
  cos 2c t  bVc2 km(t )
2 2
 bVc2 km(t ) cos 2c t      (8)
Square law detector
• From Eq.(8), the desired term is identified as
V2 (t )  bV 2 c km(t )      (9)

• The equation (9) can be extracted by using LPF


Square law detector
• From Eq.(8), the desired term is identified as
V2 (t )  bV 2 c km(t )      (9)

• The equation (9) can be extracted by using LPF

1 2 2 2
• The term bV c k m (t ) rise to plurality of the similar frequency
components. 2
Square law detector
• The ratio of wanted signal to distortion is given as
bVc2 km(t )

1 2 2 2
bV c k m (t )
2
2
      (10)
km(t )

• |km(t)| - Modulation index


• If M.I is lower, SNR is good
• If M.I is higher, SNR is poor
Envelope detector

• Suitable for narrow band AM wave (fc>>fm and m<1)


• Output signal follows the envelope of input signal exactly
• Used in commercial AM radio receivers
Working of envelope detector
• The envelope detector consists of diode and RC filter
• Positive half cycle – Diode is forward biased – Capacitor charges
rapidly
• Negative half cycle – Diode is reverse biased – Capacitor
discharges slowly
Working of envelope detector
• Diode is ideal – Zero impedance in F.B mode and infinite
impedance in R.B mode
1
Rs c     (1)
fc
1 1
 Rl c     (2)
fc fm

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