The document discusses different methods for demodulating DSBSC waves, including coherent detection, Costas loop, and squaring loop. Coherent detection extracts the message signal by multiplying the DSBSC wave with a local oscillator signal that is coherent in frequency and phase with the carrier. Costas loop is used to maintain phase coherence between the local oscillator and carrier. Squaring loop recovers the carrier signal by filtering the output of a squaring circuit to extract the signal at twice the carrier frequency.

1. DSB-SC Demodulation
Prof.Dr.G.Aarthi,Associate Professor,VIT

2. Demodulation of DSBSC-AM wave
• Coherent detection/Synchronous detection
• Costas receiver
• Squaring loop
The process of extracting an original message signal from DSBSC wave is known as
detection or demodulation of DSBSC. The following demodulators (detectors) are used
for demodulating DSBSC wave.

3. Coherent Detection
• In this process, the message signal can be extracted from DSBSC wave by multiplying it
with a local carrier.
• Local oscillator signal is exactly coherent (both frequency and phase) with the carrier
signal used in DSBSC modulation process.

4. Coherent Detection
•The resulting signal is then passed through a Low Pass Filter. Output of this
filter is the desired message signal.

5. Coherent Detection
• The local oscillator signal is given as
Vccos(2fct )     (1)
Where, ϕ is the phase difference between the local oscillator signal and the
carrier signal, which is used for DSBSC modulation.
s(t) Vc cos(2fct)m(t)    (3)
The DSB-SC wave is given as

6. Coherent Detection
• The local oscillator signal is given as
Vccos(2fct )     (1)
• The output of product modulator is given as

7. Coherent Detection
• The local oscillator signal is given as
Vccos(2fct )     (1)
• The output of product modulator is given as
v(t) Vccos(2fct )s(t)      (2)
s(t) Vc cos(2fct)m(t)     (3)
• Sub Eq.(3) in Eq.(2)

8. Coherent Detection
• The local oscillator signal is given as
Vccos(2fct )     (1)
• The output of product modulator is given as
v(t) Vccos(2fct )s(t)      (2)
s(t) Vc cos(2fct)m(t)     (3)
• Sub Eq.(3) in Eq.(2)
v(t) VcVccos(2fct)cos(2fct )m(t)

9. Coherent Detection
• The local oscillator signal is given as
Vccos(2fct )     (1)
• The output of product modulator is given as
v(t) Vccos(2fct )s(t)      (2)
s(t) Vc cos(2fct)m(t)     (3)
• Sub Eq.(3) in Eq.(2)
v(t) VcVccos(2fct)cos(2fct )m(t)
2 2
c c c c c
v(t) 
1
V Vcos( 4f t )m(t)
1
V Vcos()m(t)   (5)
In the above equation, the second term is the scaled version of the message
signal. It can be extracted by passing the above signal through a low pass filter.

10. Coherent Detection
• After passing to LPF,
• The local oscillator signal is given as
Vccos(2fct )     (1)
• The output of product modulator is given as
v(t) Vccos(2fct )s(t)      (2)
s(t) Vc cos(2fct)m(t)     (3)
• Sub Eq.(3) in Eq.(2)
v(t) VcVccos(2fct)cos(2fct )m(t)
2 2
c c c c c
v(t) 
1
V Vcos(4 f t )m(t) 
1
V Vcos()m(t)   (5)
1
2
0

V V cos( )m(t)
v (t)  c c     (6)

11. Coherent Detection
• The amplitude of the demodulated signal is maximum when Ф=0 (That’s
why the local oscillator signal and the carrier signal should be in phase, i.e., there
should not be any phase difference between these two signals)
• The amplitude of the demodulated signal is minimum when Ф=+/- π/2
• Zero demodulated signal occurs when Ф=+/- π/2 – The effect is called as
Quadrature Null effect
2
0 c c
v (t) 
1
V Vcos()m(t)   (6)

12. Costas Loop
•Costas loop is used to make both the carrier signal (used for
DSBSC modulation) and the locally generated signal in phase.

13. Costas Loop
Costas loop consists of two product modulators with common input s(t), which is DSBSC wave. The
other input for both product modulators is taken from Voltage Controlled Oscillator (VCO)
with −90o
phase shift to one of the product modulator as shown in figure.

14. Costas Loop
• Upper path – Inphase coherent detection – I-channel
• Lower path – Quadrature phase coherent detection – Q-channel
• The P.D and VCO is used to correct the phase errors

15. Costas Loop
Let the output of VCO be
This output of VCO is applied as the carrier input of the upper product modulator.
Hence, the output of the upper product modulator is
Substitute, s(t) and c1(t) values in the above equation.
We know that the equation of DSBSC wave is

16. Costas Loop
After simplifying, we will get v1(t) as
This signal is applied as an input of the upper low pass filter. The output of this low pass filter is
Therefore, the output of this low pass filter is the scaled version of the modulating signal.
The output of −90o
phase shifter is

17. Costas Loop
This signal is applied as the carrier input of the lower product modulator.The output of the lower
product modulator is
Substitute, s(t) and c2(t) values in the above equation.
After simplifying, we will get v2(t) as
This signal is applied as an input of the lower low pass filter. The output of this low pass filter is
The output of this Low pass filter has −90o
phase difference with the output of the upper low pass filter.

18. Costas Loop
 The outputs of these two low pass filters are applied as inputs of the phase discriminator.
 Based on the phase difference between these two signals, the phase discriminator produces a
DC control signal
 This signal is applied as an input of VCO to correct the phase error in VCO output.
 When the P.Doutput is zero, there is no need to correct the L.O.
 Therefore, the carrier signal (used for DSBSC modulation) and the locally generated signal
(VCO output) are in phase.

19. Squaring Loop
• It is used to recover the carrier signal from DSBSC signal (carrier recovery)
• The recovered carrier signal is used in the coherent detection process

20. Squaring Loop
• The output of the squarer is
y(t)  s2
(t) [A cos(2 f t)m(t)]2
c c

21. Squaring Loop
• The output of the squarer is
y(t)  s2
(t) [A cos(2 f t)m(t)]2
c c
c
 A2
c cos2
(2 f t)m2
(t)

22. Squaring Loop
• The output of squarer is given the narrow band filter which is centered at
+/- 4πfc
• The output of filter is
• The output of the squarer is
y(t)  s2
(t) [A cos(2 f t)m(t)]2
c c
c
 A2
c cos2
(2 f t)m2
(t)
2
2
c
f t)]
m (t)[1 cos(4
2

A c

23. Squaring Loop
• The output of squarer is given the narrow band filter which is centered at
+/- 4πfc
• The output of filter is
• The output of filter is given to PLL to provide constant frequency signal
cos(4πfct)
• Any drift in frequency is corrected by the error signal e(t) generated by LPF
• The output of VCO is connected to frequency divider(/2) to get cos(2πfct)
• The output of the squarer is
y(t)  s2
(t) [A cos(2 f t)m(t)]2
c c
c
 A2
c cos2
(2 f t)m2
(t)
2
2
c
f t)]
m (t)[1 cos(4
2

A c
2
2
c
A 2
c
f t)
v(t)  m (t)cos(4