DSB-SC

1. Module 3
Bandwidth and Power Efficient AM Systems
Prof.Dr.G.Aarthi,Associate Professor,VIT

2. Drawback of conventional AM

3. Why DSB-SC

5. DSBSC-AM
• DSBSC – Double Side Band Suppressed Carrier
• Carrier signal is suppressed
• Modulated wave contains only upper and lower sidebands
• Transmitted power is saved
• Bandwidth is same as DSBFC-AM (2fm)

6. Time domain representation of DSBSC-AM wave

7. Time domain representation of DSBSC-AM wave
• Let the modulating signal is mathematically expressed as
Vm (t)  Em cos(mt m)     (1)

8. Time domain representation of DSBSC-AM wave
• Let the modulating signal is mathematically expressed as
Vm (t)  Em cos(mt m)     (1)
• Let the carrier signal is mathematically expressed as
Vc (t)  Ec cos(ct c)      (2)

9. Time domain representation of DSBSC-AM wave
• The instantaneous amplitude of the modulated
mathematically expressed as
VDSBSC (t) Vm (t)Vc (t)      (3)
wave is

10. Time domain representation of DSBSC-AM wave
• The instantaneous amplitude of the modulated
mathematically expressed as
VDSBSC (t) Vm (t)Vc (t)      (3)
wave is
VDSBSC (t)  Em cosmt Ec cosct      (4)

11. Time domain representation of DSBSC-AM wave
• The instantaneous amplitude of the modulated
mathematically expressed as
VDSBSC (t) Vm (t)Vc (t)      (3)
wave is
VDSBSC (t)  Em cosmt Ec cosct      (4)
[cos(
2
V (t) 
E E
c m c m
  )t  cos(  )t]     (5)
m c
DSBSC

12. Time domain representation of DSBSC-AM wave
• The instantaneous amplitude of the modulated
mathematically expressed as
VDSBSC (t) Vm (t)Vc (t)      (3)
wave is
VDSBSC (t)  Em cosmt Ec cosct      (4)
[cos(
2
V (t) 
E E
c m c m
  )t  cos(  )t]     (5)
m c
DSBSC
2
cos2
2
E cos2
V (t) 
mE
m
c
mEc
cos 2 (f  f )t      (6)
c m
 (f  f )t 
c
c
c  f t 
AM

13. Frequency spectrum of DSBSC-AM wave

14. Bandwidth of DSB-SC signal

15. Differentiation between DSBFC and DSBSC signals

16. Phasor diagram
Carrier is suppressed Indicated by dotted lines

17. DSBSC-AM power distribution
• The total power in AM-DSBFC envelope is expressed as
PUSB PLSB
Pt  Pc      (1)
m2
Pt  Pc 
2
Pc     (2)
     (3)
2


m2




P  P 1
t c

18. DSBSC-AM power distribution
• The total power in AM-DSBFC envelope is expressed as
• The total power in AM-DSBSC envelope is expressed as
PUSB PLSB
Pt  Pc      (1)
m2
Pt  Pc 
2
Pc     (2)
     (3)
2


m2




P  P 1
t c
     (4)
Pt  PUSBPLSB
2
m2
 c
P      (`5)
t
P 

19. Power saving in DSBSC-AM
• Power saving in DSBSC wave is

Pt
SavDSBSC
t
P
 Pt
     (1)
P

20. Power saving in DSBSC-AM
• Power saving in DSBSC wave is

Pt
SavDSBSC
t
P
 Pt
     (1)
P
     (1)
2 m2
2

PSavDSBSC

21. Power saving in DSBSC-AM
• Power saving in DSBSC wave is
• If modulation index is equal to 1, the total power saving in DSBSC-
AM wave is 66.7%

Pt
SavDSBSC
t
P
 Pt
     (1)
P
     (1)
2 m2
2

PSavDSBSC

22. Modulation Efficiency

23. Generation of DSBSC-AM wave
• Balanced Modulator
• Ring Modulator

24. Balanced Modulator (BM)
• Two nonlinear devices are connected in balanced mode
• Two transistors are identical and the circuit is symmetrical
• Voltage across the windings of centre tap transformer is equal and
opposite in phase (Vm-Vm)

25. Balanced Modulator (BM)
• The modulating signal is fed in push-pull and the carrier voltage is fed
in parallel to a pair of identical transistors.
• The carrier voltage is thus applied to the two transistors in phase,
whereas the modulating voltages appear 180o
out of phase.

26. Balanced modulator
• The input voltage to the transistor T1 is expressed as

27. Balanced modulator
• The input voltage to the transistor T1 is expressed as
Vbc Vc (t) Vm (t)      (1)
Vbc Vc cosct Vm cosmt      (2)
• The input voltage to the transistor T2 is expressed as

28. Balanced modulator
• The input voltage to the transistor T1 is expressed as
Vbc Vc (t) Vm (t)      (1)
Vbc Vc cosct Vm cosmt      (2)
• The input voltage to the transistor T2 is expressed as
VbcVc (t) Vm(t)      (3)
VbcVc cosct Vm cosmt      (4)
• Using nonlinearity property, the collector current can be expressed
as

29. Balanced modulator
1 bc bc
i  aV  bV 2
     (5)
• The input voltage to the transistor T1 is expressed as
Vbc Vc (t) Vm (t)      (1)
Vbc Vc cosct Vm cosmt      (2)
• The input voltage to the transistor T2 is expressed as
VbcVc (t) Vm(t)      (3)
VbcVc cosct Vm cosmt      (4)
• Using nonlinearity property, the collector current can be expressed
as
i  aV  bV2
     (6)
1 bc bc

30. Balanced modulator
• Sub Eq.(2) and Eq.(4) in Eq.(5) an Eq.(6), we get
i  a[V cos t V cos t] b[V cos t V cos t]2
   (7)
1 c c m m c c m m

31. Balanced modulator
• Sub Eq.(2) and Eq.(4) in Eq.(5) an Eq.(6), we get
i  a[V cos t V cos t]  b[V cos t V cos t]2
   (7)
1
c c m m c c m m
i  a[V cos t V cos t]  b[V2
cos2
 t V 2
cos2
 t
1
c c m m c c m m
 2VcVm cosc tcos mt]   (8)

32. Balanced modulator
• Sub Eq.(2) and Eq.(4) in Eq.(5) an Eq.(6), we get
i  a[V cos t V cos t]  b[V cos t V cos t]2
   (7)
1 c c m m c c m m
i  a[V cos t V cos t] b[V2
cos2
 t V 2
cos2
 t
1 c c m m c c m m
 2VcVm cosctcos m t]   (8)
i  a[V cos t V cos t] b[V cos t V cos t]2
   (9)
1 c c m m c c m m

33. Balanced modulator
• Sub Eq.(2) and Eq.(4) in Eq.(5) an Eq.(6), we get
i  a[V cos t V cos t]  b[V cos t V cos t]2
   (7)
1 c c m m c c m m
i  a[V cos t V cos t] b[V2
cos2
 t V 2
cos2
 t
1 c c m m c c m m
 2VcVm cosctcos mt]   (8)
i  a[V cos t V cos t] b[V cos t V cos t]2
   (9)
1 c c m m c c m m
i  a[V cos t V cos t] b[V2
cos2
 t V 2
cos2
 t
1 c c m m c c m m
 2VcVm cosctcos mt]   (10)

34. Balanced modulator
• The output AM voltage is given as

35. Balanced modulator
• The output AM voltage is given as
V0  K(i1 i1)     (11)
• Sub Eq.(8) and Eq.(10) in Eq.(11)

36. Balanced modulator
• The output AM voltage is given as
V0  K(i1 i1)     (11)
• Sub Eq.(8) and Eq.(10) in Eq.(11)
V0  2KaVm cosmt  4KbVcVm cosctcosmt      (12)

37. Balanced modulator
• The output AM voltage is given as
V0  K(i1 i1)     (11)
• Sub Eq.(8) and Eq.(10) in Eq.(11)
V0  2KaVm cosmt  4KbVcVm cosctcosmt      (12)






V  2KaV cos
a
2bV
c
cos t      (13)
c
m
0 m  t 1

38. Balanced modulator
• The output AM voltage is given as
V0  K(i1 i1)     (11)
• Sub Eq.(8) and Eq.(10) in Eq.(11)
V0  2KaVm cosmt  4KbVcVm cosctcosmt      (12)
V0  2KaVm cosmt 
1 m cosct     (14)
a
ModulationIndex, m 
2bVc



 

a
2bV
V  2KaV cos c
c
m
0 m cos t      (13)
 t 1

39. Ring Modulator or Diode Balanced Modulator

40. Working principle of ring modulator
• Diodes act as a perfect switches
• Amplitude and frequency of the carrier is higher than that of the
modulating signal
• Switching operation of diodes is controlled by the RF carrier signal

41. Mode 1: Carrier suppression
Operating in the positive half cycle of the carrier

42. Mode 1: Carrier suppression
Operation in the negative half cycle of the carrier

43. Expression for Vo(t)

44. Output of BPF

45. Advantages of Ring Modulator