Wideband Frequency Modulation.pdf

In this presentation we discuss about a particular type of analog communication waves that is wideband frequency modulation. In this slide, its expression is discussed along with graphical visuals. Not forgetting its power and bandwidth as well. We also see the use of bessel function and the block diagrams that help to form this type of waves.

1. WIDEBAND
FREQUENCY MODULATION
PresentedBy :
Group 9
Ayan Das ▪Arnab Paul ▪Arnab Chatterjee ▪Arijit Dhali
11500320072 ▪11500320075 ▪11500320076 ▪11500320078

2. TABLE OF CONTENTS
WBFM Overview
01
Mathematical Analysis
02
Power and Bandwidth
03
Conclusion and Refernces
04
Frequency Modulation
05

3. Inthisarticle,wearegoingtoaddressapplications
andtechniquesforWBFMwithmodulationindexes
muchlargerthan1,goingupto100andbeyond.In
suchapplicationsspectralefficiencyislessimportant
andsometimeslargespectralspreadisactually
desired.Thepurposeofthisarticleistopresent
somemajorapplicationsinthecommercialand
defencemarkets.Withinthisframework,the
common techniquesofgeneratingWBFM are
presented.
Abstract

4. What is Frequency Modulation?
Frequencymodulation(FM)istheencodingofinformationin
acarrierwavebyvaryingtheinstantaneousfrequencyof
themodulatingwave.Thetechnologyisused
intelecommunications,radiobroadcasting,signalprocessing,
andcomputing.
Thereare2typesofFrequencyModulation:
•NarrowBandFrequencyModulation
•WideBandFrequencyModulation

5. From the expression of Frequency Modulation we
can narrate,
S(t) = A
ccos(w
ct+ βsin(w
mt))
where, A
c= Carrier Amplitude
β= Modulation Index
However when β>1, then FM is said to be Wide
Band FM (WBFM)
When Wideband Frequency
Modulation occurs?

6. Direct Method
Methods of Generating Wideband Frequency Modulation
Indirect Method
Voltage
Controlled
Oscillator
NBFM
Modulator
Frequency
Multiplier
Modulating
Signal
Modulating
Signal
WBFM
Wave
WBFM
Wave
NBFM
Wave
A
ccos(2πf
ct)

7. Bessel Function:
Wideband Frequency Modulation using Bessel Function
J
n(x) =
�
�??????
׬
−??????
??????
�
??????(??????????????????????????????−????????????)
�??????
Properties of Bessel Function:
•J
n(x) ↓when n ↑
∴J
0(x) > J
1(x) > J
2(x)…
•J
-n(x) = (-1)
n
J
n(x)
∴J
-n(x) = J
n(x), when n is even
J
-n(x) = -J
n(x), when n is odd
•׬
??????=−∞
∞
??????
??????
�
??????=�
•J
n(x) always result in real quantity

8. Plot of Bessel Function

9. Mathematical analysis
General Expression of WBFM:
S
FM(t) = A
Ccos [2π�
??????+βsin(2π�
�??????)]=??????
??????cosθ. Thus,
cos??????=Ree
�??????
Since, �
�θ
=cosθ+jsinθ
Therefore,�
??????????????????=??????
??????�
��
�2??????�
??????�+??????sin2π�
??????�
=??????
??????�
��
�2??????�
??????�
+�
�(??????sin2π�
??????�)
. . . . . . .(1)
In eq(1) , let �??????=�
�βsin2π�
??????�
is a periodic function with
�=
1
�??????
We know exponential Fourier series,
�??????=σ
�=−∞
∞
??????
��
��??????
0�
,where ??????
0=
2??????
??????
=2??????�
�
and ??????
�=
1
??????
׬
−??????/2
??????/2
�??????�
−��??????0�
�??????
�
�βsin2π�
??????�
=σ
�=−∞
∞
??????
��
��2π�
??????�
. . . . . .(2)
C
n= f
m׬
−1/�
�
1/�
�
�
�??????���2??????���
.�
−��2??????�
�
�
.dt
= fm׬
−1/�
�
1/�
�
�
�(??????���2??????���−�2??????�
�
�)
We Know that,
J
n(x) = -1/2??????׬
−??????
??????
�
�(??????���??????−�??????)
.d??????
Assume 2??????f
mt= ??????
or, d??????= 2??????fmdt
or, dt = d??????/2??????�
m

10. t = -1/2f
m
??????=2??????�
??????.−(
1
2�
�
)= -??????
t = 1/2f
m
??????=2??????�
??????.(
1
2�
�
)= ??????
C
n= f
m׬
−??????
??????
�
�(??????���??????−�??????)
.d??????/2f
m(f
mgets cancelled out)
= 1/2??????׬
−??????
??????
�
�(??????���??????−�??????)
.d??????= J
n(??????)
Substituting C
nin equation (2)
�
�??????���2??????�
�
�
= σ
�=−∞
∞
J
n(??????).�
��2??????�
�
�
Now substituting this expression with the main equation
S
fm(t) = A
cR
c[�
�2??????�??????�
.σ
�=−∞
∞
J
n(??????).�
��2??????���
]
= A
cR
c
σ
�=−∞
∞
J
n(??????).cos2??????(f
c+nf
m)t
S
WBFM(t) = A
c
σ
??????=−∞
∞
J
n(??????).cos2??????(f
c+nf
m)t (for ??????>1)

11. Power of Wideband Frequency Modulation
We know total power is the sum of carrier power and side
bands power,
P(t) = P
C+ P
USB1+ P
LSB1+ P
USB2+ P
LSB2+ . . . . . .
=
??????
??????
2
??????
0
2
(??????)
2??????
+
??????
??????
2
??????
1
2
(??????)
2??????
+
??????
??????
2
??????
−1
2
(??????)
2??????
+
??????
??????
2
??????
2
2
(??????)
2??????
+
??????
??????
2
??????
2
2
(??????)
2??????
+ . . . . .
=
??????
??????
2
2??????
[ J
0
2
(β) + J
1
2
(β) + J
-1
2
(β) + J
2
2
(β) + J
-2
2
(β) + . . . . . .]
P(t) =
??????
??????
2
2??????
׬
�=−∞
∞
??????
�
2
??????
∴P(t) =
??????�
�
�??????

12. Spectrum of Wideband Frequency Modulation
We know, S
WBFM(t) = A
c
σ
�=−∞
∞
J
n(??????).cos2??????(f
c+nf
m)t
= A
cJ
0(β)cos(2πf
ct) + A
cJ
1(β)cos(2πf
ct) +
A
cJ
-1(β)cos(2πf
ct) + A
cJ
2(β)cos(2πf
ct) + A
cJ
-2(β)cos(2πf
ct) + . . . . .
= A
cJ
0(β)cos2π(f
ct) + A
cJ
1(β)cos2π(f
c+f
m)t -
A
cJ
1(β)cos2π(f
c-f
m)t + A
cJ
2(β)cos2π(f
c+2f
m)t +
A
cJ
2(β)cos2π(f
c-2f
m)t + . . . . .
??????
????????????
0(??????)
2
??????
????????????
2(??????)
2
??????
????????????
2(??????)
2
??????
????????????
1(??????)
2
??????
????????????
1(??????)
2
(f
c+f
m) (f
c+2f
m)
(f
c-f
m)
(f
c-2f
m)
(f
c)
S
WBFM
Spectrum of WBFM

13. Practical Bandwidth using Carson’s Rule
∴For (β+1)
th
Order, BW = (β+1) x 2f
m
= (
∆�
�??????
+1) x 2f
m
BW = 2(∆f + 2f
m)
For 3
rd
Order: BW = 6f
m
For 2
nd
Order: BW = 4f
m
For 1
st
Order: BW = 2f
m
2
3
1
(f
c+f
m)
(f
c+2f
m)
(f
c-f
m)
(f
c-2f
m)
(f
c)

14. Applications
The Wide-Band Frequency Modulation is used in the following fields:
•It is used in the entertainment broadcasting applications such as FM radio, TV etc.
•It is used extensively in audio communication and data transfer.
•It is used in free running Voltage Controlled Oscillator(VCO).
•It is used in commercial and defence markets.

15. Conclusion
WhenspectrumefficiencyisimportantNarrowbandFM(NBFM)is
usedbutwhenbettersignalqualityisrequiredWidebandFM
(WBFM)isusedattheexpenseofgreaterspectrumusage.The
termWBFMisusedinapplicationswherethemodulationindexis
equaltoorlargerthan1.

16. References
●http://contents.kocw.net/KOCW/document/ 2011/korea/koyoungchai/lecturenote1
7may12.pdf
●https://www.kratosmed.com/gmcatalog/wideband -frequency-modulation-
applications-and-techniques-for-microwave-products
●https://www.researchgate.net/figure/a-The-mathematical-equation-for-Frequency-
Modulation-and-definition-of-terms_fig9_243778275
●https://www.rcet.org.in/uploads/academics/rohini_27413753398.pdf
●https://slideplayer.com/slide/5668316/

17. THANK
YOU
Foryour patience towards
our presentation