Wideband frequency modulation (WBFM) is a technique where the modulation index is greater than 1, resulting in a wider signal bandwidth. WBFM is used when spectral efficiency is less important and a large spectral spread is desired, such as in entertainment broadcasting, audio communication, and military applications. The mathematical analysis of WBFM shows that its spectrum consists of a carrier signal along with upper and lower sidebands determined by Bessel functions. Its total power is distributed among these components, with greater power in lower order sidebands. WBFM provides better signal quality than narrowband FM but uses more spectrum.
2. TABLE OF CONTENTS
WBFM Overview
01
Mathematical Analysis
02
Power and Bandwidth
03
Conclusion and Refernces
04
Frequency Modulation
05
3. In this article, we are going to address applications
and techniques for WBFM with modulation indexes
much larger than 1, going up to 100 and beyond. In
such applications spectral efficiency is less important
and sometimes large spectral spread is actually
desired. The purpose of this article is to present
some major applications in the commercial and
defence markets. Within this framework, the
common techniques of generating WBFM are
presented.
Abstract
4. What is Frequency Modulation?
Frequency modulation (FM) is the encoding of information in
a carrier wave by varying the instantaneous frequency of
the modulating wave. The technology is used
in telecommunications, radio broadcasting, signal processing,
and computing.
There are 2 types of Frequency Modulation:
• Narrow Band Frequency Modulation
• Wide Band Frequency Modulation
5. From the expression of Frequency Modulation we
can narrate,
S(t) = Accos(wct + βsin(wmt))
where, Ac = 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
Accos(2πfct)
7. Bessel Function:
Wideband Frequency Modulation using Bessel Function
Jn(x) =
𝟏
𝟐𝝅
−𝝅
𝝅
𝒆𝒋(𝒙 𝐬𝐢𝐧 𝜽−𝒏𝜽)
𝒅𝜽
Properties of Bessel Function:
• Jn(x) ↓ when n ↑
∴ J0(x) > J1(x) > J2(x)…
• J-n(x) = (-1)nJn(x)
∴ J-n(x) = Jn(x), when n is even
J-n(x) = -Jn(x), when n is odd
•
𝒏=−∞
∞
𝑱𝒏
𝟐
𝒙 = 𝟏
• Jn(x) always result in real quantity
13. Practical Bandwidth using Carson’s Rule
∴ For (β+1)th Order, BW = (β+1) x 2fm
= (
∆𝑓
𝑓𝑚
+ 1) x 2fm
BW = 2(∆ f + 2fm)
For 3rd Order: BW = 6fm
For 2nd Order: BW = 4fm
For 1st Order: BW = 2fm
2
3
1
(fc+fm)
(fc+2fm)
(fc-fm)
(fc-2fm)
(fc)
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
When spectrum efficiency is important Narrowband FM (NBFM) is
used but when better signal quality is required Wideband FM
(WBFM) is used at the expense of greater spectrum usage. The
term WBFM is used in applications where the modulation index is
equal to or larger than 1.