# Frequency Modulation and Its Applications

The FM or Frequency modulation has been available approximately since AM (Amplitude Modulation) although it has only some issues. FM itself didn’t have a problem apart from we couldn’t recognize the FM transmitter potential. In the earlier time of wireless communication, it was measured that the required bandwidth of this was narrower, and necessary to decrease noise as well as interference.  Under such a measure, frequency modulation was suffered whereas AM increased. After that, an American Engineer- “Edwin Armstrong” finished the conscious attempt to discover the intensity of FM transmitters. Edwin initiated the design of using FM intended for transmitting which was not in favor of the trend at that moment in time.

## What is a Frequency Modulation?

The frequency modulation can be defined as; the frequency of the carrier signal is varied proportional to (in accordance with) the Amplitude of the input modulating signal. The input is a single tone sine wave. The carrier and the FM waveforms also are shown in the following figure.

The frequency of a carrier (fc) will increase as the amplitude of modulating (input) signal increases. The carrier frequency will be maximum (fc max) when the input signal is at its peak. The carrier deviates maximum from its normal value. The frequency of a carrier will decrease as the amplitude of the modulating (input) signal decreases. The carrier frequency will be minimum (fc min) when the input signal is at its lowest. The carrier deviates minimum from its normal value. The frequency of the carrier will be at its normal value (free running) fc when the input signal value is 0V. There is no deviation in the carrier. The figure shows the frequency of the FM wave when the input is at its max, 0V and at its min.

### Frequency Deviation

• The amount of change in the carrier frequency produced, by the amplitude of the input modulating signal, is called frequency deviation.
• The Carrier frequency swings between fmax and fmin as the input varries in its amplitude.
• The difference between fmax and fc is known as frequency deviation. fd = fmax – fc
• Similarly, the difference between fc and fmin also is known as frequency deviation. fd = fc –fmin
• It is denoted by Δf. Therefore Δf = fmax – fc = fc – fmin
• Therefore fd = fmax – fc = fc – fmin
 Modulating signal Amplitude Frequency of Carrier Deviation 0V 100 MHz Nil (Center frequency) +2 V 105 MHz + 5 MHz ─ 2 V 95 MHz – 5 MHz

Freq deviation = 105 -100 = 5 MHz (or) Freq deviation = 95-100 = -5 MHz

## Frequency Modulation Equation

The FM equation include the following

v = A sin [ wct + (Δf / fm) sin wmt ]

= A sin [ wct + mf sin wmt ]

A = Amplitude of the FM signal. Δf = Frequency deviation

mf = Modulation Index of FM

mf = ∆f/fm

mf is called the modulation index of frequency modulation.

wm = 2π fm wc = 2π fc

### What is Modulation Index of Frequency Modulation?

The modulation index of FM is defined as the ratio of the frequency deviation of the carrier to the frequency of the modulating signal

mf = Modulation Index of FM = f/fm

### The bandwidth of Frequency Modulation Signal

Recall, the bandwidth of a complex signal like FM is the difference between its highest and lowest frequency components, and is expressed in Hertz (Hz). Bandwidth deals with only frequencies. AM has only two sidebands (USB and LSB) and the bandwidth was found to be 2 fm.

In FM it is not so simple. FM signal spectrum is quite complex and will have an infinite number of sidebands as shown in the figure. This figure gives an idea, how the spectrum expands as the modulation index increases. Sidebands are separated from the carrier by fc ± fm, fc ± 2fm, fc ± 3fm and so on.

Only the first few sidebands will contain the major share of the power (98% of the total power) and therefore only these few bands are considered to be significant sidebands.

As a rule of thumb, often termed as Carson’s Rule, 98% of the signal power in FM is contained within a bandwidth equal to the deviation frequency, plus the modulation frequency doubled.

Carson’s rule: Bandwidth of FM BWFM = 2 [ Δf + fm ].

= 2 fm [ mf + 1 ]

#### FM is known as Constant Bandwidth System. Why?

The frequency modulation is known as a constant bandwidth system and an example of this system is given below.

• Δf = 75 KHz fm = 500 Hz BWFM = 2 [75 + (500/1000)] KHz = 151.0 KHz
• Δf = 75 KHz fm = 5000 Hz BWFM = 2 [75 + (5000/1000)] KHz = 160.0 KHz
• Δf = 75 KHz fm = 10000 Hz BWFM = 2 [75 + (10000/1000)] KHz = 170.0 KHz
• Although modulating frequency increased 20 times (50 Hz to 5000 Hz), deviation increased only marginally (151 KHz to 170 KHz). Hence FM is known as constant bandwidth system.
• Commercial FM (Carson’s Rule.)
• Max freq deviation = 75 KHz
• Max Modulating freq = 15 KHz
• BWFM = 2 [ 75 + 15 ] = 180.0 KHz

### Difference between AM and FM

The main difference between AM and FM include the following.

• Equation for FM: V= A sin [ wct +Δf / fm sin wmt ] = A sin [ wct + mf sin wmt ]
• Equation for AM = Vc ( 1 + m sin ωmt ) sin ωct where m is given by m = Vm / Vc
• In FM, the Modulation Index can have any value greater than 1 or less than one
• In AM, the Modulation Index will be between 0 and 1
• In FM, carrier amplitude is constant.
• Therefore transmitted power is constant.
• Transmitted power does not depend on the modulation index
• Transmitted power depends on the modulation index
• PTotal = Pc [ 1+ (m2/2) ]
• The number of significant sidebands in FM is large.
• Only two sidebands in AM
• A bandwidth of FM depends on the modulation index of FM
• Bandwidth does not depend on the modulation index of AM. Always 2 sidebands. BW of AM is 2 fm
• FM has better noise immunity.FM is rugged/robust against noise. The quality of FM will be good even in the presence of noise.
• In AM, quality is affected seriously by noise
• The bandwidth required by FM is quite high.FM bandwidth = 2 [Δf + fm].
• The bandwidth required by AM is less (2 fm)
• Circuits for FM transmitter and receiver are very complex and very expensive.
• Circuits for AM transmitter and receiver are simple and less expensive

Thus, this is all about frequency modulation. The applications of frequency modulation include in FM radio broadcasting, radar, seismic prospecting, telemetry, & observing infants for seizure through EEG, music synthesis, two-way radio systems, magnetic tape recording systems, video broadcast systems, etc. From the above information, finally, we can conclude that, in frequency modulation, both efficiencies as well as bandwidth depends on the maximum the modulation index and modulating frequency. Contrasted to amplitude modulation, the frequency modulation signal has a larger bandwidth, superior efficiency, & improved immunity toward the noise. What are the different types of modulation techniques in communication system?