# 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.

The frequency modulation block diagram is shown below. The message signal holds the specific data whereas the next signal has no data known as the carrier signal.

The modulation of these signals will result in an FM modulated signal. This signal is more essential because the frequency of this signal will flow up & down depending on the amplitude of the signal. So this frequency change can be represented in kHz (kilohertz). For instance, once the frequency variation is 3 kHz up & down, then it is signified like ±3 kHz.

### FM History

At the time of radio, the static was the main problem &the way everybody attempted to decrease the static effects was to decrease the bandwidth. So in this method, less noise was received through the receiver. Edwin Armstrong was an American engineer, so he examining this problem & whether FM, rather than AM might give a benefit.

In 1928, he simply started to expand the idea with the help of FM & he increased the BW instead of decreasing it. But, for different reasons, his ideas don’t accept by others. Immediately, he approached Radio Corporation of America or RCA, they were impressed by his ideas, but RCA was simply focusing on TV, so they don’t want to redirect any resource to a new type of broadcasting.

After many troubles, he launched a radio station in the year 1939 to exhibit the efficiency of FM. To hold this & other stations following a band of frequencies among 42 MHz & 50 MHz frequencies. But after the war, the FCC within the USA modified the assigned frequency band between 88 MHz and 108 MHz.
Even though, there was some basic pain as thousands of radios had been sold and the band was accepted worldwide that is VHF FM band at present. In addition to this, a kind of narrowband FM became famous for UHF & VHF mobile communications.

### 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 varies 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 the 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

#### Frequency Modulation in Communication Systems

In telecommunications, there are two types of frequency modulation techniques used like analog frequency modulation & digital frequency modulation.

In analog frequency modulation, the data signal can be modulated through a continuously changing sine carrier signal. This carrier signal includes different properties like frequency, amplitude & phase which are mainly used for creating AM & PM.

The digital frequency modulation can be categorized as either FSK (Frequency Shift Key), ASK (Amplitude Shift Key), or PSK (Phase Shift Key) which works like analog. Analog modulation technique is normally used for AM, FM & short-wave broadcasting whereas digital modulation technique used to transmit binary signals like 0 & 1.

The techniques used in FM are the varactor diode oscillator and phase-locked loop. In the varactor diode oscillator technique, the diode is arranged in the circuit to change the frequency. So this technique provides simply narrowband transmissions. In the PLL technique, it provides an outstanding FM. So in this technique, phases are constrained in the loop to change the frequency.

#### FM in Vibration Analysis

The process of measuring as well as analyzing the vibration signals levels, patterns otherwise machinery frequency for noticing irregular vibration actions & estimate the complete machine’s strength along with their components. This kind of analysis is particularly very helpful by revolving machinery, where exist fault devices that may reason for amplitude & frequency modulation deviations.

The demodulation method directly detects these modulation frequencies, so it is used for recovering the data from the modulated carrier signal.

#### The Bandwidth of Frequency Modulation Signal

Bandwidth is one of the main elements of FM signal. In FM signal, the sidebands will extend either side which will extend to infinity; however, the strength of them drops away. Auspiciously, it is the potential to restrict the BW of an FM signal without changing its value excessively.

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 a 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 Amplitude Modulation and Frequency Modulation

The Amplitude Modulation Vs Frequency Modulation is discussed below.

 Amplitude Modulation Frequency Modulation In Amplitude modulation, the amplitude of a carrier signal changed based on the data signal. AM radio broadcast signals utilize low-carrier frequencies to travel long distances. Sometimes, amplitude modulation signals are capable of bouncing off the ionosphere. As compared to FM, the distance traveled through the AM is high. In frequency modulation, the carrier wave frequency can be changed based on the signal that holds data. The radio signals include high BW as compared to AM radio signals. These signals assist to provide good sound quality. FM also allows sending stereo signals. In the mid-1870s, the first audio transmission was developed Fm was developed in the year 1930 in the US, by Edwin Armstrong. In AM, the radio signal is known as a carrier signal & both the phase & frequency remain the same In FM, the radio signal is known as a carrier signal, however, the amplitude, as well as phase, remain the same More liable to noise Less liable to noise The sound clarity of AM is poor, however, can transmit long distances FM has high BW including good sound quality The AM frequency ranges from 535 kHz – 1705 kHz The FM frequency ranges from 88 MHz – 108 MHz in the higher spectrum The modulation index of AM ranges from 0 to 1 The modulation index of FM is higher than 1 It includes simply two sidebands It includes a number of sidebands It has an easy circuit It has a difficult circuit In AM, the carrier signal’s amplitude can be changed to transmit the information. In FM, the carrier signal’s frequency can be changed to transmit the information It has less bandwidth like 10 kHz. It has high bandwidth like 200 kHz AM operates in the MF (medium frequency) & HF( high frequency). FM works with very high frequency

The key differences 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

The advantages of frequency modulation include the following.

• Less noise and interference
• Service areas are well defined for specified transmitter power.
• As compared to amplitude modulation, FM includes low power consumption.
• The radiated power is less.
• Guard bands separate nearby FM channels.
• Lesser geographical interference among adjacent stations.
• Enhanced S/N (signal to noise) ratio like 25dB with respect to manmade intrusion
• Modulation technique is easily applied at a low power phase of the transmitter:
• It is the potential to employ efficient RF amplifiers including frequency modulated signals.

The disadvantages of frequency modulation include the following.

• High equipment cost is high
• High bandwidth
• The receiving area of the FM signal is small.
• The antennas for FM systems should be kept close for better communication
• Much more Bandwidth (as much as 20 times as much).
• More complicated receiver and transmitter.
• FM has poorer spectral efficiency than some other modulation formats:
• Requires more complicated demodulator:
• Some other modes have higher data spectral efficiency:
• Sidebands expand to infinity any side
• The spectral efficiency of FM is poor as compared to other modulation methods
• It uses a more complicated demodulator:
• Other modes include high data spectral efficiency
• Sidebands extend to infinity on either side

Thus, this is all about an overview of frequency modulation. The applications of frequency modulation include 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 depend on the maximum modulation index and modulating frequency. In contrast to amplitude modulation, the frequency modulation signal has larger bandwidth, superior efficiency, & improved immunity toward the noise. What are the different types of modulation techniques in communication systems?