Any wave has three significant characteristics viz amplitude, frequency and phase and modulation is a process of impressing information to be transmitted on a high frequency wave called the carrier wave, by changing its one of the characteristics (amplitude, frequency or phase angle). Modulation may also be defined as the process of altering some characteristics of the carrier wave in accordance with the instantaneous value of some other wave called the modulating wave.
Carrier wave is a high frequency, constant amplitude, constant frequency and non-interrupted wave generated by radio-frequency oscillators. These waves are inaudible i.e. by themselves they are not able to produce any sound in the loudspeaker.
We need modulation because low frequency signals cannot be transmitted over long distances if radiated directly into the space. This is due to the following hurdles:

Short operating range
Poor radiation efficiency
Mutual interference
Huge antenna requirement

Since there are three variables which can be varied (amplitude, frequency and phase) so there are mainly three types of modulations:

Amplitude Modulation (AM)
Frequency Modulation (FM)
Phase Modulation (PM)

Some common analog modulation techniques are:

Amplitude modulation (AM) (here the amplitude of the carrier signal is varied in accordance to the instantaneous amplitude of the modulating signal)

Double-sideband modulation (DSB)

Single-sideband modulation (SSB, or SSB-AM),

SSB with carrier (SSB-WC)
SSB suppressed carrier modulation (SSB-SC)

Vestigial side band modulation (VSB)
Quadrature amplitude modulation (QAM)
· Angle modulation
Frequency modulation (FM) (here the frequency of the carrier signal is varied in accordance to the instantaneous frequency of the modulating signal)
Phase modulation (PM) (here the phase shift of the carrier signal is varied in accordance to the instantaneous phase shift of the modulating signal)
We have to discuss mainly the frequency modulation because we have to study the design of an fm signal. So we will first discuss frequency modulation, an fm signal and how it is generated and what are its applications.
II. FREQUENCY MODULATION
As the name indicates, frequency modulation is achieved by controlling the frequency of the carrier by the amplitude of the modulating signal. In frequency modulation, the carrier frequency is varied in accordance with the amplitude of the signal to be transmitted.
In frequency modulation the amplitude is kept constant and the frequency is modulated by the amplitude of the modulating signal. The modulation index for fm is m = maximum frequency deviation/modulating frequency.
FM signal can be represented as:-
v = acsin(wct + m sin wmt)
III. FM SIGNAL
An fm signal is obtained by altering the frequency of a signal.
Here is a simple FM signal:
Frequency modulated signal consists the information signal, Vm(t) to vary the carrier frequency within some small range about its original value and carrier signal, Vc(t). Here are the three signals in mathematical form:

Information: Vm(t)
Carrier: Vc(t) = Vco sin ( 2 p fc t + f )
FM: VFM (t) = Vco sin (2 p [fc + (Df/Vmo) Vm (t) ] t + f)

We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: Df, the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: fc + (Df/Vmo) Vm (t) now varies between the extremes of fc – Df and fc + Df. The interpretation of Df becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the “swing” in the frequency.
We can also define a modulation index for FM, analogous to AM:
b = Df/fm , where fm is the maximum modulating frequency used.
The modulation index, b, is as a measure of the peak frequency deviation, Df. In other words, b represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, fm, i.e. Df = b fm.
Example: suppose in FM radio that the audio signal to be transmitted ranges from 20 to 15,000 Hz (it does). If the FM system used a maximum modulating index, b, of 5.0, then the frequency would “swing” by a maximum of 5 x 15 kHz = 75 kHz above and below the carrier frequency.
IV. GENERATION OF FM SIGNAL
There are two ways to generate an FM signal: Direct and Indirect.
Direct generation, as its name implies, directly generates FM from a carrier. Indirect generation normally begins with PM, which is converted to FM.
A simple FM generator is shown below:
The capacitor microphone consists of two metal plates, insulated from one another, one of which can move in response to sound waves striking hit. This causes small changes in the microphone’s capacitance. Since the microphone is part of the parallel LC circuit that determines the frequency of the carrier oscillator, the carrier oscillator frequency varies with the amplitude of the sound waves that hit the microphone. We can make the following two statements about the modulated signal:
This circuit shows an example of direct FM generation. The amount of frequency deviation depends on the amplitude of the sound waves and the rate at which the carrier frequency changes depends on the frequency of the sound waves.
This type of circuit is rarely used in practice because it is difficult to prevent carrier frequency drift and because the frequency deviation produced is very small.
DIRECT FM GENERATION
The direct method or parameter variation method can be further divided into:

Reactance method
Varactor diode modulators

The simplest method for generating FM directly is to vary the frequency of an oscillator. A capacitance microphone or a varactor diode may be used as part of the oscillator’s frequency determining network. The capacitor microphone’s capacitance varies in response to the intensity of the sound waves striking it, making the oscillator’s frequency vary as the amplitude of the sound varies. The varactor diode’s capacitance depends on the voltage across it. Audio signals placed across the diode cause its capacitance to change, which in turn, causes the frequency of the oscillator to vary.
A second method of direct FM generation is to use a reactance modulator. A reactance modulator is a circuit in which a transistor is made to act like a variable reactance. The reactance modulator is placed across the LC circuit of the oscillator and as the modulator’s reactance varies in response to an applied audio signal, the oscillator frequency varies as well.
The third technique is to use a voltage controlled oscillator (VCO). The VCO’s output frequency is proportional to the voltage of the input signal. If audio is applied to the input of a VCO, the output is an FM signal.
All three of these methods suffer from a serious drawback. There is no way to prevent drift of the carrier frequency. It is necessary that the carrier frequency stay constant so that the FM signal does not drift out of its assigned channel. Although a crystal oscillator is very stable, it is not possible to directly frequency modulate a crystal oscillator because the circuit Q is too high. To address this issue, the Crosby modulator was developed. The Crosby circuit incorporates an automatic frequency control (AFC). The circuit operation is as follows:

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The FM output signal is sampled and converted to a low frequency (~ 2 MHz) by a mixer. The mixer output is applied to a discriminator, which is a frequency controlled voltage source (the opposite of a VCO). The output of the discriminator is exactly 0 when the carrier is on its assigned frequency. If the carrier drifts, the discriminator outputs an error voltage, which is fed back to the modulator to compensate for the drift. The discriminator circuit has a sufficiently long time constant that it does not respond to the frequency variations due to modulation, but only to the slow drift of the carrier.
The maximum deviation possible with direct FM is typically 5 KHz, which is too small for wideband FM. To overcome this difficulty, frequency multiplication is used. A frequency multiplier is an amplifier that operates class C (non-linearly), whose output network is tuned to a multiple of the input network (the multiple is usually 2 or 3). A non linear amplifier has an output rich in harmonics of the input signal. The output network is tuned to select one of these harmonics. The efficiency of a multiplier decreases as the multiplier rises, so typically multipliers are designed to be doublers or triplers. Several multipliers can be placed in series to reach higher frequency multiples. For example, a frequency can be multiplied 12 times by feeding it through two doublers and a tripler.
A frequency multiplier multiplies all frequencies in its input pass band. Consider a frequency tripler whose input is an FM signal with a carrier frequency of 5 MHz and a deviation of 5 KHz. The input frequency varies from 4.995 to 5.005 MHz. At the output of the frequency multiplier, everything is tripled, so the output frequency varies from 14.985 to 15.015 MHz. The carrier is now 15 MHz, so the deviation has tripled to 15 KHz. This technique can be used to generate a high frequency wideband FM(WBFM) signal from a low frequency narrowband FM (NBFM) signal.
Let us look at an example. An FM station operates at 106.5 MHz with a maximum deviation of 75 KHz. The FM signal is generated by a reactance modulator that operates at 3.9444 MHz, with a maximum deviation of 2.7778 KHz. The resulting FM signal is fed through 3 frequency triplers, multiplying the carrier frequency and deviation 27 times. The final carrier frequency is 27*3.9444 = 106.5 MHz and the final deviation is 27*2.7778 = 75 KHz.
It is important to remember that frequency multiplication multiplies both the carrier frequency and the deviation.
INDIRECT FM GENERATION
The indirect method or Armstrong method is used when it is not possible to vary the frequency of a crystal oscillator directly but it is possible to vary its phase. The resulting PM signal can be used to create FM. This is the basis of the Armstrong modulator.
The mathematics required to analyze the Armstrong modulator completely are complex, so we will discuss only the basic circuit operation. An audio signal is passed through a preemphasis network and then an integrator, a special network whose output is the time integral of the input signal. The preemphasized integrated signal is used to phase modulate a crystal oscillator. Mathematically, it can be shown that PM using the integral of the audio signal is identical to FM using the audio signal itself. In this way an FM signal is generated.
The Armstrong modulator cannot produce much deviation, so combination of multipliers and mixers are used to raise the carrier frequency and the deviation. The multipliers are used to multiply the carrier and the deviation. The mixers are used to decrease the carrier, while keeping the deviation constant so that additional multiplier stages can be used to obtain more deviation. It is worth going through an example:
An FM station is authorized to operate at 90.9 MHz, with maximum deviation of 75 KHz. The FM signal is generated with an Armstrong modulator whose output is 500 KHz with a deviation of 15.432 Hz. The modulator output is applied to 3 triplers and a doubler to obtain a frequency of 81 MHz and a deviation of 2.5 KHz. The 81 MHz signal is mixed with a 77.97 MHz signal to produce a 3.03 MHz signal whose deviation is still 2.5 KHz. This signal is fed through a doubler, tripler and quintupler to multiply the carrier to 90.9 MHz and the deviation to 75 KHz.
V. FM SIGNAL PERFORMANCE
Bandwidth
The bandwidth of a FM signal may be predicted using:
BW = 2 (b + 1) fm
where b is the modulation index and fm is the maximum modulating frequency used.
FM radio has a significantly larger bandwidth than AM radio, but the FM radio band is also larger. The combination keeps the number of available channels about the same.
The bandwidth of an FM signal has a more complicated dependency than in the AM case (recall, the bandwidth of AM signals depend only on the maximum modulation frequency). In FM, both the modulation index and the modulating frequency affect the bandwidth. As the information is made stronger, the bandwidth also grows.
Efficiency
The efficiency of a signal is the power in the side-bands as a fraction of the total. In FM signals, because of the considerable side-bands produced, the efficiency is generally high. Recall that conventional AM is limited to about 33 % efficiency to prevent distortion in the receiver when the modulation index was greater than 1. FM has no analogous problem.
The side-band structure is fairly complicated, but it is safe to say that the efficiency is generally improved by making the modulation index larger (as it should be).
Noise
FM systems are far better at rejecting noise than AM systems. Noise generally is spread uniformly across the spectrum (the so-called white noise, meaning wide spectrum). The amplitude of the noise varies randomly at these frequencies. The change in amplitude can actually modulate the signal and be picked up in the AM system. As a result, AM systems are very sensitive to random noise. An example might be ignition system noise in your car. Special filters need to be installed to keep the interference out of your car radio. FM systems are inherently immune to random noise.
VI. APPLICATION
Broadcasting
FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (see FM broadcasting). The type of FM used in broadcast is generally called wide-FM, or W-FM. In two-way radio, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.
Hardware
FM is also used at intermediate frequencies by all analog VCR systems, including VHS, to record both the luminance (black and white) and the chrominance portions of the video signal. FM is the only feasible method of recording video to and retrieving video from magnetic tape without extreme distortion, as video signals have a very large range of frequency components. FM also keeps the tape at saturation level, and therefore acts as a form of noise reduction, and a simple limiter can mask variations in the playback output, and the FM capture effect removes print-through and pre-echo. correction.
Sound
FM is also used at audio frequencies to synthesize sound. This technique, known as FM synthesis, was popularized by early digital synthesizers and became a standard feature for several generations of personal computer sound cards.
Radio
An FM signal can also be used to carry a stereo signal: see FM stereo. However, this is done by using multiplexing and demultiplexing before and after the FM process. The rest of this article ignores the stereo multiplexing and demultiplexing process used in “stereo FM”, and concentrates on the FM modulation and demodulation process, which is identical in stereo and mono processes.
A high-efficiency radio-frequency switching amplifier can be used to transmit FM signals (and other constant-amplitude signals).
VII. CONCLUSION
We discussed modulation and our main focus was on frequency modulation and the fm signal. We concluded that In FM signals, the efficiency and bandwidth both depend on both the maximum modulating frequency and the modulation index. Compared to AM, the FM signal has a higher efficiency, a larger bandwidth and better immunity to noise. So it has more applications some of them are given in this paper.
VIII. ACKNOWLEDGMENT
I, Madhurima Maggo am highly greatful to my esteemed university for giving a task to prepare a paper on “Design of an FM signal” . I am very thankful to the almighty. I pay my deep sense of gratitude to my teacher Mr. Dhananjay Devangan, who supported me throughout this task and helped me to correct the mistakes in my document. The credit for completion of this work goes to my parents, my friends and my teachers who supported me, without them it wouldn’t have been so easy to complete the work.
IX. REFERENCES
[1] www.google.com
[2] www.bing.com
[3] www.wikipedia.com
[4] some pdf files
[5] Electronic Devices and Circuits, by J.B. Gupta
[6] Analog Communication Systems, by Sanjay Sharma