II.

Angle Modulation

Frequency Modulation

In amplitude modulation, the amplitude of the carrier signal varies. Whereas, in Frequency
Modulation (FM), the frequency of the carrier signal varies in accordance with the
instantaneous amplitude of the modulating signal.
Hence, in frequency modulation, the amplitude and the phase of the carrier signal remains
constant. This can be better understood by observing the following figures.

Fig 2.1 Frequency Modulation

The frequency of the modulated wave increases, when the amplitude of the modulating or
message signal increases. Similarly, the frequency of the modulated wave decreases, when the
amplitude of the modulating signal decreases. Note that, the frequency of the modulated wave
remains constant and it is equal to the frequency of the carrier signal, when the amplitude of
the modulating signal is zero.

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Mathematical Representation

The equation for instantaneous frequency fi in FM modulation is

Where,
fc is the carrier frequency
kt is the frequency sensitivity
m(t) is the message signal
We know the relationship between angular frequency ωi and angle θi(t) as

This is the equation of FM wave.

Modulation Index of FM

The ratio of frequency deviation to the modulating frequency is knwn as the modulation
index of FM.

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Frequency Deviation

The difference between FM modulated frequency (instantaneous frequency) and normal carrier
frequency is termed as Frequency Deviation. It is denoted by Δf, which is equal to the product
of kf and Am.

Deviation Ratio

Accordingly the FM deviation ratio can be defined as: the ratio of the maximum carrier
frequency deviation to the highest audio modulating frequency.

m=Max frequency deviation/Max modulation frequency

Carson’s Rule for Bandwidth of FM

This rule states that the bandwidth of an FM system is double the sum of the maximum
frequency deviation and the highest modulating frequency fm. Thus, if B is the bandwidth of
the system; then according to Carson's rule:

B=2( fd + fm)

Comparison of AM and FM

Table 2.1 Comparison of AM and FM

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Narrow Band and Wideband FM Comparison

Narrowband FM

Following are the features of Narrowband FM.

 This frequency modulation has a small bandwidth when compared to wideband FM.
 The modulation index ββ is small, i.e., less than 1.
 Its spectrum consists of the carrier, the upper sideband and the lower sideband.
 This is used in mobile communications such as police wireless, ambulances, taxicabs,
etc.

Wideband FM

Following are the features of Wideband FM.

 This frequency modulation has infinite bandwidth.

Generation of FM Using Varactor Diode Modulator (Direct Method)

 The varactor diode FM modulator has been shown below in figure .

Fig 2.2 Varactor Diode Modulator

 A varactor diode is a semiconductor diode whose junction capacitance varies linearly

Working Operation

 The varactor diode is reverse biased by the negative dc source –Vb.

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  The modulating AF voltage appears in series with the negative supply voltage. Hence,
the voltage applied across the varactor diode varies in proportion with the modulating
voltage.
 This will vary the junction capacitance of the varactor diode.
 The varactor diode appears in parallel with the oscillator tuned circuit.
 Hence the oscillator frequency will change with change in varactor dioide capacitance
and FM wave is produced.
 The RFC will connect the dc and modulating signal to the varactor diode but it offers a
very high impedance at high oscillator frequency. Therefore, the oscillator circuit is
isolated from the dc bias and modulating signal.

Indirect Method of FM Generation

In the direct methods of generation of FM, LC oscillators are to be used. The crystal oscillator
cannot be used. The LC oscillators are not stable enough for the communication or broadcast
purpose. Thus, the direct methods cannot be used for the broadcast applications.

The alternative method is to use the indirect method called as the Armstrong method of FM
generation.

In this method, the FM is obtained through phase modulation. A crystal oscillator can be used
hence the frequency stability is very high and this method is widely used in practice.

Fig 2.3 Armstrong Method for FM Generation

The Armstrong method uses the phase modulator to generate a frequency modulated wave.

Working Principle

The working operation of this system can be divided into two parts as follows:

Part I: Generate a narrow band FM wave using a phase modulator.

Part II: Use the frequency multipliers and mixer to obtain the required values of
frequency deviation, carrier and modulation index.

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Part I: Generate a narrow band FM using Phase Modulator

As discussed carrier, we can generate FM using a phase modulator.

The modulating signal x(t) is passed through an integrator before applying it to the phase
modulator as shown in figure 1.

Let the narrow band FM wave produced at the output of the phase modulator be represented
by s1(t) i.e.,

where Vc1 is the amplitude and f1 is the frequency of the carrier produced by the crystal
oscillator.

The phase angle Φ1(t) of s1(t) is related to x(t) as follows:

where k1 represents the frequency sensitivity of the modulator.

If Φ1(t) is very small then,

Hence, the approximate expression for s1(t) can be obtained as follows:

After approximation, we get,

Substituting,

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This expression represents a narrow band FM. Thus, at the output of the phase modulator, we
obtain a narrow band FM wave.

Part II: Implementation of the Phase Modulator

Figure.2.4 shows the block diagram of phase modulator circuit.

Fig 2.4 Phase Modulator Circuit

The crystal oscillator produces a stable unmodulated carrier which is applied to the 90° phase
shifter as well as the combining network through a buffer.

The 90° phase shifter produces a 90° phase shifted carrier. It is applied to the balanced
modulator along with the modulating signal.

Thus, the carrier used for modulation is 90° shifted with respect to the original carrier.

At the output of the product modulator, we get DSB SC signal i.e., AM signal without carrier.

This signal consists of only two sidebands with their resultant in phase with the 90° shifted
carrier.

The two sidebands and the original carrier without any phase shift are applied to a combining
network (∑). At the output of the combining network, we get the resultant of vector addition
of the carrier and two sidebands as shown in figure 2.5.

Fig 2.5 Phasor explaining the generation of PM

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Now, as the modulation index is increased, the amplitude of sidebands will also increase.
Hence, the amplitude of their resultant increases. This will increase the angle Φ made by the
resultant with unmodulated carrier.

The angle Φ decreases with reduction in modulation index as shown in figure2.6.

Fig 2.6 Effect of modulation index on frequency

Thus, the resultant at the output of the combining network is phase modulated. Hence, the block
diagram operates as a phase modulator.

Part III: Use of Frequency Multipliers Mixer and Amplifier

The FM signal produced at the output of phase modulator has a low carrier frequency and low
modulation index. They are increased to an adequately high value with the help of frequency
multipliers and mixer.

Phase Modulation

In frequency modulation, the frequency of the carrier varies. Whereas, in Phase Modulation
(PM), the phase of the carrier signal varies in accordance with the instantaneous amplitude of
the modulating signal.

So, in phase modulation, the amplitude and the frequency of the carrier signal remains constant.
This can be better understood by observing the following figures.

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