Frequency Modulation Circuit

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In this type of angle modulation, the instantaneous frequency is varied linearly with a modulating signal f(t) about an unmodulated frequency. In other words, the instantaneous value of the angular frequency is equal to the frequency of the unmodulated carrier plus a time varying component proportional to f(t). Mathematically,

ωi = ωc + Kf f(t)

The term Kf represents the frequency sensitivity of the modulator expressed in Hz/V.
Frequency Modulation Circuit:

The varactor diode is a semiconductor diode whose junction capacitance changes appreciably with d.c. bias voltage. This diode is shunted with the tuned circuit (tank circuit) of the carrier oscillator as shown in the figure.

Frequency modulation circuit

The capacitor C is kept much smaller than the diode capacitance (Cd), in order to keep the radio frequency (r.f.) voltage from oscillator across the diode small as compared to V0. V0 is the polarizing voltage to maintain a reverse bias across the varactor diode. Also, reactance of C at the highest modulating frequency is kept large as compared to R, so that the shunting of ...
... the modulating signal through the tank circuit is avoided.
Working Principle:

The capacitance Cd of the diode is given by the relation

Cd = K(Vd)^-(1/2) ____________(1)

Where Vd is the total instantaneous voltage across the diode given by

Vd = V0 + f(t) And K is a constant of proportionality.

The total capacitance of the oscillator tank circuit is (C0 + Cd) and, hence, the instantaneous frequency of oscillation is given as

ωi = 1/ sqrt(Lo(Co + Cd)) [ As the frequency of oscillation is given by ωc = 1/sqrt(LC) ]

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Substituting Cd from equation (1), we get

ωi = [Lo(Co + KVd-1/2)]-1/2

This frequency is dependent on Vd which in turn depends on the modulating signal f(t). Therefore, the oscillator frequency is dependent on the modulating signal f (t) and thus frequency modulation is generated.

The bandwidth of an FM signal depends on the deviation Kff(t). When the deviation is high, the bandwidth will be large, and vice-versa. From the equation Δω = Kf f(t) (where Δω = frequency deviation) it is clear that deviation is controlled by Kff (t). Thus, for a given f (t), the deviation, and hence, bandwidth will depend on frequency sensitivity Kf. If Kf is too small then the bandwidth will be narrow and vice-versa. Thus depending on the value of Kf, FM can be divided into two categories.

(1) Narrowband FM.

(2) Wideband FM.
Wide Band Frequency Modulation :

When Kf has larger value, then the signal has a wide bandwidth, ideally infinite and the signal is called wideband signal. The general equation of wideband FM is given by

ΦFm (t) = AJ0(mf)cosωct + AJ1(mf)[cos(ωc+ωm)t - cos(ωc-ωm)t] +AJ2(mf)[cos(ωc + 2ωm)t + cos(ωc - 2ωmt)] +

AJ3(mf) [cos(ωc + 3ωm)t - cos(ωc - 3ωm)t] + _ _ _ _ _ _
Wide Band Frequency Modulation : Frequency Components

The FM signal has the following frequency components:

Carrier term cosωct with magnitude AJ0 (mf), i.e. the magnitude of the carrier term is reduced by a factor J0 (mf) here, J0 is the Bessel function coefficient and mf is known as modulation index of the FM wave. It is defined as the “ratio of frequency deviation to the modulating frequency. The modulation index mf decides whether an FM wave is a narrowband or a wideband because it is directly proportional to the frequency deviation. Normally mf = 0.5 is the transition point between a narrowband and a wideband FM. If mf0.5, then FM is a narrowband, otherwise it is a wideband. As discussed, when mf is large, the FM produces a large number of sidebands and the bandwidth of FM is quite large. Such systems are called wideband FM.

Theoretically infinite numbers of sidebands are produced, and the amplitude of each sideband is decided by the corresponding Bessel function Jn (mf). The presence of infinite number of sidebands makes the ideal bandwidth of the FM signal is infinite. However, the sidebands with small amplitudes are ignored. The sidebands having considerable amplitudes are known as significant sidebands. They are finite in numbers.

Power content in FM signal: Since the amplitude of FM remains unchanged, the power of the FM signal is same as that of unmodulated carrier. (i.e.` A^2/2` ) where A is amplitude of signal.

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