## FM Modulation & Demodulation |

## FM Modulation and Demodulation |

**TUNED COLLECTOR OSCILLATOR ::**

An oscillator is a system consisting of active and passive circuit elements to
produce a sinusoidal or other repetitive waveforms at the output without the
application of an external input signal. The function of an oscillator is to
convert DC power into AC power. In an oscillating circuit the amplitude of
voltage or current oscillation decays with time owing to the dissipation of
energy in the resistance contained in the circuit. If a –ve resistance is
incorporated in the circuit to generate energy that compensates for the loss of
energy through the passive resistance, oscillations with undiminished amplitude
can occur. Basically therefore a –ve resistance must be provided in an
oscillator. This is accomplished in a feedback oscillator by providing an
external +ve feedback to make the overall gain infinite. The initial signal to
trigger the oscillation is obtained from the noise voltage, which is produced
from the power supply of the system. The frequency spectrum of noise being very
wide it always has a voltage component at the frequency required for the
oscillation. So the primary requirements of a feedback oscillator are: -

- An amplifier with external regenerative feedback to give a –ve resistance in the system.
- A frequency determining networks to produce oscillation of the desirable frequency.
- Some system non-linearity to limit the amplitude of oscillation.
- A DC Power source to supply the energy.

Tuned Collector Oscillator is a LC feedback oscillator. Here we use a transistor in CE configuration which gives 180 degree phase shift between its input and output voltage. Also we use a transformer, which gives another 180-degree phase shift needed for oscillation. The frequency determining circuit is made up bye the capacitor C together with the transformer primary inductance L. The LC tuned circuit connected to the collector accounts for the name ‘Tuned Collector Oscillator’. The LC tuned circuit is called tank circuit because this circuit determines the frequency of oscillation. There is a large value of resistance called R2 connected in series with the transformer secondary winding. The main purposes served by R2 are to: -

- Reduce the loading of the collector circuit by the low input resistance of the transistor.
- Introduce regenerative feedback just require to sustain oscillations.
- Decrease the input non-linear distortion.

The frequency of oscillation `ƒ`

is approximately
given by the natural resonant frequency of the LC tank circuit. Thus_{0
}

`ƒ`

_{0}= 1/2`П√LC`

**FM TRANSMITTER:: **

A FM transmitter is usually a VHF tuned collector oscillator with center
frequency `ƒ`

_{0}= 1/2`П√LC`

. Frequency range is around 80-108Mhz. We can choose value of L or C
such that center frequency can be changed between the frequency band. Usually
30-300Mhz VHF range is optimal for FM TRANSMITTER. Transmitter is a combination
of an oscillator, Modulator and a suitable Antenna system. Carrier is generated
in the oscillator. Then it is modulated with the information signal then
transmitted through transmission channel via an interface of antenna system.
Antenna system converts the carrier current to electromagnetic waves, which
easily travels through the space.

Now we consider our circuit. The CE mode transistor is a tuned collector with a
tuned LC circuit. The center frequency of oscillator is determined by this LC
value. The center frequency is thus `ƒ`

_{0}=
1/2`П√LC`

. Now we go in to the modulation part. When
a signal is applied in to the base, the base–emitter (B-C) voltage is changed.
The voltage across the varactor diode also changed. The capacitance of base to
emitter junction also changed. This capacitance falls series with the tank
circuit. The operating frequency also changed. Thus the change of frequency is
achieved which is the main criteria of FM modulation.

The change of frequency should not be such that it can track by a PLL. The FM
wave is now coupled with a telescopic antenna for broadcast.

**VHF oscillator and FM Transmitter**

**FM DEMODULATION USING PLL ::**

In FM modulation when the bandwidth becomes so large that the input noise power
is relatively large, the performance of the FM system degrades rapidly and the
system exhibits a threshold. When input noise power is quite large we would be
inclined to use FM and allows a sacrifice of bandwidth for the sake of improved
output signal-to-noise ratio. But FM threshold prevents such use of
FM. Conventional FM discriminators does not occur threshold improvement while FM
demodulator using Phase-Locked Loop (PLL) improves threshold.

**DEFINITION OF PLL ::**

The Phase-Locked Loop (PLL) is a feedback system that may be used to extract a
base band signal from a FM carrier, especially under low SNR conditions. Thus
PLL tracks the phase and the frequency of the carrier component of an incoming
signal.

A PLL has three basic components: -

- A voltage-controlled oscillator (VCO)
- A multiplier, serving as a phase detector or a phase comparator
- A loop filter having response H(s)

The operation of PLL is similar to that of a feedback system except that the quantity feedback and compared is phase, but not amplitude.

**OPERATION OF VCO ::**

An oscillator whose frequency can be controlled by an external voltage is a
Voltage Controlled Oscillator (VCO). In a VCO, the oscillation frequency varies
linearly with the input voltage. If a VCO input voltage Eo(t), its output is a
sinusoid of frequency given by,

`ω`

_{VCO }= ω_{c} + Ce_{o}(t)

Where C is a constant of the VCO and ω_{c} is the free-running frequency of the VCO.
The multiplier output is further low pass filtered by the loop filter and then
applied to the input of the VCO. This voltage changes the frequency of the
oscillator and keeps the loop locked, i.e. the frequency and phase of the input
and output sinusoidal signals becomes identical.

**OPERATION OF PHASE COMPARATOR ::**

A Phase Comparator is a device with two input ports and a single output port.
If periodic signals of identical frequency but with a timing difference are
applied to the inputs, the output is a voltage, which depends on the timing
difference. After phase comparator the signal is low pass filtered to get the
error voltage.

**PLL ACTING AS A DEMODULATOR ::**

In PLL the output _{Eo}(t) of the loop filter H(s) acts as an input to the VCO. The
free-running frequency of the VCO is set at the carrier frequency ω_{c}. The
instantaneous frequency of the VCO is given by,

`ω`

---------(1)_{vco} =ω_{c} + Ce_{o}(t)

If the VCO output is, `Bcos [ω`

, _{c}t +
θ_{o}(t)]

then its instantaneous frequency is
`[ω`

. _{c}t + d(θ_{o}(t))]

Therefore,
`d(θ`

= Ce_{o}(t))_{o}(t) ----------(2), where C and B are constants of the PLL.

Let the incoming signal be, `Asin [ω`

. At the multiplier this incoming
signal and the VCO output are fed so that the output X(t) is given by,_{c}t +ω_{i} (t)]

X(t) =

A B sin(ω_{c}t +`θ`

)cos(ω_{i}_{c}t +`θ`

_{0})

`=[½AB {sin (`

`θ`

_{i}` -`

`θ`

_{0}`) + sin(2ω`

_{c}t +`θ`

_{i}```
+
```

`θ`

_{0}```
)}]
```

---------(3)

The sum frequency term is suppressed by the loop filter, Hence the effective
input to the loop filter is `[½AB {sin (`

`θ`

_{i}`(t) -`

`θ`

_{0}`(t))]`

. If h(t) is the unit impulse
response of the loop filter,

e_{o}(t) = h(t) * [`½`

ABsin{`θ`

_{i}`(t) -`

`θ`

_{0}`(t)`

}] = [`½`

(AB)]_{0}∫^{t} h(t –
x)sin[`θ`

_{i}`(t) -`

`θ`

_{0}`(t)`

]dx
-(4)

Substituting eq.(2) in eq.(4) we get ```
d(θ
```

= AK_{o}(t))_{-α}∫^{t}h(t –
x)sin[`θ`

e(x)]dx
----------------(5)

where K =CB
and `θ`

e
(t) is the phase error,
defined as `θ`

e
(t) = `θ`

_{i}(t) – ```
θ
```

_{o}(t).

When the incoming FM carrier is Asin[ω_{c}t + `θ`

_{i}(t)],

`θ`

_{i}(t)= k_{f-α}∫^{t}m(α)dα -------------(6)

Hence,

`θ`

_{o}(t)
= [k_{f-α}∫^{t}m(α)dα] – 0e(t)

and assuming a small error e(t) we get from eq.(2)

e_{o}(t) =1/c[`d(θ`

]~
1/ck_{o}(t))_{f }m(t) ---------------(7)

Thus, the PLL acts as an FM demodulator.

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