**THEORY OF FREQUENCY AND PHASE MODULATION:**

**Frequency modulation:**

- The process of changing the frequency of the carrier signal in accordance with the modulating signal transmitted, keeping the amplitude and phase of the carrier wave unchanged is known as frequency modulation.

**Phase modulation****:**

- The process of changing the phase of the carrier signal in accordance with the modulating signal transmitted, keeping the amplitude and frequency of the carrier wave unchanged is known as phase modulation.

**Direct frequency modulaton:**

- The process of changing the frequency of a constant amplitude carrier directly proportional to the amplitude of moulating signal at a rate equal to the frequency of the modulated signal.

**Direct phase modulation:**

- The process of changing the phase of aconstant amplitude carrier directly proportional to the amplitude of odulating signal at a rate equal to the frequency of the modulatingb signal.

**Instantaneous phase deviation:**

- It gives the instantaneous change in the phase of the carrier at a given instant of time and indicates how much the phase of the carrier changes with respect to its reference phase.
- Instantaneous phase deviation is indicated as θ(t).
- Its unit is radians.

**Instantaneous phase:**

- Precise phase of carrier of the carrier at a given instant of time is given by,

Instantaneous phase = w_{c}t + θ(t).

- Its unit is radians.

**Instantaneous frequency devation:**

- Instantaneous cahnge in the frequency of carrier,defined as the first time deviation of instantaneous phase deviation.
- Instantaneous frequency deviation is indicated as θ’(t)
- Its unit is radians/sec.

**Instantaneous frequency:**

- Precise frequency of carrier at a given instant of time and is defined as the first time deviation of the instantaneous phase.
- Instantaneous frequency w
_{i}(t) = d/dt [w_{c }+θ(t)]

= w_{c }+θ’(t) (or) 2∏f_{c} + θ’(t)

- Its unit is radians/sec.

**Deviation sensitivity:**

- Instantaeous frequency deviaton, instantaneous phase deviation depends on the modulating signal voltage.That is,

θ(t) α V_{m}(t)

θ’(t) α V_{m}(t)

θ(t) = k V_{m}(t)

θ’(t)= k1V_{m}(t)

where, k – phase deviation or deviation sensitivity.

k1 –frequency deviation or deviation sensitivity.

**Modulation index for PM:**

The generalm term of phase modulaton,

m(t) = V_{c }cos[w_{c}t + θ(t)]

where w_{c} is angle modulation.

m(t) = V_{c }cos[w_{c}t +k V_{m}(t)] [since θ(t) = k V_{m}(t) ]

m(t) = V_{c }cos[w_{c}t +k V_{m}sin w_{m}(t)] [ sinceV_{m}(t)= V_{m}sin w_{m}(t) ]

m(t) = V_{c }cos[w_{c}t + m sin w_{m}(t)] [since modulation index m= kV_{m}]

_{ }i.e., moduation index m α amplitude of modulating signal.( m α V_{m} )

m = k V_{m}

**Modulation index or FM:**

The generalm term of phase modulaton,

m(t) = V_{c }cos[w_{c}t + θ(t)]

where w_{c} is angle modulation.

m(t) = V_{c }cos[w_{c}t + ∫θ’(t) dt]

m(t) = V_{c }cos[w_{c}t +∫ k1 V_{m}(t)dt] [since θ’(t) = k1 V_{m}(t) ]

m(t) = V_{c }cos[w_{c}t +∫ k1 V_{m}cos w_{m}t dt]

m(t) = V_{c }cos[w_{c}t + k1 V_{m}/w_{m }sin w_{m}t]

Therefore modulation index,

m = k1 V_{m}/w_{m }

**Modulation index in FM:**

m = δ / f_{m }= maximum frequency deviation / modulating frequency

* It has no unit.

**Percentage modulation:**

% modulation = actual frequency deviation / max. allowable frequency deviation

**Corson’s rule:**

- Carson’s rule gives approximate maximum minimum bandwidth of angle modulated signal as,
- BW = 2 [ δ + f
_{m (max)}] Hz - Here f
_{m (max) }is the maximum modulating frequency.

- As per Corson’s rule,the bandwidth accomaodates almost 98% of total transmitted power.

**PLL transmitter:**** (Direct FM transmitter)**

**Introduction to PLL**

The concept of Phase Locked Loops (PLL) first emerged in the early 1930’s.But the technology was not developed as it now, the cost factor for developing this technology was very high. Since the advancement in the field of integrated circuits, PLL has become one of the main building blocks in the electronics technology. In present, the PLL is available as a single IC in the SE/NE560 series (560, 561, 562, 564, 565 and 567) to further reduce the buying cost ,the discrete IC’s are used to construct a PLL.

**PLL Block Diagram**

- The block diagram of a basic PLL is shown in the figure below.
- It is basically a flip flop consisting of a phase detector, a low pass filter (LPF),and a Voltage Controlled Oscillator (VCO).

- The input signal Vi with an input frequency fi is passed through a phase detector.
- A phase detector basically a comparator which compares the input frequency fiwith the feedback frequency fo
- The phase detector provides an output error voltage Ver (=fi+fo),which is a DC voltage.
- This DC voltage is then passed on to an LPF. The LPF removes the high frequency noise and produces a steady DC level, Vf (=Fi-Fo). Vf also represents the dynamic characteristics of the PLL.
- The DC level is then passed on to a VCO.
- The output frequency of the VCO (fo) is directly proportional to the input signal.
- Both the input frequency and output frequency are compared and adjusted through feedback loops until the output frequency equals the input frequency.
- Thus the PLL works in these stages – free-running, capture and phase lock.
- As the name suggests, the free running stage refer to the stage when there is no input voltage applied.
- As soon as the input frequency is applied the VCO starts to change and begin producing an output frequency for comparison this stage is called the capture stage.
- The frequency comparison stops as soon as the output frequency is adjusted to become equal to the input frequency.
- This stage is called the phase locked state.

**PLL Applications**

- Frequency Modulation (FM) stereo decoders, FM Demodulation networks for FM operation.
- Frequency synthesis that provides multiple of a reference signal frequency.
- Used in motorspeed controls, tracking filters.
- Used in frequency shift keying (FSK) decodes for demodulation carrier frequencies.

**Indirect FM transmitter: (Amstrong method)**

** **

**Working:**

*Crystal oscillator:*

- It generates the carrier signal.
- It will be act as a reference oscillator.

*Buffer amplifier:*

- It acts as a isolation block and amplifies the carrier signal.
- It joins the characteristics of two different components.
- The output of this Buffer amplifier is carrier signal.

*90 ̊ phase shft:*

- It is a part of the carrier signal.
- It is also called as sub-carrier.

*Balanced modulator:*

- A relatively low frequency subcarrier (f
_{c}) is phase shifted by 90 ̊ and given to BM and it is mixed with input modulating signal (f_{m}). - The output of Balanced modulator isDSB-SC that is combined with original carrier in combining network to produce low-index PM wave.

*Combining network:*

- The output of combining network is a signal whose phase is varied at a rate equal to f
_{m}and magnitude is directly proportional to V_{m}. - Peak phase deviation θ = m = arctan V
_{m}/V_{c} - For very small angles, tangent of angle is approximately equal to angle
- θ = m = V
_{m}/V

- θ = m = V
- When V
_{c}is varied, unwanted AM produces and V_{c(max) }is produced when V_{USF , }V_{LSF}are in phase. - Maximum phase deviation that can be produced is 1.67milliradians, frequency of modulating signal = 15kHz.
- Therefore maximum frequency deviation is,
- ∆f
_{max}= (0.00167)(15000) = 25Hz.

- ∆f

**72 multiplier:*

- Since the modulating signal at the output of combining network is insufficient to produce wideband GM, it is multiplied by 72, to produce the following,
- f
_{1 }= 72 * 200 kHz = 14.4 MHz - m = 72 * 0.00096 = 0.06912 radians

- f

∆f = 72 * 14.4 Hz = 1036.8 Hz

*BPF:*

- It will allow only the particular range of frequency.

*Mixer and down-convertor:*

- The output of first multiplier is mixed with 13.15 MHz crystal controlled frequency (f
_{0}) to give different signal (f_{2}).

f_{2} = 14.4 MHz – 13.15 MHz = 1.25 MHz (decreasing)

m = 0.06912

∆f= 1036.8 Hz

- Mixer output is again multiplied by 72,

f_{2} =1.25 * 72 = 90 MHz

m = 0.06912 * 72 = 4.98 radians

∆f = 1036.8 * 72 = 74.650 Hz

**Power amplifier:**

- It increase the power of the signal outputted from BPF
- The final output of the the transmitter is FM modulated signal.

**Advantages of FM:**

- Noise immunity
- Power utilization
- Capture effect

**Disadvantages:**

- Costly
- Complex circuit.
- Bandwidth is increasing rather than AM.

**COMPARISION OF VARIOUS ANALOG COMMUNICATION SYSTEMS (AM-FM-PM):**

S.No | Amplitude modulation | Frequency modulation |

1 | Amplitude of the carrieris varied according to amplitude of modulating signal | Frequency of the carrieris varied according to amplitude of modulating signal |

2 | AM has poor fidelity due to narrow bandwidth | FM has better fidelity due to large bandwidth |

3 | Less efficient | More efficient |

4 | Noise interference is more | Noise interference is less |

5 | Adjacent channel interference is present | Adjacent channel interference s avoided due to wide frequency spectrum |

6 | AM broadcast operates in MH and HF range | FM broadcast operates in VHH and UHF range |

7 | In AM only carrier and sidebands are present | Infinite number of sidebands are present |

8 | The transmission equipment is simple | The transmission equipment is complex |

9 | Transmission power depends on modulation index | Transmission power ies irresponsible of modulation index |

S.No | Frequency modulation | Phase modulation |

1 | The maximum frequency deviation depends upon amplitude of modulating voltage and modulating frequency | The maximum phase deviation depends only upon amplitude of modulating voltage |

2 | Frequency of the carrier is modulated by modulatng signal | Phase of the carrier is modulated by modulating signal |

3 | Modulation index is increased as modulation frequency is reduced and vice versa | Modulation index remains same if modulating frequency is changed |