**Modulation and Demodulation-II**consists of topics such as

**Types of AM and its classification, Angle Modulation and Demodulation, Phase and Frequency Modulation, Types of FM, Armstrong Method.**

**Types of AM:**

**1. DOUBLE-SIDEBAND SUPPRESSED-CARRIER MODULATION**

In the standard form of amplitude modulation, the carrier wave c(t) is completely independent of the message signal m(t), which means that the transmission of the carrier wave represents a waste of power. This is a disadvantage of amplitude modulation; namely that only a fraction of the total transmitted power is affected by m(t). To overcome this , we may suppress the carrier component from the modulated wave, resulting in double-sideband suppressed carrier modulation.

**(i) Time-Domain Description**

To describe a double-sideband suppressed-carrier (DSBSC) modulated wave as a function of time, we write

s(t) = c(t)m(t) = A_{c} cos(2πf_{c}t) m(t)

**(ii) Frequency-Domain Description**

The suppression of the carrier from the modulated wave is well-appreciated by examining its spectrum. Specifically, by taking the Fourier transform whereas before, S(f) is the Fourier transform of the modulated wave s(t) and M(f) is the Fourier transform of the message signal m(t). When the message signal m(t) is limited to the interval –W ≤ f ≤ W, except for a change in scale factor, the modulation process simply translates the spectrum of the baseband signal ±f_{c}. Of course, the transmission bandwidth required by DSBSC modulation is the same.

**(iii) Generation of DSBSC Wave:**

A double-sideband suppressed-carrier modulated wave consists simply of the product of the message signal and the carrier wave.For achieving this requirement the device is called a product modulator.

**(a) Balanced Modulator:-**

A balanced modulator is combination of two standard amplitude modulators arranged in a balanced configuration so as to suppress the carrier wave. We assume that the two modulators are identical except for the sign reversal of the modulating wave applied to the input of one of them. The outputs of the two modulators may be expressed as follows.

Let there are two signals s_{1}(t) = A_{c}[1 + k_{a}m(t)]cos(2πf_{c}t)

and s_{2}(t) = A_{c}[1 – k_{a}m(t)]cos(2πf_{c}t)

Subtracting s_{2}(t) from s_{1}(t), we obtain

s(t) = s_{1}(1) – s_{2}(t) = 2k_{a}A_{c}cos(2πf_{c}t) m(t)

Hence, the balanced modulator output is equal to the product of the modulating wave, except for the scaling factor 2k_{a }and the carrier, as required.

Transmission B.W = 2ω_{m}

**(b) Ring Modulator**

One of the most useful product modulators that is well suited for generating a DSBSC modulated wave is the ring modulator, it is also known as double-balanced modulator or lattice. The four diodes in figure shown below forms a ring in which they all point the same way. These diodes are controlled by a square-wave carrier c(t) of frequency f_{c} which is applied by means of two center-tapped transformers. We assume that the diodes are ideal, and the transformers are perfectly balanced When the carrier supply is positive, the outer diodes (D_{1}, D_{2}) are switched on, presenting zero impedance, whereas the inner diodes (D_{3}. D_{4}) are switched off, presenting infinite impedance.

We see that there is no output from the modulator at the carrier frequency; that is, the modulator output consists entirely of modulation products.

- Four diodes are connected to form a ring.
- Used for the generation of DSB-SC waves.

**(iv) Operation of the Circuit**

From the circuit diagram of ring modulator, we can explain the operation of the circuit as follows.

- The operation is explained with the assumptions that the diodes act as perfect switches and they are switched on and off by the RF carrier signal. This is because the amplitude and frequency of the carrier is higher than that of the modulating signal.
- The operation can be divided into different modes without the modulating signal and with modulating signal as follows:

**For (+)ve half cycle of c(t) **

Diode D_{1} and D_{2} is ON.

**For (–)ve half cycle of c(t)**

Diode D_{3} and D_{4} ON.

**(v) Hilbert Transform:**A signal x(t) and its Hilbert transform X

_{h}(t) has the following characteristics

- A signal x(t) and its Hilbert transform X
_{h}(t) have the same energy density spectrum. - A signal x(t) and its Hilbert transform X
_{h}(t) have the same autocorrelation function. - A signal x(t) and its Hilbert transform X
_{h}(t) are mutually orthogonal

- If X
_{h}(t) is a Hilbert transform of x(t), then the Hilbert transform of X_{h}(t) is - x(t), i.e If H[x(t)] = X_{h}(t), then H[X_{h}(t)] = - x(t)

**2. Single Sideband Technique:**

Assume the above spectrum an SSB signal in which lower side band is removed.

Let m(t) have a Fourier transform M(f), thus to eliminate the LSB we write the equation as

**(i) Generation of SSBSC Wave:**

**(ii) Advantage SSB-SC over DSB-SC and AM**

In SSB-SC, B.W = ω_{m}, while in DSB-SC or AM, B.W = 2ω_{m}. This reduction in B.W allows signals to be transmitted in the same frequency range. In SSB-SC, more power is saved, and this saved power can be used to produce a stronger signal.

**(iii) Conventional AM Over DSBSC and SB Signals**

- The demodulation or detection of AM signal is simpler than DSBSC and SSB systems. The conventional AM can be demodulated by rectifier or envelope detector. Detection of DSBSC and SSB is rather difficult and expensive.
- Furthermore, it is quite easier to generate conventional AM signals at high power levels as compared to DSBSC and SSB signals. For this reason, conventional AM systems are used for broadcasting purpose.
- The advantage of DSBSC and SSB systems over conventional AM system is that the former requires lesser power to transmit the same information.

**(iv) Vestigial Sideband (VSB) Modulation Technique:**

- When there is vestige or relaxed in one of the sidebands in DSBSC signal then this is called VSB modulation technique.
- VSB wave equation is:

- where F represents the fraction.

**(v) Power Saving**

**In DSB-SC:**

**(vi) Power Relations in VSB Wave:**

_{VSB}can be calculated as

**(vii) SSB Over DSBSC and VSB**

- Demodulation of DSBSC and SSB waves is done using coherent carrier signal at a receiver.
- Envelope detector can also be used to recover message by passing received VSB signal through it.
- SSB scheme needs only one-half of the bandwidth required in DSBSC system and less than that required in VSB also. Thus, we can say that SSB modulation scheme is the most efficient scheme among DSBSC and VSB schemes. SSB modulation scheme is used for long distance transmission of voice signals because it allows the longer spacing between repeaters.
- A device that performs the frequency translation of a modulated signal is known as a frequency mixer. The operation is often collect frequency mixing, frequency conversion or heterodyning.

**3. Performance Comparison of AM Techniques:**

**4. Angle modulation and demodulation**

**Angle Modulation:**

- Angle modulation may be defined as the process in which the total phase angle of a carrier wave is varied in accordance with the instantaneous value of the modulating or message signal while keeping the amplitude of the carrier constant.
- There are two types of angle modulation schemes as under
- Phase Modulation (PM)
- Frequency Modulation (FM)

- These modulation schemes are also called as non-linear modulation schemes.

**(i) Phase Modulation (PM):**

- PM is that type of angle modulation in which the phase angle φ is varied linearly with a baseband or modulating signal x(t) about an unmodulated phase angle:

_{p}= Phase sensitivity of the modulator

**(ii) Frequency Modulation (FM):**FM is that type of angle modulation in which the instantaneous frequency ω

_{i}is varied linearly with a message or baseband signal x(t) about an unmodulated frequency ω

_{c}.

_{f}= Frequency sensitivity of the modulator

**(iii) Representation of FM and PM Signals:**

_{c }cos [θ(t)]

_{p}and k

_{f}are phase and frequency deviation constants respectively.

**Key Points**

- By passing message through a differentiator, then through a FM modulator we get PM modulated signal.
- By passing message through a integrator and then PM modulator we get FM modulated signal.

**(iv) PM and FM Modulated Signals for Sinusoidal Message Signal:**

_{c}is called

**frequency deviation**which depends upon the magnitude and sign of k

_{f }m(t). Frequency deviation:

**Carrier Swing:**The total variation in frequency from the lowest to the highest point is called carrier swing.

**Key Points**

- The amount of frequency deviation or variation depends upon the amplitude (loudness) of the modulating (audio) signal. This means that louder the sound, greater the frequency deviation and vice-versa.
- The frequency deviation is useful in determining the FM signal bandwidth.
- In FM broadcast, the highest audio frequency transmitted is 15 kHz.

**Modulation Index:**For FM, the modulation index is defined as the ratio of frequency deviation to the modulating frequency.

_{f}= frequency deviation / modulating frequency

**Note:**The m

_{f}may be greater than unity.

**Per cent Modulation:**The term 'per cent modulation as it is used in reference to FM' refers to the ratio of actual frequency deviation to the maximum allowable frequency deviation.

- Maximum modulating frequency is 15 kHz.
- Maximum frequency deviation is ± 75 kHz.
- Frequency stability of the carrier is ± 2 kHz.
- Allowable bandwidth per channel is 200 kHz.

**(iv) Types of FM:**The FM signal can be classified based on sensitivity constant as:

**Narrow Band FM:**In this case, k_{f}is small and hence the bandwidth of FM is narrow.**Wide Band FM:**In this case, k_{f}is large and hence the FM signal has a wide bandwidth.

**(v) Another Representation of PM and FM Signals for Sinusoidal Message:**

**Bandwidth of the Angle Modulated Signal:**In general, the effective bandwidth of an angle modulated signal, which contains atleast 98% of the signal power is given by.

_{c}= 2 (β + 1) f

_{m}is also known as Carson's formula

- By seeing the graph of angle modulation signal we can't tell whether it is PM or FM.
- FM receiver may be fitted with amplitude limiters to remove the amplitude variations caused by noise.

**Relation between PM and FM:**

**(vi) Generation of FM Using Phase Modulator**

**(vii) Generation of PM using a Frequency Modulator**

It is also possible to generate a PM wave using a frequency modulator as shown in figure 3. The modulating signal is first passed through a differentiator and then applied to a frequency modulator.

This discussion has revealed that it is possible to obtain all the properties of FM from a PM wave and vice versa. At the output of the differentiator, we get the differentiated version of modulating signal i.e. dm(t)/dt. Hence, output of the frequency modulator will be,

**(viii) FM Over AM:**

- It is possible to reduce noise still further by increasing the frequency deviation but in AM this is not possible.
- Standard frequency allocations provide a guard band between commercial FM stations. Due to this, there is less adjacent channel interference than in AM.
- FM broadcasts operate in the upper VHF and UHF frequency ranges at which there happens to be less noise than in the MF and HF ranges occupied by AM broadcasts.

**Note:**A much wider channel typically 200 kHz is required in FM as against only 10 kHz in AM broadcast. This form serious limitation of FM.

**(ix) Generation of FM:**The FM modulator circuits used for generating FM signals may be put into two categories as under

- The direct method or parameter variation method.
- The indirect method or the Armstrong method.

**Direct Method**

This method is most widely used for generation of WBFM signal.

**Drawbacks of Direct Method for FM Generation**

Following are the drawbacks of the direct method:

- In direct method of FM generation, it is not easy to get a high order stability in carrier frequency. This is due to the fact that generation of carrier signal is directly affected by the baseband or modulating signal. The baseband signal directly controls the tank circuit of the carrier generator and thus a stable oscillator circuit (i.e. crystal oscillator) cannot be used. This means that the carrier generation cannot be of high stability which is a necessary requirement. A solution to this problem is the indirect method i.e. Armstrong method of FM generation. In fact, in this method, the carrier oscillator does not respond to the modulating signal directly rather the generation of the carrier is made isolated from other parts of the circuit. Thus, stable crystal oscillators may be used to generate carrier signal.
- The non-linearity of the varactor diode produces a frequency variation due to harmonics of the modulating or baseband signal and therefore the FM signal is distorted. We will have to take the proper cares to keep this type of distortion minimum.

Despite all above drawbacks, the direct method is utilized for high power FM generation in several applications.

**[Note: **A low-pass filter compensates for higher phase shift and frequency deviation at the higher modulating frequencies to produce indirect FM.**]**

**(x) ARMSTRONG METHOD**

DC component is eliminated using an amplifier of gain 2 then o/p = cos 4πfct. when one more square law device is connected frequency gets multiplied again by 2. Thus 2 square law devices in cascade multiplies the frequency by 4.

Assume that the message signal and carrier are applied to a NBFM modulate. The output signal is A_{c} cos [2πf_{c}t + βsin 2πf_{m}t]. If the signal is passed through frequency multiplier the final output is A_{c} cos [n(2π f_{c}t + βsin 2πf_{m}t)]. In a frequency multiplier, carrier frequency and β are increased by a factor of n. But the message frequency is same. (As multiplier changes the carrier frequency, it must be brought back to the original carrier frequency. This is done by using a mixer)

**(xi) Demodulation of FM:**

The demodulation process of FM waves is exactly opposite to that of the frequency modulation. The AM detector is nothing but a rectifier, but FM demodulator is a frequency to amplitude converter. It is necessary to convert the frequency variations in FM wave at its input into amplitude variations at its output to recover the original modulating signal.

**(xii) Requirements of FM demodulator (Detector)**

The FM demodulator must satisfy the following requirements:

- It must convert frequency variations into amplitude variations.
- This conversion must be linear and efficient.

** **3**. **The demodulator circuit must be insensitive to amplitude changes. It should respond only to the frequency changes.

4. Its adjustment and operation should not be critical.

**(xiii) Performance comparison of FM & PM System**

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