Types of Modulation & Demodulation Study Notes for Instrumentation Engineering

1. Frequency discrimination method or filter method
2. Phase discrimination method or phase-shift method: The phase-shift method avoids the filter. This method makes use of two balanced modulators and two phase-shifting networks.

Conventional AM Over DSBSC and SB Signals

• The demodulation or detection of AM signals is simpler than DSBSC and SSB systems. The conventional AM can be demodulated by a 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 purposes.
• The advantage of DSBSC and SSB systems over conventional AM systems is that the former requires lesser power to transmit the same information.

Vestigial Sideband (VSB) Modulation Technique:

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

• where F represents the fraction.

Power Relations in VSB Wave: The power of VSB wave P_VSB can be calculated as

SSB Over DSBSC and VSB

• Demodulation of DSBSC and SSB waves is done using a coherent carrier signal at a receiver.
• An envelope detector can also be used to recover a message by passing the received VSB signal through it.
• SSB scheme needs only one-half of the bandwidth required in the DSBSC system and less than that required in VSB also. Thus, we can say that the 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 longer spacing between repeaters.
• A device that performs the frequency translation of a modulated signal is known as a frequency mixer. The operation often collects frequency mixing, frequency conversion, or heterodyning.

Performance Comparison of AM Techniques

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 nonlinear modulation schemes.

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:

where k_p = Phase sensitivity of the modulator

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.

where k_f = Frequency sensitivity of the modulator

Representation of FM and PM Signals: An angle-modulated signal, in general, can be written as

S(t) = A_c cos [θ(t)]

where θ (t) is the phase of the signal and its instantaneous frequency is given by

If m(t) is the message signal, then in the PM system, we have

For FM system, we have

where k_p and k_f are phases and frequency deviation constants respectively.

Key Points

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

PM and FM Modulated Signals for Sinusoidal Message Signal:

The maximum change in instantaneous frequency from the average frequency ω_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.

The carrier swing = 2 x frequency deviation = 2 x Δω

Key Points

• The amount of frequency deviation or variation depends upon the amplitude (loudness) of the modulating (audio) signal. This means that the louder the sound, the 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.

m_f = frequency deviation / modulating frequency

for FM (sinusoidal message signal)

for PM

for PM (sinusoidal message signal)

Note: The m_f may be greater than unity.

Percent Modulation: The term ‘percent modulation as it is used in reference to FM’ refers to the ratio of actual frequency deviation to the maximum allowable frequency deviation.

Percent modulation :

where,

 is Actual frequency deviation,

 is Maximum frequency deviation

In percent modulation, the following features will be considered

• The maximum modulating frequency is 15 kHz.
• The maximum frequency deviation is ± 75 kHz.
• The frequency stability of the carrier is ± 2 kHz.
• Allowable bandwidth per channel is 200 kHz.

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.

Another Representation of PM and FM Signals for Sinusoidal Message:

where β is the modulation index. In (β) is known as the Bessel function of the first kind of order n. The total bandwidth requirement for angle modulated signal is infinite. Basically, the effective bandwidth is the separation between the two extremely significant side frequencies on either side of the carrier.

The bandwidth of the Angle Modulated Signal: In general, the effective bandwidth of an angle-modulated signal, which contains at least 98% of the signal power is given by.

B_c = 2 (β + 1) f_m is also known as Carson’s formula

where β is the modulation index.

For

A number of harmonics in the bandwidth (including the carrier) is:

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

The relation between PM and FM

PM signal:

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.

The amplitude of the FM wave is constant. It is thus independent of the modulation depth, whereas, in AM, modulation depth governs the transmitted power.

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

In a direct method or parameter variation method, the baseband or modulating signal directly modulates the carrier. The carrier signal is generated with the help of an oscillator circuit. This oscillator circuit uses a parallel-tuned L-C circuit having the frequency.

Varactor Diode Method: The varactor diode is a semiconductor diode whose junction capacitance changes with DC bias voltage. This varactor diode is connected in a shunt with the tank circuit of the carrier oscillator.

Armstrong Method (Indirect Method): The working principle of the Armstrong method is to generate a narrow band FM (NBFM) indirectly by utilizing the phase modulation technique and then changing this narrow band FM into a wide band FM.

Demodulation of FM: The FM wave can be demodulated by using the following methods.

Frequency Discriminators Circuit It converts the frequency-modulated (FM) signal into a corresponding amplitude-modulated (AM) signal with the help of frequency-dependent circuits, i.e., the circuits whose output voltage depends upon the input frequency.

Slope Detector: The principle of operation of slope detectors depends upon the slope of the frequency response characteristics of a frequency-selective network. The two main FM detectors, which use detuned resonant circuits come under this category, are as under

• Single-tuned detector circuit or balanced slope detector
• Stagger-tuned detector circuit or balanced slope detector

The following two circuits come under this category.

• Faster-Seeley detector
• Ratio detector

Schematic of an FM demodulator based on FM to AM conversion

Superheterodyne Receiver: In a superheterodyne receiver, the incoming RF signal frequency is combined with the local oscillator signal frequency through a mixer and is converted into a signal of a lower fixed frequency.

The essential idea of the superheterodyne receiver is to change the radio frequency of the signal to a lower, fixed value, where the amplifying circuits can be designed to have great stability and gain, and proper selectivity and fidelity This lower fixed frequency is known as intermediate frequency.

Receiver Characteristics: A receiver has the following characteristics.

• Sensitivity: The sensitivity of a radio receiver may be defined as its ability to amplify weak signals.
• A superheterodyne receiver’s characteristics are discussed as under
• Selectivity: The selectivity of a receiver may be defined as the ability to reject unwanted signals. It also expresses the attenuation that the receiver offers to signal at a frequency adjacent to the one to which it is tuned.
• Fidelity: The facility is the ability of a receiver to reproduce all the modulating frequencies equally. The fidelity basically depends on the frequency response of the RF amplifier.
• Double Spotting: When a receiver picks up the same short wave station at two nearby points on the receiver dial, the double spotting phenomenon takes place. The main cause for double spotting is poor-front end selectivity i.e., inadequate image frequency rejection.

A superheterodyne receiver suffers from a major drawback known as an image frequency problem.

Pulse Modulation

Digital Transmission:

• Digital Transmission is the transmittal of digital signals between two or more points in a communications system. The signals can be binary or any other form of discrete-level digital pulses. Digital pulses can not be propagated through a wireless transmission system such as Earth’s atmosphere or free space.
• Alex H. Reeves developed the first digital transmission system in 1937 at the Paris Laboratories of AT & T for the purpose of carrying digitally encoded analog signals, such as the human voice, over metallic wire cables between telephone offices.

Advantages & Disadvantages of Digital Transmission:

• Advantages
  • Noise immunity
  • Multiplexing(Time domain)
  • Regeneration
  • Simple to evaluate and measure
• Disadvantages
  • Requires more bandwidth
  • Additional encoding (A/D) and decoding (D/A) circuitry

Pulse Modulation:

• Pulse modulation consists essentially of sampling analog information signals and then converting those samples into discrete pulses and transporting the pulses from a source to a destination over a physical transmission medium.
• The four predominant methods of pulse modulation:
  • pulse width modulation (PWM)
  • pulse position modulation (PPM)
  • pulse amplitude modulation (PAM)
  • pulse code modulation (PCM).

Pulse Width Modulation

• PWM is sometimes called pulse duration modulation (PDM) or pulse length modulation (PLM), as the width (an active portion of the duty cycle) of a constant amplitude pulse is varied proportionally to the amplitude of the analog signal at the time the signal is sampled.
• The maximum analog signal amplitude produces the widest pulse, and the minimum analog signal amplitude produces the narrowest pulse. Note, however, that all pulses have the same amplitude.

Pulse Position Modulation:

• With PPM, the position of a constant-width pulse within a prescribed time slot is varied according to the amplitude of the sample of the analog signal.
• The higher the amplitude of the sample, the farther to the right the pulse is positioned within the prescribed time slot. The highest amplitude sample produces a pulse to the far right and the lowest amplitude sample produces a pulse to the far left.

Pulse Amplitude Modulation:

• With PAM, the amplitude of constant width, the constant-position pulse is varied according to the amplitude of the sample of the analog signal.
• The amplitude of a pulse coincides with the amplitude of the analog signal.
• PAM waveforms resemble the original analog signal more than the waveforms for PWM or PPM.

Pulse Code Modulation:

• With PCM, the analog signal is sampled and then converted to a serial n-bit binary code for transmission.
• Each code has the same number of bits and requires the same length of time for transmission

Other Facts:

• PAM is used as an intermediate form of modulation with PSK, QAM, and PCM, although it is seldom used by itself.
• PWM and PPM are used in special-purpose communications systems mainly for the military but are seldom used for commercial digital transmission systems.
• PCM is by far the most prevalent form of pulse modulation and will be discussed in more detail.
• PCM is the preferred method of communication within the public switched telephone network because with PCM it is easy to combine digitized voice and digital data into a single, high-speed digital signal and propagate it over either metallic or optical fiber cables.
• With PCM, the pulses are of fixed length and fixed amplitude.
• PCM is a binary system where a pulse or lack of a pulse within a prescribed time slot represents either a logic 1 or a logic 0 condition.
• PWM, PPM, and PAM are digital but seldom binary, as a pulse does not represent a single binary digit ( a bit).

PCM System Block Diagram

• The bandpass filter limits the frequency of the analog input signal to the standard voice-band frequency range of 300 Hz to 3000 Hz.
• The sample-and-hold circuit periodically samples the analog input signal and converts those samples to a multilevel PAM signal.
• The analog-to-digital converter (ADC) converts the PAM samples to parallel PCM codes, which are converted to serial binary data in the parallel-to-serial converter and then outputted onto the transmission linear serial digital pulses.
• The transmission line repeaters are placed at prescribed distances to regenerate the digital pulses.
• In the receiver, the serial-to-parallel converter converts serial pulses received from the transmission line to parallel PCM codes.
• The digital-to-analog converter (DAC) converts the parallel PCM codes to multilevel PAM signals.
• The hold circuit is basically a low-pass filter that converts the PAM signals back to their original analog form.

The block diagram of a single-channel, simplex (one-way only) PCM system.

PCM Sampling

• The function of a sampling circuit in a PCM transmitter is to periodically sample the continually changing analog input voltage and convert those samples to a series of constant-amplitude pulses that can more easily be converted to binary PCM code.
• A sample-and-hold circuit is a nonlinear device (mixer) with two inputs: the sampling pulse and the analog input signal.
• For the ADC to accurately convert a voltage to a binary code, the voltage must be relatively constant so that the ADC can complete the conversion before the voltage level changes. If not, the ADC would be continually attempting to follow the changes and may never stabilize on any PCM code.
• Essentially, there are two basic techniques used to perform the sampling function
  • natural sampling
  • flat-top sampling

Natural Sampling on the left and Flat top sampling on right

• Natural sampling is when the tops of the sample pulses retain their natural shape during the sample interval, making it difficult for an ADC to convert the sample to a PCM code.
• The most common method used for sampling voice signals in PCM systems is flat-top sampling, which is accomplished in a sample-and-hold circuit.
• The purpose of a sample-and-hold circuit is to periodically sample the continually changing analog input voltage and convert those samples to a series of constant-amplitude PAM voltage levels.

Sampling Rate

• The Nyquist sampling theorem establishes the minimum Nyquist sampling rate (f_s) that can be used for a given PCM system.
• For a sample to be reproduced accurately in a PCM receiver, each cycle of the analog input signal (f_a) must be sampled at least twice.
• Consequently, the minimum sampling rate is equal to twice the highest audio input frequency.
• Mathematically, the minimum Nyquist sampling rate is:

f_s ≥ 2f_a

• If f_s is less than two times f_a an impairment called alias or foldover distortion occurs.

Quantization and the Folded Binary Code:

• Quantization
  • Quantization is the process of converting an infinite number of possibilities to a finite number of conditions.
  • Analog signals contain an infinite number of amplitude possibilities.
  • Converting an analog signal to a PCM code with a limited number of combinations requires quantization.
• Folded Binary Code
  • With quantization, the total voltage range is subdivided into a smaller number of sub-ranges.
  • The PCM code shown in Table is a three-bit sign-magnitude code with eight possible combinations (four positive and four negative).
  • The leftmost bit is the sign bit (1 = + and 0 = -), and the two rightmost bits represent magnitude.
  • This type of code is called a folded binary code because the codes on the bottom half of the table are a mirror image of the codes on the top half, except for the sign bit.

Quantization key points:

• With a folded binary code, each voltage level has one code assigned to it except zero volts, which has two codes, 100 (+0) and 000 (-0).
• The magnitude difference between adjacent steps is called the quantization interval or quantum.
• For the code shown in Table 10-2, the quantization interval is 1 V.
• If the magnitude of the sample exceeds the highest quantization interval, overload distortion (also called peak limiting) occurs.
• Assigning PCM codes to absolute magnitudes is called quantizing.
• The magnitude of a quantum is also called the resolution.
• The resolution is equal to the voltage of the minimum step size, which is equal to the voltage of the least significant bit (V_lsb) of the PCM code.
• The smaller the magnitude of a quantum, the better (smaller) the resolution and the more accurately the quantized signal will resemble the original analog sample.

• For a sample, the voltage at t3 is approximately +2.6 V. The folded PCM code is
• sample voltage/resolution = 2.6/1 = 2.6
• There is no PCM code for +2.6; therefore, the magnitude of the sample is rounded off to the nearest valid code, which is 111, or +3 V.
• The rounding-off process results in a quantization error of 0.4 V.
• The likelihood of a sample voltage being equal to one of the eight quantization levels is remote.
• Therefore, as shown in the figure, each sample voltage is rounded off (quantized) to the closest available level and then converted to its corresponding PCM code.
• The rounded-off error is called the called the quantization error (Qe).
• To determine the PCM code for a particular sample voltage, simply divide the voltage by the resolution, convert the quotient to an n-bit binary code, and then add the sign bits.

Linear input-versus-output transfer curve:

• For the PCM coding scheme shown in the figure, determine the quantized voltage, quantization error (Qe), and PCM code for the analog sample voltage of + 1.07 V.
• To determine the quantized level, simply divide the sample voltage by resolution and then round the answer off to the nearest quantization level:
• +1.07V/1V = 1.07 = 1
• The quantization error is the difference between the original sample voltage and the quantized level, or Qe = 1.07 -1 = 0.07
• From Table, the PCM code for + 1 is 101.

Dynamic Range (DR):

• It determines the number of PCM bits transmitted per sample.
• Dynamic range is the ratio of the largest possible magnitude to the smallest possible magnitude (other than zero) that can be decoded by the digital-to-analog converter in the receiver. Mathematically,
• 
• 
• DR= 20 log (V_max/V_min)
• where DR = dynamic range (unitless)
• V_min = the quantum value
• V_max = the maximum voltage magnitude of the DACs
• n = number of bits in a PCM code (excluding the sign bit)
• For n > 4,

Signal-to-Quantization Noise Efficiency:

• For linear codes, the magnitude change between any two successive codes is the same.
• Also, the magnitude of their quantization error is also same.
• The maximum quantization noise is half the resolution. Therefore, the worst possible signal voltage- to-quantization noise voltage ratio (SQR) occurs when the input signal is at its minimum amplitude (101 or 001). Mathematically, the worst-case voltage SQR is
• SQR = resolution/Q_e  = V_lsb/ V_lsb /2
• 

For input signal minimum amplitude:

• SQR = minimum voltage/quantization noise
•  

For input signal maximum amplitude:

• SQR = maximum voltage/quantization noise
• 

Linear vs. Nonlinear PCM codes:

Companding:

• Companding is the process of compressing and then expanding
• High amplitude analog signals are compressed prior to txn. and then expanded in the receiver
• Higher amplitude analog signals are compressed and Dynamic range is improved
• Early PCM systems used analog companding, where as modern systems use digital companding.

Basic companding process

Analog companding:

PCM system with analog companding

• In the transmitter, the dynamic range of the analog signal is compressed and then converted o a linear PCM code.
• In the receiver, the PCM code is converted to a PAM signal, filtered, and then expanded back to its original dynamic range.
• There are two methods of analog companding currently being used that closely approximate a logarithmic function and are often called log-PCM codes.
• The two methods are
  • μ-law
  • A-law

μ-law companding:

• where V_max = maximum uncompressed analog input amplitude(volts)
• V_in = amplitude of the input signal at a particular instant of time (volts)
• μ = parameter used to define the amount of compression (unitless)
• V_out = compressed output amplitude (volts)

A-law companding:

• A-law is superior to m-law in terms of small-signal quality
• The compression characteristic is given by

• where y = V_out
• x = V_in/V_max

Digital Companding:

• With digital companding, the analog signal is first sampled and converted to a linear PCM code, and then the linear code is digitally compressed.
• In the receiver, the compressed PCM code is expanded and then decoded back to analog.
• The most recent digitally compressed PCM systems use a 12- bit linear PCM code and an 8-bit compressed PCM code.

Digital compression error:

• To calculate the percentage error introduced by digital compression

PCM Line speed:

• Line speed is the data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line. Mathematically,
• Line speed= samples/second X bits/sample

Delta Modulation:

• Delta modulation uses a single-bit PCM code to achieve digital transmission of analog signals.
• With conventional PCM, each code is a binary representation of both the sign and the magnitude of a particular sample. Therefore, multiple-bit codes are required to represent the many values that the sample can be.
• With delta modulation, rather than transmit a coded representation of the sample, only a single bit is transmitted, which simply indicates whether that sample is larger or smaller than the previous sample.
• The algorithm for a delta modulation system is quite simple.
• If the current sample is smaller than the previous sample, a logic 0 is transmitted.
• If the current sample is larger than the previous sample, a logic 1 is transmitted.

Differential DM:

• With Differential Pulse Code Modulation (DPCM), the difference in the amplitude of two successive samples is transmitted rather than the actual sample. Because the range of sample differences is typically less than the range of individual samples, fewer bits are required for DPCM than for conventional PCM.

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