Module 2 Modulation

Communication Process….. Source / Transmitter User / Receiver Channel / Medium

General Model…..

Elaborated Model of Communication system

Information Source: Audio, image, data, etc Information Source: Audio, image, data, etc. This is converted (if conversion required) into digital form by an ADC. Source Encoder: Here the “bits” are encoded or compressed to reduce bandwidth - e.g. Lempel-Ziv, MPEG/JPEG, LPC, Huffman, etc. Channel Encoder: Here additional bits are added to allow for detection and/or correction of errors at the receiver - e.g. linear block codes, cyclic codes, convolution codes and compound codes. Modulation: Translation of the baseband message signal to a higher frequency suitable for transmission over the channel. Multiple Access: more than one user over the same channel - e.g. TDMA, FDMA, CDMA, SDMA, etc. Channel: Twisted copper pair, coaxial cable, optical fibre, wireless, mobile radio, satellite, etc.

What is Modulation…. Its defined as the process by which some characteristics of a carrier is varied in accordance with a modulating (baseband) signal. Baseband signal is directly generated by the source. Carrier is generated specifically depending on our specific requirement.

Need of Modulation…. what would be the scenario if we send the baseband signal itself or instead use an un-modulated carrier…..!!!!!

Conditions……. Antenna size: Multiplexing : For efficient radiation & reception the transmitting and receiving antennas would have to have lengths comparable to a quarter wavelength of the frequency used. e.g.: for transmitting any signal at 1 Megahertz we need a antenna length of 75 meters or an antenna length of 5000 meter for transmitting 15 kHz. Calculate what it would require for 300 Hz….!!! Multiplexing : All sound is concentrated in the range of 20 Hz to 20 kHz, so that all the signal if transmitted together would be hopelessly and inseparably mixed up. In order to separate its necessary to convert them all to a different part of the electromagnetic spectrum.

Example of Multiplexing

Noise: any unwanted introduction of random energy tending to interfere with the proper reception & reproduction of the transmitted signals. At lower frequencies they have greater impact on the signal. (e.g., atmospheric noise becomes less severe at frequencies above about 30MHz because the nature of mechanism generating this noise is such that very little of it is created at VHF and above). Security: its achieved by changing the original signal to another form that helps in hiding the original signal – its also called encryption or cryptography.

Narrow banding : when we transmit a signal having its lowest frequency component at 50 Hz and highest frequency at 1000 Hz the max to min frequency ratio is 200. therefore an antenna suitable for use at one end of frequency would be too short or too long for the other end. But if it is translated to a different frequency range Hz to Hz, then the ratio becomes 1.01. thus the process of frequency translation may be used to make a ‘wideband’ signal to a ‘narrowband’ signal.

Types of Modulation… A sine wave is described by three parameters – amplitude, frequency and phase. Often we use a high frequency sine wave as the carrier. So we can have three types of modulation Amplitude Modulation (AM) Frequency Modulation (FM)& Phase Modulation (PM) FM & PM are closely related. AM radio band : 500 – 1600 kHz FM radio band : 88 – 108 MHz

Method of Frequency Translation… A signal may be translated to a new spectral range if it is multiplied with another signal of different frequency. As explained for a signal having amplitude Am with frequency fm = ωm / 2π.

Now if we have another sinusoidal signal with amplitude Ac and frequency fc = ωc / 2π. Then similarly as we did before, we will have

Now if we multiply both the signals, from the property of trigonometry we apply we find N.B. it comes a signal which has both side bands excluding the carrier component, i.e., DSBSC.

Recovery of baseband signal Two methods : Method 1: multiplication with carrier waveform. Method 2: squaring the received signal and processing.

In the following circuit, the filter selects the spectral component which is then applied to a circuit which divides the frequency by a factor of 2. The output of the divider is then used to demodulate the incoming signal and recover the baseband signal. S(t) Sync signal Squaring Circuit. Filter centred at 2fc Divide by 2

Amplitude Modulation

% modulation

Expression of AM

Waveform of AM

example http://cnyack.homestead.com/files/modulation/modssb.htm

Bandwidth of AM

Bandwidth & Spectrum of AM

Power Relationship in AM In a simplified form, its possible to write an equation for the amplitude of AM wave as ; as m=Vm / Vc the instantaneous voltage of the resulting waveform is given by so it gives the frequency components only in the positive direction. - The first term in the un-modulated carrier - Second (LSB) and third (USB)terms are sidebands.

The total power in the modulated wave will be

Current Calculation Sometimes we can calculate the modulated or un modulated currents easily and then we need to find the modulation index from them. If, Ic be the carrier or un modulated current and It the total current, both in r.m.s. values and R is the resistance in the system, then

Modulation by Several Sine Waves Let, be the simultaneous modulation voltages. Then the total modulating voltage will be the square root of the sum of the squares of the individual voltages, i.e., dividing both the sides by Vc ,we get

Power Efficiency Efficiency in AM is given by the ratio of power required for transmission of information by the total transmitted power. η= (Psb/Pt) when m = modulation index for AM.

Problems: A 400 watt carrier is modulated to a depth of 75%. Calculate the total power. A broadcast radio transmitter radiates 10kW when the modulation percentage is 60. Calculate its carrier power. A certain transmitter radiates 9 kW with carrier un modulated and 10.125 kW when the carrier is sinusoidally modulated. Calculate the modulation index. If another sine wave, corresponding to 40% modulation, is transmitted simultaneously, calculate the total radiated power.

Types of AM: Double Sideband Full Carrier (DSBFC): This is the most widely used type of AM modulation. In fact, all radio channels in the AM band use this type of modulation. Double Sideband Suppressed Carrier (DSBSC): This is the same as the AM modulation above but without the carrier.   Single Sideband (SSB): In this modulation, only half of the signal of the DSBSC is used. Vestigial Sideband (VSB): This is a modification of the SSB to ease the generation and reception of the signal.

Task Do the power relation ship of DSBFC, DSBSC & various kinds of SSB calculations – as discussed in the class…

SSB Conventional AM double-side band communication system, such as those discussed, have two inherent disadvantage: Carrier constitute two-third or more of the total transmitter power. This is a major drawback because the carrier contains no information. Conventional AM systems utilize twice as much bandwidth as needed with single-sideband systems. With double sideband (AM) transmission, the information contained in the upper sideband is identical to the information contained in the lower sideband. Therefore transmitting both sidebands is redundant.

There are several types of sideband communication systems There are several types of sideband communication systems. Some of them conserve bandwidth, some conserve power, and some conserve both. They are: Full-Carrier Single Sideband Suppressed-Carrier Single Sideband Reduce-Carrier Single Sideband Independent Sideband Vestigial Sideband

Full carrier single sideband. Transmit at full power but only one sideband is transmitted. Thus require only half AM DSBFC bandwidth. In DSBFC power of the carrier is 2/3 and signal 1/3. Suppressed carrier single sideband. Carrier is completely suppressed and so signal power is equal to transmission power. One sideband transmitted and so require half bandwidth of DSBFC.

Reduced carrier single sideband. Carrier amplitude reduce to approximately 10% of its un modulated value. Consequently, as much as 96% of total power transmitted is in the sideband. Only one sideband transmitted so only half the bandwidth of the DSBFC needed. Independent sideband also known as twin sideband suppressed carrier. Carrier modulated with two independent intelligence signal and so bandwidth is conserved. Carrier is reduced and so intelligent signal as a higher transmission power.

Vestigial sideband. The carrier and one complete sideband are transmitted, but only part of the second sideband is transmitted. The lower modulating-signal frequencies are transmitted double sideband and the higher modulating-signal frequencies single sideband.

Advantage of Single Side Band Transmission Power Conservation One sideband transmitted Carrier suppressed or reduced Bandwidth Conservation Requires half as much bandwidth as DSBFC Selective Fading With double sideband transmission the two sidebands may travel different paths and therefore experience different impairments this condition is called selective fading. Noise Reduction Less bandwidth and so less thermal noise. Selective fading also reduce.

Disadvantages of SSB Complex Receivers Tuning Difficulties Require complex and expensive receiver Require carrier regeneration and synchronization. Tuning Difficulties Require more complex and precise tuning

Advantages & Disadvantages of AM It is simple to implement it can be demodulated using a circuit consisting of very few components AM receivers are very cheap as no specialized components are needed. Disadvantages: It is not efficient in terms of its power usage It is not efficient in terms of its use of bandwidth, requiring a bandwidth equal to twice that of the highest audio frequency It is prone to high levels of noise because most noise is amplitude based and obviously AM detectors are sensitive to it.

Angle Modulation Angle modulation is the process by which the phase angle of a carrier is varied according to the message signal. Angle modulation is sub-classified into frequency modulation (FM) and phase modulation (PM). In PM, the instantaneous phase deviation of the carrier is proportional to the message signal. In FM, the instantaneous frequency deviation of the carrier is proportional to the message signal

Angle Modulation Why need angle modulation? Disadvantages Applications Better noise reduction Improved system fidelity Disadvantages Low bandwidth efficiency Complex implementations Applications FM radio broadcast TV sound signal Two-way mobile radio Cellular radio Microwave and satellite communications

Basic Concept…

Angle modulation has two forms Frequency modulation (FM): message is represented as the variation of the instantaneous frequency of a carrier Phase modulation (PM): message is represented as the variation of the instantaneous phase of a carrier

PM (phase modulation) signal

FM (frequency modulation) signal (Assume zero initial phase)

Can you say which one is FM, which one is PM? Characteristics of FM signals Zero-crossings are not regular Envelope is constant FM and PM signals are similar Can you say which one is FM, which one is PM?

Example

Relations between FM and PM

An important term: frequency deviation Δf difference between the maximum instantaneous frequency and carrier frequency Definition: Relationship with instantaneous frequency Question: Is bandwidth of s(t) just 2Δf? No, instantaneous frequency is not equivalent to spectrum frequency (with non-zero power)! S(t) has ∞ spectrum frequency (with non-zero power).

Another important term: modulation index β Indicate by how much the modulated variable (instantaneous frequency) varies around its unmodulated level (message frequency) FM modulation index definition:

Example

Narrowband FM

Narrowband FM For this type of FM value of β is small compared to one radian or β << 1. Though ideally an FM signal has a constant envelop and for the case of a sinusoidal modulating signal of frequency fm the angle is also sinusoidal with same frequency. Specifications: Bandwidth is small, easy to analyze, but not useful practically. The narrow band FM requires essentially the same bandwidth (2 fm ) as the AM signal. bandwidth is due to a different effect than AM: nonlinearity

Wide Band FM(WBFM) In this case the value of β is large compared to one radian or β >> 1. As we know the expression for FM is given by : - This gives a function of cos (sin(θ)) which could be solved using the Bessel’s function.

Wideband FM Wideband FM signal Fourier series representation

Properties of Bessel’s function: For all values of n , positive and negative For small values of modulation index β And in general we have:

Bessel Function… Unlike AM, the spectrum of FM contains a carrier component and infinite no of side frequencies located symmetrically on either side of carrier at frequency separations of fm, 2 fm , 3 fm etc. For the special case of β small compared to unity, only the Bessel coefficients J0(β) and J1(β) have significant values, so the FM signal is effectively composed of a carrier and a single pair of side frequencies at . This special case corresponds the case of AM. The J coefficients eventually decrease as the value of n increases but not linearly. As the J coefficients represents the amplitude of a particular side band they also decreases but only past a certain value of n. The modulation index (β) determines how many side frequencies have significant amplitude.

Bessel Function… As β increases, so does the value of a particular J coefficient. Keeping in mind that β is inversely proportional to the modulating frequency, the relative amplitude of the distant side bands increases when the modulating frequency is lowered. We assume here that the deviation or the modulating voltage remains constant. In AM, increased depth of modulation increases the side band power and therefore the total transmitted power. In FM, the total transmitted power always remains constant but with the increased depth of modulation required bandwidth is increased( to transmit the relatively undistorted signals) .

Bessel Function… In FM, unlike in AM, the amplitude of the carrier component does not remain constant. As J is a function of β . Keeping the overall amplitude of the FM wave constant would be very difficult if the amplitude of the carrier were not reduced when the amplitude of the various side bands increased. Its possible for the carrier component to disappear completely and for certain values of modulation index, eigenvalues, this happens.

Side Bands in FM…

Power in FM In the general form the power in FM is given by

Carson’s Rule Carson's bandwidth rule defines the approximate bandwidth requirements for a carrier signal that is frequency modulated by a continuous or broad spectrum of frequencies rather than a single frequency. Carson's rule does not apply well when the modulating signal contains discontinuities, such as a square wave. Carson's bandwidth rule is expressed by the relation BT = 2 (Δf + f m) where BT is the bandwidth requirement, Δf is the peak frequency deviation, and f m is the highest frequency in the modulating signal.

BW for FM It’s the separation between the two frequencies beyond which none of the side frequencies is greater than 1% of the carrier amplitude obtained when the modulation is removed. We can define the transmission BW as where, fm is the modulating frequency and nmax is the largest value of the integer n which satisfies the requirement , the value of nmax varies with β and can be determined from the tabulated values of Bessel Function.

Bessel functions of the 1st kind for varying order n J0(.5) J1(.5) J2(.5)

Comparison of AM & FM AM requires a simple circuit, and is very easy to generate. It is simple to tune, and is used in almost all short wave broadcasting. The area of coverage of AM is greater than FM (longer wavelengths (lower frequencies) are utilized-remember property of HF waves?) However, it is quite inefficient, and is susceptible to static and other forms of electrical noise. The main advantage of FM is its audio quality and immunity to noise. Most forms of static and electrical noise are naturally AM, and an FM receiver will not respond to AM signals. The audio quality of a FM signal increases as the frequency deviation increases (deviation from the center frequency), which is why FM broadcast stations use such large deviation. The main disadvantage of FM is the larger bandwidth it requires

AM transmitter… DSBSC modulator using Diode:

BPF passes frequency ; where is carrier frequency and is the maximum baseband signal frequency. Diode is taken as ideal and carrier signal is stronger than baseband signal. Diode conducts when the combined signal is positive. Since carrier is stronger than baseband signal diode switching is regulated by the carrier only. Switching action of a pulse train is given as -

So, combined signal message will appear across the output when the diode is switched on. So the diode output can be written as

Books 1. Principle of Communications – Taub, Schilling 2. Communication Systems – Simon Haykin 3. Electronic Communication Systems – Kennedy, Davis. IMPORTANT : you should include all the points and topics I discussed in the class and mentioned important, all of them are not included in the slides.