Analog Modulation

Analog Modulation
A
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Submitted By:
Rakesh Kumar Bazad

Analog Modulation
Introduction :
In analog modulation, the modulation is applied continuously in response to the analog information signal. in this used analog signal with carrier frequency.
Common analog modulation techniques are:
• Amplitude modulation (AM)
o Double-sideband modulation (DSB)
 Double-sideband modulation with unsuppressed carrier (DSB-WC) Double-sideband suppressed-carrier transmission (DSB-SC)
 Double-sideband reduced carrier transmission (DSB-RC)
o Single-sideband modulation (SSB, or SSB-AM),
 SSB with carrier (SSB-WC)
 SSB suppressed carrier modulation (SSB-SC)
o Vestigial sideband modulation (VSB, or VSB-AM)
o Quadrature amplitude modulation (QAM)
• Angle modulation
o Frequency modulation (FM)
o Phase modulation (PM)

 
Amplitude modulation (AM)
Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. For example, changes in the signal strength can be used to reflect the sounds to be reproduced by a speaker, or to specify the light intensity of television pixels.
Double-sideband modulation (DSB)
A key consequence of the usual Double-sideband modulation (DSB) is that, usually, the range of frequencies the signal spans (its spectral bandwidth) is doubled. Thus, the RF bandwidth of a signal (measured from the lowest frequency as opposed to 0 Hz) is usually twice its baseband bandwidth. Steps may be taken to reduce this effect, such as single-sideband modulation; the highest frequency of such signals greatly exceeds the baseband bandwidth.
Double-sideband suppressed-carrier transmission (DSB-SC):
Transmission in which frequencies produced by amplitude modulation are symmetrically spaced above and below the carrier frequency and the carrier level is reduced to the lowest practical level, ideally completely suppressed.
In the double-sideband suppressed-carrier transmission (DSB-SC) modulation, unlike AM, the wave carrier is not transmitted; thus, a great percentage of power that is dedicated to it is distributed between the sidebands, which implies an increase of the cover in DSB-SC, compared to AM, for the same power used.
Double-sideband reduced carrier transmission (DSB-RC):
Transmission in which (a) the frequencies produced by amplitude modulation are symmetrically spaced above and below the carrier and (b) the carrier level is reduced for transmission at a fixed level below that which is provided to the modulator.
 
Single-sideband modulation (SSB):
Single-sideband modulation (SSB) is a refinement of amplitude modulation that more efficiently uses electrical power and bandwidth. Amplitude modulation produces a modulated output signal that has twice the bandwidth of the original baseband signal. Single-sideband modulation avoids this bandwidth doubling, and the power wasted on a carrier, at the cost of somewhat increased device complexity. Amateur radio operators began serious experimentation with SSB after World War II. It has become a de facto standard for long-distance voice radio transmissions since then.
Formulation :
SSB and vestigial side band (VSB) can also be regarded mathematically as special cases of analog quadrature amplitude modulation.
Let be the baseband waveform to be transmitted. Its Fourier transform, , is Hermitical symmetrical about the axis, because is real-valued. Double sideband modulation of to a radio transmission frequency, , moves the axis of symmetry to , and the two sides of each axis are called sidebands.
Let represent the Hilbert transform of . Then

is a useful mathematical concept, called an analytic signal. The Fourier transform of equals , for , but it has no negative-frequency components. So it can be modulated to a radio frequency and produce just a single sideband.
The analytic representation of is:

Fourier transform is .
When is modulated (i.e. multiplied) by , all frequency components are shifted by , so there are still no negative-frequency components. Therefore, the complex product is an analytic representation of the single sideband signal:

where is the real-valued, single sideband waveform. Therefore:





The presence of two out-of-phase (quadrature) carrier waves is now evident.
Lower sideband
represents the baseband signal's upper sideband, . It is also possible, and useful, to convey the baseband information using its lower sideband, , which is a mirror image about f=0 Hz. By a general property of the Fourier transform, that symmetry means it is the complex conjugate of :

Note that:

The gain of 2 is a result of defining the analytic signal (one sideband) to have the same total energy as (both sidebands).
As before, the signal is modulated by . The typical is large enough that the translated lower sideband (LSB) has no negative-frequency components. Then the result is another analytic signal, whose real part is the actual transmission.


Note that the sum of the two sideband signals is

which is the classic model of suppressed-carrier double sideband AM.
Demodulation :
The front end of an SSB receiver is similar to that of an AM or FM receiver, consisting of a super heterodyne RF front end that produces a frequency-shifted version of the radio frequency (RF) signal within a standard intermediate frequency (IF) band.
To recover the original signal from the IF SSB signal, the single sideband must be frequency-shifted down to its original range of baseband frequencies, by using a product detector which mixes it with the output of a beat frequency oscillator (BFO). In other words, it is just another stage of heterodyning.(mixing down to base band). For this to work, the BFO frequency must be exactly adjusted. If the BFO frequency is off, the output signal will be frequency-shifted (up or down), making speech sound strange and "Donald Duck"-like, or unintelligible. For audio communications, there is a common agreement about the BFO oscillator shift of 1.7kHz. A voice signal is sensitive to about 50Hz shift, with up to 100Hz still bearable. Some receivers use a carrier recovery system, which attempts to automatically lock on to the exact IF frequency. The carrier recovery doesn't solve the frequency shift. It gives better S/N ratio on the detector output.
As an example, consider an IF SSB signal centered at frequency = 45000 Hz. The baseband frequency it needs to be shifted to is = 2000 Hz. The BFO output waveform is . When the signal is multiplied by (aka 'heterodyned with') the BFO waveform, it shifts the signal to and to , which is known as the beat frequency or image frequency. The objective is to choose an that results in = 2000 Hz.

 
Vestigial sideband (VSB):
A vestigial sideband (in radio communication) is a sideband that has been only partly cut off or suppressed. Television broadcasts (in analog video formats) use this method if the video is transmitted in AM, due to the large bandwidth used. It may also be used in digital transmission, such as the ATSC standardized 8-VSB. The Milgo 4400/48 modem used vestigial sideband and phase-shift keying to provide 4800-bit/s transmission over a 1600 Hz channel.

 
Quadrature amplitude modulation

Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers or quadrature components — hence the name of the scheme. The modulated waves are summed, and the resulting waveform is a combination of both phase-shift keying (PSK) and amplitude-shift keying (ASK), or (in the analog case) of phase modulation (PM) and amplitude modulation. In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used. PSK modulators are often designed using the QAM principle, but are not considered as QAM since the amplitude of the modulated carrier signal is constant. QAM is used extensively as a modulation scheme for digital telecommunication systems. Spectral efficiencies of 6 bits/s/Hz can be achieved with QAM.
Digital QAM :
Like all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, or the carrier wave, (usually a sinusoid) in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (modulated or keyed) to represent the data signal. Amplitude modulating two carriers in quadrature can be equivalently viewed as both amplitude modulating and phase modulating a single carrier.
Phase modulation (analog PM) and phase-shift keying (digital PSK) can be regarded as a special case of QAM, where the magnitude of the modulating signal is a constant, with only the phase varying. This can also be extended to frequency modulation (FM) and frequency-shift keying (FSK), for these can be regarded as a special case of phase modulation.
 
Analog QAM
When transmitting two signals by modulating them with QAM, the transmitted signal will be of the form:
,
where and are the modulating signals and is the carrier frequency.
At the receiver, these two modulating signals can be demodulated using a coherent demodulator. Such a receiver multiplies the received signal separately with both a cosine and sine signal to produce the received estimates of and respectively. Because of the orthogonality property of the carrier signals, it is possible to detect the modulating signals independently.
In the ideal case is demodulated by multiplying the transmitted signal with a cosine signal:

Using standard trigonometric identities, we can write it as:

Low-pass filtering removes the high frequency terms (containing ), leaving only the term. This filtered signal is unaffected by , showing that the in-phase component can be received independently of the quadrature component. Similarly, we may multiply by a sine wave and then low-pass filter to extract .
The phase of the received signal is assumed to be known accurately at the receiver. If the demodulating phase is even a little off, it results in crosstalk between the modulated signals. This issue of carrier synchronization at the receiver must be handled somehow in QAM systems. The coherent demodulator needs to be exactly in phase with the received signal, or otherwise the modulated signals cannot be independently received. For example analog television systems transmit a burst of the transmitting colour subcarrier after each horizontal synchronization pulse for reference.
Analog QAM is used in NTSC and PAL television systems, where the I- and Q-signals carry the components of chroma (colour) information. "Compatible QAM" or C-QUAM is used in AM stereo radio to carry the stereo difference information.

Fourier analysis of QAM
In the frequency domain, QAM has a similar spectral pattern to DSB-SC modulation. Using the properties of the Fourier transform, we find that:

where S(f), MI(f) and MQ(f) are the Fourier transforms (frequency-domain representations) of s(t), I(t) and Q(t), respectively.


Quantized QAM
Like many digital modulation schemes, the constellation diagram is a useful representation. In QAM, the constellation points are usually arranged in a square grid with equal vertical and horizontal spacing, although other configurations are possible (e.g. Cross-QAM). Since in digital telecommunications the data are usually binary, the number of points in the grid is usually a power of 2 (2, 4, 8 ...). Since QAM is usually square, some of these are rare—the most common forms are 16-QAM, 64-QAM and 256-QAM. By moving to a higher-order constellation, it is possible to transmit more bits per symbol. However, if the mean energy of the constellation is to remain the same (by way of making a fair comparison), the points must be closer together and are thus more susceptible to noise and other corruption; this results in a higher bit error rate and so higher-order QAM can deliver more data less reliably than lower-order QAM, for constant mean constellation energy.
If data-rates beyond those offered by 8-PSK are required, it is more usual to move to QAM since it achieves a greater distance between adjacent points in the I-Q plane by distributing the points more evenly. The complicating factor is that the points are no longer all the same amplitude and so the demodulator must now correctly detect both phase and amplitude, rather than just phase.
64-QAM and 256-QAM are often used in digital cable television and cable modem applications. In the United States, 64-QAM and 256-QAM are the mandated modulation schemes for digital cable (see QAM tuner) as standardised by the SCTE in the standard ANSI/SCTE 07 2000. Note that many marketing people will refer to these as QAM-64 and QAM-256. In the UK, 16-QAM and 64-QAM are currently used for digital terrestrial television (Freeview and Top Up TV) and 256-QAM is planned for Freeview-HD.
structure
Transmitter:
The following picture shows the ideal structure of a QAM transmitter, with a carrier frequency and the frequency response of the transmitter's filter :

First the flow of bits to be transmitted is split into two equal parts: this process generates two independent signals to be transmitted. They are encoded separately just like they were in an amplitude-shift keying (ASK) modulator. Then one channel (the one "in phase") is multiplied by a cosine, while the other channel (in "quadrature") is multiplied by a sine. This way there is a phase of 90° between them. They are simply added one to the other and sent through the real channel.
The sent signal can be expressed in the form:

where and are the voltages applied in response to the th symbol to the cosine and sine waves respectively.
Receiver:
The receiver simply performs the inverse process of the transmitter. Its ideal structure is shown in the picture below with the receive filter's frequency response :

Multiplying by a cosine (or a sine) and by a low-pass filter it is possible to extract the component in phase (or in quadrature). Then there is only an ASK demodulator and the two flows of data are merged back.
In practice, there is an unknown phase delay between the transmitter and receiver that must be compensated by synchronization of the receivers local oscillator, i.e. the sine and cosine functions in the above figure. In mobile applications, there will often be an offset in the relative frequency as well, due to the possible presence of a Doppler shift proportional to the relative velocity of the transmitter and receiver. Both the phase and frequency variations introduced by the channel must be compensated by properly tuning the sine and cosine components, which requires a phase reference, and is typically accomplished using a Phase-Locked Loop (PLL).
 
Angle modulation

Angle modulation is a class of analog modulation. These techniques are based on altering the angle of a sinusoidal carrier wave to transmit data, as opposed to varying the amplitude, such as in AM transmission.

ANGLE MODULATION is modulation in which the angle of a sine-wave carrier is varied by a modulating wave. FREQUENCY MODULATION (fm) and PHASE MODULATION (pm) are two types of angle modulation. In frequency modulation the modulating signal causes the carrier frequency to vary. These variations are controlled by both the frequency and the amplitude of the modulating wave.

 
Frequency modulation:

In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency (contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant). In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. Digital data can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying.
If the baseband data signal (the message) to be transmitted is and the sinusoidal carrier is , where fc is the carrier's base frequency and Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:



In this equation, is the instantaneous frequency of the oscillator and is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.
Although it may seem that this limits the frequencies in use to fc ± fΔ, this neglects the distinction between instantaneous frequency and spectral frequency. The frequency spectrum of an actual FM signal has components extending infinitely, although they become negligible beyond a certain point.
Sinusoidal baseband signal
Simply stated, a baseband modulated signal may be approximated by a sinusoidal continuous wave signal with a frequency fm. The integral of such a signal is:

In this case, equation (1) above simplifies to:

where the amplitude of the modulating sinusoid is represented by the peak deviation (see frequency deviation).
The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.
Modulation index
As in other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the carrier frequency:

where is the highest frequency component present in the modulating signal xm(t), and is the peak frequency-deviation—i.e. the maximum deviation of the instantaneous frequency from the carrier frequency. If , the modulation is called narrowband FM, and its bandwidth is approximately .
If , the modulation is called wideband FM and its bandwidth is approximately . While wideband FM uses more bandwidth, it can improve the signal-to-noise ratio significantly; for example, doubling the value of , while keeping constant, results in an eight-fold improvement in the signal-to-noise ratio.[4] (Compare this with Chirp spread spectrum, which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).
With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases but the spacing between spectra remains the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.
Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index >1) than the signal frequency. [5] For example, narrowband FM is used for two way radio systems such as Family Radio Service, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for FM broadcasting, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20-kHz bandwidth.
Carson's rule
A rule of thumb, Carson's rule states that nearly all (~98 percent) of the power of a frequency-modulated signal lies within a bandwidth of:

where , as defined above, is the peak deviation of the instantaneous frequency from the center carrier frequency .
Noise quieting
Noise power decreases as signal power increases; therefore, the SNR increases significantly.
Modulation
FM signals can be generated using either direct or indirect frequency modulation:
• Direct FM modulation can be achieved by directly feeding the message into the input of a VCO.
• For indirect FM modulation, the message signal is integrated to generate a phase-modulated signal. This is used to modulate a crystal-controlled oscillator, and the result is passed through a frequency multiplier to give an FM signal.[6]
Demodulation
Many FM detector circuits exist. A common method for recovering the information signal is through a Foster-Seeley discriminator. A phase-locked loop can be used as an FM demodulator. Slope detection demodulates an FM signal by using a tuned circuit which has its resonant frequency slightly offset from the carrier. As the frequency rises and falls the tuned circuit provides changing amplitude of response, converting FM to AM. AM receivers may detect some FM transmissions by this means, although it does not provide an efficient means of detection for FM broadcasts.
Applications
Magnetic tape storage
FM is also used at intermediate frequencies by analog VCR systems (including VHS) to record both the luminance (black and white) portions of the video signal. Commonly, the chrominance component is recorded as a conventional AM signal, using the higher-frequency FM signal as bias. FM is the only feasible method of recording the luminance ("black and white") component of video to (and retrieving video from) magnetic tape without distortion; video signals have a large range of frequency components – from a few hertz to several megahertz, too wide for equalizers to work with due to electronic noise below −60 dB. FM also keeps the tape at saturation level, acting as a form of noise reduction; a limiter can mask variations in playback output, and the FM capture effect removes print-through and pre-echo. A continuous pilot-tone, if added to the signal – as was done on V2000 and many Hi-band formats – can keep mechanical jitter under control and assist timebase correction.
These FM systems are unusual, in that they have a ratio of carrier to maximum modulation frequency of less than two; contrast this with FM audio broadcasting, where the ratio is around 10,000. Consider, for example, a 6-MHz carrier modulated at a 3.5-MHz rate; by Bessel analysis, the first sidebands are on 9.5 and 2.5 MHz and the second sidebands are on 13 MHz and −1 MHz. The result is a reversed-phase sideband on +1 MHz; on demodulation, this results in unwanted output at 6−1 = 5 MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.[7]
Sound
FM is also used at audio frequencies to synthesize sound. This technique, known as FM synthesis, was popularized by early digital synthesizers and became a standard feature in several generations of personal computer sound cards.
Radio
Edwin Howard Armstrong (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio.[8] He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922.[9] Armstrong presented his paper, "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation", (which first described FM radio) before the New York section of the Institute of Radio Engineers on November 6, 1935. The paper was published in 1936.[10]
As the name implies, wideband FM (WFM) requires a wider signal bandwidth than amplitude modulation by an equivalent modulating signal; this also makes the signal more robust against noise and interference. Frequency modulation is also more robust against signal-amplitude-fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio transmission, hence the term "FM radio" (although for many years the BBC called it "VHF radio" because commercial FM broadcasting uses part of the VHF band—the FM broadcast band). FM receivers employ a special detector for FM signals and exhibit a phenomenon known as the capture effect, in which the tuner "captures" the stronger of two stations on the same frequency while rejecting the other (compare this with a similar situation on an AM receiver, where both stations can be heard simultaneously). However, frequency drift or a lack of selectivity may cause one station to be overtaken by another on an adjacent channel. Frequency drift was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.


Phase modulation

Phase modulation (PM) is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.
Unlike its more popular counterpart, frequency modulation (FM), PM is not very widely used. This is because it tends to require more complex receiving hardware and there can be ambiguity problems in determining whether, for example, the signal has changed phase by +180° or -180°.


PM changes the phase angle of the complex envelope in direct proportion to the message signal.
Suppose that the signal to be sent (called the modulating or message signal) is and the carrier onto which the signal is to be modulated is

Annotated:
carrier(time) = (carrier amplitude)*sin(carrier frequency*time + phase shift)
This makes the modulated signal

This shows how modulates the phase - the greater m(t) is at a point in time, the greater the phase shift of the modulated signal at that point. It can also be viewed as a change of the frequency of the carrier signal, and phase modulation can thus be considered a special case of FM in which the carrier frequency modulation is given by the time derivative of the phase modulation.
The mathematics of the spectral behaviour reveals that there are two regions of particular interest:
• For small amplitude signals, PM is similar to amplitude modulation (AM) and exhibits its unfortunate doubling of baseband bandwidth and poor efficiency.
• For a single large sinusoidal signal, PM is similar to FM, and its bandwidth is approximately
,
where and is the modulation index defined below. This is also known as Carson's Rule for PM.
Modulation index
As with other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase of the carrier signal:
,
where is the peak phase deviation. Compare to the modulation index for frequency modulation.
 
Reference
1. www.google.com

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