There are a number of methods of modulation where the amplitude of the carrier is varied by the information signal but the most commonly used is double sideband AM (DSB). Figure 8.2 shows a radio frequency carrier modulated by a low frequency signal.
The amount or depth of modulation is expressed as percentage ratio, m%, of the maximum to minimum amplitude:Mod. depth = m%
max. amplitude− min. amplitude × 100%= max. amplitude+ min. amplitude
When the modulation is increased to the point where the minimum amplitude falls to zero, 100% modulation occurs. Any further increase in modulation produces spurious, out-of-band frequencies (AM splash), a source of interference for other radio users. For this reason, the depth of amplitude modulation is usually limited to 70%.
Input or audioEmAn alternative expression for modulation depth is in terms of a modulation index from 0 to 1. The peak carrier voltage in Figure 8.2 is Ec and the peak modulation voltage, Em. The modulation index, m,is: Emm = Ec
Amplitude modulation produces a band of frequencies above and below the carrier frequency – the upper and lower sidebands. The width of each sideband is equal to the highest modulating frequency so the bandwidth of an AM wave is 2× the highest modulating frequency. To conserve spectrum, the range of modulating frequencies
Input or
audio
frequencies Lowerfc Upper sideband sideband
300 Hz 3 kHz
Output options
Double sideband
is restricted. For example, radio communication quality speech is limited to 300 Hz to 3000 Hz. The bandwidth occupied by a double sideband, amplitude modulated carrier for this service is 6 KHz (Figure 8.3).
Ecarr2+ Elsb2+ Eusb2Pt = R R R
where all values are RMS and R is the resistance in which the power is dissipated. From the peak voltages shown in Figure 8.2 the power in the unmodulated carrier is:
Ec/√2 2 Ec2Pc = R = 2RThe power in the sidebands
P
lsb
=
P
usb
=
mEc/22 m2Ec2 √2 ÷R =8R
The ratio of the total power in the wave to the carrier power is:
Pt = 1+ m2 Pc 2
As m cannot exceed 1, the maximum RMS power in the wave is Pt = 1.5Pc; but if m reaches 1, the peak sum of Ec and Em is 2Ec and so the instantaneous peak power is 2Pc. Circuitry must be capable of handling this power level without distortion.
Double sideband amplitude modulation wastes power and spectrum. Two-thirds of the power is in the carrier which conveys no information and one sideband is discarded in the receiver. Also, the modulation must be accomplished either in the final power amplifier of the transmitter necessitating a high power modulator, or in an earlier, low power stage when all subsequent amplifiers must operate in a linear, but inefficient, mode.
In an amplitude modulated wave the carrier conveys no information yet contains 2/3 of the transmitted power. It is possible to remove the carrier by using a balanced modulator (Figure 8.4), and improve the power efficiency by this amount.
ModulatingC1DSBSCsignal outputinput C2In a balanced modulator, the modulating voltage is fed in push–pull to a pair of matched diodes or amplifiers while the carrier is fed to them in parallel. The carrier components in the output cancel leaving the two sidebands. The result is a double sideband suppressed-carrier (DSBSC) wave, which is not sinusoidal, formed by the sum of the two sidebands. The carrier must be re-introduced in the receiver and its accuracy in both frequency and phase is critical.
• removal of the carrier saves 2/3 of the total power
• removal of one sideband saves 50% of the remaining power
• an SSBSC transmitter only produces power when modulation is present
• the occupied bandwidth is halved; a spectrum saving
• the received signal-to-noise ratio is improved by 9 dB for a 100% modulated carrier. Halving the bandwidth accounts for 3 dB, the remainder from the improved sideband power to total power ratio. The S/N ratio improves further with lower modulation levels
• reduced susceptibility to selective fading and consequent distortion.
Two methods of generating a single sideband wave are in general use. One filters out the unwanted sideband after removal of the carrier by a balanced modulator. The other is a phase shift method (Figure 8.5). Here, the modulating signal is fed to two balanced modulators with a 90æ phase difference. The output from both modulators contains only the sidebands but, while both upper sidebands lead the input carrier voltage by 90æ, one of the lower sidebands leads it by 90æ and the other lags it by 90æ. When applied to the adder, the lower sidebands cancel each other while the upper sidebands add.
Balanced modulatorAdder 90°C shift
Carrier
input
A single sideband AM wave modulated by a sinusoid consists of a constant amplitude signal whose frequency varies with the frequency of the modulating wave. Note that this is not the same as FM: the frequency in SSB does not swing to either side of the carrier. It is higher than the carrier frequency if the upper sideband is transmitted, and lower if the lower sideband is selected. The single sideband waveform is sinusoidal and, although the frequency of the reintroduced carrier must be highly accurate (±2Hz), the phase is unimportant making a single sideband receiver less complex than one for DSBSC.
On some systems a pilot carrier is transmitted and the transmitter output power is then specified in terms of peak envelope power (pep), the power contained in a wave of amplitude equal to the pilot carrier and transmitted sideband power. Where no pilot carrier is transmitted, the power is specified as peak sideband power (psp).
Both frequency and phase modulation (both may be referred to as angle modulation) effectively vary the frequency of the carrier rather than its amplitude. Frequency modulation varies the carrier frequency directly but its amplitude remains constant regardless of the modulating voltage. Angle modulation is employed at VHF and above for both communications and broadcasting services.
When frequency modulated, a carrier frequency either increases or decreases when the modulation voltage is positive and varies in the opposite sense when the modulating voltage is negative (Figure 8.6). The amount of modulation, i.e. the ‘deviation’ of the carrier from its nominal frequency, is proportional to the amplitude, and not the frequency, of the modulating voltage. The modulation index, M,is defined as the deviation divided by the modulating frequency:
M =
fd or ωd fm ωm
where
fd = deviation in hertz
fm = modulating frequency in hertz
frequency frequency Varied
amplitude
Modulated carrier
Fixed
amplitude
ωd = 2πfd = deviation in radians
ωm = 2πfm = modulating frequency in radians The ‘deviation ratio’, D, is given by:
fd(max)D = fm(max)
The peak deviation is the maximum amount of modulation occurring (equivalent to 100% amplitude modulation). With FM, this is limited only by the need to conserve spectrum; there is no technical limit where distortion occurs, as with 100% AM. The maximum permitted deviation for a service is determined by regulation.
The bandwidth of a frequency modulated signal is made up of the carrier and a series of sidebands, sometimes referred to as sidecurrents, spaced apart from each other at the modulating frequency. The number of sidebands is proportional to the modulation index and their amplitudes decrease with spacing from the carrier. It is generally considered satisfactory to transmit those sidebands M + 1 in number, with amplitudes greater than 10% of that of the carrier for that modulation index (Figure 8.7). The sidebands occur on both sides of the carrier and:
1st order sidebands = fc ±fm
2nd order sidebands = fc ± 2fm, etc.
When the modulation index approaches 6 a good approximation of the bandwidth (δf) required for an FM transmission is 2(fd+fm)Hz. For example, speech 300–3000 Hz, max deviation 15 kHz (relevant to a VHF, 50 kHz channel spacing system):
δf = 2(fd +fm) = 2(15+ 3)kHz = 36 kHz M = 15/3 = 5The bandwidth is also given by δf = fm× highest needed sideband× 2. From Bessel functions (Figure 8.7), a modulation index of 5 requires the 6th order sideband to be transmitted (M + 1). Therefore:
δf = fm× 6× 2 = 3× 6× 2 = 36 kHzFor specific values of M the carrier of an FM wave disappears. The successive disappearances and the modulation index are given in Table 8.2.
1.0
0.9
0.8 Carrier
6th order8th order 9th order 0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
Table 8.2 Successive disappearances and modulation index
12.40
25.52
38.65
4 11.79
5 14.93
6 18.07
n(n > 6) 18.07+π(n− 6)
Systems where the modulation index exceeds π/2 are considered to be wide band FM (WBFM), those with a modulation index lower than π/2, narrow band FM (NBFM). The bandwidth of an NBFM signal is 2fm(max).
Pressure on spectrum necessitates narrower channel spacings for communications and, at VHF, 12.5 kHz is normal with±2.5 kHz as the maximum permitted deviation. Lower standards of performance with a restricted modulation index and a highest modulating frequency of 3 kHz have had to be accepted.
For transmitters used on 12.5 kHz channel spaced systems the highest modulating frequency is, in practical terms, 2700 Hz because the specification requires the frequency response to fall above 2.55 kHz.
The modulation index on such systems, assuming a highest modulating frequency of 3 kHz, is 2.5/3 = 0.8333 (<π/2and so system is NBFM) and the amplitude of the 2nd order sideband is <10% of carrier amplitude (Figure 8.7), so the bandwidth = 2fm(max) = 6 kHz.
The end result of phase modulation is frequency modulation, but the method of achieving it and the definition of the modulation index is different. Phase modulation is used in VHF and UHF transmitters where the carrier frequency is generated directly by a crystal oscillator. The frequency of a crystal oscillator can be varied by only a few radians but if the oscillator frequency is multiplied to produce the final carrier frequency the phase variation is also multiplied to produce a frequency deviation.
In frequency modulation deviation is proportional to the modulating voltage, but in phase modulation the frequency deviation is proportional to both the modulating voltage and frequency.
The phase modulation, φd radians, equals the modulation index so, for phase modulation, the modulation index is φd = ωd/ωm.
Phase modulation has, therefore, a frequency response for the deviation that rises at 6 dB per octave of the modulating frequency. The flat frequency response of FM can be produced on a phase modulated transmitter by installing a filter with a response falling at 6 dB per octave in the audio amplifier, and the rising response of PM can be produced in an FM transmitter with a rising response filter.
Phase modulation, and FM modified to give a rising frequency response (pre-emphasis), offer an improved signal-to-noise ratio in the receiver. The+6 dB per octave response produced in the transmitter is restored to a flat response in the receiver by a −6 dB per octave filter in the audio circuitry which reduces both the enhanced levels of the higher speech frequencies and the high frequency noise (de-emphasis).
Table 8.3 Advantages and disadvantages of AM and FM
Narrower bandwidth than Audio strength falls with wide-band FM decreasing RF signal strength Inefficient power usage Limited dynamic range Transmitter output power not
easily adjusted FM Less susceptible to noise Wider bandwidthConstant audio level to almost the
end of radio range
reception of the left and right audio signals, to produce a stereo image. However, the introduction of stereo had to be achieved while still catering for large numbers of listeners who wanted to continue receiving in mono. The introduction of stereo FM radio had to go unnoticed by anyone using old mono radios. Without this condition, a simpler method could have been chosen.
The standard FM stereo system used by broadcasters around the world is illustrated in the block diagram of Figure 8.8. It uses frequency division multiplexing (FDM) to combine the two signals of the left and right channels. The signals are filtered to limit the bandwidth to 15 kHz. The left (L) and right (R) signals are then added to produce a sum signal and subtracted one from the other to produce a difference signal.
Stereo FM system diagramStereo FM spectrum
19 kHz 38 kHz pilot
The sum signal provides a monophonic signal, which provides a baseband signal for the frequency modulator. This was the technique used in mono FM and thus was the obvious choice for stereo FM, to allow backward compatibility. An mono FM radio can receive this signal and recover the combined L and R channels, thereby satisfying the requirement for providing unchanged service to mono radios.
The difference signal is used to amplitude modulate a 38 kHz sinewave. By utilizing a balanced mixer, double sideband suppressed carrier (DSBSC) is generated. However, the modulation method must take into account the ease of demodulation. In particular, demodulating a DSBSC signal can be difficult. Both frequency and phase of the carrier are needed to perform faithful demodulation.
In the stereo system the DSBSC demodulation problem is dealt with by including a 19 kHz pilot tone in the broadcast. This tone is generated by a divide-by-two frequency converter circuit, which takes the 38 kHz carrier and produces the 19 kHz pilot tone. The 19 kHz pilot tone falls midway in the spectral region between the mono sum signal (up to 15 kHz) and below the DSBSC difference signal information. The DSBSC signal extends from 23 kHz to 53 kHz, since the input modulating signals are band limited to 15 kHz. The DSBSC output is added to the baseband (L and R sum) signal and the 19 kHz pilot tone before being sent to the FM modulator.
A mono FM receiver ignores the stereo information by using a filter after its FM demodulator to block everything above 15 kHz. It passes the combined L and R channel signal, which is monophonic.
A stereo receiver has an additional circuit after the FM demodulator to detect and demodulate the DSBSC signal. The stereo receiver detects a 19 kHz pilot tone and uses this to generate a 38 kHz signal. This is then used to demodulate the DSBSC signal that carries the L and R channel difference information. The stereo receiver then has both the sum and difference signals, which is all that is needed to recreate the separate left and right signals. Separation is achieved by adding and subtracting sum and difference signals.
The noise power spectral density of a demodulated FM signal tends to increase with the square of the modulation frequency. This is why pre-emphasis is used to boost the high frequency baseband signals for maintaining the signal-to-noise ratio of the transmitted signal. However, this means that there will be more noise in the 23 kHz to 53 kHz band used for the difference signal than for the 0–15 kHz band used for the sum signal. Consequently a significantly higher input signal level is required to receive a stereo transmission compared with a mono signal for the same output signal-to-noise ratio. Thus stereo reception requires far higher radio signal levels than for mono reception and is more susceptible to interference from other radio sources.