## Modulation and Demodulation of Signals

Information to be transmitted in a radio system, such as voice or music, is first transformed to a low frequency, for example, an audio frequency, electric signal. This baseband signal cannot be directly transmitted through a radio channel, or at least that would be very inefficient. The signal is first fed into a modulator, which modulates some property (amplitude, frequency, phase) of a high-frequency carrier according to the baseband signal. The high-frequency signal obtained is then transmitted by a transmitting antenna. A receiving antenna receives the high-frequency signal and feeds it into a receiver. In the receiver the signal is often downconverted to an intermediate frequency and then demodulated, that is, the original baseband signal is detected; for example, in the case of voice radio, the original voice signal is recovered. In other words, with a modulator the information is attached into a carrier, and with a demodulator it is detached.

There are a number of different modulation schemes, which can be divided into analog and digital methods. Modulation is important not only in communication (radio broadcasting, radio links, mobile phone systems) but also in radar, radionavigation, and so on. Modulation is treated in many communication textbooks, for example, [8—10].

11.3.1 Analog Modulation

A sinusoidal waveform can be presented as

A(t) = A0 cos (m0 t + ^o) = A0 cos (2^/01 + (11.27)

Information can be attached into this carrier by modulating one of its basic properties according to the baseband signal. Modulation methods are:

1. Amplitude modulation (AM): Information is attached to the carrier amplitude.

2. Frequency modulation (FM): Information is attached to the carrier frequency.

3. Phase modulation (PM): Information is attached to the carrier phase.

AM is in principle the simplest method, but it has high requirements, especially for the linearity of the transmitter. It is used in radio broadcasting in the LF, MF, and HF bands, and in TV broadcasting. FM is used, for example, in FM radio.

Let us consider a signal that is amplitude modulated by a sinusoidal signal at frequency fm :

Thus, the amplitude varies between values of Ao(1 — m ) and Ao(1 + m). Factor m is the modulation index or modulation depth. The signal envelope follows the modulating signal as shown in Figure 11.9(a), if m < 1. The carrier frequency should be much higher than the modulating frequency. Equation (11.28) can be presented as

mm cos (Oo t + — cos (Mo + Mm ) t + — cos (Mo — Mm ) t

The graphical interpretation of this equation is presented in Figure 11.9(b). A constant voltage phasor A0 corresponds to the carrier frequency. Two voltage phasors with an amplitude of (m/2) A 0 rotate in opposite

Figure 11.9 Amplitude-modulated signal: (a) in time domain; (b) phasor presentation; and (c) frequency spectrum.

directions at an angular frequency of œm. The resultant of these three voltage phasors gives the total voltage. The spectrum contains the components at frequencies f), fo + fm, and fo — fm, as shown in Figure 11.9(c).

If the modulating baseband signal is more complicated, it can be considered as consisting of several sinusoidal components, which have a given amplitude and phase. The modulating signal has a given spectrum and each spectral component modulates the carrier independently.

Figure 11.10 presents the spectrum of an AM signal when the modulating signal is distributed over a given frequency range. The AM is using lavishly both the power and frequency spectrum, because also the carrier not containing information is transmitted and one sideband is only a mirror image of the other. Transmitter power can be saved using DSB modulation, in which the carrier is suppressed, that is, it is not transmitted. This modulation scheme is also called double-sideband suppressed carrier (DSBSC) modulation. The frequency spectrum is saved by removing the other sideband, which leads to SSB modulation.

If the modulating signal contains frequency components near the zero frequency, use ofSSB modulation becomes complicated, because it is difficult to separate the sidebands. Vestigial sideband (VSB) modulation is a compromise between SSB and DSB modulations. In VSB, one sideband is trans-

Modulating signal

Figure 11.10 Spectra of basic AM, DSB, and SSB modulation.

mitted nearly in full, but only a small part of the other sideband is transmitted, as illustrated in Figure 11.11. VSB can be realized more easily than SSB by filtering from DSB.

### 11.3.1.2 Amplitude Modulators and Demodulators

A mixer can be used as an amplitude modulator. The modulating waveform is fed into the IF port and the carrier into the LO port, and the modulated signal is obtained from the RF (signal) port, as in Figure 11.12. In a double-balanced mixer there is a good isolation between the LO and RF ports. In that case the carrier is suppressed, and a DSB signal is obtained. The SSB modulation can be realized using the circuit shown in Figure 11.13.

Figure 11.11 VSB modulation.

Figure 11.11 VSB modulation.

Modulating IF RF ^ Modulated signal fm V^S' signal f0±fm i i

Carrier fD

Figure 11.12 A mixer as an amplitude modulator.

JF^VN RF

90°

« Jt

180°

hybrid

Figure 11.13 An SSB modulator.

An AM signal can be demodulated by an envelope detector. The output of an envelope detector follows the envelope of the input signal, as shown in Figure 11.14. During one half forward cycle the capacitance C is charged rapidly to the peak voltage value of the signal. The time constant Rg C must be much shorter than the cycle length 1/f 0. In the reverse direction the capacitor C discharges slowly, but it has to be able to follow the modulating signal. This leads to a condition 1/fo << Rl C << 1/B, where B is the bandwidth of the modulating signal.

In order to demodulate a DSB signal, the carrier must be generated in the receiver. Both the frequency and phase must be correct. The DSB demodulator shown in Figure 11.15 is called the Costas loop, and it resembles the PLL. The input signal is mixed with orthogonal LO signals from a VCO. The difference signals selected by the lowpass filters are proportional to m (t) cosf and m (t) sin (, where (f is the phase error of the LO. The third mixer produces a signal that adjusts the VCO phase and frequency until the output signal of the upper branch is at maximum and that of the lower branch vanishes. Also, demodulation of an SSB signal requires generation

A0cos(2ttf0t)m(t)

cos(Z7rfDt+0)

Demodulated

sin(2jrfot+0

sin(2jrfot+0

Phase detector

Figure 11.15 A DSB demodulator.

of the carrier. In order to aid this process, a pilot carrier may be transmitted together with the sideband.

QAM is a modulation method that combines two orthogonal DSB signals into the same band. In the transmitter shown in Figure 11.16(a), the phase difference between the two carriers is 90°. In the receiver there is also a 90° phase difference between the two LO signals, and the original baseband signals can be separated. QAM is used in TV broadcasting.

The amplitude ofa frequency-modulated signal is constant, and the instantaneous frequency varies according to the modulating signal. If the modulating signal is sinusoidal, the instantaneous frequency is f (t ) =

Figure 11.16 QAM: (a) transmitter and (b) receiver.

r<S>

\

~m,(t)

>

cos (27rf0t)

Figure 11.16 QAM: (a) transmitter and (b) receiver.

where Af is the maximum frequency deviation. The equation for an FM signal waveform is

The spectrum of the FM signal contains, besides the carrier, an infinite number of sidebands with a separation of fm. The required bandwidth is wider than that in AM, but tolerance to noise and interference is better. The amplitudes of the carrier and sidebands depend on the modulation index m = Af/fm. The amplitude Asp of a sideband p relative to the amplitude A 0 of an unmodulated carrier is obtained from

where Jp is the p th order Bessel function of the first kind. Figure 11.17 presents Bessel functions and Figure 11.18 shows an FM power spectrum when the modulation index is m = 5.52. In this case the normalized amplitude J0 of the carrier component is small.

If m is small—less than unity—there is in the spectrum only one important sideband on both sides of the carrier, and A^/A0 ~ m/2. The

Figure 11.17 Bessel functions (first kind).

Figure 11.18 Spectrum of a frequency-modulated signal when the modulation index is m = 5.52.

spectrum looks like the AM spectrum, but the phases of the sidebands are different.

In theory the FM signal requires an infinite bandwidth. If we allow a given maximum distortion, we can limit the bandwidth. According to Carson's rule the required bandwidth is [10]

B « 2Af + 2fm = 2Af (1 + 1/m) = 2fm (1 + m) (11.33) 11.3.1.5 Frequency Modulators and Demodulators

FM can be realized with a VCO. The output frequency of some oscillators can be controlled directly by changing the operation point of the nonlinear element. In other VCOs the frequency is controlled by voltage tuning the resonance frequency of the high-Q embedding circuit, which contains a voltage-dependent element such as a varactor.

Figure 11.19 shows a Hartley oscillator. The input network contains a varactor. The resonance frequency of the input resonator is f=

Let us assume that C changes sinusoidally an amount of AC around C0 and that the ratio AC /C0 is small. Then

Figure 11.19 A Hartley oscillator.

2^(L1 + L2) C0 V1 + (AC/C0) cos 2wfmt " f0 (1 _ cos = f) + Af cos 2 7rfm t which shows that we have a frequency modulator.

A frequency demodulator produces a voltage, the instantaneous value of which is proportional to the instantaneous frequency of the signal. Networks capable of doing so include, for example, a frequency discriminator, such as the one shown in Figure 11.20, and a PLL, shown in Figure 11.21. In the frequency discriminator there are two resonance circuits, each followed by an envelope detector. One resonance circuit is tuned to a frequency above the carrier frequency, the other one below. One detector produces a positive output voltage, the other one a negative output voltage. The sum of these voltages is linear in the vicinity of the carrier frequency, if the difference between the resonance frequencies has a proper value. Usually there is an amplitude limiter before the frequency discriminator to eliminate the effects of signal amplitude variations. In the PLL, the control voltage of the VCO contains the demodulated signal, if the frequency depends linearly on the control voltage.

PM is closely linked to FM because frequency f(t) is obtained from the derivative of phase (f)(t) = co(t) t + tp(t) and accordingly the phase is obtained as an integral of the frequency:

Normalized output voltage 1.0

Normalized output voltage 1.0

Filter tuned below f,

Figure 11.20 FM demodulator based on a frequency discriminator and its normalized output voltage.

Filter tuned below f,

Figure 11.20 FM demodulator based on a frequency discriminator and its normalized output voltage.

FM signal

Loop filter

Demodulated signal

Figure 11.21 A PLL as an FM demodulator.

A PM signal can be presented as

= A0 [cos (2 wfo t) cos if(t) — sin (2 wf) t) sin if/(t)]

If ) is small, cos if/(t) ~ 1 and sin if(t) ~ if/(t), and (11.38) is simplified into form

A (t) - A0 [cos (2wf) t) - sin (2wf) t) ^(t)] (11.39)

When the modulating signal is sinusoidal if(t) = 2wM cos (2 wfmt), we obtain

A (t) - A 0 {cos (2 wf 01) - wMsin [2w( f 0 + fm) t] - wMsin [2w( f 0 - fm) t]}

Equation (11.40) shows that the spectrum of a PM signal contains frequencies f0 , f0 + fm , and f0 - fm , as an AM signal does, but now the phases of these components are different. Figure 11.22 represents a phasor diagram of the PM signal.

### 11.3.2 Digital Modulation

An analog signal, such as a voice signal in the form of an audio-frequency electric signal, can be transformed into a digital form by sampling it frequently

Figure 11.22 Phasor presentation of a PM signal.

enough. A digital signal may be binary, that is, containing only symbols 0 and 1, or m-ary, containing m different levels or states. The digital modulation has many advantages over the analog modulation; the total use of spectrum is effective, immunity to interference is good, frequency reuse is effective, TDM is easily realized, and it allows the use of encryption for privacy.

The basic digital modulation methods are amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase-shift keying (PSK). Figure 11.23 shows the waveforms of binary ASK, FSK, and PSK signals when a symbol chain 01101001 is transmitted. In ASK, the maximum amplitude corresponds to symbol 1 and a zero amplitude corresponds to symbol 0. In FSK, the symbols are presented by signals with frequencies f1 and f2 . In PSK, signals corresponding to symbols 1 and 0 have a phase difference of 180°. While analog FM and PM signals closely resemble each other, FSK and PSK signals are easily distinguishable.

In digital modulation, rapid waveform changes occur and thus the power spectrum of a digitally modulated signal is broad. Figure 11.24 shows the spectra of a binary baseband signal consisting of rectangular pulses and a PSK signal modulated with it. The envelopes of the spectra have the shape of a sinc function. The width between the first nulls of the PSK spectrum is twice the bit rate 1/Tb, where Tb is the symbol period. In practice, the signal is filtered and the spectrum is narrower.

0 -1

### Responses

• mirrin bruce
What is modulation in radio engg?
3 years ago
• Roger
Why voice signals are modulated and demodulated?
2 years ago