Application of Amplitude Modulation

The main hardware component of an amplitude modulator is an analog multiplier. It is commercially available in the monolithic IC form. Alternatively, it can be assembled using IC op-amps and various discrete circuit elements. Schematic representation of an amplitude modulator is shown in Figure 2.31.

In practice, to achieve satisfactory modulation, other components such as signal preamplifiers and fil-ters would be needed.

There are many applications of AM. In some applications, modulation is performed intentionally. In others, modulation occurs naturally as a consequence of the physical process, and the resulting signal is used to meet a practical objective. Typical applications of AM include the following:

1. Conditioning of general signals (including dc, transient, and low frequency) by exploiting the advantages of ac signal-conditioning hardware

2. Making low-frequency signals immune to low-frequency noise

(a) Time t

|X( f )|

–f_b 0 f_b

x(t) M

Frequency f

(b)

–f_c– f_b –f_c–f_c+ f_b f_c– f_b f_c f_c+ f_b

t f

0

x_a(t) = x(t)a_ccos 2πf_ct |X_a( f )|

Ma_c 2

(c)

(d)

x(t) = a cos 2πf_ot

x_a(t) = aa_c cos2πf_ot cos2πf_ct

–f_o 0 f_o f

a2

|X( f )|

t

aa_c 4

t –fc– fo –fc–fc+ fo0 fc– fo fc fc+ fo f

|X_a( f )|

FIGURE 2.30 Illustration of the modulation theorem: (a) a transient data signal and its Fourier spectrum mag-nitude, (b) Amplitude-modulated signal and its Fourier spectrum magmag-nitude, (c) a sinusoidal data signal, and (d) amplitude modulation by a sinusoidal signal.

3. Transmission of general signals (dc, low frequency, etc.) by exploiting the advantages of ac signal transmission

4. Transmission of low-level signals under noisy conditions

5. Transmission of several signals simultaneously through the same medium (e.g., same telephone line, same transmission antenna, etc.)

6. Fault detection and diagnosis of rotating machinery

The role of AM in many of these applications should be obvious if one understands the frequency-shifting property of AM. Several other types of applications are also feasible due to the fact that power of the carrier signal can be increased somewhat arbitrarily, irrespective of the power level of the data (modulating) signal. Let us discuss, one by one, the listed six categories of applications.

Signal conditioning: AC signal-conditioning devices such as ac amplifiers are known to be more stable than their dc counterparts. In particular, drift (instability) problems are not as severe and nonlin-earity effects are lower in ac signal-conditioning devices. Hence, instead of conditioning a dc signal using dc hardware, we can first use the signal to modulate a high-frequency carrier signal. Then, the resulting high-frequency modulated signal (ac) may be conditioned more effectively using ac hardware.

Noise immunity: The frequency-shifting property of AM can be exploited in making low-frequency signals immune to low-frequency noise. Note from Figure 2.30 that using AM, the low-frequency spectrum of the modulating signal can be shifted out into a very high frequency region, by choos-ing a carrier frequency fc that is sufficiently large. Then, any low-frequency noise (within the band 0 to fc − fb) would not distort the spectrum of the modulated signal. Hence, this noise could be removed by a high-pass filter (with cutoff at fc − fb) so that it would not affect the data. Finally, the original data signal can be recovered using demodulation. Since the frequency of a noise com-ponent can very well be within the bandwidth fb of the data signal, if AM was not employed, the noise would directly distort the data signal.

AC signal transmission: Transmission of ac signals is more efficient than that of dc signals. Advantages of ac transmission include lower energy dissipation problems. As a result, a modulated signal can be transmitted over long distances more effectively than could the original data signal alone.

Furthermore, the transmission of low-frequency (large wave-length) signals requires large anten-nas. Hence, when AM is employed (with an associated reduction in signal wave length), the size of broadcast antenna can be effectively reduced.

Weak signal transmission: Transmission of weak signals over long distances is not desirable because further signal weakening and corruption by noise could produce disastrous results. Even if the power of the data signal is low, by increasing the power of the carrier signal to a sufficiently high level, the strength of the resulting modulated signal can be elevated to an adequate level for long-distance transmission.

Modulated signal Carrier

signal Modulating

input

(data) Multiplier

Out

FIGURE 2.31 Representation of an amplitude modulator.

Simultaneous signal transmission: It is not possible to transmit two or more signals in the same fre-quency range simultaneously using a single telephone line. This problem can be resolved by using carrier signals with significantly different carrier frequencies to amplitude modulate the data signals. By picking the carrier frequencies sufficiently farther apart, the spectra of the modu-lated signals can be made nonoverlapping, thereby making simultaneous transmission possible.

Similarly, with AM, simultaneous broadcasting by several radio (AM) broadcast stations in the same broadcast area has become possible.

2.6.2.1 Fault Detection and Diagnosis

A manifestation of AM that is particularly useful in the practice of electromechanical systems is in the fault detection and diagnosis of rotating machinery. In this method, modulation is not deliber-ately introduced, but rather results from the dynamics of the machine. Flaws and faults in a rotating machine are known to produce periodic forcing signals at frequencies higher than, and typically at an integer multiple of, the rotating speed of the machine. For example, backlash in a gear pair will generate forces at the tooth-meshing frequency (equal to the product: number of teeth × gear rotating speed).

Flaws in roller bearings can generate forcing signals at frequencies proportional to the rotating speed times the number of rollers in the bearing race. Similarly, blade passing in turbines and compressors, and eccentricity and unbalance in a rotor can generate forcing components at frequencies that are integer multiples of the rotating speed. The resulting system response (e.g., acceleration in the hous-ing) is clearly an amplitude-modulated signal, where the rotating response of the machine modulates the high-frequency forcing response. This can be confirmed experimentally through Fourier analysis (FFT) of the resulting response signals. For a gearbox, for example, it will be noticed that, instead of getting a spectral peak at the gear tooth-meshing frequency, two sidebands are produced around that frequency. Faults can be detected by monitoring the evolution of these sidebands. Furthermore, since sidebands are the result of modulation of a specific forcing phenomenon (e.g., gear-tooth meshing, bearing-roller hammer, turbine-blade passing, unbalance, eccentricity, misalignment, etc.), one can trace the source of a particular fault (i.e., diagnose the fault) by studying the Fourier spectrum of the measured response.

AM is an integral part of many types of sensors. In these sensors, a high-frequency carrier signal (typ-ically the ac excitation in a primary winding) is modulated by the motion that is sensed. Actual motion signal can be recovered by demodulating the output. Examples of sensors that generate modulated out-puts are differential transformers (linear variable differential transducer or transformer [LVDT], and its rotatory counterpart RVDT), magnetic-induction proximity sensors, eddy-current proximity sensors, ac tachometers, and strain-gauge devices that use ac bridge circuits. These are discussed in Chapter 5.

Signal conditioning and transmission are facilitated by AM in these cases. The signal has to be demodu-lated at the end, for most practical purposes such as analysis and recording.

2.6.3 Demodulation

Demodulation or discrimination, or detection is the process of extracting the original data signal from a modulated signal. In general, demodulation has to be phase sensitive in the sense that the algebraic sign of the data signal should be preserved and determined by the demodulation process. In full-wave demodulation, an output is generated continuously. In half-wave demodulation, no output is generated for every alternate half period of the carrier signal.

A simple and straightforward method of demodulation is by detection of the envelope of the modulated signal. For this method to be feasible, the carrier signal must be quite powerful (i.e., signal level has to be high) and the carrier frequency also should be very high. An alternative method of demodulation, which generally provides more reliable results, involves a further step of

modulation performed on the already modulated signal, followed by low-pass filtering. This method can be explained by referring to Figure 2.30.

Consider the amplitude-modulated signal xa(t) shown in Figure 2.30b. Multiply this signal by the scaled sinusoidal carrier signal 2/ac cos 2πfct. We get

x t a x t f t

c

a c

( )= 2 ( )cos2p (2.77)

Now, by applying the modulation theorem (Equation 2.76) to Equation 2.77, we get the Fourier spectrum of x t() as

The magnitude of this spectrum is shown in Figure 2.32a. Observe that we have recovered the spectrum X(f) of the original data signal, except for the two sidebands that are present at locations far removed (centered at ±2fc) from the bandwidth of the original signal. We can conveniently low-pass filter the signal x t() using a filter with cutoff at fb to recover the original data signal. A schematic representation of this method of amplitude demodulation is shown in Figure 2.32b.

2.6.3.1 Advantages and Disadvantages of AM

The main advantage of AM is the use of a carrier signal (of higher power and higher frequency) to carry the information of the data signal (modulating signal). The data is transmitted at a much higher

M

FIGURE 2.32 Amplitude demodulation: (a) spectrum of the signal after the second modulation and (b) demodu-lation schematic diagram (modudemodu-lation + filtering).

frequency (as the sidebands) than that of the data signal and is recovered (through demodulating) at the received end. Also, the modulation process is quite simple (multiplication of two signals). However, there are several disadvantages of AM. They include the following:

1. Since analog signal of high power and high frequency is transmitted, power loss during transmis-sion is high. Hence it is somewhat wasteful and not quite efficient.

2. Since the amplitude of the transmitted signal varies with that of the data signal, it is prone to noise (at low signal to noise ratio—SNR), when the signal level is low.

3. AM signal uses up more bandwidth since the carrier signal has to be transmitted as well as the data signal.

The key disadvantages of AM can be overcome by using digital AM (or PCM) or other methods of modulation such as FM and PWM where the modulated signal has a constant amplitude (and also digi-tal methods can be used with added advantages).

2.6.3.2 Double Sideband Suppressed Carrier

The amplitude modulation given by Equation 2.74: x_a(t) = x(t)x_c(t) is called suppressed carrier AM or double sideband suppressed carrier (DSBSC) AM. As shown in Figure 2.30b, its spectrum consists of the two sidebands, which are the frequency-shifted spectra of the data signal (modulating signal). Since it is these two sidebands that are transmitted, it is rather efficient with respect to signal power. Often, however, AM is represented by

x ta( )=x tc( )+x t x t( ) ( ) (c = +1 x t x t( )) ( )c (2.79) Here the carrier signal is added to the product signal, so that the product signal rides on the carrier sig-nal. This overall modulated signal has more power. Then, a modulation index is defined as

Modulation index = Amplitude of data signal

Amplitude of carrier siignal (2.80)

Clearly, Equations 2.74 and 2.79 carry the same information content. So, in theory, they are equivalent.

In particular, at high levels of modulation index, the two modulated signals are quite similar, as shown in Figure 2.33. However, the nature and the power content of the two types of modulated signals are dif-ferent. When power efficient modulation is important, the AM given by Equation 2.65 is suitable. When high-power AM is desired, the AM given by Equation 2.79 is preferred.

2.6.3.3 Analog AM Hardware

The most critical component in analog AM is the analog multiplier, where the data signal and the carrier signal are multiplied. Analog hardware multipliers are commercially available. For example, an analog multiplier that can multiply two analog signals and add to the product another signal (say, add the car-rier, which is exactly the AM operation given by Equation 2.79) in the frequency range DC to 2 GHz is available as an IC package. The feature of product scaling (called, gain scaling) is available as well, which corresponds to setting the modulation index.

Note: The miniature (3 mm) analog multiplier (or amplitude modulator) IC package ADL5391 from Analog Devices has 16 leads corresponding to 3 differential signal inputs (6), differential output (2), dc supply voltage leads (3) for 4.5–5.5 V, device common leads (2), scaling input (1), chip enable (1), and dc reference output (1).

(a)

(b)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

–0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4

Time (s)

Modulated signal

Amplitude modulation (suppressed carrier)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

–1.5 –1 –0.5 0 0.5 1 1.5

Modulated signal

Modulated signal (carrier added; modulation index = 0.4)

Time (s)

Modulating frequency = 0.25 Hz Carrier frequency = 10.0 Hz Modulating frequency = 0.25 Hz Carrier frequency = 10.0 Hz

(c)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

–5 –4 –3 –2 –1 0 1 2 3 4 5

Modulated signal

Time (s)

Modulated signal (carrier added; modulation index = 4.0)

Modulating frequency = 0.25 Hz Carrier frequency = 10.0 Hz

FIGURE 2.33 (a) Modulated signal with suppressed carrier, (b) modulated signal with added carrier at modula-tion index = 0.4, and (c) modulated signal with added carrier at modulamodula-tion index = 4.0.

There are some drawbacks of analog multiplication. It is a nonlinear operation with corresponding disadvantages. The noise in either signal will affect the product. Furthermore, the effect on the phase angle is much more complex.