T 7.2.1.3 Amplitude Modulation

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TPS 7.2.1.3 Review Special cases are depicted in Fig. 3-3. The spectrum of amplitude modulation The expression in the brackets of (3-6) describes the envelope of amplitude modulation. If you multiply the dynamic (time) characteristic of the carrier oscillation in this expression, you obtain: s AM (t) = A C [cos (2 π f C t) + m cos (2 π f T t) cos (2 π f M t)] (3-7) The application of the addition theorem: 1 cos x⋅ cos y= cos( x−y)+ cos x+ y 2 provides: s ( t) A cos 2π f t AM C C [ ( )] = ( ) m + cos 2π ( fC − fM ) t 2 [ ] m + cos 2π ( fC + fM ) t 2 [ ] (3-8) From (3-8) you can see the spectral composition of amplitude modulation, see Fig. 3-4. From the spectrum we can see that besides the carrier oscillation with the frequency f C , there are also 2 side oscillations with the frequencies f C + f M and f C – f M contained in s AM (t). According to (3-8) the amplitudes of the equal side oscillations depend on the modulation index. The oscillation with the lower frequency f C – f M is called the lower sideline, the one with the higher frequency is the upper sideline f C + f M . The lower sideline (LSL) slips further into the range of lower frequencies as the signal frequency f M increases. This frequency response of the LSL is referred to as inverted position. The upper sideline (USL) shifts into the higher range of frequencies with increasing signal frequency. It lies in the normal position. In Fig. 3- 5 the terms are in standard representation for the transmission of an information band, which extends from a lower frequency limit f u up to the upper frequency limit f o . The representation according to Fig. 3-5 is standard particularly in carrier frequency technology. The bandwidth requirement of AM equals twice the maximum message frequency f Mmax : b = 2 f Mmax (3-9) Representing amplitude modulation with a vector diagram The vector diagram constitutes an important tool in the representation of modulation methods. It frequently permits the immediate assessment of interference effects or manipulations during modulation. For example, asymmetrical attenuation of the sideband oscillations in AM can lead to the formation of parasitic angular modulation. From Fig. 3-6 the following features of amplitude modulation can be read off directly: An AM signal can be represented by 3 complex vectors ( 2 sideband vectors and a vector for the carrier). The 3 vectors are displayed in a joint diagram for any given point in time, see Fig. 3-6. S AM S AM A C m/2 A C m/2 f M f C (f) f C – f M Fig. 3-4: The spectrum of amplitude modulation s M f u f o s AM f C – f o f C f C + f o 1 1 f C f C + f M (f) f Fig. 3-5: Normal and inverted position f 24
TPS 7.2.1.3 Review t = t 1 s AM USL USL t = t 2 LSL LSL s C s C s AM Fig. 3-6: Amplitude modulation in a vector diagram Fig. 3-7: Relationship between envelope and vector representation 1. The carrier oscillation is depicted with a constant direction (normally perpendicular upwards), although in absolute terms it rotates in counterclockwise rotation with 2 π f C . 2. The length of the carrier vector remains constant. 3. The sideband vectors are symmetrical with respect to the carrier. The vector of the USL rotates counterclockwise around the tip of the carrier vector. The vector of the LSL rotates in clockwise rotation. 4. The vector for the amplitude modulated oscillation is obtained through vector addition, i.e. construction of the vector parallelogram, made up of the vector of the carrier and the side oscillations. The resulting vector always has the direction of the carrier vector. As you can see from Fig. 3-7, the tips of the resulting vectors, if you draw them as a function of time, again produce the envelope of the amplitude modulated oscillation. 1. A DC voltage component 2. The original signal with the frequency f M . 3. Components with higher frequencies f C , f C + f M , 2 f C + f M , etc. Fourier expansion shows that rectification of the AM signal produces many new spectral components which are not present at the input of the rectifier. A suitable filter is used to suppress these unwanted spectral components. Envelope demodulation belongs to the so-called incoherent demodulation methods, as neither the carrier phase nor the carrier frequency are of any importance. Fig. 3-9 reproduces the possible circuit configuration of an envelope demodulator. AM demodulation Envelopes and synchronous demodulation 1st envelope demodulation First the AM signal is rectified, see Fig. 3-8. The dynamic characteristic of the current passing through the recifier can be subjected to Fourier series expansion. It can be shown that a rectified AM signal contains the following signal components: Fig. 3-8: Envelope curve demodulation 25
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T 7.2.1.3 Amplitude Modulation

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