T 7.2.1.3 Amplitude Modulation

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TPS 7.2.1.3 Solutions 3 Review of amplitude modulation Answers 3.1 Modulation means the frequency conversion of an information signal from the AF position of the baseband into the RF band of the carrier. Here, the modulating signal influences an appropriate parameter of the carrier oscillation, e.g. the amplitude or frequency. While f C >> f M always holds true in modulation, mixing entails frequency conversion being generated between signals with comparable frequencies. 3.2 Modulation offers the following advantages: – Matching to the features of the transmission channel, i.e. improved efficiency during transmission of information signals. – Multiple utilization of transmission channels, e.g. in frequency multiplexing methods. – Improved signal-to-noise ratios (modulation gain) 3.3 The DSB is something "new" produced by combining the carrier oscillation and the modulating signal. While the dynamic characteristic of the AM signal can be observed as a whole on the oscilloscope the spectrum analyzer shows the AM broken down into its components. With constant modulation signal these components have amplitudes contstant with respect to time. 3.4 In the dynamic characteristic of the beat a phase shift of 180° arises in the envelope curve. The frequency of the envelope curve is approx. half the differential frequency of the oscillation components involved. The beat frequency corresponds to the arithmetic mean value. 3.5 The amplitude deviation ∆A C indicates the maximum change permissible for the carrier amplitude A C . It is dependent on the modulator constant α and the amplitude A M of the modulating signal. The modulation index m is the quotient formed out of the amplitude deviation and the carrier amplitude. The modulation index m can assume values between 0 and 1. Overmodulation occurs for m > 1. 3.6 In addition to envelope demodulation, synchronous or coherent demodulation are common demodulation methods particularly in commercial communications systems. In contrast to envelope demodulation, it requires an auxiliary carrier which is stable in terms of frequency, phase and amplitude. 3.7 The reduction in carrier power means an improvement in the transmission efficiency. The amount of power and amplifier circuitry in the transmitter can be reduced. Bandwidth is saved by limiting modulation to one sideband. However, coherent demodulation becomes problematic when the carrier is completely suppressed. For that reason a residual carrier is transmitted with which the receiver is synchronized. 3.8 The following applies for the efficiency η: useful power η = total power Expressed by the modulation index m the following holds true: η = m 2 2+ m 2 For the maximum modulation index m = 100% you obtain the best efficiency of the DSB when η = 33%! Regarding the power needed in DSB at least 2/3 is “squandered” in the carrier. Since the carrier contains no information it can be suppressed to increase the efficiency. 3.9 Methods of carrier suppression – Suppress the carrier using a bandpass filter with very sharp cutoffs. – Addition of a carrier in phase opposition and of equal amplitude to the modulated signal. – Use of a modulation method which does not permit the carrier to reach the modulation product, e.g. balanced or ring modulator. 3.10 Here only coherent demodulation still constitutes a viable alternative. For this an auxiliary oscillation is needed in the receiver, which is in agreement with the original carrier in terms of frequency and phase and whose amplitude remains constant. 52
TPS 7.2.1.3 Solutions 5 The Double Sideband AM Experiment results 5.1 Investigating the dynamic characteristic of the DSB 5.1.1 DSB modulation signal. At the same time the amplitude of the modulated signal drops. Consequently in XY display modus a trapezoid is produced which the its broad side on the left. 5.1.2 DSB SC Diagram 5.1.1-1: Dynamic characteristic of the DSB signal (1): Modulating signal s M (t) (2): Modulation product at the output M2 The envelope curve of the AM signal nearly coincides completely with the modulating signal and immediately follows its changes in frequency and amplitude. Diagram 5.1.2-1: Dynamic characteristic of the DSB SC signal (1): Modulating signal s M (t) (2): Modulation product at output M2 The DSB SC signal has the characteristic of a beat, i.e. it is the linear superpositioning of 2 harmonic oscillations with very close frequencies. The envelope curve of the beat shows zero crossings. There the beat signal experiences phase shifts of 180°. Also the DSB SC signal follows the frequency changes of the AF signal without any visible phase delay. There is no overmodulation caused by amplitude changes in the modulating signal, as in the case of DSB. The modulation trapezoid for DSB SC . Diagram 5.1.1-2: The modulation trapezoid m D − d 65 . − 2 = ≈ ≈ 53% D+ d 65 . + 2 The modulation index amounts to approx. m = 53%. Observation: the trapezoid chords are distorted "cigar-shaped". This is an indication for a phase shift between the signals at the X and Y input. These kinds of distortions can scarcely be seen in Diagrams like 5.1.1-1. Generating the modulation trapezoid Oscilloscope set to XY mode. Set the coordinate origin in the middle of the screen using the X-position and Y-position controllers. If the modulating AF signal reaches its negative maximum value, then the X-deviation is at the far left. From there it increases horizontally to the right with a rising Diagram 5.1.2-2: The modulation trapezoid Observations: In the display of the modulation trapezoid in XY mode Lissajous figures appear resembling a double conic section depending on the modulation frequency f M . These figures rotate as a function of the frequency f M . The modulation trapezoid is bet- 53
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T 7.2.1.3 Amplitude Modulation

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