Single and Double Sideband Amplitude

Transcription

1 Experiment: Single and Double Sideband Amplitude Modulation Introduction Modulation is one of the basic principles in communications technology. The purpose in using modulation is: a) multiplexed operation of a transmission path, b) transposition of the signals into a frequency band favorable for signal transfer, c) obtaining favorable signal-to-noise ratios when source and noise power are given. Depending upon the type of modulation, modifications can be done in - amplitude (amplitude modulation, AM), - phase angle (angular modulation), or - both (quadrature-amplitude modulation ). In detail, more distinctions can be made: - types of amplitude modulation double-sideband amplitude modulation suppressed carrier = linear AM, (SC-AM) - double-sideband amplitude modulation with carrier = DSB-AM (usual) - single-sideband amplitude modulation without carrier = SSB-AM (ESB-AM) - vestigial (residual) sideband AM without carrier = VSB-AM (RSB-AM) - quadrature AM without carriers = QAM - types of angular modulation - phase modulation = PM - frequency modulation = FM In this experiment usual AM, DSB-AM and SSB-AM are treated.. Linear Amplitude Modulation The amplitude Û of a sinusoidal carrier Uˆ sin (Ω 0 t + Φ s ) is modified in such a manner that Û is a proportional to the signal s (t), i.e. Û û(t) = k s( t). (.) Thus the modulated signal can be written as s M (t) == k s( t) sin(ω 0 t + Φ S ). (.2) A signal s (t) is any function in time with a continuous spectrum []and k is a constant

2 + jωt ( ω ) = s( t) e dt S (.3) The exponential form for the sine function from Eq. (.2) is written as sin( j 0t jω0t Ω t) = j e Ω + j e, (l.4) thus one receives the spectrum of the modulated signal S M + jωt = sm ( t e dt ( ω ) ) k + + j ( ω Ω k 0 ) t j( ω +Ω0 ) t = j s ( t) e dt + j s( t) e dt 2 2 k k = j S ( ω Ω 0 ) + j S ( ω + Ω 0 ). (.5) 2 2 The zero phase angle Φ s of the carrier signal was assumed here to be zero. Proceeding from signal with limited frequency band, then the amplitude spectrum from Eq. (.5) has for example the form represented in Fig. b. Fig. : Amplitude spectrum a) S (ω) : example for a band-limited signal b) S M (ω) : with S (ω) modulated carrier The spectral components of the carrier and the signal do not appear in the modulation product. Sufficient information for rebuilding (or demodulating) the signal is contained both in the upper and in the lower sideband of the modulated signal. Linear AM therefore is also called double-sideband amplitude modulation (DSB-AM) without carrier... How to Modulate Signals Following Eq. (.2), linear amplitude modulation is in theory simply generated by multiplying of the signal s (t) with [ k sin (Ω 0 t)]. This means, that a modulator could 2

3 be implemented by a multiplier circuit; its inputs have to be connected to the sine carrier and the signal. For high frequency applications, the implementation of linear semiconductor multipliers causes difficulties. In some cases an approximation of the sine by a square wave is sufficient. Using this, the modulated signal can be described as the signal periodically reversed with the carrier frequency and multiplied by a factor. The modulated signal then naturally contains parts in its frequency spectrum that have to be removed by filtering. In very high frequency applications, the semiconductor switches are implemented using fast diodes. Such a circuit for linear AM is called a ring modulator or doublebalanced modulator. One setup for such a device is displayed within Fig. 2. Fig. 2 Circuit diagram of a ring modulator The amplitude of the carrier u T (t) has to be high enough to make the diodes conducting, which means that the forward voltage of the diodes has to be exceeded. If the amounts of the magnetic flux in the windings w 2 and w 3 or w 4 and w 5 are equal, then no voltage is induced in windings w and w 6. In w 6 the signal s (t) appears, only switched in polarity in the same clock period as the carrier signal. As shown in [ ], this represents the linear modulated oscillation s M (t)...2 Synchronous or Coherent Demodulation If the modulated signal is modulated again with the carrier u T (t) = Uˆ sin(ω E t + Φ E ) (.6) then the upper and lower sideband are shifted by +/-Ω E. The same occurs to the negative upper and lower sideband. In case of Ω E = Ω 0, the by -Ω E shifted upper and lower sideband and the by +Ω E shifted negative upper and lower sideband are found again in the baseband and add up following the cosine law. Signal components also will be shifted around double the carrier frequency 2Ω 0, which must be filtered out by a low-pass. 3

4 If the zero phase angles Φ S and Φ E of the carrier waves at the transmitter and receiver are equal, then the signal s (t) is transmitted at maximum receivable power. If the phase angle is shifted by +/-90, the power of the received signal reaches zero []. For the demodulation of the linear AM, the carrier must be supplied to the receiver, corresponding the transmit carrier in frequency and phase. For the synchronization of frequency and phase at the receiver, either the carrier rest or a subcarrier at a different frequency has to be transmitted as well..2 Single-sideband Amplitude Modulation (SSB-AM) Since with linear AM the message is contained both in the lower sideband and in the upper, the transfer of only one sideband is sufficient. This saves bandwidth in the transfer system. Additionally, the demodulation of SSB-AM is simpler than for DSB- AM without carrier..2. How to Generate SSB-AM For the generation of SSB-AM, DSB- AM is used, where one of the sidebands of the modulated signal is filtered out (other procedures see [ ]). Since filters are available only with a finite edge steepness, SSB-AM can only be implemented for the signal having a lower cut-off frequency not equal to zero. This is the case with speech signals, where the frequency range spans from 0.3kHz < f < 3.4 khz. Many different filter methods can be used for the suppression of the unwanted sideband. If a Nyquist-filter is used instead of a filter with a very good edge steepness, the modulation method is called vestigial (residual) sideband AM. It enables the transfer of signals with an only slightly higher bandwidth than as for example with SSB-AM. The advantage is, that it can also carry DC voltage signals like TV video signal. SSB- modulation can be performed also by a so-called Hilbert-Transformer, which flips the signal phase by - 90 for positive frequencies and + 90 for negative frequencies. []. This procedure is of interest, if SSB- modulation is implemented by digital signal processing..2.2 Demodulation Here the baseband can be recovered by modulating again with the carrier on the receiver side. u T (t) = Uˆ sin(ω E t + Φ E ) (.7) 4

5 If Ω 0 = Ω E, the positive and negative upper and lower sideband are shifted by +/-Ω E. Thereby the positive and negative baseband are reconstructed and additionally double frequency components are generated. The higher frequency parts have to be removed by appropriate filters, so that only the original signal remains. In Fig.3a, the amplitude spectrum S M (ω) of the demodulated signal is represented. Only the upper sideband was transferred. Fig. 3b shows the shift over +/-Ω with repeated linear modulation of SSB-AM with Ω 0 =Ω E. The dashed line in the spectrum represents the modulated signal which will not be contained in the spectrum S E (ω) of the resulting signal. It easily can be shown that to demodulate SSB-AM the receiver only requires a carrier with the same frequency. This means, that the carrier frequency on the receiver side can also be produced by a separate generator (Beat Frequency Oscillator, BFO). Fig. 3 Demodulation of SSB-AM a) amplitude spectrum of the signal which can be demodulated b) amplitude spectrum of the demodulated signal With the use of vestigial sideband AM, the frequency-shifted sidebands supplement themselves to form the baseband spectrum again, which is done by the symmetrical copy of the sideband with the Nyquist filter edge. Obviously the important edge symmetry requires more effort for the Nyquist filter..3 Amplitude Modulation Double sideband amplitude modulation with carrier is called (usual)am. This modulation is the oldest transmission method depending on a carrier-signal (Marcani, 895) and allows very simple implementations by using nonlinear components. Long-, medium- and short-wave broadcast uses AM due to minimal needs for the receivers. 5

6 .3. How to Generate AM Signals The amplitude Û of a sinusoidal carrier is changed in accordance with Û û(t) = A 0 + k s( t), (.8) which means for the modulated signal u T (t) = A0 sin(ω 0 t + Φ S ) + k s( t) sin(ω 0 t + Φ S ). (.9) Therefore, a carrier-frequency spectral line appears next to the two sidebands in the spectrum. The peak value of the signal S (t) is called modulation factor m, and is calculated by the quotient k ˆ S m =. (.0) A Envelope Demodulation For m <, the envelope of the modulated signal s M (t) never crosses the zero line, see Fig. 4, which permits the use of a very simple envelope detector. Fig. 4 Envelope of AM A rectifier cuts off the negative portions of s M (t), a low-pass smoothens high frequency carrier components, and a high-pass eliminates the DC component A 0. This envelope demodulator can be implemented technically very easily with a diode and RC elements, see Fig. 5. 6

7 Fig. 5 Block diagram of an envelope detector.4 Description of the setup In Fig. 6, the block diagram of the experimental setup is displayed. In the transmitter modulator (multiplier) the signal s (t) is linearly modulated and with a linear amplifier magnified by factor 2.7. By substituting the band filters, both SSB-AM and DSB-AM can be implemented. With additional amplification, the modulated signal is fed into the transmission link. In the receiver amplifier, the transmission losses are compensated. In the receiver modulator, the signal is demodulated where the carrier is either taken from the transmitted signal itself and phase shifted by the phase shifting device or is supplied separately onto the modulator. The low-pass filter on the receiver side is suppressing the unwanted frequency band. Fig. 6 Block diagram of the experimental setup 2 References [] K. Steinbuch, W. Rupprecht: Nachrichtentechnik Band I und II, dritte, neubearbeitete Auflage, Springer-Verlag Berlin, Heidelberg, New York 7

8 3 The Experiment 3. Measurement Equipment Oscilloscope Selective signal level meter Level meter Frequency generator Frequency generator Carrier frequency generator loudspeaker amplifier tape recorder frequency counter distortion generator 0.Hz to 00kHz 0.Hz to 20kHz 0.2Hz to 00kHz 20 Hz to 20kHz 20 khz quartz-stabilized Ri = 600Ω 3.2 Quantities in the experimental setup The input and output resistances on the low frequency side of the experimental setup are R i =600 Ω; all other blocks have an input and output impedance of Z =50Ω. The voltage level of the carrier signal at the transmitter- and receiver modulator is set up to -9 db. The carrier generator should have an internal resistance of approximately 0Ω, and the signal generator has to have Ω. 3.3 Tasks.) Build up the setup for DSB-AM. Use the same carrier for receiver and transmitter. To simulate the transmission line a capacitor of 0.05µF has to be applied. l.2) A low frequency signal of 2 khz and a voltage level of 0 db is supplied to the input of the transmission modulator. At the signal output of the receiver the received level ( with R i = 600Ω) has to be measured. For this, find out the optimal adjustment of Φ E. Adjust the potentiometer at the low-pass of the receiver amplifier at central position..3) With the selective signal level meter, the residual carrier of the transmission modulator can be measured, and has to be adjusted to the minimum. The achieved carrier suppression in db is to be written into a table..4) Using the setup of task.2, the time signals at test points, 3, 4, 7 and 8 of the experimental setup have to be measured with the oscilloscope. The pictures have to be recorded and to be sketched in the block diagram of the experimental setup. The oscilloscope is to be triggered with the LF signal via its second channel. 8

9 .5) The amplitude spectrum at the output of the transmission modulator has to be recorded with a setup in accordance with task.2. Use a selective signal level meter and display the result on logarithmically scaled paper (3 decades). The result has to be described..6) The amplitude spectrum of the output signal at the receiver modulator has to be measured and displayed on logarithmically scaled paper (3 decades). Remove the block low-pass filter and amplifier" and insert the level meter instead(r i =600Ω). Then the block "low-pass filter and amplifier" has to be inserted again..7) The frequency response of the entire transfer model has to be measured for a direct connection between transmitter and receiver (no capacitor). The phase error caused by the bandpass filter has to be compensated by adjusting the zero phase angle Φ E of the receiver carrier. The frequency response measurement has to be done for optimal adjustment of Φ E. The results of measurement have to be depicted on logarithmically scaled paper. 2.) The experiment for DSB-AM has to be built up. In addition, the receiver demodulator has to be replaced by an envelope detector. The level of the 2 khz low frequency signal has to be lowered to -20 db, and by superimposing a DC offset at the transmission modulator, a modulation factor of approximately 0.5 has to be adjusted. As transmission circuit a direct connection between senders and recievers is used. The receiver level has to be measured at R i = 600Ω. Compare the result with those of task.2 (discussion). 2.2) Like in task.4 the time signals at test points 3, 4, 7 and 8 of the experimental setup have to be recorded. 3.) The experimental setup for SSB-AM has to be built up. As transmission line a direct connection between transmitter and receiver is used. The transmission modulator is to be wired with a signal of the frequency 2 khz and a level of 0 db. The receiver level is to be measured at R i = 600Ω and compared with the result of task ) Like in task.4, the time signals at test points 3, 4, 7 and 8 have to be recorded. 3.3) The frequency response of the transfer model has to be measured and drawn into the diagram of task.7. 4.) A disturbance generator has to be inserted into the transmission line in accordance to Fig. 7. 9

10 Fig. 7 A disturber in the transmission line 4.2) The signal-to-noise ratio (η) has to be measured for a) SSB-AM b) DSB-AM. c) AM (usual), m = 0,5. The signal-to-noise ratio η is calculated in accordance with η = P 0dB lg P S N For this, the signal power P S of the unimpaired system (disturbance OFF, Fig. 7) is measured with a transmitter side wiring according to the task.2, 2. and 3.. Afterwards, the interference power P N in the disturbed system has to be measured (disturbance ON, Fig. 7), whereby the low-frequency signal at the sender is switched off and the transmission band filter is removed. The signal-to-noise ratio is measured at the receiver input (test point 6) and at the receiver output (test point 8). 4.3) The signal-to-noise ratio gain is determined between receiver input and output for SSB -, DSB - and (usual)am. These gains have to be compared with the theoretical values in the references (i.e. []). How has the experimental setup to be extended, so that the theoretical signal-to-noise ratio gains are obtained? 5.) Perform an auditory test with SSB-AM without distortion. In addition the transmitter side signal input has to be connected to the tape recorder with a special cable. At the receiver output a loudspeaker amplifier is attached. As transmission line a direct connection between transceiver and receiver is used. a) the transmitter and receiver modulator use the same carrier frequency (splitting jacks closed) and the tape recorder is started. What is observed during a phase shift between transceiver and receiver carrier of 0, 45 and 90. What would be observed for DSB-AM? c) the splitting jack is opened and the receiver modulator is supplied by a separate frequency generator (f = 20 khz). After rewinding the tape the test is started again. By slight changing the frequency of the receiver carrier (check with the frequency counter) the influence of the frequency difference between transmitter and receiver carrier have to be evaluated. The influence has to be described and explained. 0

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