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Experiment ECE #2
DSBSC GENERATION AND DEMODULATION (A1 manual pp.33-46 and portions of pp.97-108) General procedure for lab reports is given in another document. If you see any errors please bring them to my attention. Tutorial comments are enclosed in boxes. Read carefully the definition of DSBSC. The principle comes from a well-known trigonometric identity: cos(1t+1)cos(2t+ 2) = [cos[(1+2)t+1+2]+cos[(1-2)t+1- 2] (1)
[Also note: cos(A-B) = cos(B-A), because the cosine is an even function. For example, cos[(510)t] = cos[(10-5)t] If, for example, cos(1t) represents a low (such as baseband in a communications context) frequency waveform and cos(2t) represents a high frequency (carrier) waveform, this equation tells us that the low frequency waveform can be upconverted to a pair of higher frequencies centered around the carrier. One of these has the frequency of carrier minus baseband) and the other has the frequency of carrier plus baseband. Our interest is in some arbitrary low frequency waveform, say m(t). Think now of one of the cosines in Eq. 1 being replaced by a collection of cosines and sines of the different frequencies contained in m(t), all of them low frequency compared with carrier frequency c. Then, as in Eq. 1, we can upconvert this entire group of frequencies using the operation (i.e., modulation) expressed in the equation:
DSBSC
(t) = m(t)cos(ct).
(we say m(t) modulates the carrier, cos(ct).)
(2)
In numerous applications including cell phone transmissions, m(t) is the voice signal, although generally after some processing. The frequency spectrum of m(t) we will call M() Its frequencies are in the range 100-3500 Hz, whereas the carrier frequency for cell phone transmission is in a range around 1 GHz, or 109 Hz. Although cos(ct) implies precise timing with respect to the t = 0 point, that is not the case; actually cos(ct+) would be more accurate. But since the timing of m(t) is arbitrary, for our analysis we can set the time origin anywhere we please, so we set the carrier phase = 0. (Cosines are slightly more convenient than sines in terms of the math manipulations.) We use complex algebra for M() simply because it carries both magnitude and phase. Phase (a frequency domain concept) is how we keep track of time shifts in the time domain. Phase = to informs us that the frequency is time shifted by an amount to. It can be shown (as, for example, by convolving M() with the two delta functions representing the cosine) that:
DSBSC
() = [M(+c)+M(-c)]
(3)
Thus, multiplication by cos(ct) upconverts the entire low frequency spectrum M() up to where one replica is centered at the carrier frequency c and another at - c. The latter is a mathematical convenience and is not seen in a laboratory spectral display, which essentially folds it over to add to the M(-c) term. Upconversion is essential in wireless communication in order for the antennas to be of reasonable size. For cell phones, reasonable size is in the context of handheld. For commercial AM, however, where the listener is never involved in the transmission, it is only necessary for the size to be reasonable structurally in the vertical direction. Since in that case the receiving antenna is used only for reception, it needs only to be of sufficient length to pick up to the rather strong field strength that is transmitted by the AM radio station. In general, the low frequency spectrum or baseband M() may originate from speech, music, low rate digital waveforms, the baseband video output of a video camera, etc. To recover baseband from a received modulated carrier we need a downconversion or demodulation step. For DSBSC this requires multiplication of (t) (Eq. 2, above) by a signal synchronous with the carrier, A cos(ct). We recall from Exp. 1 that a product of cosines with same frequency and phase yields a constant (DC) voltage and a cosine with double the original frequency. Here that constant part of the product is invaluable! It is the part that enables us to recover a voltage proportional to m(t), as we see below:
DSBSC
A cos(ct)[
DSBSC
(t)]=Am(t)cos2(ct)=(A/2)m(t +(A/2)m(t)cos(2ct).
(4)
A low pass filter is used to block the second of these, that is, the high frequency (A/2)m(t)cos(2ct) part, leaving only (A/2) m(t), directly proportional to the baseband signal. Considerable amplification is generally required in the demodulation process to bring the recovered m(t) to the point where it can drive a loudspeaker. DSBSC modulation is very similar to that of ordinary AM, but in ordinary AM a carrier is added to the DSBSC signal before transmission. As it turns out, this makes it unnecessary for the receiver to supply a sinuosoid that is synchronous with the carrier. Receivers can be built much more inexpensively than if they had to operate synchronously in order to receive DSBSC. If the spectrum you record is different than that of some one else, this is entirely to be expected. Random choices in timing among different experimenters will result in different spectral displays. Some of the Picoscope recordings I incorporated in the Instructions sheets will be very relevant here, so be sure you look at them. As noted, however, do not expect recordings of spectrum to be identical. Procedure (Note: Sketches called for in the manual are unnecessary.) For all spectral recordings be sure you use the average setting (Under Settings go to options and then to display mode) to get a relatively stable display (because it is integrating m(t) over longer time intervals). This is especially important when m(t) is constantly varying, as with speech. The averaging is cumulative, so allow up to a minute or so between to changes be sure it has settled down a bit. 1. T1 - T5: I wouldnt worry too much about precise synchronization of the scope display, since for both the oscilloscope and Picoscope you can freeze it for easy viewing (but it wouldnt hurt). Also when you copy a waveform or spectrum from Picoscope there is an automatic freeze.
Using 1 kHz audio and the setup of Fig. 5, take a look at the waveform. You should see something like Fig. 4 in the manual. However the details will be clearer (as per Fig. 2 in the A1 manual) if the carrier is at a lower frequency. To get a lower carrier frequency than that available next to the frequency counter you can use one of the VCOs as a variable oscillator, free-running mode (that is, no voltage applied to the in terminal). The gain control is irrelevant when the VCO is free-running. A frequency around 65 kHz works well (lower end of the high range) or often you can use the high end of the low range, somewhere around 15 kHz. The exact value is usually immaterial in these experiments, and the reason for using a frequency lower than 100 kHz for the carrier is so that in the time display of the waveforms you can see both the low frequency modulating waveform and the high frequency carrier. When the carrier frequency is too high it just becomes black for a sweep speed matched to the low frequencies. Save a display as in Fig. 2; also save a display of the spectrum. In your report, state why we dont see the carrier frequency itself in the DSBSC spectrum. (This is more or less obvious from Eq. 1 but needs to be stated.) 2. T-6. Record time domain and spectrum with the overload condition. You should see new frequencies in the spectrum resulting from the distortion due to overload. 3. Omit Bandwidth section, T7 through T22. Your spectral displays provide all the bandwidth information you need. Examine your spectrum of the DSBSC waveform and state what its bandwidth is. How does this relate to the audio frequency? Explain. 4. Modulation with speech: In place of the audio oscillator use the output of either of the channels of the speech module after amplification with the buffer amplifier to bring up the voltage. (You can verify its existence by listening to it on the earphones through the earphone amplifier. (Be careful with the earphone amplifier gain control, dont blast your eardrums.) Get a snapshotof the speech signal and the multiplier output showing the DSBSC signal, as in Fig. 9 of the manual, but adjust the scroll bars of Picoscope to get an overlay of speech and DSBSC as in Example 1, below. Choose a time segment when theres some action going on. As noted before you can freeze the display any time. Also obtain a spectrum average; again, freeze when it is at a reasonably high level. A sample of a speech spectrogram is shown in the Instructions and Lab Reports document. Side comment: The speech module has a microphone and a channel for live viewing of the signal into it. By using this output instead of the oscillaltor to modulate the carrier and talking into the microphone you can get a Picoscope spectral display of your own voice. (That of a partner might be easier, because the voice input needs to be close to the microphone, and that makes it hard to see what shows up on Picoscope.)] 5. Demodulation: As already noted above, to recover the baseband from a DSBSC signal you have to multiply synchronously; that is,...