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PSK signal modelling



Modelling of PSK31 Signals
Introduction
The following signal modelling discussion concludes on the importance of ensuring the settings of the transmitter, and the PC sound card producing the PSK31 audio drive, are both optimised to ensure that the gain of the transmitter amplifying chain is held constant and below any ALC activity.
The PSK Signal is modelled by generating a 32Hz bit stream, with cosine shaping, and applying this signal to a balanced modulator (multiplier).  The second input to the balanced modulator is a cosine wave at the “carrier” frequency—1kHz.  If the bit stream is all “zeroes”, the modulating signal (after applying the cosine shaping) is simply a cosine wave and the output signal from the balanced modulator is a “double sideband suppressed carrier” or two-tone signal.  The modulating signal is shown in Figure 1, and the two-tone output signal is shown in Figure 2. 
An FFT (Fast Fourier Transform) is used to convert the time-domain output signal of the balanced modulator to the frequency spectrum of the resulting BPSK signal (Figure 3). Note that the two “desired” tones are at frequencies equal to the carrier frequency plus, or minus, half the modulating frequency.

 


Figure 1



Figure 2



Figure 3

Nonlinearity is modelled by assuming that the PSK signal is passed through an amplifier whose gain is dependent on the amplitude of the input signal.  For simplicity, the gain is assumed to be constant at unity whenever the amplitude of the PSK signal is below one volt.  When the amplitude is greater than one volt, the model assumes the gain to be constant at some value between 0 and 1.
If the constant is 1, then there is no change in gain as the amplitude varies, and the system is “linear”.  –i.e. gain is independent of amplitude.
If the constant is 0, then all signals above one volt in amplitude will be “hard limited” to one volt.  “Flat-topping” is evident on the signal.  See Figure 4.


Figure 4







Figure 5
For any constant less than 1, there will be distortion of the signal, and subsequent alteration of the spectrum.  For example,  see Figure 6, generated with the constant equal to 0.95.  In this case, the distortion is not visually evident.  However, Figure 7 shows the frequency domain (spectrum) where spurious sidebands are clearly evident.


Figure 6

As you will see in the following figure, this is about the most nonlinearity that should be tolerated, as it produces spurious outputs that are only slightly more than 20 dB below the desired outputs.  This is an IMD of about –23dB.  (The largest spurious output is 23 dB below the desired output—which has been normalised to 0 dB).


Figure 7

For the case of “hard-limiting”, note that the spurious sidebands of Figure 5, corresponding to time domain signal of Figure 4, are less than 10 dB below the two desired sidebands.  We see far too many such signals on the bands.
The following two figures (8 and 9) show the balanced modulator waveform and corresponding spectrum when there is only 1% gain reduction above 1 volt.


Figure 8







Figure 9

From these figures, it is evident that we want to keep the gain of our amplifying systems (transceivers) constant over all amplitudes, to within one or two percent.  Since ALC (Automatic Level Control) implies a reduction in gain at high amplitudes, we must adjust the signal generated by the sound card so that no ALC action is detected.  This means no “overdriving” of the rig.  One of the easiest ways to accomplish this is follow these procedures:
  1. Tune the rig for normal output on CW.
  2. Change to the appropriate sideband setting (USB for PSK31 is standard)
  3. Turn off the speech processor and leave it off
  4. Set the audio control of the rig as you would for normal SSB operation
  5. Set the PSK software to Transmit, with no data being transmitted.
  6. Adjust the audio output from the soundcard so that the RF power output from the rig is no more than 25% of the cw output.  (e.g. 25 watts for a 100 watt rig)  There should be no ALC indication at this power level.

Although you might be able to set the power higher in step 6 with no ALC, this should ensure that a very clean signal is transmitted.
A few words of caution—If driving the microphone input of the rig, an attenuator between the soundcard output and the transceiver input may be needed.  Distortion can also occur in the sound card at very low, or very high output levels.  An attenuator can ensure that the soundcard output is near the middle of its dynamic range, giving the cleanest audio signal to the transceiver.

Milton E. Cram, W8NUE
December 8, 2002




 
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