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Implementation of Analog Modulation on SpinCore PulseBlasterDDS And RadioProcessor Boards

Introduction:

Analog modulation refers to the process of transferring an analog baseband (low frequency) signal, like an audio or TV signal over a higher frequency signal such as a radio frequency band.

There are two ways to modulate an RF carrier:

1. Amplitude Modulation

In analog modulation, the amplitude of the carrier signal is made to follow that of the modulating signal. Several variants of amplitude modulation are used in practice. They are Double Side Band Suppressed Carrier (DSBSC) Modulation, Single Sideband Suppressed Carrier (SSBSC) Modulation and Vestigial Sideband Amplitude Modulation (VSBAM).

PBDDS Board Implementation:

For generation of AM waveforms on SpinCore PulseBlasterDDS Boards, the basic form of amplitude modulation is given by:

AM (t) = Ca*sin(wc*t)*[A+(Ma*sin(wm*t))]

For this formula:

t = time
Ca = amplitude of Carrier waveform (1 Vp-p here)
wc = angular frequency of the carrier signal in radians/sec
wm = angular frequency of the modulating signal in radians/sec
Ma = amplitude of the modulating waveform.
AM(t) = the resulting AM waveform


A and Ma are set and scaled so that the amplitude of [A+(Ma*Sin(wmt))] does not exceed the value of 1Vp-p for the given modulation index.

The scaling factor and the values are chosen by the formula given below:

Ma = 1/((100/MI) + 1)
Where MI=Modulation Index specified by the user in between 0-100% value. And A = Ma*100/MI

Note: Tm=1/Fm can not be less than (9 * clock time period) for proper results where Fm is the frequency of the message signal in Hz.

The carrier waveform and the message signals can be generated using the PulseBlasterDDS and RadioProcessor's NCO and AWG respectively.

The generation of carrier waveform in C code is as below :

void shape_make_carrier (float *dds_data)
{
  int i;

  for (i = 0; i < 1024; i++)
    {
      dds_data[i] = sin (2.0 * pi * ((float) i / 1024.0));
    }
}

The message signal in which amplitude is scaled in accordance with modulation index is generated as given below.

void shape_make_sin (float *shape_data)
{
  int i;
  float MI, A, Ma;
  printf ("Enter Modulation Index from 0 to 100 percent: ");
  scanf ("%f", &MI);

  Ma = 1/((100/MI) + 1);
  A = Ma*100/MI ;

  for (i = 0; i < 1024; i++)
    {
      shape_data[i] = A+(Ma*sin (2.0 * pi * ((float) i / 1024.0)));
    }
}

Both the above generated signals are loaded in the board by using the SpinAPI function as given below:

pb_dds_load (shape_data, DEVICE_SHAPE);
pb_dds_load (dds_data, DEVICE_DDS);

The complete C code demonstrating this implementation is available for direct download. The code generates an amplitude modulated wave for any given modulation index, carrier frequency, and message signal frequency. In the code, the message signal is assumed to be a sine wave, but the user can edit the code to make the message signal into any waveform.

Some examples of output obtained with this code is given below. Note that the code only demonstrates a basic version of amplitude modulation. A similar setup can also be used for the DSBSC, SSBSC and VSBAM techniques mentioned above.

AM1


Figure 1 shows the output AM waveform generated.

Channel 1 shows the ouput AM wave for carrier frequency Fc =1 MHz and a message signal frequency of Fm = 100 kHz and modulation index = 100%.

Channel 2 shows the TTL output with frequency = Fm/2. Each cycle of the TTL output corresponds to the time taken to execute the two SpinAPI functions given below:

pb_inst_radio_shape (0, 0, 0, 0, TX_ENABLE, NO_PHASE_RESET, NO_TRIGGER,
USE_SHAPE, 0, 0x0F, CONTINUE, 0, (1/fm) * us);

pb_inst_radio_shape (0, 0, 0, 0, TX_ENABLE, NO_PHASE_RESET, NO_TRIGGER,
USE_SHAPE, 0, 0x00, BRANCH, start, (1/fm) * us);


The execution of these instructions results in the generation of two full cycles of the AM signal.

Also note that Channel 1 is delayed by (9 * clock cycle) time period.

                                         





Spectrum

Figure 2 shows the frequency spectrum of the output AM waveform for the specifications given in Figure 1.

The carrier is centered around at 1 MHz and two sidebands are present at 900 kHz and 1100 kHz. The sidebands are offset from the carrier by the frequency of the modulating signal.

This basic variant of AM has a prominent carrier signal displayed in the frequency spectrum. Some of the other methods of achieving AM mentioned, such as DSBSC and SSBSC above are designed to reduce this carrier component in the frequency spectrum. Methods such as SSBSC and VSBAM are designed to remove or suppress one of the sidebands.





AM3


Figure 3 shows an AM waveform generated using the example code.

Channel 1 shows the ouput AM wave for a carrier frequency Fc = 1 MHz and message signal frequency Fm = 100 kHz with Modulation Index = 30%.

Channel 2 shows the TTL output with frequency = Fm/2.





2. Angle Modulation

In Angle Modulation, the message signal's amplitude is used to control the frequency or phase of the carrier signal. This gives rise to the two methods known as Frequency Modulation and Phase Modulation, respectively.

Frequency Modulation implementation on SpinCore PulseBasterDDS Boards:

In the SpinCore PulseBasterDDS board, the frequency modulated waveform is generated using the NCO by controlling the frequency registers in accordance with the instantaneous amplitude of the message signal using the PulseBlaster Timing Core.

The complete C code demonstrating this implementation is available for direct download.

The code performs basic frequency modulation using a sinusoidal carrier for any given carrier frequency within the board specifications. The message signal is also assumed to be a sine wave, as in the case of amplitude modulation. This code can be extended to use different types of carrier and message signals.

The equation implemented in the code is:
FM(t)= Ca*sin(wc*t + phi)

For this formula:

phi = change in the frequency of the carrier with respect to amplitude of modulating waveform. 
wc = angular frequency of the carrier signal in radians/sec (also equal to 2*pi*fc)
Ca = amplitude of the carrier signal (set to 1 in the code)
FM(t) = the resulting FM waveform

The modulating signal chosen is a sine wave as given by:
m(t) = Ma*sin(wm*t)

For this formula:

m(t) = the modulating or message signal
wm = angular frequency of the message signal in radians/sec (also equal to 2*pi*fm)
Ma = amplitude of the modulating signal (set to 1 in the code)

Also, in this example, the TTL outputs are used to trigger the oscilloscope.

Following the similar method described in amplitude modulation, the carrier and message signal is generated in the C code.

In this implementation, the modulating waveform amplitude (which is in the range of -1V to +1V) is quantized into a number of value as set by the user (with greater numbers offering a better FM implementation). These values are in turn used to compute one of that many possible frequency shifts around the carrier frequency. This is done by choosing a step size such that a +1V amplitude would produce a shift resulting in a instantaneous carrier frequency of fs + (fm/2) and a -1V would result in fs - (fm/2). The quantization size should be set to the number of frequency registers available on the particular SpinCore PulseBlasterDDS or RadioProcessor board being used. If more frequency registers are desired, please contact SpinCore.

The frequency registers can be loaded with the required value by using the following SpinAPI functions.:

    for (i=0;i<N;i++)
    {
        pb_set_freq (fc[i]);

    }

where fc[i] contains the values of the frequency shift in accordance to the quantized amplitude.
The SpinAPI functions used for frequency modulation is given by:

              pb_inst_radio(i,0,0,0, TX_ENABLE, NO_PHASE_RESET, NO_TRIGGER, 0xFF,CONTINUE, 0, Ti*ns);

where the index "i" represents the ith frequency register.

Some examples of output obtained with this code is given below. Note that the code only demonstrates a basic version of frequency modulation. It can also be used to implement the phase modulation by using the phase registers of the PulseBlasterDDS and RadioProcessor boards instead of the frequency registers.
 

FM1

Figure 4: In this example, for the purpose of visualizing the results on the oscilloscope, the instantaneous frequency of the carrier signal is quantized to only 9 possible values.

The figure shows the output FM waveform on channel 2 with TTL outputs on Channel 1 being used for triggering the oscilloscope for a carrier frequency of Fc = 1 MHz and a message signal frequency of Fm = 500 kHz.

Each pulse in the TTL waveform corresponds to the execution of an instruction that generates a portion of the FM signal corresponding to 1/9th of the period of the message signal.



FM2

Figure 5 is the result obtained with the same parameters that were used in the previous example. Here, the number of frequency values for the carrier signal was quantized to 5 values to give a even better visualization of the frequency modulation.

FM4

Figure 6 shows the FM spectrum on channel 2  of the oscilloscope when 1024 frequency values are used in the carrier signal. The same parameters as the examples given above were used for this example as well.
 


 


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