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.
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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.
|
|
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.
|
|
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.
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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.
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.
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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.
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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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