App Note 003
Applying the AN10E40
Amplitude Modulation and Demodulation
Introduction
This application note describes one practical method of generating an Amplitude Modulated signal using just a fraction
of the resources available within an AN10E40. This particular example was designed to accept a low audio band input
signal and use it to amplitude modulate a 100 kHz carrier. These frequencies were selected out of convenience for
demonstration purposes. You can easily adapt all of the parameters to better suit your specific requirements. This note
also demonstrates the convenience and utility of AnadigmDesigner's built in simulator.
Theory of Operation
The above screen shot shows just how few resources are required to accomplish the modulation task, leaving the
balance of the array available for other signal processing functions (like demodulation). Strictly speaking, the amplitude
modulation is accomplished with just the two IPmodules, G03a and D01. Recall that the Anadigm FPAA is a sampled
data system; each IPmodule is fed by a sampling clock. For this circuit, the device is supplied with a 1MHz master
clock and G03a uses a divided down (by 10) version of that clock. The resultant 100 kHz clock establishes the carrier
frequency. On Phase 1 of this 100 kHz clock, G03a samples the incoming baseband signal (fed from the LBX analog
input pin). The output of G03a reflects this input signal only during the Phase 2 (F2) of the 100 kHz clock; during
Phase 1 (F1) the G03a output is switched back to VMR. (The intervening summing amplifier is discussed later.)
F2
F1
e = ∆V
∆T
Slop
Sl
op
e=
(
fn
dV
dT
)
This chopped baseband signal is fed into an inverting differentiator, IPmodule D01. In a continuous time system (a
sample input waveform is shown on the left), the output of a differentiator circuit at a particular instant will be
proportional to the slope of the input signal
at that same instant. In a sampled system
such as ours (a sample input waveform is
shown on the right), the output signal will be
proportional to the change in voltage (DV)
over the change in time (DT). The "slope"
,V
during
this
sample
is
/,T.
The
differentiation constant k of the D01 sets the
gain for the circuit. D01's output is thus
V
given by: Vout = -k, /,T
For this application k has been set to 1 ms. Setting a low value for k ensures that the output of the differentiator will not
V
rail (clip) with large amplitude input waveforms (waveforms which present a large , /,T value to D01). For the clock
phase shown in our example, the input signal slope is positive and so produces a negative step at the D01 IPmodule's
output. In the very next phase, the slope will have the same magnitude, but opposite sign, and so the D01 output will
now be a positive step of the same amplitude. The result of all this will be square wave centered about VMR (Channel
3 below), with each phase's amplitude proportional to the input signal. In plainer language, we now have an AM signal.
A summing amplifier is used to provide a DC offset to the input signal to keep it always above VMR. Failing to do so
will result in an over-modulated signal (modulation index > 1) which precludes the use of simple envelope detection for
demodulation. A much more complex synchronous demodulation scheme would otherwise be required. This is rarely
used in AM receiver circuits. Please see this note's addendum for additional information on modulation index.
The resultant wave forms are shown in the simulation results window below. The summing amplifier inverted the input
signal, so the waveforms below are negative with respect to the description above, but the operation is otherwise as
described.
In order from top to bottom, Channel 1 shows the 2 kHz input signal. Channel 2 shows the output of G03a. Channel 3
shows the output of D01 and Channel 4 shows the output of the second of the two low pass filters.
Of course, an AM signal is not typically modulated square wave as we now have on Channel 3 (precisely known as a
Pulse Amplitude Modulated signal), but rather a modulated sine wave. The final processing elements in our circuit then
are a pair of low pass filters. With their sample clock running at 1 MHz, they are able to achieve the requested 100 kHz
corner frequency. The final waveform shown above on Channel 4 now has the characteristics we were looking for. A
100 kHz sine carrier, amplitude modulated by a baseband signal. Further smoothing of the output signal is of course
possible with the use of higher order filters or the addition of an output smoothing filter on the FPAA's I/O pins, though
as we shall see this is not required for this particular application.
The simulation result above gives a better overall perspective of the behavior of the modulation circuit. Here again,
Channel 1 shows the 2 kHz input signal. Channel 2 shows the output of G03a. Channel 3 shows the output of D01 and
Channel 4 shows the output of the second of the two low pass filters. We have left the signal somewhat undermodulated in our example to stress an important point; changing a parameter such as the modulation index is very
easily accomplished with programmable analog. In this instance a quick adjustment to either the differentiation
constant parameter in D01 or the offset voltage provided by V02a is all that is required.
Demodulation
The classic AM demodulation circuit uses nothing more than a diode followed by a low pass filter. The diode cuts away
half of the AM envelope and the low pass filter gets rid of the carrier. In our example design, demodulation is achieved
by using an inverting full wave rectifier with built in low pass filtering (R01b) followed by two additional low pass filters.
The simulation result for the demodulator portion of the circuit is shown in the screen shot above. In order from top to
bottom: the AM signal (input to R01b) is on Channel 1, the R01b output is on Channel 2, the output of the G05
summing amplifier is on Channel 3 and finally the fully recovered signal on the RBZ analog output pin is on Channel 4.
In this example, the R01b stage has done a pretty fair job of demodulating the signal all by itself, the positive half of the
AM signal has been rectified down, and this IPmodule's built in low pass filter has begun the job of removing the carrier
frequency. It is obvious however that there is still some carrier frequency present that yet needs to be filtered out.
A complete modulator - demodulator circuit will be presented in a bit later in the note, but in order to keep things simple
for now the screen shot below shows only the demodulator portion.
The signal to be demodulated is applied to the LDX analog input pin. The signal is rectified and filtered in the R01b
IPmodule.
While it probably isn't necessary for most applications, we have included another summing amplifier and voltage
source in the demodulation circuit to remove the DC offset introduced by the modulator. The re-programmable nature
of the FPAA allows the modulator circuit's offset to be adjusted in order to affect a change in its modulation index. In a
like fashion, the demodulator's offset can also be readily adjusted. Please see this note's addendum for additional
information on modulation index.
The series pair of F01 low pass filters completes the job of removing the carrier frequency and restoring signal
amplitude.
In the screen shot above, we have the composite design, including both modulator and demodulator circuits. In order
to demonstrate the complete functionality of the system the following external connections are required:
•
•
•
Signal generator connected to the input pin of the modulator (LBX) (2 kHz, 2 Vpp, centered about VMR)
Jumper wire, connecting the modulator output pin (RBZ) to the demodulator input pin (LDX).
Oscilloscope probes at various signal points of interest
If you don't happen to have a signal generator handy to drive the LBX pin, don't worry. Just drop in an O01 Sine Wave
Oscillator IPmodule in the open positions in the upper right of the array and connect it in. The same holds for the
jumper wire; for ease of experimentation, it too may be achieved with an internal connection. In a single FPAA, we can
build the modulator, the demodulator, and a signal generator which provides the modulating input signal. We have a
whole bench's worth of analog breadboard circuitry built into a single chip.
Simulation vs. Actual Results
While simulations provide a convenient experimentation and learning environment, the true test is of course what
happens in the real world. In order from top to bottom, the simulation results for the input signal, the AM output and the
recovered signal are shown in the screen shot above. The actual bench results are shown in the same order in the
scope shot below.
AnadigmDesigner hooks up easily to the AN10DS40 demonstration board and evaluating circuits is an easily
accomplished task. For this particular circuit a standard signal generator was used to drive the baseband input pin
LBX. A 2 Vpp amplitude sine wave centered around VMR at 2 kHz was applied and is shown as the "A1" trace below.
The AM output was taken off of the RDZ pin and is shown as the "A2" trace below. The "A3" trace shows the
recovered baseband signal. It is slightly phase shifted with respect to the input signal, but otherwise is an accurate
reconstruction of the input.
End Notes
In this note, the carrier frequency was limited only by our decision to filter the AM signal using on chip IPmodules. If we
had instead elected to use external filtering, higher corner frequencies could have been set and the carrier could have
been set as high as 1 MHz.
Experiment. Learn. Have fun. Build an AM transmitter (no kidding). (A length of wire driven by the modulator output
laid out along side your radio's whip antenna has been shown to be workable for quick experiments.) With Anadigm,
you've got the world's only truly programmable analog design system. The way you approach design will never be the
same. You've got programmable analog solutions, "in a click".
Addendum - Modulation Index
The basic principle of Amplitude Modulation is familiar to most engineers, but there are some subtle points of the
subject that should be reviewed before circuit design is attempted. One of these is the circuit's modulation index. In this
note's design example, the input signal to the modulator first passes through a summing amplifier where a DC offset is
added. The need for such an offset arises from the requirement that the modulation index (m) should always be less
than 1. This addendum to the note explains the concept in detail.
Consider the signal shown in Figure 1. It is a
representative input signal to the first stage of the actual
modulator circuit, the G03a IPmodule.
f(t)
A
Voltage Mid Rail (VMR)
f(t)min
Recall that all analog signals within the FPAA are
referenced to Voltage Mid Rail (VMR, 2.5 Volts above
AVDD). In Figure 1, the modulating signal f(t), is shown to
swing about an average value that is "A" above VMR. The
value of "A" is the DC offset supplied by the summing
amplifier. The most negative value of the modulating
signal is noted as f(t)min. For any AM modulator circuit, the
modulation index is given as:
µ=
Figure 1. The modulating input signal.
− f(t)min
A
For the rest of this discussion, two examples will be developed in parallel. The left side figures will illustrate a
modulator designed to produce an under modulated signal and the right will show an over modulating design. The
figures below show the AM signal outputs for each of these circuit types.
f(t)
Phase Inversions
min
A
A'
µ=
− f(t)min − ( −0.6)
=
= 0. 5
A
1.2
Figure 2. An Under Modulated Signal
f(t)min
µ=
− f(t)min − ( −0.6)
=
= 3 .0
A'
0.2
Figure 3. An Over Modulated Signal
For the purpose of explaining the principle, estimating numbers graphically off the plots will suffice. In Figure 2, f(t)min is
-0.6, or 0.6 units below the average value of the input signal (A), and A is 1.2 units above VMR. Plugging in the
numbers we get a modulation index of 0.5 (also referred to as 50% modulation). Anytime a modulation index is less
than 1 (100% modulation), the signal is referred to as under modulated.
Running through the similar calculation for Figure 3, we find the modulation index to be 3.0. Any signal with a
modulation index greater than 1 is referred to as over modulated.
The critical thing to note in Figure 3 is the phase inversion that occurs as the input signal f(t) passes through VMR. The
significance of this does not become obvious until you consider the demodulation of the signal. There is nothing wrong
per se with an over modulated signal, but as we shall see in the following discussion, the recovery of an over
modulated signal is much more difficult. In most AM designs, over modulation is strictly avoided.
As discussed in the application note, the most common AM demodulation scheme involves passing the AM signal
through a diode and then on to a low pass filter. The diode serves to cut away exactly one half of the signal. The low
pass filter then removes the high frequency component (the carrier), leaving only the original modulating signal. This
demodulation scheme is referred to as "diode detection" or alternatively "envelope detection".
Figure 4. The Rectified Under Modulated Signal
Figure 5. The Rectified Over Modulated Signal
Rather than using a single diode, our note's demodulation circuit used a full wave rectifier IPmodule. In doing so, rather
than "cutting away" half of the signal it is instead rectified up as shown in Figures 4 and 5.
Figure 6. The Recovered Under Modulated Signal
Figure 7. Failed Recovery of the Over Modulated Signal
Figure 6 illustrates the successful recovery of the original signal. But, as you can see in Figures 5 and 7, attempting to
use the simple envelope detection scheme on an over modulated signal will result in a signal that may be badly
distorted. Increasing A' (decreasing the signal's modulation index) is the job of the modulator's summing amplifier.
When A' is large enough to ensure that f(t) (the input signal to the modulator) never gets below VMR, then the simple
envelope detection scheme will work.
Recovery of an over modulated signal is not impossible, it is just more difficult. Recall from Figure 3, that the carrier
underwent a phase inversion every time f(t) crossed VMR. That information is critical to the coherent recovery of an
over modulated AM signal. The only way to detect that phase inversion at the receiver (demodulator) is to regenerate
(and lock to) the carrier frequency. This is called a synchronous demodulator and as mentioned above is almost never
employed. It is much easier to transmit an under modulated signal and use simple envelope detection at the receiver.
The programmable voltage source and summing amplifier prior to the modulator circuit are there to ensure that the AC
input signal to the FPAA (symmetric about VMR) gets biased up and thus yields a lower modulation index. If your
system already has the input signal biased up, or you prefer to bias the signal up appropriately outside of the FPAA
then obviously these elements will not be required components of the modulator circuit.
The demodulator circuit also included a voltage source and summing amplifier; these to subtract back out the DC
offset from the recovered signal. One could imagine that this might not be a required feature of the demodulator. For
example, an AC coupled output would achieve the same results.
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1.04