Classical modulation procedures - Signals, Processes, and Systems - page 230

The following R-C-circuit is something like a lowpass filter. In the language of the time
domain the circuit is so sluggish that it cannot keep up with the rapid changes of the
rectified sine. Given the correct time dimensions of the R-C circuit (

= R < C) something
ressembling a sliding average value of the rectified signal appears at the output. This
sliding average value is however nothing other than the source signal.

τ

Note:

A television set provides an appropriate example. It shows 50 half-pictures or 25
full pictures a second. As a result of the sluggishness of our eye in time and the
subsequent processing of the signal in the brain we do not perceive 25 individual
images per second but a picture which changes continuously. The “sliding average
value” of this sequence of pictures, so to speak.

In Illustration 157 instead of a diode the module “absolute value” was selected. The
absolute value corresponds here to the so-called full wave rectification - the negative
region of the sine is in addition represented positively - and represents a non-linear
process which we should look at again more closely at this point.

According to Illustration 147 a kind of doubling of the frequency takes place in the
frequency domain as a result of the “absolute value process“ of a pure sine , just as in the
multiplication of a sine by itself in Illustration 143. As analog multipliers did not exist 50
years ago rectification was used as a kind of substitute multiplication of the AM signal by
a carrier signal of the same frequency.

Just as in Illustration 143 we obtain by means of this „absolute value process“- carried out
in the time domain - an AM signal in the frequency domain with double the carrier
frequency and one with the “carrier frequency” 0Hz , i.e. the original source signal. This
cannot be seen in the time domain.

Now all that remains is to filter out the AM signal with double the carrier frequency by
means of a lowpass filter and the demodulation is complete (see Illustration 157).

Wasting energy: double sideband AM with carrier
The classical process described has serious drawbacks which become apparent when the
AM spectrum is examined. On closer examination the following results from Illustration
154 and Illustration 155:

• By far the larger part of the energy of the AM signal is accounted for by the carrier,
which does not contain any information. Please note that the electrical energy is
proportional to the square of the amplitude, i.e. ~ Û 2 .

• The information of the source signal seems to be present twice over, once in the upper
sideband and once in the lower sideband. As a result the frequency domain is
unnecessarily large.

We shall therefore first try to generate and demodulate a double sideband AM signal
without a carrier in the spectrum. This is shown in Illustration 158. Demodulation is now
carried out by a method based on the above remarks about multiplication by a sinusoidal
carrier of the same frequency. As in Illustration 144 we expect two bands in the range of
the sum and difference frequency, i.e. in the double carrier frequency and at 0 Hz.