Physics · Ch 15 — Communication Systems

Production of Amplitude Modulated Wave

15.9

Production of Amplitude Modulated Wave

A conceptually simple way to generate an AM wave is to first add the modulating signal to the carrier:

x(t) = A_m\sin(\omega_m t) + A_c\sin(\omega_c t)

and then pass this sum through a square-law device - a non-linear device whose output is:

y(t) = Bx(t) + Cx(t)^2 \quad \text{(Eq. 15.6)}

with $B$ and $C$ constants characteristic of the device. Expanding this (using $\sin^2A = \tfrac{1}{2}(1-\cos 2A)$ and the product identity for sines) produces a DC term plus sinusoidal terms at frequencies $\omega_m$ , $2\omega_m$ , $\omega_c$ , $2\omega_c$ , $(\omega_c-\omega_m)$ and $(\omega_c+\omega_m)$ (Eqs. 15.7-15.8).

This composite signal is then passed through a band-pass filter centred at $\omega_c$ (Figure 15.10), which rejects the DC term and the $\omega_m$ , $2\omega_m$ and $2\omega_c$ components, while allowing $\omega_c$ , $(\omega_c-\omega_m)$ and $(\omega_c+\omega_m)$ through - exactly the three components of Eq. 15.5. So the filter's output is precisely the desired AM wave. …

Figure 15.10Block diagram of a simple modulator for obtaining an AM signal.

What this figure shows. Block diagram, left to right: two inputs, 'm(t) = Am sin(omega_m t) (Modulating Signal)' entering from the top-left and 'c(t) = Ac sin(omega_c t) (carrier)' entering from the bottom-left, both feed into a circular summing-junction node marked '+', whose output labelled x(t) feeds into a rectangular block labelled 'SQUARE LAW DEVICE'; its output labelled y(t) (with the expression Bx(t)+Cx(t)^2 written beneath, pointing to the same arrow) feeds into a rectangular block labelled 'BANDPASS FILTER CENTRED AT omega_c', whose output arrow on the right i …

Figure 15.11Block diagram of a transmitter.

What this figure shows. Block diagram, left to right: an arrow labelled 'm(t)' with the caption 'Message signal' below feeds into a rectangular block labelled 'AMPLITUDE MODULATOR' (which also has a vertical arrow labelled 'Carrier' entering from below); its output feeds into a rectangular block labelled 'POWER AMPLIFIER'; its output feeds via a horizontal line up to a simple antenna symbol (a short mast with an angled line) labelled 'TRANSMITTING ANTENNA' at the top right …

Start your 14-day free trial to unlock the full solution →

← Previous · 15.8Amplitude Modulation Next · 15.10 →Detection of Amplitude Modulated Wave