Introduction to Modulation

• Basic concept is to vary a carrier signal c(t) = A_c cos (2πf_ct relative to an analog (information) wave form m(t) orbits {b_i}.

• Analog modulation varies the amplitude (AM), frequency (FM), or phase (PM) of the carrier c(t).

• Digital modulation varies the amplitude (M-AM), phase (PSK), pulse characteristics (PAM), or amplitude and phase (MQAM) of the carrier.

Amplitude Modulation

• Amplitude modulation varies the carrier amplitude according to an analog information signal m(t)

•In standard AM modulation, a constant term is added to the information signal to yield the transmitted signals(t)=Ac[1+k_am(t)] cos(2πf_ct).

•The constant term greatly simplifies demodulation but is wasteful of power.

•The envelope of the transmitted signal is a(t)=Ac|1+k_am(t)|.

•If |kam(t)|<=1t then a(t) is always nonnegative, which simplifies demodulation (can demodulate envelope only), but hurts SNR.

•The spectrum of modulated signal is S(f) = .5 k_a A_c [M (f−f_c) + M(f+f_c)] + .5 A_c [ (f−f_c) + δ(f+f_c)]

•The percentage modulation of the signal is defined as max t[100|k_am(t)|].

•The band width of the modulated signal is twice that of the information signal.

Generation of AM Waves

• Multipliers difficult to build in hardware (at least circa 1920)

• AM waves typically generated using a nonlinear device to obtain the desired multiplication

• Square law modulator sums carrier c (t) and information m (t) signals, and then squares the m using a nonlinear device. Unwanted terms are filtered out with a band pass filter.

• Switched modulation sums c (t) and m (t) then passes sum through a switch, which approximately multiplies it by a periodic square wave. This generates the desired signal plus extra terms that are filtered out.

Detection of AM Waves

• AM detection typically entails tradeoffs between performance and complexity (cost).

• Square law detector squares the received signal followed by a low pass filter. This detection is simple but introduces an unwanted distortion term proportional to m²(t).

• Envelope detector is a simple circuit for AM detection consisting of resistors, a capacitor, and a diode. It only works when |k_am(t)| <= 1t (Can’t detect sign change). The RLC circuit must track envelope but not the carrier (f−1c<<

Main Points:

• Modulation is the process of encoding a message signal orbits into a carrier signal.

• AM modulation modulates the amplitude of the carrier wave form with a message signal.

• A constant term is added to the message signal to simplify demodulation: this is wasteful of power and hurts SNR.

• AM waves are typically generated using nonlinear devices.

• AM waves can be demodulated using nonlinear devices with some distortion.

• Envelope detectors are simple cheap devices to detect AM waves with no distortion, but they have poor SNR.