1. Multiplier Modulators: in this case the modulation is performed in a straightforward manner by...2. Nonlinear Modulators: in this case modulation is obtained by passing the message signal m(t) t...3. Switching Modulators: In this case the multiplication operation required for modulation is rep...1. Direct method is based on a voltage-controlled oscillator (VCO) to which the message signal m(...2. Indirect method uses a narrowband frequency modulator (NBFM) followed by a frequency multiplie...Table 1: Summary of the different continuous-wave (CW) modulation schemesECEN 4242 Communication Theory Belkacem DerrasUniversity of Colorado at Boulder, ECE Department 1 10/6/01Chapter 2 Summary: Continuous-Wave ModulationBelkacem Derras2.1 ModulationModulation is a process in which a parameter of a carrier waveform is varied in accordance with a given message(baseband) signal. In continuous-wave (CW) modulation, the modulated carrier is a sinusoidal signal of the form c(t)= Accos(2πfct+φ), where fcis the carrier frequency. It is clear that c(t) is characterized by 3 parameters: the amplitudeAc, the frequency fc, and the phase φ. Varying each of these 3 parameters proportionally to a meassage signal m(t) willresult in a certain type of modulation. Thus we can have amplitude modulation (AM), frequency modulation (FM),and phase modulation (PM). FM and PM are related and sometimes they are called angle modulation. Within AM wehave several variants which are: AM, DSB-SC, SSB, and VSB. SSB and VSB can be with or without carrier.The modulation process is performed on baseband signal for several reasons: (1) to adapt the signal bandwidth tothe transmission channel bandwidth, (2) to be able to frequency-multiplex many message signals and transmit themaltogether across the same channel, and (3) to be able to use a small size receiving antennas.2.2 Amplitude ModulationFor the different amplitude modulation methods the modulated signals have the following formsAM signal: s(t) = Ac[1 + kam(t)]cos(2πfct)DSB-SC signal: s(t) = Acm(t)cos(2πfct)SSB signal:VSB signal:where is the Hilbert transform of m(t) and m’(t) is the response of VSB filter to an input m(t).In commercial TV broadcasting a VSB plus a carrier is used for the modulation of video signals. This makes thereceiver much simpler since in the presence of a carrier, an envelope detector is used to demodulate the transmittedsignal.2.3 Angle ModulationThis includes FM and PM. In FM, the instantaneous frequency of a carrier wave is proportional to the message signalm(t), i.e. fi(t)=fc+ kfm(t) and in PM the instantaneous phase is proportional to m(t), i.e. φ(t)=2πfct + kpm(t). There-fore an FM generator is simply an integrator followed by a phase modulator and a PM generator is simply a differen-tiator followed by a frequency modulator.FM signal:PM signal:In fact FM and PM signals may be written using a single expression ,where h(t)=δ(t) for PM and h(t)=u(t) (unit step function) for FM. In commercial FM broadcasting h(t) is chosen asthe impulse response of a preemphasis filter used before the modulation. Strictly speaking, such a modulation is infact neither FM nor PM but a mixture of the two. The preemphasis filter is used to boost high frequency componentsof the message signal m(t) because in FM modulation noise affects more high frequency components of m(t). At thereceiver and after demodulation, a filter called deemphasis filter is used to undo the effect of the preemphasis filterused at the transmitter.st()Ac2------mt() 2π fct()Ac2------mˆt() 2π fct()sin±cos=st()Ac2------mt() 2π fct()Ac2------m′ t() 2π fct()sin±cos=mˆt() mt()∗1πt-----=st() Ac2π fct 2πkfm τ()τd0t∫+cos=st() Ac2π fctkpmt()+()cos=st() Ac2π fct 2πkfm τ()ht τ–()τd0t∫+cos=ECEN 4242 Communication Theory Belkacem DerrasUniversity of Colorado at Boulder, ECE Department 2 10/6/012.4 Generation of Amplitude-Modulated SignalsThe generation of the different amplitude-modulated signals can be performed using 3 different types of modulators:1. Multiplier Modulators: in this case the modulation is performed in a straightforward manner by multiplyingm(t) by Accos(2πfct).2. Nonlinear Modulators: in this case modulation is obtained by passing the message signal m(t) through a nonlin-ear device, then by using an appropriate bandpass filter we can extract the desired component.3. Switching Modulators: In this case the multiplication operation required for modulation is replaced by a simpleswitching operation. This is done in the following way. If we multiply the message signal m(t) by any periodicsignal q(t) (not necessarily a pure sinusoid) that has a fundamental frequency fc. Such a signal q(t) can beexpressed in terms of Fourier series as . This shows that the frequency content(spectrum) of m(t)q(t) is the spectrum M(f) shifted to , , ..., , .... With a bandpass filter of band-width 2W and centered at fc, we can get the desired AM signal, where W is the bandwidth of m(t). In this method,an appropriate and simple switching signal q(t) should be employed.For SSB and VSB signals, in addition to the steps of these three methods, one more step is required which is a band-pass filtering to extract one side band for SSB or to extract one side band and a vestige of the other side band for VSB.2.5 Generation of Angle-Modulated SignalsThere are two methods for generating FM signals: direct method and indirect method.1. Direct method is based on a voltage-controlled oscillator (VCO) to which the message signal m(t) is applied asinput. And since the output frequency of a VCO varies proportionally to the input signal, the result is an FM sig-nal at the VCO output. This method is not used for high precision applications since it is based on varying one ofthe reactive parameters (C or L) of a resonnant circuit of an oscillator.2. Indirect method uses a narrowband frequency modulator (NBFM) followed by a frequency multiplier. TheNBFM uses m(t) as input and produces sNBFM(t)=Accos(2πfct)-2πAckfsin(2πfct)a(t) as output, where. The frequency multiplier is a nonlinear device followed by a bandpass filter to extract