EE160 - Digital and Analog Communication SystemsSan Jos´e State University. Spring 2003.Lecture on PM/FM Modulator and Demodulator StructuresModulators• VCO modulator: The simplest way to generate an FM signal is to design an oscillatorwhose frequency changes with the input voltage, or voltage-controlled oscillator (VCO).• Indirect modulator: This modulator consists of two parts: (i) a narrowband anglemodulator followed by (2) a frequency multiplier and bandpass filter.IntegratorFM-m(t)+90oPMA narrowband phase modulatorBPFNarrowbandangle modulatorFrequencymultiplierxnInput OutputIndirect phase modulatorDemodulatorsMost FM demodulators transform the FM signal into an AM signal and have a bandwithequal to the channel bandwidth Bc.• FMFB demodulator: An FM demodulator with feedback (FMFB demodulator) isshown below.ReceivedsignalBPFLPFDiscriminator(FM-to-AM)OutputVCO1An FMFB demodulator• PLL demodulator: An alternative implementation is the use of a phase-locked loop(PLL). Next, the principle of operation of this type of demodulator is presented. Forsimplicity, the presence of noise is ignored.e(t) v(t)ReceivedsignalPhasecomparatorLoop filterG(f)OutputVCOA PLL-FM demodulatorIn the following, we will show that the output of the PLL-FM demodulator is propor-tional to the message signal m(t).The input to the demodulator is the angle modulated signalu(t)=Accos [2πfct + φ(t)] ,where (FM),φ(t)=2πkft−∞m(τ)dτ.When its input equals zero, the VCO generates a sinusoidal waveform of frequency fc.Let the output of the loop filter be v(t). Then the instantaneous frequency of the VCOis given byfv(t)=fc+ kvv(t),where kvis a deviation constant (Hz/volt). The output of the VCO isφv(t)=Avsin [2πfct + φv(t)]= Avsin2πfct +2πkvt0v(τ )dτ .The phase comparator is a multiplier and lowpass filter with outpute(t)=12AvAcsin [φ(t) − φv(t)] =12AvAcsin [φe(t)] .Assuming the the PLL is in lock, φe(t)  1, and sin [φe(t)] ≈ φe(t). This means thatan equivalent linear model of the PLL can be employed, using phase as input signal.As such, it has a transfer function that is derived next.The phase error can be expressed asφe(t)=φ(t) − 2πkft0v(τ )dτ,2that is,ddtφe(t)+2πkfv(t)=ddtφ(t),from which it follows thatddtφe(t)+2πkf∞0φe(τ)g(t − τ)dτ =ddtφ(t),where g(t) is the impulse response of the loop filter. The Fourier transform of theabove equation is(j2πf)Φe(f)+2πkvΦe(f)G(f )=(j2πf)Φ(f).Consequently,Φe(f)=11+kvjfG(f)Φ(f).Therefore the control voltage isV (f)=Φe(f)G(f )=G(f)1+kvjfG(f)Φ(f).Assuming that |kvG(f)jf| 1, in the range |f| <W,V (f)=jfkvΦ(f)=j2πf2πkvΦ(f).As a result,v(t)=12πkvddtφ(t)=kfkvm(t).Errorphasev(t)-Loop filterG(f)Inputphase+OutputVCOphaseVCOEquivalent linear model of a PLL-FM