%The?phase?locked?loop（PLL）adjusts?the?phase?of?a?local?oscillator?
%w.r.t?the?incoming?modulated?signal.In?this?waythe?phase?of?the?
%incoming?signal?is?locked?and?the?signal?is?demodulated.This?scheme
%is?used?in?PM?and?FM?as?well.
%We?will?implement?it?by?using?a?closed?loop?system.Control?systems
%techniques?are?applied?here.
%**************************************************************


%STEP?RESPONSE?OF?THE?FIRST?ORDER?CLOSED?LOOP?TRANSMITTANCE?OF?PLL
%H（S）?=?1;
%SYSTEM?TYPE?NUMBER?=?1;
%THETAo/THETAi?（output?phase/input?phase）


close?all
kv?=?1;
kd?=?1;
dt?=?0.01
t?=?0:dt:2
u?=?ones（1length（t））
g11?=?[tf（[2*pi*kv*kd][1?2*pi*kv*kd]）]??%its?the?transfer?function?given?in?the?handout
[y11?t]?=?lsim（g11ut）
figure
plot（ty11）
xlabel（‘TIME?IN?SECONDS‘）
ylabel（‘AMPLITUDE‘）
title（‘STEP?RESPONSE?OF?1st?ORDER?CLOSED?LOOP?TRANSMITTANCE‘）
%***************************************************************


%STEP?RESPONSE?OF?THE?FIRST?ORDER?CLOSED?LOOP?ERROR?TRANSMITTANCE?OF?PLL
%ALL?THE?OTHER?FACTORS?H（S）?etc?ARE?SAME?HERE
%THETAe/THETAi?（same?interp.?as?above）

g12?=?[tf（[1?0][1?2*pi*kv*kd]）]???%error?transmittance?given?in?the?handout
[y12?t]?=?lsim（g12ut）
figure
plot（ty12）
xlabel（‘TIME?IN?SECONDS‘）
ylabel（‘AMPLITUDE‘）
title（‘STEP?RESPONSE?OF?1st?ORDER?CLOSED?LOOP?ERROR?TRANSMITTANCE‘）
%****************************************************************

%STEP?RESPONSE?OF?THE?FIRST?ORDER?CLOSED?LOOP?TRANSMITTANCE?OF?PLL
%BETWEEN?VCO?AND?INPUT?SIGNAL?PHASE
%H（S）?=?1;
%SYSTEM?TYPE?NUMBER?=?1;
%V2/THETAi
Kd?=1;
g13?=?[tf（[Kd?0][1?2*pi*kv*kd]）]???%vco?voltage?and?input?signal?transmittance
[y13?t]?=?lsim（g13