Question

Three radio stations broadcast at three different carrier frequencies:

TIL Ulaucasts at three different carrier frequencies: 700 kHz, 1000 kHz, and 1400 Hz The antenna at the radio receiver front-end receives the voltage signals from all three stations, so the input to the radio receiver (tuner) will be the sum of these signals. You are asked to design a parallel resonant RLC circuit with a quality factor of 15 to be used as a tuner to receive only the broadcast voltage signal at carrier frequency 1000 kHz while significantly attenuating the voltage signals from the other two stations. (a) Sketch your parallel resonant RLC circuit and determine the appropriate values for the inductor and the resistor if the capacitance of the capacitor used is 1 nF = 10°F. 15 points (b) Write down the transfer function and the exact analytical expressions for both the magnitude response and the phase response of your tuner circuit. 12 points

Answer 1

Ans: Giuen camier freq P2= 1000 KM A3= 14OO KH 700 KH facdox Quality s Part Ca)- Here we need to receioe only ignal ohich has a carrier freq 1000 KH2. This means his fYea reachve comporemt cancel eo ch o the at XL 2TFL where, f 1000 KM2 C2TF) C C2TT 1000 7103)16 4TI03 -3 00253 IO Now we cal culad e the R

Know the quo lity facdor we Q- for RLC circut quality factor calcala deal as Q=R nocw me value of C,L,Q here we Q IS 10 15 J0.02 X10 R 2.386 X10 2-386 K PaTt Cb) for RLC circat phase diag coill be 100k like this V TR = L90 L-90 Phase diagram

VIC Vs=UV t000kn to 9p Parallel RLC ciTcuit So, from phase diagram have aken uoltage as reference becoase in parallel cireaie remain ond we haue plottedl all Somer Componend current accondi ng can sa From Phase diagram toe TRt (I-Ie) Is FRtCF-Te) Ts 11 X c Ts where nd TesV V TRe R wwwgp 17

then according to Kirchoff's Current Law Is-TR du Ts Svdt-c diw.nit Is-du dt R cdrs olt .1. V L dicide whole ea dv + dt + RC dt main differendial ea this is lap lase taansfox mation, Now ta lke a V US+ Lc Vs2 . Ts + 1 RC T's RC LC this is foT CuTTemd Res 2 2 RC S t RC LC

Magni kude response 3 f rom t Cimpendan ce) where YL ref ot eq take a 1 Y Codlmittance) Xt 2nfC can also write OT you 4 + i cwc- R this eao from ite Can Co e TR CJce

+j Cwc 1+ CwCR- magnikude re sponse R2 1+ CwcR+ to calcaldte magnikude you use Can for mula below atb) Ca-b) a-b from e Phase So response dan CocR- OCiw

Here in question we have given 3 carrier frequencies, but while calculating value of inductor and resistor we need to focus on only one frequency that we need to receive i.e 1000kHz. This is part a. Then in part b using a kirchoff's current equation we have derived transfer equation. This is a parallel circuit hence voltage remain same in all branches. Then from the transfer equation we have derived impendance and from there magnitude response and phase response.