A Few Basics Modulation AM FM Your favorite music The A m plitude Modulated AM version of your music Your station s carrier frequency The Frequency Modulated FM version of your music Demodulation is about recovering the original signal Crystal Radio Example Antenna Long WFM ire AM A simple Diode Tuning Circuit Demodulation Circuit Basically a tapped Inductor L and variable Capacitor C envelop of AM Signal Filter Mechanical Signal Flow in Crystal Radio Circuit Level Issues V W ire Antenna V time BW Filter fo set by LC B W set by RLC music fo tuning ground 0V KX KY KZ frequency time V only Series Resonant Tank Circuit R C L o Z j R 1 jQs o where o L Xs Qs R Rs o 1 LC Parallel Resonant Tank Circuit R t C L o Y j G t 1 jQp o where Rp Rt oC Qp 1 Gt X oC p About notation and components We ll use the p and s subscripts per text and their definitions in terms of respective R and X values where X is either L or 1 C Components are NOT ideal see Chapter 6 reading Basically when talking about resonant circuits we want to have equivalent tank circuit either series or parallel per above to cases Example of non ideal Inductor and transforming back to equivalent tank circuit R t C L R R t C Lp Conversion series to parallel Qs2 1 Lp L 2 Qs Rt R Qs2 1 where Qs o L R Final equivalent resonant tank circuit transformed L now sets resonant frequency let s see how these transformations work A bit more about Q We can think about and or measure the quality factor Q in two ways parallel sub p or series sub s As discussed in text section 6 7 2 there is ultimately only one Q for the circuit we ll call it Q c The definitions of the parallel and series component Q s are as follows Q p R p X p parallel or shunt Q s X s R s series Based on simple math comparing the series and parallel cases for either capacitor or inductor R p Q c 2 1 R s and Q c Q p Q s We can derive all of the following relationships based on using the above relationships Conversion Relationships Capacitors C R p p r a p Cs eq Qp2 1 Cp 2 Qp Rs eq Rp 1 Q Rp Qp Xp X p 1 Cp 2 p se rie le l a l to se rie s R C Cp eq s to p ar al s s Qs2 Cs 2 Qs 1 Rp eq Rs Q 1 2 s le l Xs Qs Rs X s 1 Cs Conversion Relationships Inductors L Ls eq p Q 2p Lp 2 Qp 1 Rs eq Qp R p Rp 1 Q Rp Xp X p Lp 2 p p se a r a rie lle l to r se i es Lp eq s to p ar al le R s L s Qs2 1 Ls 2 Qs 2 Rp eq Rs 1 Qs l Xs Qs Rs X s Ls Another Example a k a Lab 1 original circuit R L t C R 2 t C L 1 R 1 L L R 2 1se se convert to series Following steps Combine L 1 L 2 series equivalent L new Convert L new R se back to parallel Result gives final equivalent tank circuit Design Oriented Example including use of transformer concepts text Sect 6 8 2 L1 L2 N L1 Rt N2 R1 R per book notation n N n1 LT L L2 L1 L 2 t L 1 R 1 Example R 1 50 In order to have R t 2K N 2 40 or N 6 3 L T L 1 caution this simple relationship works for Q p 10 otherw ise one needs to do the transformations per above example Useful more complete Design Equations per supplemental book by Krauss last year s text For Qc Qt o BW 10 1 2 BW Rt 1 L 2 oC C L 2 R t C L RN 1 1 Qt Q Qp If t 10 N N For Qp 10 L1 se L1Qp2 2 Qp 1 L2 L L1 se 0 1 Qp 0 R1 o Qp 1 L1 1 2 Qp Q 1 1 Qp 2 N 2 t Rt R1 1 2 For Qp 10 Qt N L L1 N L2 N 1 L1 L L1 Qp