AM Demodulation (peak detect.)

Transcription

1 AM Deodulaion (peak deec.) Deodulaion is abou recovering he original signal--crysal Radio Exaple Anenna = Long Wire FM AM Tuning Circui A siple Diode! Deodulaion Circui (envelop of AM Signal) Filer (Mechanical) Basically a apped Inducor (L) and variable Capacior (C) We ll no spend a lo of ie on he AM crysal radio, alhough I love i dearly as a COOL, ulra-inial piece of elecronics-- Iagine, you ge radio FREE wih no baeries required. Bu The hings we will look a and acually do a bi in lab is o consider he peak deecor (I.e. he eans for deodulaing he AM signal) Fro a block diagra poin of view, he circui has a uning coponen (frequency selecive filer) aached o he anenna (basically a wire for he basic X-al radio). The deodulaion consiss of a diode (called he crysal fro he good old days of Epire of he Air ovie we ll wach) and an R-C filer o ge rid of he carrier frequency. In he Radio Shack version here is no C needed; your ear bones can respond o he carrier so hey ac as he filer. The following slide gives a ore elecronics-oriened view of he circui

2 +V Signal Flow in Crysal Radio-- Circui Level Issues -V BW fo ie Filer: fo se by LC BW se by RLC uning Wire=Anenna usic KX KY KZ frequency ground=0v +V (only) ie So, here s he incoing (odulaed) signal and he parallel L-C (so-called ank circui) ha is hopefully selecive enough (having a high enough Q --a er ha you ll soon coe o know and love) ha unes he radio o he desired frequency. Selecive enough eans ha you receive KX and don also ge KY and KZ (for AM you definiely won ge KZSU:) The diode recified signal looks as shown; basically we keep he posiive side of he signals (referenced o GROUND) [Coen abou X-al Radios; To ge a good signal, you do indeed need a solid ground an ineresing challenge uno iself] Back o he deecion Now, our challenge is o keep he envelop and ge rid of he carrier basically o filer i ou. Per he NEW EE0A diodes are used o creae power supplies (a lab experience now in progress:). Here we are using he incoing AM signal o creae a power supply (I.e. no baery needed) where he ripple is he inforaion (usic ec.) ha we wan o hear. 2

3 Abou Peak Deecion and Wavefors dν i d dν o d Generally..we..wan : dν o dν i d d So, le s look a a cycle of he usic ha rides on op of he uch higher frequency carrier. By analogy o he power supply exaple we will use an R-C filer o decay a a rae ha hopefully follows he odulaed signal bu doesn decay oo fas and herefore follow he carrier. This plo shows us ha he odulaed signal has a slope and he resul of he R-C filer will also have a slope. Generally speaking, we wan he slope of he filering o be seeper han he envelope. If i is NOT seeper, we re no following he odulaing signal (he very las slide in his se corresponds o Diagonal Clipping -- he consequence of going oo slowly). If i s TOO STEEP, we re no filering ou he carrier. OK Le s ry and pu ha in a ore foral (aheaical) for 3

4 Condiion for Opiu RC Incoing Signal Req Vo() Wha happens peak o peak (afer diode) R ν C refresh needed fro nex phase pulse, via diode T ω c ω = RC 2 T ω Here we define he circui o be considered (and used in lab!) a bi ore forally. We have he diode ha ges us half-wave recificaion. Going fro one carrier peak o he nex, we have an RC fall-off as shown. A he end of he following few pages we will deerine an opiu C value (in ers of R, and ω ) This figure siply is showing graphically boh he circui RC in relaionship o he carrier period and also how ha copares o he period of he odulaing signal. The BOXED equaion ells us he final resul in ers of how he RC and odulaion index should uliaely relae o he odulaing frequency Now le s ake a very quick sroll hrough he derivaion of he real inequaliy ha is involved. 4

5 Abou he Equaion for opiu v i = V i ( + cosω ) v o = Ve V e V i ω sinω equaing_v i = v o _(a _ soe _ ) + cosω ω sinω Generally..we..wan : dν o dν i d d Given ha we wan This is THE consrain equaion now le s ake i useful. Assue ha he incoing (envelop) wavefor looks as shown above (firs equaion) The R-C circui will have a response ha looks like ha shown in he second equaion. Taking he derivaive of boh equaions wih respec o ie and applying he desired inequaliy (per he previous slide), he hird equaion is obained. Also, a soe poin in ie he op wo equaions can be equaed and ha resul, cobined wih he hird equaion, gives he fourh equaion--an inequaliy ha relaes: RC ie consan Modulaion index Modulaion frequency ω Unforunaely, how o work wih his equaion is NOT so easy and anoher page of equaion hacking is needed. [We won spend uch ie on he hacking bu we need o ge o he final resul!] 5

6 And he answer is afer _ soe _"rig"_ anipulaions... ( 2 ) 2 ω where _ = RC _ hen : C ( 2) 2 ω R = 2 ω R The KEY equaion for C (in ers of:,ω &R) There are soe rigonoeric ideniies ha allow us o siplify he inequaliy fro he previous page o he one shown here. The RC ie consan is defined as shown. The [bracked/boxed] equaion ells us how sall o ake C (in he RC) in ers of ω, and R. If C is larger, hen we sar o loose inforaion in he envelop due o diagonal clipping. If C is oo sall (I.e. why no ake i ZERO?) hen we cerainly follow he envelop bu we are NOT geing rid of he carrier Basically, if C is oo sall we ve kep oo uch and we haven really deodulaed he signal. 6

7 Wha we DON T wan--clipping envelope V =0 e() Diagonal Clipping Considering he dark side wha we DON T wan If he slopes in he above inequaliy are reversed, here s wha i looks like. Basically, if he RC ie consan is oo long hen as he odulaed signal decreases he sapled poin shown siply falls off and ignores he suff below i. This is called Diagonal Clipping and eans ha he envelop (e()) is no followed by he circui. 7