Signal Rectification


 Dwight Morris
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1 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, halfwae and fullwae. Le s firs consider he ideal halfwae recifier. I is a = f : circui wih he ransfer funcion ( ) S Ideal S ( ) ½ Wae ( )  Recifier for S < = S for S > S Jim Siles he Uni. of Kansas Dep. of EECS
2 9/3/25 Signal Recificaion.doc 2/ Prey simple! When he inpu is negaie, he oupu is zero, whereas when he inpu is posiie, he oupu is he same as he inpu. Q: Prey simple and prey supid I d say! his migh be your mos poinless circui ye. How is his circui een remoely useful?? : o see why a halfwae recifier is useful, consider he ypical case where he inpu source olage is a sinusoidal signal wih frequency ω and peak magniude : s () ( ) = sinω S  hink abou wha he oupu of he halfwae recifier would be! Remember he rule: when S () is negaie, he oupu is zero, when S () is posiie, he oupu is equal o he inpu. Jim Siles he Uni. of Kansas Dep. of EECS
3 9/3/25 Signal Recificaion.doc 3/ he oupu of he halfwae recifier for his example is herefore: ()  S () Q: ha s he lames resul I e eer seen. Wha good is half a sine wae? Why een boher? : lhough i may appear ha our recifier had lile useful effec on he inpu signal S (), in fac he difference beween inpu S () and oupu () is boh imporan and profound. o see how, consider firs he DC componen (i.e. he imeaeraged alue) of he inpu sine wae: VS = S( ) d = sinωd = Jim Siles he Uni. of Kansas Dep. of EECS
4 9/3/25 Signal Recificaion.doc 4/ hus, (as you probably already knew) he DC componen of a sine wae is zero a sine wae is an C signal! Now, conras his wih he oupu () of our halfwae recifier. he DC componen of he oupu is: V = ( ) d 2 = sinωd d = π 2 Unlike he inpu, he oupu has a nonzero (posiie) DC componen ( V = π )! () V = π  Q: I see. nonzero DC componen eh? So refresh my memory, why is ha imporan? Jim Siles he Uni. of Kansas Dep. of EECS
5 9/3/25 Signal Recificaion.doc 5/ : Recall ha he power disribuion sysem we use is an C sysem. he source olage S () ha we ge when we plug our power cord ino he wall socke is a 6 Hz sinewae a source wih a zero DC componen! he problem wih his is ha mos elecronic deices and sysems, such as Vs, sereos, compuers, ec., require a DC olage(s) o operae! Q: Bu, how can we creae a DC supply olage if our power source S () has no DC componen?? : ha s why he halfwae recifier is so imporan! I akes an C source wih no DC componen and creaes a signal wih boh a DC and C componen. We can hen pass he oupu of a halfwae recifier hrough a lowpass filer, which suppresses he C componen bu les he DC alue ( V = π ) pass hrough. We hen regulae his oupu and form a useful DC olage source one suiable for powering our elecronic sysems! Power Supply Jim Siles he Uni. of Kansas Dep. of EECS
6 9/3/25 Signal Recificaion.doc 6/ Q: K, now I see why he ideal halfwae recifier migh be useful. Bu, is here any way o acually build his magical deice? : n ideal halfwae recifier can be buil if we use an ideal diode. i i D i D  S () R () _ If we follow he ransfer funcion analysis seps we sudied earlier, hen we will find ha his circui is indeed an ideal halfwae recifier! for S < = S for S > S Jim Siles he Uni. of Kansas Dep. of EECS
7 9/3/25 Signal Recificaion.doc 7/ f course, since ideal diodes do no exis, we mus use a juncion diode insead: i ()  S () D () R () Q: his circui looks so familiar! Haen we sudied i before? : Yes! I was an example where we deermined he juncion diode circui ransfer funcion. Recall ha he resul was: S 7. for S > 7. = for S < 7. S.7 V Noe ha his resul is slighly differen from ha of he ideal halfwae recifier! he.7 V drop across he juncion diode causes a horizonal shif of he ransfer funcion from he ideal case. Q: So hen his juncion diode circui is worhless? Jim Siles he Uni. of Kansas Dep. of EECS
8 9/3/25 Signal Recificaion.doc 8/ : Hardly! lhough he ransfer funcion is no quie ideal, i works well enough o achiee he goal of signal recificaion i akes an inpu wih no DC componen and creaes an oupu wih a significan DC componen! Noe wha he ransfer funcion rule is now:. When he inpu is greaer han.7 V, he oupu olage is equal o he inpu olage minus.7 V. 2. When he inpu is less han.7 V, he oupu olage is zero. So, le s consider again he case where he source olage is sinusoidal (jus like he source from a wall socke!): s () ( ) = sinω S.7  he oupu of our juncion diode halfwae recifier would herefore be: Jim Siles he Uni. of Kansas Dep. of EECS
9 9/3/25 Signal Recificaion.doc 9/ ().7  S () lhough he oupu is shifed downward by.7 V (noe in he plo aboe his is exaggeraed, ypically >>.7V), i should be apparen ha he oupu signal (), unlike he inpu signal S (), has a nonzero (posiie) DC componen. Because of he.7 V shif, his DC componen is slighly smaller han he ideal case. In fac, we find ha if >>.7, his DC componen is approximaely: V 35. V π In oher words, jus 35 mv less han ideal! Q: Way back on he firs page you said ha here were wo ypes of recifiers. I now undersand halfwae recificaion, bu wha abou hese socalled fullwae recifiers? Jim Siles he Uni. of Kansas Dep. of EECS
10 9/3/25 Signal Recificaion.doc / : lmos forgo! Le s examine he ransfer funcion of an ideal fullwae recifier: Ideal S ( ) ( )  FullWae Recifier S for S < = S for S >  S If he ideal halfwae recifier makes negaie inpus zero, he ideal fullwae recifier makes negaie inpus posiie! For example, if we again consider our sinusoidal inpu, we find ha he oupu will be: ()  S () Jim Siles he Uni. of Kansas Dep. of EECS
11 9/3/25 Signal Recificaion.doc / he resul is ha he oupu signal will hae a DC componen wice ha of he ideal halfwae recifier! V = ( ) d 2 = sinω d sinω d = () 2 2 π V = 2 π  Q: Wow! Fullwae recificaion appears o be wice as good as halfwae. Can we build an ideal fullwae recifier wih juncion diodes? : lhough we canno build an ideal fullwae recifier wih juncion diodes, we can build fullwae recifiers ha are ery close o ideal wih juncion diodes! Jim Siles he Uni. of Kansas Dep. of EECS
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