Signal Rectification

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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, half-wae and fullwae. Le s firs consider he ideal half-wae 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 half-wae 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 half-wae 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 half-wae 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 half-wae recifier. he DC componen of he oupu is: V = ( ) d 2 = sinωd d = π 2 Unlike he inpu, he oupu has a non-zero (posiie) DC componen ( V = π )! () V = π - Q: I see. non-zero 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 half-wae 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 half-wae recifier hrough a low-pass 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 half-wae recifier migh be useful. Bu, is here any way o acually build his magical deice? : n ideal half-wae 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 half-wae 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 half-wae 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 half-wae 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 non-zero (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 so-called full-wae 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 full-wae recifier: Ideal S ( ) ( ) - Full-Wae Recifier S for S < = S for S > - S If he ideal half-wae recifier makes negaie inpus zero, he ideal full-wae 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 half-wae recifier! V = ( ) d 2 = sinω d sinω d = () 2 2 π V = 2 π - Q: Wow! Full-wae recificaion appears o be wice as good as halfwae. Can we build an ideal full-wae recifier wih juncion diodes? : lhough we canno build an ideal full-wae recifier wih juncion diodes, we can build full-wae recifiers ha are ery close o ideal wih juncion diodes! Jim Siles he Uni. of Kansas Dep. of EECS

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