Full-wave Bridge Rectifier Analysis

Transcription

1 Full-wave Brige Recifier Analysis Jahan A. Feuch, Ocober, 00 his aer evelos aroximae equais for esigning or analyzing a full-wave brige recifier eak-eecor circui. his circui is commly use in A o D cverers, an csiss of ly six circui elemens. Even so, he circui analysis for he full-brige recifier circui is no as simle as firs imressis migh lea e o believe. Figure. Full brige recifier circui Figure shows he schemaic for he full-wave brige recifier. he four-ioe brige cvers boh olariies of he inu waveform ino osiive volage a he u. he caacior cnece o he u noe acs as a charge reservoir, which smoohes he u volage an makes he circui more like csan D volage source. Figure. Ouu volage an inu curren As shown in Figure, he u volage waveform has a rile, which is eenen he caacior size an he amoun of u curren. he inu curren, i in (), csiss of a rail of riangular ulses, which occur when he ioes urn. o analyze he full-wave brige recifier, we will analyze e cuci cycle for he circui. Each cuci cycle lass half a erio, an csiss of wo hases: he hase, when no curren is flowing hrough he ioes o he u; an he hase, when curren is being sulie hrough he ioes o he u. Figure 3 shows he u volage an caacior curren los uring e cuci cycle. Figure 3. Ouu volage an caacior curren for he full-wave recifier uring e cuci cycle

2 o begin he analysis, le vin ( ) V his equai for v in () is chosen so ha he cuci cycle sars in he hase. V is he eak amliue of he inu signal. During he hase, he u volage is equal o v in () minus wo ioe volage ros. he hase sars a ime an ens a + /, which is he beginning of he nex cuci cycle., V VD A he beginning of he hase, he ioes urn, an he caacior sulies all of he u curren. ica (, ) I he value is he beginning of he hase. o fin, we fin he ime a which he ioes urn. his occurs a he ime he sloes of v (,) for he curren cycle an v (,) for he revious cycle are equal.,, V V VD V sin sin V o simlify calculais, we use he rigomeric ieniy sin ( x) x. I V We fin V by lugging + / ino v (,). V V,, V VD he ischarging caacior causes he u volage o ro. V is he volage a he beginning of he hase. he u volage eclines linearly wih ime wih a sloe eenan he u curren an he caacior value. ca, V i x, x V I Base he revious equai, he u volage can be mae seaier by increasing he caacior size. Alhough he circui more resembles an ieal csan volage source, he ioe curren uring he hase is higher, meaning higher ower ioes are necessary. In he esign of recifier circuis, limis are usually lace he amoun of rile allowe in he u volage, so V (he minimum u volage reache uring each cycle) is usually secifie for he circui alg wih he u curren I. he nex se is o fin he caacior values ha woul rovie he secifie amoun of rile. We firs solve for, he ime a he beginning of he hase, a which ime he u volage has roe he secifie amoun. VD, V VD V

3 3 During he firs ar of he hase, he caacior curren is osiive, an he u curren is fe irecly of he brige ioes. A he eak u volage, he caacior curren reverses, an he caacior an ioes boh cribue o he u curren. he curren going ino he caacior uring he hase is ica (,), V sin( ) We now have enough informai o solve for he caacior value. We solve for by seing V equal o v (,). V, V I V V V D V V We will use he hir-orer aylor series olynomial o aroximae ine: ( x) x. I V V V D V V V VD V VD V V he equai above is a rough aroximai for he u caacior, an will give higher caacior values han neee. he lower he value of V is, he higher he error from he aroximai. he seleci of recifier ioes mus ake ino accoun he iniial surge curren, I max. his curren is a resul of he caacior having no charge sore a he beginning of he firs cuci cycle. he iniial surge curren is I max V I is he maximum curren uring he cuci cycle, which is a ime. I V sin he roo mean square (rms) ioe curren is useful, since i is use for calculaing he ower issiai in he ioes. he ioe curren is he same as he inu curren i in (), exce for ha each ioe urns every oher cycle. o fin he rms curren, we inegrae he square of he inu curren over he hase, fin he average square curren over a wo-cycle inerval by iviing by, hen ake he square roo of he resul. iin, V sin We will work wih he inegral ar of he equai. I sin V V sin V sin

4 I V I V sin V V I V V sin V We use he rigomeric ieniy sinxx sinyy I he final equai for RMS curren is V V I V sin sin I x sin y sin o simlify his equai. V sin sin V sin sin V V

5 5 Ouu volage an caacior curren for he full-wave recifier uring e cuci cycle Summary of equais for he full-wave brige recifier Variable Equai Off hase k k k k On hase v () i ca () V I s V VD V sin( ) i in () ca V V max i I Off hase On hase Off hase On hase VD V V VD V I V V D V V VD V sin I I max V I V sin sin V V