AN-953 ᆌᆩԴऻ One Technology Way t P.O. Box 9106 t Norwood, MA 02062-9106, U.S.A. t Tel: 781.329.4700 t Fax: 781.461.3113 t www.analog.com ਏᆶՊײఇຕڦথຕጴೕ୲ࢇׯഗ(DDS) ፕኁǖKen Gentile ACCUMULATOR C TUNING WORD C C Q C D P ANGLE-TOAMPLITUDE CONVERSION D DAC 07234-001 SAMPLE CLOCK 1. एᇀેेഗۆڦ႙DDSॐࠓ ߁ຎ Պײఇຕएᇀેेഗۆڦ႙DDSॐࠓڦႪ۩ӲLj ॽDDSڦ๑ᆩકቛڟᄲ൱ඓᆶຕೕ୲ࢇڦׯᆌᆩ )૩සඪᅪೕ୲ᆌᆩ*ăAD9913ADIࠅິڼڦᅃ༵ࠃ ՊײఇຕॐࠓĂएᇀેेഗڦDDSׂă एᇀેेഗۆڦ႙DDS एᇀેेഗۆڦ႙DDSᅈડᇀᅃ߲ેेഗᅜ֑ᄣ้ዓ ୲ࡃڿ൱ࢅຕጴۙၿጴ)֖९1*ăኄࣷሞેेഗ ڦิׂ܋ᅃ้߲क़ႾଚڦຕጴጴLjຕጴጴ၍Ⴀሺ ٷLjेેڟഗڟٳഄፌٷኵ2CժገăᅺُLjેेഗ ਏᆶᅃ߲ࠦۨఇຕ2Că ેेഗཚࣷԥপP࿋)ৈ๑ᆩMSB*LjᅜՍ३ ၭໜഄࢫڦঙ܈ናޗገ࣑ఇٷڦၭࢅްሗ܈ăኄᄣLj ሞঙ܈ናޗገ࣑ഗڦ܋Ljેेഗׂิ้ڦक़Ⴞଚຕ ጴጴྺྷݔڦଭڟ2P − 1ă ঙ܈ናޗገ࣑ഗॽP࿋ጴᆙพڇڟ࿋ᇶฉڦᅃංฉLjन ॽ02Pܾڦాྷݔኵ၍Ⴀᆙพྺ02πࢷڦాྷݔ ܈ঙăኄዖᆙพ݆ݛ๑ঙ܈ናޗገ࣑ഗీݥᆶၳॽں P࿋ጴገ࣑ྺD࿋ናޗኵ(A)ă ඹᅟॽঙ܈ናޗገ࣑ࠀీકቛྺཞ้ኴႜኟ၀ࢅᇆ၀ ገ࣑LjᅺُLjཞ้༵ࠃኄଇዖገ࣑ݛӄڦDDS९ă ߶ঙ܈ናޗገ࣑ഗኮࢫڦᅃD࿋DACLjॽঙ܈ ናޗገ࣑ഗׂิڦD࿋ຕጴናޗኵገ࣑ྺఇె႑ࡽă ࡕྺDAC܋ฉڦᅃ߲ኟ၀հႚLjഄೕ୲ᆯેेഗ ڦೝገ୲ਦۨă ኍܔएᇀેेഗۆڦ႙DDSLjᅜူײݛ๕ٳକDAC ܋ฉ၄ڦኟ၀հڦೕ୲ǖ fO = M fS 2C ഄዐǖ fOྺࢇׯೕ୲ă fSྺ֑ᄣೕ୲ă M/2CྺၭຕԲ૩ᅺጱ)MࢅCྺኟኝຕ*ă ᅃӯܸჾLjM๔ዕၭᇀ2C – 1LjޏሶՍࣷࢇׯᅃ߲లઊຯ ༬ၟೕ୲ă2CྺેेഗڦఇຕLjഄዐCྺેेഗڦ࿋ ܈ăኝຕMᅃӯྺೕ୲ۙၿጴăMྺኝຕLjᅺُfO ๔ዕሞᅜူೕ୲णኮాǖ { f O ∈ 0, ገ࣑ࡗײᅜ๖ྺᅜူෙঙࡧຕ࠲ဣǖ x = sin(2πk/2P) ഄዐǖ Pྺٗેेഗइڦڥ࿋ຕă kྺඪᅪߴ้ۨਗ਼ܾڦኵă ߲kኵܔᆌڦAኵऺ໙ྺ݆ݛǖܔxኵႜݣĂೋᅎ ࢅปتLj๑ڥAྺׯଭ2D − 1ڦాྷݔኝຕኵă ( 1) 2 S C , 2 fS 3 fS , , 2C 2C (2 , C −1 ) − 1 fS 2 C } (2) ᅺُLjٗDCৎ½fSڦೕ୲णਏᆶ၎ڪक़߰fS/2Căኄ ᅃक़߰fS/2CྺDDSڦೕ୲ݴՐ୲ăॠֱfOೕ୲णᅜ ݀၄LjDDSેेഗڦఇຕ(2C)ཞ้ਦۨକDDSڦೕ୲ݴ Ր୲ࢅీڦೕ୲ຕă૩සLjܔᇀߴ֑ۨᄣ୲ (f S )Lj ֑ ᆩ 32࿋ ે े ഗ ڦDDS ڦ ೕ ୲ ण ਏ ᆶ 2,147,483,648DŽन231Dž߲ీڦೕ୲ă Rev. 0 | Page 1 of 4 AN-953 ᆌᆩԴऻ न๑ᆛᆶසُڦٷᆩೕ୲णLjएᇀેेഗۆڦ႙DDS ධփీׂิᅃၵᆶᆩڦೕ୲)ၟඓڦfS/10*Ljᅺྺેे ഗఇຕྺࠦۨኵLjܸۙၿጴ(M)ՂႷྺኝຕăײݛ๕1 ၂๖Ljೕ୲֑ܔᄣೕ୲ڦԲኵՂႷፁᅜူ࠲ဣǖ fO M = C fS 2 ՊײఇຕDDSॐࠓ๑ײݛ๕3Վႚྺူ๕ǖ fO M = fS N (3) ኍڪܔᇀ֑ᄣ୲గᅃኝຕሀຕڦೕ୲)૩ස f S/10*LjfOᅜ๖ྺfO = fS/Q)Qྺኝຕ*ăᆩfS/Qݛ༺پ ײ๕3ዐڦfOᅜڟڥǖ 1 M = Q 2C ݛܾڼ௬ሗොႠీăසࡕፔ݆փړLjႪ߀ેेഗఇຕ ࣷᆅೕ࿁ၟăՊײఇຕํแᄲ൱႐ยऺLjፌٷ ں܈ײইܔگሗොႠీڦඪࢆ௬ᆖၚă ( 4) ൱MڟڥM = 2C/QăᅺྺMࢅQՂႷྺኝຕLjᅜ ྸᅃፁײݛ๕4ڦQኵྺᅜ๖ྺ2Kႚ๕ڦኵLjഄዐ Kྺኝຕăᄺ৽ຫLjM = 2C/2K = 2C − K )CࢅKྺኝຕ*ă ਉ૩ܸჾLjସf O = f S/8Ljժ्ยCྺ32LjሶQ = 8 = 2 3Lj M = 232 − 8 = 224 = 536,870,912)ኝຕ*ăଷᅃݛ௬LjසࡕfO = fS/10Lj ሶQྺ10LjM = 232/10 = 429,496,729.6)ݥኝຕ*Ljኄᅪ࿆ጣ ۆ႙DDSփీׂิඓೕ୲fS /10ăۆ႙DDSᅜࢇׯᅃ ߲टഄথৎfS /10ڦೕ୲)एᇀೕ୲ݴՐ୲*Ljڍփ ඓڦfS /10ೕ୲ăܠٷຕ൧ူLjटഄথৎᅜথ ڦLjڍሞగၵ൧ူ)૩සྪஏ้ዓ*LjՂႷइڥඓڦ ೕ୲ă ࠵ִײݛ๕4ᅜ݀၄Ljᆸ֨ڦԲኵᆯેेഗڦఇຕ(2C) ඓۨLjܸఇຕྺᆯેेഗٷၭਦۨۨࠦڦଉă၂Lj ેेഗۨࠦڦఇຕ၌କᆩೕ୲णăڍLjසࡕ ેेഗఇຕۙLjሶQኵॽփ၌ᇀ2Kႚ๕ڦኵLjኄ৽ ՊײఇຕDDSॐࠓڦएԨᇱă ՊײఇຕDDS Պײఇຕᆯएᇀેेഗۆڦ႙DDSॐࠓՎࣅܸઠ )֖९2*ăՊײఇຕरຍీࠀڦ߀Վેेഗ ఇຕLjํڍा֡ፕഐઠඐԲডްሗăްሗႠภतଇݛ௬ă ڼᅃݛ௬ঙ܈ናޗገ࣑ഗॽኝ߲P࿋)ྷݔ02P* ᆙพྺ02πྷݔ܈ࢷڦăঙ܈ናޗገ࣑ഗኮᅜీߛ ၳ߾ፕLjኟڥᅮᇀኄዖएຕྺ2ڦᆙพ݆ݛăॽેे ഗఇຕඪᅪՎ߸ྺ2ڦᅜྔڦഄኵՂࣷྵݒঙ܈ ናޗገ࣑ഗᄲ൱ڦᆙพ݆ݛăྺਖ਼ޜኄᅃઓవLjՊײ ఇຕॐࠓ૧ᆩޤዺેेഗ๑ዷેेഗੂഐઠ߀Վକఇ ຕLjڍධԍঙ܈ናޗገ࣑ഗᄲ൱ڦᅜ2ྺएຕڦ ڦᆙพă (5) ഄዐMࢅNྺኝຕLjժ1 ≤ M < N/2ă ൩ጀᅪLjՊײఇຕDDSڦೕ୲Բ)ײݛ๕5*ᇑएᇀેे ഗۆڦ႙DDSڦೕ୲Բ)ײݛ๕3*ݥ၎ຼăྸᅃڦ൶՚ ሞᇀLjՊײఇຕփᄲ൱Nྺ2ڦኸຕăᅜඪ ڦኝຕăܔNྸڦᅃ၌LjݴړຕM/Nሀፌၭၜ้Lj NՂႷፁ0 < N < 232ăኄᅃ၌क़থԍኤକঙ܈ናޗ ገ࣑ഗᄲ൱ڦ2ڦԲ૩ă AD9913ڦՊײఇຕࠀీܔෙ߲32࿋स٪ഗՊײNĂ YࢅXڦኵઠํ၄ڦLjኄၵኵ2ዐఇຕ੦இडڦ ăNĂXࢅYڦຕኵՊྺྷݔײ0232 − 1)ࡤԨຕ*LjڍNڦ ူ၌M၌LjनN > 2Mă fSĂfOĂMĂNĂYࢅXኮक़࠲ڦဣጺᇀײݛ๕6ăfOࢅfS ڦኵඓۨକMᇑN࠲ڦဣLjनڪᇀሀፌၭၜݴڦຕ M/NăMĂNࢅેेഗڦఇຕ(2C)ཚࡗ݆أඓۨକXᇑ Y࠲ڦဣă fO M = fS N X → N 2C M − XN Y → Y = 2 C M − XN (6) ഄዐǖ Xྺڦ݆أኝຕฆă Yྺኝຕᇆຕă ᆶڦLjMඓۨକેेഗႾଚڦዜႠLjनેे ഗՂႷՓ૦Mኵ֍ీྜׯᅃ߲Ⴞଚժ࣮ݓഐ๔ۅă ኄᅃႾଚ൬ںዘްăኵڥጀᅪڦLjසࡕY ྺ0LjሶՊײఇຕܠᇆڦLjनfOᅜ૧ᆩՔጚDDS থٗfSࢇׯă Rev. 0 | Page 2 of 4 AN-953 ᆌᆩԴऻ MODIFIED ACCUMULATOR MODULUS (N) REMAINDER (Y) C MODULUS CONTROL LOGIC C Q C D P ANGLE-TOAMPLITUDE CONVERSION D DAC 07234-002 TUNING WORD (X) SAMPLE CLOCK 2. ՊײఇຕDDSॐࠓ Պײఇຕ๖૩ ୯ኄዖ൧ǖfS = 250 MHzLjႴfOኵྺ25 MHzăኄ ዖ൧ᄲ൱ࢇڦׯೕ୲ྺ֑ᄣ୲ڦኝຕሀຕLj नf O = f S/10ăf O/f Sڦೕ୲Բ(25,000,000/250,000,000)ሀ ፌၭၜՍڟڥMᇑNLjनǖ M/N = 25,000,000/250,000,000 = 1/10 ᅺُLjM = 1LjN = 10ăᆯMࢅNڦኵᆼ໙ڥXࢅYڦኵǖ X = 429,496,729LjY = 6ă ॽኄၵኵՊײAD9913ዐՍሞߴۨڦ250 MHz֑ᄣ้ ዓׂ้ิඓڦ25 MHzೕ୲ă ՔጚDDS݆ሞf S = 250 MHz้ࢇׯඓڦ25 MHz ೕ ୲ Lj ᅜ ࢇ ڦ ׯፌ থ ৎ ೕ ୲ ྺ 25.000000023283064365386962890625 MHzăሞྪஏᆌᆩ ዐLjኄᅃৎຼኵփথڦLjᅺྺᄲ൱ڦೕ୲ਨܔ ၭຕဃֶڦ25 MHză ୯ᅺ໎! ՂႷຫڦLjܠٷຕऺ໙ײႾ)සExcel®ĂMathcad®ࢅ MATLAB®*ڪሞऺ໙XࢅY้ࣷۼᆅຕኵဃֶLjኄၵဃ ֶᇸᇀాևปईপتLjሞႜٷຕ݆أࢅ݆ױ ้Սࣷ၄ઠăᆶڦLjWindows® XP֡ፕဣཥڦ ऺڦ໙ഗײႾሶᅜ༵ࠃፁࠕߛڦຕኵ܈ઠኴႜኄၵ ऺ໙Ljܸփׂࣷิฉຎဃֶ)ณܔᇀAD9913Պײ၎࠲ ڦ32࿋ຕසُ*ă๚ํฉLjAD9913ೠࠚӱॲਸ݀ට ᇵ६କ࠲ᇀຕኵ܈࿚༶ڦ၎࠲ኪ๎Ljᅙঢ়३ၭକป ईপဃֶă ྺକຫปࢅপتڦᆖၚLjምْ୯ኄዖ൧ǖ ႴfOኵྺ25 MHzLjڍfSྺ249,999,999.5 MHz)ܸփ250 MHz*ăfO/fSڦೕ୲Բ(25,000,000/249,999,999.5)ሀፌၭ ၜՍڟڥMᇑNLjनǖ M/N = 25,000,000/249,999,999.5 = 50,000,000/499,999,999 ᅺُLjM = 50,000,000LjN = 499,999,999ǗᆯMࢅNڦኵᅜ ໙ڥǖX = 429,496,730LjY = 229,496,730ă සࡕ๑ᆩExcelऺ໙LjXኵᇑฉຎኵ၎ཞLjڍYኵሶྺ 229,496,736ăጀᅪፌگᆶၳ࿋ྺ6Ljܸփ0)ኟඓኵ*ă ဃֶटഄၭ)ৈ0.026 ppm*Ljڍධࣷڞዂೕ୲փ ඓڦ25 MHzLjܸ25.000000000000000698492 MHzăᄲ ൱ඓfO/fSԲኵڦᆌᆩॽփీথኄᅃဃֶă ࠲॰ሞᇀLjᆩᇀऺ໙NĂXࢅYऺڦ໙ᆅՂႷਏᆶፁࠕ ߛڦຕኵ܈LjՆ௨ټઠপईปဃֶă Rev. 0 | Page 3 of 4 AN-953 ᆌᆩԴऻ ጀ 2008-2009 Analog Devices, Inc ԍାᆶ૧ă ᆶฆՔࢅጀ֩ฆՔຌᇀഄ၎ᆌࠅິă AN07234-0-1/08(0) Rev. 0 | Page 4 of 4