AN-953: 具可编程模数的直接数字频率合成器(DDS) (Rev. 0)

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
ਏᆶ੗Պ‫ײ‬ఇຕ‫ڦ‬኱থຕጴೕ୲ࢇ‫ׯ‬ഗ(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
੗Պ‫ײ‬ఇຕ๟एᇀેेഗ‫ۆڦ‬႙DDSॐࠓ‫ڦ‬Ⴊ۩ӲLj໲
ॽDDS‫ڦ‬๑ᆩકቛ‫ڟ‬ᄲ൱৛ඓᆶ૙ຕೕ୲ࢇ‫ڦׯ‬ᆌᆩ
)૩සඪᅪೕ୲ᆌᆩ*ăAD9913๟ADIࠅິ‫ڼڦ‬ᅃ੼༵ࠃ
੗Պ‫ײ‬ఇຕॐࠓĂएᇀેेഗ‫ڦ‬DDSׂ೗ă
एᇀેेഗ‫ۆڦ‬႙DDS
एᇀેेഗ‫ۆڦ‬႙DDSᅈડᇀᅃ߲ેेഗᅜ֑ᄣ้ዓ໏
୲‫ࡃڿ‬൱ࢅຕጴ๼෇ۙၿጴ)֖९཮1*ăኄࣷሞેेഗ
‫ڦ‬๼‫ิׂ܋؜‬ᅃ้߲क़Ⴞଚ‫ڦ‬ຕጴጴLj޿ຕጴጴ၍Ⴀሺ
‫ٷ‬Lj኱‫ेેڟ‬ഗ‫ڟٳ‬ഄፌ‫ٷ‬ኵ2Cժ‫݋‬ገăᅺُLjેेഗ
๼‫؜‬ਏᆶᅃ߲ࠦۨఇຕ2Că
ેेഗ๼‫؜‬ཚ‫ࣷ׉‬ԥপ܏዁P࿋)ৈ๑ᆩMSB*LjᅜՍ३
ၭ৆ໜഄࢫ‫ڦ‬ঙ‫܈‬ና‫ޗ‬ገ࣑ఇ੷‫ٷڦ‬ၭࢅްሗ‫܈‬ăኄᄣLj
ሞঙ‫܈‬ና‫ޗ‬ገ࣑ഗ‫ڦ‬๼෇‫܋‬Ljેेഗׂิ‫้ڦ‬क़Ⴞଚຕ
ጴጴ‫ྺྷݔڦ‬ଭ‫ڟ‬2P − 1ă
ঙ‫܈‬ና‫ޗ‬ገ࣑ഗॽP࿋ጴᆙพ‫ڇڟ‬࿋ᇶฉ‫ڦ‬ᅃංฉLjन
ॽ0዁2P‫ܾڦాྷݔ‬৊዆ኵ၍Ⴀᆙพྺ0዁2π‫ࢷڦాྷݔ‬
‫܈‬ঙăኄዖᆙพ‫݆ݛ‬๑ঙ‫܈‬ና‫ޗ‬ገ࣑ഗీ‫׉ݥ‬ᆶၳ‫ॽں‬
P࿋ጴገ࣑ྺD࿋ና‫ޗ‬ኵ(A)ă
࢔ඹᅟॽঙ‫܈‬ና‫ޗ‬ገ࣑ࠀీકቛྺཞ้ኴႜኟ၀ࢅᇆ၀
ገ࣑LjᅺُLjཞ้༵ࠃኄଇዖገ࣑‫ݛ‬ӄ‫ڦ‬DDS࢔‫׉‬९ă
৆߶ঙ‫܈‬ና‫ޗ‬ገ࣑ഗኮࢫ‫ڦ‬๟ᅃ੼D࿋DACLj໲ॽঙ‫܈‬
዁ና‫ޗ‬ገ࣑ഗׂิ‫ڦ‬D࿋ຕጴና‫ޗ‬ኵገ࣑ྺఇె႑ࡽă
঳ࡕྺDAC๼‫܋؜‬ฉ‫ڦ‬ᅃ߲ኟ၀հႚLjഄೕ୲ᆯેेഗ
‫ڦ‬ೝ਩‫݋‬ገ୲ਦۨă
ኍ‫ܔ‬एᇀેेഗ‫ۆڦ‬႙DDSLjᅜူ‫ײݛ‬๕՗‫ٳ‬କDAC๼
‫܋؜‬ฉ‫؜‬၄‫ڦ‬ኟ၀հ‫ڦ‬ೕ୲ǖ
fO =
M
fS
2C
ഄዐǖ
fOྺࢇ‫ׯ‬ೕ୲ă
fSྺ֑ᄣೕ୲ă
M/2CྺၭຕԲ૩ᅺጱ)MࢅCྺኟኝຕ*ă
ᅃӯܸჾLjM๔ዕၭᇀ2C – 1Lj‫ޏ‬ሶՍࣷࢇ‫ׯ‬ᅃ߲లઊຯ
༬৥ၟೕ୲ă2Cྺેेഗ‫ڦ‬ఇຕLjഄዐCྺેेഗ‫ڦ‬࿋
੻‫܈‬ăኝຕMᅃӯ‫ྺ׬‬ೕ୲ۙၿጴăMྺኝຕLjᅺُfO
๔ዕሞᅜူೕ୲णኮాǖ
{
f O ∈ 0,
ገ࣑ࡗ‫ײ‬੗ᅜ՗๖ྺᅜူෙঙࡧຕ࠲ဣǖ
x = sin(2πk/2P)
ഄዐǖ
Pྺٗેेഗइ‫ڦڥ‬࿋ຕă
kྺඪᅪߴ้ۨਗ਼‫ܾڦ‬৊዆ኵă
௅߲kኵ‫ܔ‬ᆌ‫ڦ‬Aኵऺ໙‫ྺ݆ݛ‬ǖ‫ܔ‬xኵ৊ႜ໫‫ݣ‬Ăೋᅎ
ࢅป෇‫ت‬૙Lj๑‫ڥ‬A‫ྺׯ‬ଭ዁2D − 1‫ڦాྷݔ‬ኝຕኵă
( 1)
2
S
C
,
2 fS 3 fS
,
,
2C 2C
(2
,
C −1
)
− 1 fS
2
C
}
(2)
ᅺُLjٗDC዁ৎ½fS‫޿ڦ‬ೕ୲णਏᆶ၎‫ڪ‬क़߰fS/2Căኄ
ᅃक़߰fS/2C‫ྺ׬‬DDS‫ڦ‬ೕ୲‫ݴ‬Ր୲ăॠֱfOೕ୲ण੗ᅜ
݀၄LjDDSેेഗ‫ڦ‬ఇຕ(2C)ཞ้ਦۨକDDS‫ڦ‬ೕ୲‫ݴ‬
Ր୲ࢅ੗ీ‫ڦ‬๼‫؜‬ೕ୲ຕă૩සLj‫ܔ‬ᇀߴ֑ۨᄣ໏୲
(f S )Lj ֑ ᆩ 32࿋ ે े ഗ ‫ ڦ‬DDS‫ ڦ‬๼ ‫ ؜‬ೕ ୲ ण ਏ ᆶ
2,147,483,648DŽन231Dž߲੗ీ‫ڦ‬๼‫؜‬ೕ୲ă
Rev. 0 | Page 1 of 4
AN-953
ᆌᆩԴऻ
न๑ᆛᆶසُ‫ڦٷ‬੗ᆩೕ୲णLjएᇀેेഗ‫ۆڦ‬႙DDS
ධփీׂิᅃၵᆶᆩ‫ڦ‬ೕ୲)ၟ৛ඓ‫ڦ‬fS/10*Ljᅺྺેे
ഗఇຕྺࠦۨኵLjܸ൐ۙၿጴ(M)ՂႷྺኝຕă‫ײݛ‬๕1
၂๖Lj๼‫؜‬ೕ୲‫֑ܔ‬ᄣೕ୲‫ڦ‬ԲኵՂႷ஢ፁᅜူ࠲ဣǖ
fO
M
= C
fS
2
੗Պ‫ײ‬ఇຕDDSॐࠓ๑‫ײݛ‬๕3Վႚྺူ๕ǖ
fO M
=
fS
N
(3)
ኍ‫ڪܔ‬ᇀ֑ᄣ໏୲గᅃኝຕሀຕ‫ڦ‬๼‫؜‬ೕ୲)૩ස
f S/10*LjfO੗ᅜ՗๖ྺfO = fS/Q)Qྺኝຕ*ăᆩfS/Q‫ݛ༺پ‬
‫ײ‬๕3ዐ‫ڦ‬fO੗ᅜ‫ڟڥ‬ǖ
1
M
=
Q 2C
‫ݛܾڼ‬௬๟ሗොႠీăසࡕፔ݆փ‫ړ‬LjႪ߀ેेഗఇຕ
ࣷᆅ෇ೕ೷࿁ၟă੗Պ‫ײ‬ఇຕํแᄲ൱৛႐ยऺLjፌ‫ٷ‬
‫ں܈ײ‬ই‫ܔگ‬ሗොႠీ‫ڦ‬ඪࢆ޶௬ᆖၚă
( 4)
൱঴M‫ڟڥ‬M = 2C/QăᅺྺMࢅQ਩ՂႷྺኝຕLj໯ᅜ
ྸᅃ஢ፁ‫ײݛ‬๕4‫ڦ‬Qኵྺ੗ᅜ՗๖ྺ2Kႚ๕‫ڦ‬ኵLjഄዐ
Kྺኝຕăᄺ৽๟ຫLjM = 2C/2K = 2C − K )CࢅK਩ྺኝຕ*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
‫ۆ‬႙DDSփీׂิ৛ඓೕ୲fS /10ă‫ۆ‬႙DDS੗ᅜࢇ‫ׯ‬ᅃ
߲टഄথৎfS /10‫ڦ‬๼‫؜‬ೕ୲)एᇀೕ୲‫ݴ‬Ր୲*Lj‫ڍ‬փ๟
৛ඓ‫ڦ‬fS /10ೕ୲ă‫ܠٷ‬ຕ൧઄ူLjटഄথৎ๟੗ᅜথ๴
‫ڦ‬Lj‫ڍ‬ሞగၵ൧઄ူ)૩සྪஏ้ዓ*LjՂႷइ‫ڥ‬৛ඓ‫ڦ‬
ೕ୲ă
࠵ִ‫ײݛ‬๕4੗ᅜ݀၄Ljᆸ֨‫ڦ‬Բኵᆯેेഗ‫ڦ‬ఇຕ(2C)
ඓۨLjܸఇຕྺᆯેेഗ‫ٷ‬ၭਦۨ‫ۨࠦڦ‬ଉă࢔၂඗Lj
ેेഗ‫ۨࠦڦ‬ఇຕ၌዆କ੗ᆩ๼‫؜‬ೕ୲णă‫ڍ‬๟Ljසࡕ
ેेഗఇຕ੗ۙLjሶQኵॽփ၌ᇀ๟2Kႚ๕‫ڦ‬ኵLjኄ৽
๟੗Պ‫ײ‬ఇຕDDSॐࠓ‫ڦ‬एԨᇱ૙ă
੗Պ‫ײ‬ఇຕDDS
੗Պ‫ײ‬ఇຕ๟ᆯएᇀેेഗ‫ۆڦ‬႙DDSॐࠓՎࣅܸઠ
)֖९཮2*ă໚඗੗Պ‫ײ‬ఇຕरຍ‫ీࠀڦ‬๟߀Վેेഗ
ఇຕLj‫ํڍ‬ा֡ፕഐઠඐԲডްሗăްሗႠภतଇ‫ݛ‬௬ă
‫ڼ‬ᅃ‫ݛ‬௬๟ঙ‫܈‬ና‫ޗ‬ገ࣑ഗॽኝ߲P࿋๼෇‫)ྷݔ‬0዁2P*
ᆙพྺ0዁2π‫ྷݔ܈ࢷڦ‬ăঙ‫܈‬ና‫ޗ‬ገ࣑ഗኮ໯ᅜీߛ
ၳ߾ፕLjኟ๟‫ڥ‬ᅮᇀኄዖएຕྺ2‫ڦ‬ᆙพ‫݆ݛ‬ăॽેे
ഗఇຕඪᅪՎ߸ྺ2‫ڦ‬௣ᅜྔ‫ڦ‬ഄ໲ኵՂ඗ࣷྵ‫ݒ‬ঙ‫܈‬
ና‫ޗ‬ገ࣑ഗᄲ൱‫ڦ‬ᆙพ‫݆ݛ‬ăྺਖ਼‫ޜ‬ኄᅃઓవLj੗Պ‫ײ‬
ఇຕॐࠓ૧ᆩ‫ޤ‬ዺેेഗ๑ዷેेഗੂഐઠ߀Վକఇ
ຕLj‫ڍ‬ධ඗ԍ‫׼‬ঙ‫܈‬ና‫ޗ‬ገ࣑ഗᄲ൱‫ڦ‬ᅜ2ྺएຕ‫ڦ‬௣
‫ڦ‬ᆙพă
(5)
ഄዐMࢅNྺኝຕLjժ൐1 ≤ M < N/2ă
൩ጀᅪLj੗Պ‫ײ‬ఇຕDDS‫ڦ‬ೕ୲Բ)‫ײݛ‬๕5*ᇑएᇀેे
ഗ‫ۆڦ‬႙DDS‫ڦ‬ೕ୲Բ)‫ײݛ‬๕3*‫׉ݥ‬၎ຼăྸᅃ‫ڦ‬൶՚
ሞᇀLj੗Պ‫ײ‬ఇຕփᄲ൱Nྺ2‫ڦ‬ኸຕă໲੗ᅜ๟ඪ჋
‫ڦ‬ኝຕă‫ܔ‬N‫ྸڦ‬ᅃ၌዆๟Lj‫ݴړ‬ຕM/Nሀ዁ፌၭၜ้Lj
NՂႷ஢ፁ0 < N < 232ăኄᅃ၌዆क़থԍኤକঙ‫܈‬዁ና‫ޗ‬
ገ࣑ഗᄲ൱‫ڦ‬2‫ڦ‬௣Բ૩ă
AD9913‫ڦ‬੗Պ‫ײ‬ఇຕࠀీ๟‫ܔ‬ෙ߲32࿋स٪ഗՊ‫ײ‬NĂ
YࢅX‫ڦ‬ኵઠํ၄‫ڦ‬Ljኄၵኵ๟཮2ዐఇຕ੦዆இड‫ڦ‬๼
෇ăNĂXࢅY‫ڦ‬ຕኵՊ‫ྺྷݔײ‬0዁232 − 1)ࡤԨຕ*Lj‫ڍ‬N‫ڦ‬
ူ၌๴M၌዆LjनN > 2Mă
fSĂfOĂMĂNĂYࢅXኮक़‫࠲ڦ‬ဣጺ঳ᇀ‫ײݛ‬๕6ăfOࢅfS
‫ڦ‬ኵඓۨକMᇑN‫࠲ڦ‬ဣLjन‫ڪ‬ᇀሀ዁ፌၭၜ‫ݴڦ‬ຕ
M/NăMĂNࢅેेഗ‫ڦ‬ఇຕ(2C)ཚࡗ‫݆أ׊‬ඓۨକXᇑ
Y‫࠲ڦ‬ဣă
fO M
=
fS
N
X
→ N 2C M
− XN
Y
→ Y = 2 C M − XN
(6)
ഄዐǖ
Xྺ‫ڦ݆أ‬ኝຕฆă
Yྺኝຕᇆຕă
ᆶ඀‫ڦ‬๟LjMඓۨକેेഗ๼‫؜‬Ⴞଚ‫ڦ‬ዜ೺ႠLjनેे
ഗՂႷՓ૦Mኵ֍ీྜ‫ׯ‬ᅃ߲๼‫؜‬Ⴞଚժ‫࣮ݓ‬ഐ๔‫ۅ‬ă
ኄᅃ๼‫؜‬Ⴞଚ࿮൬࿮৑‫ں‬ዘްăኵ‫ڥ‬ጀᅪ‫ڦ‬๟LjසࡕY
ྺ0Ljሶ੗Պ‫ײ‬ఇຕ๟‫ܠ‬ᇆ‫ڦ‬LjनfO੗ᅜ૧ᆩՔጚDDS
኱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
੊୯ኄዖ൧઄ǖfS = 250 MHzLj໯ႴfOኵྺ25 MHzăኄ
ዖ൧઄ᄲ൱ࢇ‫ڦׯ‬๼‫؜‬ೕ୲ྺ֑ᄣ໏୲‫ڦ‬ኝຕሀຕLj
नf O = f S/10ăf O/f S‫ڦ‬ೕ୲Բ(25,000,000/250,000,000)ሀ
዁ፌၭၜՍ੗‫ڟڥ‬MᇑNLjनǖ
M/N = 25,000,000/250,000,000 = 1/10
ᅺُLjM = 1LjN = 10ăᆯMࢅN‫ڦ‬ኵᆼ੗໙‫ڥ‬XࢅY‫ڦ‬ኵǖ
X = 429,496,729LjY = 6ă
ॽኄၵኵՊ‫ײ‬዁AD9913ዐՍ੗ሞߴۨ‫ڦ‬250 MHz֑ᄣ้
ዓׂ้ิ৛ඓ‫ڦ‬25 MHz๼‫؜‬ೕ୲ă
ՔጚDDS࿮݆ሞf S = 250 MHz้ࢇ‫ׯ‬৛ඓ‫ڦ‬25 MHz
๼ ‫ ؜‬ೕ ୲ Lj ໲ ੗ ᅜ ࢇ ‫ ڦ ׯ‬ፌ থ ৎ ೕ ୲ ྺ
25.000000023283064365386962890625 MHzăሞྪஏᆌᆩ
ዐLjኄᅃৎຼኵ๟փ੗থ๴‫ڦ‬Ljᅺྺᄲ൱‫ڦ‬ೕ୲๟ਨ‫ܔ‬
࿮ၭຕဃֶ‫ڦ‬25 MHză
੊୯ᅺ໎!
ՂႷຫ௽‫ڦ‬๟Lj‫ܠٷ‬ຕऺ໙‫ײ‬Ⴞ)සExcel®ĂMathcad®ࢅ
MATLAB®‫*ڪ‬ሞऺ໙XࢅY้‫ࣷۼ‬ᆅ෇ຕኵဃֶLjኄၵဃ
ֶᇸᇀాևป෇ईপ܏‫ت‬૙Ljሞ৊ႜ‫ٷ‬ຕ‫݆أࢅ݆ױ‬
้Սࣷ՗၄‫؜‬ઠăᆶ඀‫ڦ‬๟LjWindows® XP֡ፕဣཥ‫ڦ‬
‫ऺڦ‬໙ഗ‫ײ‬Ⴞሶ੗ᅜ༵ࠃፁࠕߛ‫ڦ‬ຕኵ৛‫܈‬ઠኴႜኄၵ
ऺ໙Ljܸփׂࣷิฉຎဃֶ)዁ณ‫ܔ‬ᇀAD9913Պ‫ײ‬၎࠲
‫ڦ‬32࿋ຕ๟සُ*ă๚ํฉLjAD9913ೠࠚӱ෉ॲਸ݀ට
ᇵ঺६କ࠲ᇀຕኵ৛‫܈‬࿚༶‫ڦ‬၎࠲ኪ๎Ljᅙঢ়३ၭକป
෇ईপ܏ဃֶă
ྺକຫ௽ป෇ࢅপ܏‫ت‬૙‫ڦ‬ᆖၚLjምْ੊୯ኄዖ൧઄ǖ
໯ႴfOኵྺ25 MHzLj‫ڍ‬fSྺ249,999,999.5 MHz)ܸփ๟250
MHz*ăfO/fS‫ڦ‬ೕ୲Բ(25,000,000/249,999,999.5)ሀ዁ፌၭ
ၜՍ੗‫ڟڥ‬MᇑNLjनǖ
M/N = 25,000,000/249,999,999.5 = 50,000,000/499,999,999
ᅺُLjM = 50,000,000LjN = 499,999,999ǗᆯMࢅN‫ڦ‬ኵ੗ᅜ
໙‫ڥ‬ǖX = 429,496,730LjY = 229,496,730ă
සࡕ๑ᆩExcelऺ໙LjXኵᇑฉຎኵ၎ཞLj‫ڍ‬Yኵሶྺ
229,496,736ăጀᅪፌ‫گ‬ᆶၳ࿋ྺ6Ljܸփ๟0)ኟඓኵ*ă໚඗
޿ဃֶटഄၭ)ৈ0.026 ppm*Lj‫ڍ‬໲ධ඗ࣷ‫ڞ‬ዂ๼‫؜‬ೕ୲փ
๟৛ඓ‫ڦ‬25 MHzLjܸ๟25.000000000000000698492 MHzăᄲ
൱৛ඓfO/fSԲኵ‫ڦ‬ᆌᆩॽփీথ๴ኄᅃဃֶă
࠲॰ሞᇀLjᆩᇀऺ໙NĂXࢅY‫ऺڦ‬໙ᆅ൤ՂႷਏᆶፁࠕ
ߛ‫ڦ‬ຕኵ৛‫܈‬LjՆ௨‫ټ‬ઠপ܏ईป෇ဃֶă
Rev. 0 | Page 3 of 4
AN-953
ᆌᆩԴऻ
ጀ๥
2008-2009 Analog Devices, Inc ԍା໯ᆶ඄૧ă
໯ᆶฆՔࢅጀ֩ฆՔ਩ຌᇀഄ၎ᆌࠅິă
AN07234-0-1/08(0)
Rev. 0 | Page 4 of 4
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