{"id":2428,"date":"2025-09-08T03:12:45","date_gmt":"2025-09-08T03:12:45","guid":{"rendered":"https:\/\/flj-pcb.com\/?page_id=2428"},"modified":"2025-09-26T02:56:54","modified_gmt":"2025-09-26T02:56:54","slug":"impedance-control-pcb","status":"publish","type":"page","link":"https:\/\/flj-pcb.com\/cs\/pcb-manufacturer\/impedance-control-pcb\/","title":{"rendered":"Impedan\u010dn\u00ed desky plo\u0161n\u00fdch spoj\u016f - optimalizace integrity sign\u00e1lu"},"content":{"rendered":"
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Co je \u0159\u00edzen\u00ed impedance desek plo\u0161n\u00fdch spoj\u016f?<\/h2>

\u0158\u00edzen\u00edm impedance DPS se rozum\u00ed \u0159\u00edzen\u00ed impedance stop. Tato impedance se tak\u00e9 naz\u00fdv\u00e1 \u0159\u00edzen\u00e1 impedance. \u0158\u00edzen\u00e1 impedance je charakteristick\u00e1 impedance p\u0159enosov\u00e9ho veden\u00ed tvo\u0159en\u00e9ho stopami DPS a jejich referen\u010dn\u00edmi rovinami. P\u0159i p\u0159enosu vysokofrekven\u010dn\u00edch sign\u00e1l\u016f po p\u0159enosov\u00fdch veden\u00edch DPS je to d\u016fle\u017eit\u00e9. \u0158\u00edzen\u00e1 impedance je d\u016fle\u017eit\u00e1 pro \u0159e\u0161en\u00ed probl\u00e9m\u016f s integritou sign\u00e1lu. Integrita sign\u00e1lu znamen\u00e1, \u017ee se sign\u00e1l \u0161\u00ed\u0159\u00ed bez zkreslen\u00ed.<\/p>

Impedance obvodu je d\u00e1na fyzickou velikost\u00ed desky plo\u0161n\u00fdch spoj\u016f a dielektrick\u00fdm materi\u00e1lem. M\u011b\u0159\u00ed se v ohmech (\u03a9). Mezi typy p\u0159enosov\u00fdch veden\u00ed na desce plo\u0161n\u00fdch spoj\u016f, kter\u00e9 vy\u017eaduj\u00ed \u0159\u00edzen\u00ed impedance, pat\u0159\u00ed jednop\u00e1skov\u00e9 mikrop\u00e1sky, jednop\u00e1skov\u00e9 p\u00e1skov\u00e9 veden\u00ed, diferenci\u00e1ln\u00ed mikrop\u00e1skov\u00fd p\u00e1r, diferenci\u00e1ln\u00ed p\u00e1skov\u00e9 veden\u00ed, vlo\u017een\u00e9 mikrop\u00e1sky a koplan\u00e1rn\u00ed veden\u00ed (jednop\u00e1skov\u00e9 a diferenci\u00e1ln\u00ed).<\/p>

B\u011b\u017en\u00e9 metody pro dosa\u017een\u00ed impedan\u010dn\u00ed regulace<\/h2>

1. Pou\u017eit\u00ed struktury vrstev PCB<\/h3>

Konstrukt\u00e9\u0159i desek plo\u0161n\u00fdch spoj\u016f mohou ke kontrole impedance pou\u017e\u00edt z\u00e1sobn\u00edk vrstev desky. Um\u00edst\u011bn\u00edm r\u016fzn\u00fdch sign\u00e1lov\u00fdch vrstev na r\u016fzn\u00e1 m\u00edsta lze \u0159\u00eddit kapacitu a induk\u010dnost mezi vrstvami. Obvykle se u vnit\u0159n\u00edch vrstev vol\u00ed vy\u0161\u0161\u00ed impedance a u vn\u011bj\u0161\u00edch vrstev ni\u017e\u0161\u00ed impedance, aby se sn\u00ed\u017eily odrazy a p\u0159eslechy.<\/p>

2. Pou\u017eijte diferenci\u00e1ln\u00ed sign\u00e1ln\u00ed veden\u00ed<\/h3>

Diferenci\u00e1ln\u00ed p\u00e1ry poskytuj\u00ed lep\u0161\u00ed odru\u0161en\u00ed a ni\u017e\u0161\u00ed riziko p\u0159eslech\u016f. Diferenci\u00e1ln\u00ed p\u00e1r jsou dva paraleln\u00ed vodi\u010de. Jejich nap\u011bt\u00ed jsou stejn\u011b velk\u00e1 a maj\u00ed opa\u010dnou polaritu. Diferenci\u00e1ln\u00ed p\u00e1ry poskytuj\u00ed lep\u0161\u00ed integritu sign\u00e1lu a odolnost proti \u0161umu. Impedance diferenci\u00e1ln\u00edho p\u00e1ru je \u0159\u00edzena vzd\u00e1lenost\u00ed, \u0161\u00ed\u0159kou stopy a uspo\u0159\u00e1d\u00e1n\u00edm zemn\u00ed roviny.<\/p>

3. Geometrie kontroln\u00ed stopy<\/h3>

\u0160\u00ed\u0159ka stopy, rozte\u010d a geometrie uspo\u0159\u00e1d\u00e1n\u00ed mohou rovn\u011b\u017e ovlivnit impedanci. U b\u011b\u017en\u00fdch mikrop\u00e1sk\u016f sni\u017euj\u00ed impedanci \u0161ir\u0161\u00ed stopy a v\u011bt\u0161\u00ed rozestupy. U koaxi\u00e1ln\u00edch struktur men\u0161\u00ed vnit\u0159n\u00ed vodi\u010d a v\u011bt\u0161\u00ed polom\u011br vn\u011bj\u0161\u00edho vodi\u010de zvy\u0161uj\u00ed impedanci. Geometrii stop zvolte na z\u00e1klad\u011b c\u00edlov\u00e9 impedance a frekvence sign\u00e1lu.<\/p>

4. V\u00fdb\u011br materi\u00e1l\u016f PCB<\/h3>

Dielektrick\u00e1 konstanta materi\u00e1lu DPS ovliv\u0148uje impedanci. V\u00fdb\u011br materi\u00e1l\u016f se stabiln\u00edmi dielektrick\u00fdmi vlastnostmi je sou\u010d\u00e1st\u00ed \u0159\u00edzen\u00ed impedance. Pro vysokofrekven\u010dn\u00ed a vysokorychlostn\u00ed pou\u017eit\u00ed jsou b\u011b\u017en\u00e9 materi\u00e1ly fr4 (sklo-epoxid), PTFE (teflon) a VF lamin\u00e1ty.<\/p>

5. Pou\u017e\u00edvat simula\u010dn\u00ed a n\u00e1vrhov\u00e9 n\u00e1stroje<\/h3>

P\u0159ed fin\u00e1ln\u00edm rozvr\u017een\u00edm PCB pou\u017eijte simula\u010dn\u00ed a n\u00e1vrhov\u00e9 n\u00e1stroje ke kontrole a optimalizaci impedance. Tyto n\u00e1stroje simuluj\u00ed chov\u00e1n\u00ed obvodu, ztr\u00e1ty sign\u00e1lu a elektromagnetick\u00e9 interakce. Pom\u00e1haj\u00ed naj\u00edt nejlep\u0161\u00ed parametry desky. Mezi b\u011b\u017en\u00e9 n\u00e1stroje pat\u0159\u00ed CST Studio Suite, HyperLynx a ADS.<\/p>

Vliv v\u00fdroby DPS na impedanci<\/h2>

\u0160\u00ed\u0159ka stopy<\/h3>

\u0160\u00ed\u0159ka stopy p\u0159\u00edmo ovliv\u0148uje impedanci a ztr\u00e1ty p\u0159enosov\u00e9ho veden\u00ed. V\u011bt\u0161ina dobr\u00fdch konstrukt\u00e9r\u016f d\u00e1v\u00e1 v\u00fdrobci PCB toleranci \u0161\u00ed\u0159ky stopy pomoc\u00ed soubor\u016f Gerber. Pokud je nap\u0159\u00edklad \u0161\u00ed\u0159ka stopy navr\u017eena na 6,2 mil a jej\u00ed impedance je 50 ohm\u016f, v\u00fdrobn\u00ed nestabilita, kter\u00e1 zm\u011bn\u00ed \u0161\u00ed\u0159ku stopy, zm\u011bn\u00ed impedanci. Ze zku\u0161enost\u00ed s mnoha tov\u00e1rnami se \u0161\u00ed\u0159ka stopy m\u016f\u017ee li\u0161it p\u0159ibli\u017en\u011b o 10%. Zm\u011bnu \u0161\u00ed\u0159ky stopy m\u016f\u017eeme modelovat jako Gaussovo rozd\u011blen\u00ed se sm\u011brodatnou odchylkou 10%.<\/p>

Tlou\u0161\u0165ka m\u011bd\u011bn\u00e9 f\u00f3lie \/ pokoven\u00e9 m\u011bdi<\/h3>

Tlou\u0161\u0165ka m\u011bdi se u v\u00fdrobk\u016f PCB skl\u00e1d\u00e1 ze dvou \u010d\u00e1st\u00ed: z\u00e1kladn\u00ed tlou\u0161\u0165ky m\u011bdi a tlou\u0161\u0165ky pokoven\u00e9 m\u011bdi. Z\u00e1kladn\u00ed m\u011b\u010f je relativn\u011b rovnom\u011brn\u00e1, ale rovnom\u011brnost pokoven\u00e9 m\u011bdi z\u00e1vis\u00ed na v\u00fdrobn\u00edm procesu. Tlou\u0161\u0165ka pokoven\u00e9 m\u011bdi se m\u016f\u017ee v jednotliv\u00fdch tov\u00e1rn\u00e1ch zna\u010dn\u011b li\u0161it. R\u016fzn\u00e1 tlou\u0161\u0165ka pokoven\u00e9 m\u011bdi m\u011bn\u00ed impedanci a ztr\u00e1ty stopy. Impedance se m\u016f\u017ee li\u0161it v mal\u00e9m rozsahu, nap\u0159\u00edklad mezi 49,5 a 51 ohmy. Ve srovn\u00e1n\u00ed s \u0161\u00ed\u0159kou stopy m\u00e1 tlou\u0161\u0165ka m\u011bdi men\u0161\u00ed vliv na impedanci.<\/p>

Tlou\u0161\u0165ka dielektrika<\/h3>

P\u0159i v\u00fdrob\u011b desek plo\u0161n\u00fdch spoj\u016f doch\u00e1z\u00ed ke zm\u011bn\u00e1m tlou\u0161\u0165ky dielektrika v d\u016fsledku kol\u00eds\u00e1n\u00ed surovin, tlaku p\u0159i laminov\u00e1n\u00ed a pln\u011bn\u00ed lepidlem. Pokud se zm\u011bn\u00ed tlou\u0161\u0165ka dielektrika, zm\u011bn\u00ed se impedance a ztr\u00e1ty. V z\u00e1va\u017en\u00fdch p\u0159\u00edpadech budou m\u00edt p\u0159enosov\u00e1 veden\u00ed velk\u00e9 ztr\u00e1ty. Impedance se m\u016f\u017ee pohybovat od p\u0159ibli\u017en\u011b 44 ohm\u016f do 54 ohm\u016f. Rozsah m\u016f\u017ee b\u00fdt a\u017e 10 ohm\u016f.<\/p>

Faktor lept\u00e1n\u00ed<\/h3>

Vodi\u010de maj\u00ed kone\u010dnou tlou\u0161\u0165ku. Po lept\u00e1n\u00ed nejsou stopy dokonal\u00fdmi obd\u00e9ln\u00edky. Vypadaj\u00ed sp\u00ed\u0161e jako lichob\u011b\u017en\u00edk. \u00dahel lichob\u011b\u017en\u00edku se m\u011bn\u00ed s tlou\u0161\u0165kou m\u011bdi (v\u010detn\u011b pokoven\u00ed). Kdy\u017e je m\u011b\u010f tenk\u00e1, \u00fahel bo\u010dn\u00ed st\u011bny se bl\u00ed\u017e\u00ed 90\u00b0. Velikost \u00fahlu ovliv\u0148uje impedanci. Nap\u0159\u00edklad p\u0159i \u00fahlu bo\u010dnice 70\u00b0 je impedance p\u0159ibli\u017en\u011b 50 ohm\u016f. P\u0159i \u00fahlu 90\u00b0 je impedance p\u0159ibli\u017en\u011b 48,37 ohm\u016f.<\/p>

V\u00fd\u0161e uveden\u00e9 testy m\u011bn\u00ed jeden faktor po druh\u00e9m. Ve skute\u010dn\u00e9 v\u00fdrob\u011b se m\u011bn\u00ed v\u00edce prom\u011bnn\u00fdch najednou. Impedance se m\u016f\u017ee pohybovat od 40 ohm\u016f do 56 ohm\u016f. To zna\u010dn\u011b p\u0159esahuje typick\u00fd po\u017eadavek, jako je 50\u03a9 \u00b110%. B\u011bhem v\u00fdroby zp\u016fsobuje zm\u011bnu impedance mnoho parametr\u016f. U vysokorychlostn\u00edch nebo \u0161pi\u010dkov\u00fdch v\u00fdrobk\u016f mus\u00ed n\u00e1vrh a v\u00fdrobn\u00ed proces desek plo\u0161n\u00fdch spoj\u016f p\u0159\u00edsn\u011b kontrolovat ka\u017ed\u00fd materi\u00e1l a krok. V opa\u010dn\u00e9m p\u0159\u00edpad\u011b m\u016f\u017ee v\u00fdrobek vykazovat neo\u010dek\u00e1van\u00e9 probl\u00e9my.<\/p>

Impedance a charakteristick\u00e1 impedance<\/h2>

1. Odolnost<\/h3>

Kdy\u017e ve vodi\u010di te\u010de st\u0159\u00eddav\u00fd proud, odpor, na kter\u00fd naraz\u00ed, se naz\u00fdv\u00e1 impedance (odpor). Symbol je Z. Jednotkou je st\u00e1le ohm (\u03a9). Tento odpor se li\u0161\u00ed od odporu stejnosm\u011brn\u00e9ho proudu. Ve st\u0159\u00eddav\u00e9m proudu existuje krom\u011b odporu (R) tak\u00e9 induktivn\u00ed reaktance (XL) a kapacitn\u00ed reaktance (XC).<\/p>

Pro odli\u0161en\u00ed od stejnosm\u011brn\u00e9ho odporu se naz\u00fdv\u00e1 st\u0159\u00eddav\u00e1 odporov\u00e1 impedance (Z).<\/p>

Vzorec:<\/p>

\u00a0<\/div><\/div><\/div>
Z<\/span> = \u221a(R\u00b2 + (XL - XC)\u00b2)
\n<\/code><\/div><\/div>

2. Impedance (Z)<\/h3>

S vy\u0161\u0161\u00ed integrac\u00ed integrovan\u00fdch obvod\u016f a vy\u0161\u0161\u00ed frekvenc\u00ed a rychlost\u00ed sign\u00e1lu mohou b\u00fdt sign\u00e1ly na stop\u00e1ch PCB ovlivn\u011bny samotnou stopou PCB. Kdy\u017e frekvence sign\u00e1lu dos\u00e1hne ur\u010dit\u00e9 hranice, zp\u016fsobuje stopa v\u00e1\u017en\u00e9 zkreslen\u00ed nebo ztr\u00e1tu sign\u00e1lu. To ukazuje, \u017ee stopy DPS nep\u0159en\u00e1\u0161ej\u00ed pouze proud, ale i energii ve form\u011b impuls\u016f nebo sign\u00e1l\u016f se \u010dtvercov\u00fdmi vlnami.<\/p>

3. \u0158\u00edzen\u00ed charakteristick\u00e9 impedance (Z0)<\/h3>

Odpor, kter\u00fd sign\u00e1l p\u0159i sv\u00e9 cest\u011b vid\u00ed, se naz\u00fdv\u00e1 charakteristick\u00e1 impedance. Symbol je Z0.<\/p>

Oprava pouze \u201copen\u201d, \u201cshort\u201d a konektivity tedy nesta\u010d\u00ed. U vysokorychlostn\u00edch a vysokofrekven\u010dn\u00edch p\u0159enosov\u00fdch veden\u00ed mus\u00ed b\u00fdt kvalita p\u0159\u00edsn\u011bj\u0161\u00ed. Nesta\u010d\u00ed proj\u00edt testem na otev\u0159en\u00ed\/zkrat nebo m\u00edt mal\u00e9 z\u00e1vady. Mus\u00edte m\u011b\u0159it Z0 a udr\u017eovat ji v toleranci. Pokud tomu tak nen\u00ed, mus\u00ed b\u00fdt deska vy\u0159azena. Nep\u0159epracov\u00e1vejte.<\/p>

\u0160\u00ed\u0159en\u00ed sign\u00e1lu a p\u0159enosov\u00e1 veden\u00ed<\/h2>

1. Definice veden\u00ed pro p\u0159enos sign\u00e1lu<\/h3>

  1. Z elektromagnetick\u00e9 teorie vypl\u00fdv\u00e1, \u017ee krat\u0161\u00ed vlnov\u00e1 d\u00e9lka (\u03bb) znamen\u00e1 vy\u0161\u0161\u00ed frekvenci (f). Jejich sou\u010din se rovn\u00e1 rychlosti sv\u011btla. To znamen\u00e1:<\/p><\/li><\/ol>

    \u00a0<\/div><\/div><\/div>
    C<\/span> = \u03bb - f = 3<\/span> \u00d7 10<\/span>^10<\/span> cm\/s
    \n<\/code><\/div><\/div>

    1. Jak\u00e9koli za\u0159\u00edzen\u00ed m\u016f\u017ee m\u00edt vysokou frekvenci sign\u00e1lu. Po pr\u016fchodu sign\u00e1lu stopou na desce plo\u0161n\u00fdch spoj\u016f se m\u016f\u017ee sign\u00e1l zpomalit nebo zpozdit.<\/p><\/li><\/ol>

      Krat\u0161\u00ed d\u00e9lka stopy je tedy lep\u0161\u00ed.<\/p>

      1. Pom\u00e1h\u00e1 zv\u00fd\u0161en\u00ed hustoty zapojen\u00ed nebo zmen\u0161en\u00ed velikosti vodi\u010d\u016f. Kdy\u017e se v\u0161ak frekvence sou\u010d\u00e1stek zv\u00fd\u0161\u00ed nebo se zkr\u00e1t\u00ed periody pulz\u016f, m\u016f\u017ee se d\u00e9lka stopy p\u0159ibl\u00ed\u017eit \u010d\u00e1sti vlnov\u00e9 d\u00e9lky sign\u00e1lu. Pak stopa vykazuje zjevn\u00e9 zkreslen\u00ed.<\/p><\/li>

      2. V bod\u011b 3.4.4 normy IPC-2141 se uv\u00e1d\u00ed: pokud se d\u00e9lka stopy bl\u00ed\u017e\u00ed 1\/7 vlnov\u00e9 d\u00e9lky sign\u00e1lu, pova\u017euje se stopa za veden\u00ed pro p\u0159enos sign\u00e1lu.<\/p><\/li>

      3. P\u0159\u00edklad:<\/p><\/li><\/ol>

        Za\u0159\u00edzen\u00ed m\u00e1 frekvenci sign\u00e1lu f = 10 MHz. D\u00e9lka stopy na desce plo\u0161n\u00fdch spoj\u016f je 50 cm. Je t\u0159eba \u0159\u00eddit charakteristickou impedanci?<\/p>

        Po\u010d\u00edtejte:<\/p>

        \u00a0<\/div><\/div><\/div>
        C = \u03bb - f = 3 \u00d7 10^10 cm\/s
        \n\u03bb = C \/ f = (3 \u00d7 10^10 cm\/s) \/ (1 \u00d7 10^7 \/s) = 3000 cm
        \nd\u00e9lka stopy \/ vlnov\u00e1 d\u00e9lka = 50 \/ 3000 = 1\/60
        \n<\/code><\/div><\/div>

        Proto\u017ee 1\/60 je mnohem m\u00e9n\u011b ne\u017e 1\/7, je tato stopa norm\u00e1ln\u00edm vodi\u010dem a nepot\u0159ebuje \u0159\u00edzen\u00ed charakteristick\u00e9 impedance.<\/p>

        Maxwellovy rovnice \u0159\u00edkaj\u00ed: rychlost \u0161\u00ed\u0159en\u00ed sinusov\u00e9 vlny VS v prost\u0159ed\u00ed souvis\u00ed s rychlost\u00ed sv\u011btla C a dielektrickou konstantou \u03b5r takto:<\/p>

        \u00a0<\/div><\/div><\/div>
        VS<\/span> = C \/ \u221a\u03b5r
        \n<\/code><\/div><\/div>

        Je-li \u03b5r = 1, rychlost sign\u00e1lu se rovn\u00e1 rychlosti sv\u011btla = 3 \u00d7 10^10 cm\/s.<\/p>

        2. P\u0159enosov\u00e1 rychlost a dielektrick\u00e1 konstanta<\/h3>

        Rychlost sign\u00e1lu p\u0159i 30 MHz pro r\u016fzn\u00e9 materi\u00e1ly:<\/p>

        Materi\u00e1l \/ substr\u00e1t<\/th>Tg (\u00b0C)<\/th>Dielektrick\u00e1 konstanta \u03b5r<\/th>Rychlost sign\u00e1lu (m\/\u03bcs)<\/th><\/tr><\/thead>
        Vakuum<\/td>\/<\/td>1.0<\/td>300.00<\/td><\/tr>
        PTFE (teflon)<\/td>\/<\/td>2.2<\/td>202.26<\/td><\/tr>
        Termosetov\u00fd polyfenylen ether<\/td>210<\/td>2.5<\/td>189.74<\/td><\/tr>
        Ester kyanatanu<\/td>225<\/td>3.0<\/td>173.21<\/td><\/tr>
        PTFE + E-sklo<\/td>\/<\/td>2.6<\/td>186.25<\/td><\/tr>
        Ester kyanatanu + sklo<\/td>225<\/td>3.7<\/td>155.96<\/td><\/tr>
        Polyimid + sklo<\/td>230<\/td>4.5<\/td>141.42<\/td><\/tr>
        Quartz<\/td>\/<\/td>3.9<\/td>151.98<\/td><\/tr>
        Epoxidov\u00e9 sklo (fr4)<\/td>130\u00b15<\/td>4.7<\/td>138.38<\/td><\/tr>
        Hlin\u00edk<\/td>\/<\/td>9.0<\/td>100.00<\/td><\/tr><\/tbody><\/table><\/div><\/div>

        Z tabulky vypl\u00fdv\u00e1, \u017ee s rostouc\u00edm \u03b5r kles\u00e1 rychlost sign\u00e1lu v materi\u00e1lu. Chcete-li dos\u00e1hnout vy\u0161\u0161\u00ed rychlosti sign\u00e1lu, zvolte vy\u0161\u0161\u00ed charakteristickou impedanci. Chcete-li z\u00edskat vy\u0161\u0161\u00ed Z0, zvolte ni\u017e\u0161\u00ed \u03b5r materi\u00e1lu. PTFE m\u00e1 nejmen\u0161\u00ed \u03b5r, tak\u017ee poskytuje nejvy\u0161\u0161\u00ed rychlost.<\/p>

        Deska fr4 pou\u017e\u00edv\u00e1 epoxidovou prysky\u0159ici a E-sklo. Jej\u00ed \u03b5r je p\u0159ibli\u017en\u011b 4,7. Rychlost sign\u00e1lu je 138 m\/\u03bcs. Zm\u011bna syst\u00e9mu prysky\u0159ice m\u016f\u017ee zm\u011bnit \u03b5r.<\/p>

        D\u016fvody pro kontrolu charakteristick\u00e9 impedance<\/h2>

        D\u016fvod 1<\/h3>

        Kdy\u017e b\u011b\u017e\u00ed elektronick\u00e9 za\u0159\u00edzen\u00ed (po\u010d\u00edta\u010d, komunikace), ovlada\u010d vys\u00edl\u00e1 sign\u00e1l do p\u0159ij\u00edma\u010de prost\u0159ednictv\u00edm stop na desce plo\u0161n\u00fdch spoj\u016f. Charakteristick\u00e1 impedance Z0 stopy mus\u00ed odpov\u00eddat elektronick\u00e9 impedanci ovlada\u010de a p\u0159ij\u00edma\u010de. Pokud je shodn\u00e1, energie sign\u00e1lu se p\u0159en\u00e1\u0161\u00ed \u00fapln\u011b.<\/p>

        D\u016fvod 2<\/h3>

        Pokud je kvalita PCB \u0161patn\u00e1 a Z0 je mimo toleranci, sign\u00e1ly se odr\u00e1\u017eej\u00ed, rozptyluj\u00ed, zeslabuj\u00ed nebo zpo\u017e\u010fuj\u00ed. V z\u00e1va\u017en\u00fdch p\u0159\u00edpadech mohou b\u00fdt sign\u00e1ly \u0161patn\u00e9 a za\u0159\u00edzen\u00ed se m\u016f\u017ee zhroutit.<\/p>

        D\u016fvod 3<\/h3>

        Aby v\u00edcevrstv\u00e1 deska Z0 spl\u0148ovala specifikace z\u00e1kazn\u00edka, je nutn\u00fd p\u0159\u00edsn\u00fd v\u00fdb\u011br materi\u00e1lu a kontrola procesu. Komponenty s vy\u0161\u0161\u00ed elektronickou impedanc\u00ed obvykle vy\u017eaduj\u00ed vy\u0161\u0161\u00ed Z0 desky plo\u0161n\u00fdch spoj\u016f, aby odpov\u00eddala. V\u00edcevrstv\u00e1 deska se spr\u00e1vnou Z0 je kvalifikovan\u00fd vysokorychlostn\u00ed nebo vysokofrekven\u010dn\u00ed v\u00fdrobek.<\/p>

        Vztah Z0 k materi\u00e1lu a procesu<\/h2>

        Vzorec pro charakteristickou impedanci mikrop\u00e1skov\u00e9ho veden\u00ed Z0:<\/p>

        \u00a0<\/div><\/div><\/div>
        Z0<\/span> = 87<\/span> \/ \u221a\u03b5r + 1.41<\/span> - ln [ 5.98<\/span> H \/ (0.8<\/span> W + T) ]
        \n<\/code><\/div><\/div>

        Kde:<\/p>

        • \u03b5r - dielektrick\u00e1 konstanta<\/p><\/li>

        • H - tlou\u0161\u0165ka dielektrika<\/p><\/li>

        • W - \u0161\u00ed\u0159ka stopy<\/p><\/li>

        • T - tlou\u0161\u0165ka stopy<\/p><\/li><\/ul>

          Ni\u017e\u0161\u00ed \u03b5r usnad\u0148uje zv\u00fd\u0161en\u00ed Z0, aby odpov\u00eddalo vysokorychlostn\u00edm sou\u010d\u00e1stk\u00e1m.<\/p>

          1. Z0 a \u03b5r<\/h3>

          Z0 je nep\u0159\u00edmo \u00fam\u011brn\u00e1 \u03b5r. Z0 roste s rostouc\u00edm H. Pro p\u0159\u00edsn\u00e9 Z0 vysokofrekven\u010dn\u00edch veden\u00ed mus\u00ed b\u00fdt tolerance tlou\u0161\u0165ky dielektrika p\u0159\u00edsn\u00e1. Obvykle nesm\u00ed zm\u011bna tlou\u0161\u0165ky dielektrika p\u0159ekro\u010dit 10%.<\/p>

          2. Efekt tlou\u0161\u0165ky dielektrika<\/h3>

          P\u0159i vy\u0161\u0161\u00ed hustot\u011b trasov\u00e1n\u00ed vede v\u011bt\u0161\u00ed H k v\u011bt\u0161\u00edmu elektromagnetick\u00e9mu ru\u0161en\u00ed. U vysokofrekven\u010dn\u00edch a vysokorychlostn\u00edch digit\u00e1ln\u00edch veden\u00ed je t\u0159eba s rostouc\u00ed hustotou veden\u00ed zmen\u0161it tlou\u0161\u0165ku dielektrika, aby se sn\u00ed\u017eilo EMI a p\u0159eslechy, nebo pou\u017e\u00edt materi\u00e1ly s ni\u017e\u0161\u00edm \u03b5r.<\/p>

          Ze vzorce vypl\u00fdv\u00e1, \u017ee d\u016fle\u017eit\u00fdm faktorem je tlou\u0161\u0165ka m\u011bdi T. V\u011bt\u0161\u00ed T sni\u017euje Z0, ale zm\u011bna je mal\u00e1.<\/p>

          3. Vliv tlou\u0161\u0165ky m\u011bdi<\/h3>

          Ten\u010d\u00ed m\u011b\u010f poskytuje vy\u0161\u0161\u00ed Z0, ale jej\u00ed vliv na Z0 je mal\u00fd. Pou\u017eit\u00ed tenk\u00e9 m\u011bdi pom\u00e1h\u00e1 vytvo\u0159it jemn\u00e9 stopy a to pom\u00e1h\u00e1 kontrolovat Z0 v\u00edce ne\u017e samotn\u00e1 hodnota tlou\u0161\u0165ky m\u011bdi.<\/p>

          Ze vzorce:<\/p>

          \u00a0<\/div><\/div><\/div>
          Z0<\/span> = 87<\/span> \/ \u221a\u03b5r + 1.41<\/span> - ln [ 5.98<\/span> H \/ (0.8<\/span> W + T) ]
          \n<\/code><\/div><\/div>

          Se zmen\u0161ov\u00e1n\u00edm W (\u0161\u00ed\u0159ky stopy) se Z0 zv\u011bt\u0161uje. Zm\u011bna \u0161\u00ed\u0159ky m\u00e1 na Z0 v\u011bt\u0161\u00ed vliv ne\u017e zm\u011bna tlou\u0161\u0165ky.<\/p>

          4. Efekt \u0161\u00ed\u0159ky stopy<\/h3>

          Z0 se prudce zv\u011bt\u0161uje se zu\u017euj\u00edc\u00ed se \u0161\u00ed\u0159kou W. Chcete-li kontrolovat Z0, kontrolujte pevn\u011b \u0161\u00ed\u0159ku stopy. V\u011bt\u0161ina vysokofrekven\u010dn\u00edch a vysokorychlostn\u00edch digit\u00e1ln\u00edch stop m\u00e1 dnes \u0161\u00ed\u0159ku nap\u0159\u00edklad 0,10 mm nebo 0,13 mm. Tradi\u010dn\u00ed tolerance \u0161\u00ed\u0159ky byla \u00b120%. Pro stopy, kter\u00e9 nejsou p\u0159enosov\u00fdmi linkami (d\u00e9lka stopy << vlnov\u00e1 d\u00e9lka sign\u00e1lu \/ 7), m\u016f\u017ee b\u00fdt \u00b120% v po\u0159\u00e1dku. Ale pro stopy \u0159\u00edzen\u00e9 Z0 nem\u016f\u017ee chyba \u0161\u00ed\u0159ky \u00b120% spl\u0148ovat po\u017eadavky. V takov\u00e9m p\u0159\u00edpad\u011b chyba Z0 \u010dasto p\u0159esahuje \u00b110%.<\/p>

          P\u0159\u00edklad:<\/p>

          Mikrop\u00e1ska na desce plo\u0161n\u00fdch spoj\u016f m\u00e1 \u0161\u00ed\u0159ku 100 \u03bcm, tlou\u0161\u0165ku 20 \u03bcm a tlou\u0161\u0165ku dielektrika 100 \u03bcm. P\u0159edpokl\u00e1dejte, \u017ee tlou\u0161\u0165ka m\u011bdi je rovnom\u011brn\u00e1. Pokud se \u0161\u00ed\u0159ka zm\u011bn\u00ed \u00b120%, m\u016f\u017ee Z0 spl\u0148ovat \u00b110%?<\/p>

          Podle vzorce:<\/p>

          Nech\u0165 W0 = 100 \u03bcm, W1 = 80 \u03bcm, W2 = 120 \u03bcm, T = 20 \u03bcm, H = 100 \u03bcm. Pak Z01 \/ Z02 = 1,20. Z0 tedy pr\u00e1v\u011b dosahuje \u00b110%, nikoliv v r\u00e1mci \u00b110%. Aby se Z0 dostalo do \u00b110%, mus\u00ed b\u00fdt odchylka \u0161\u00ed\u0159ky mnohem men\u0161\u00ed ne\u017e \u00b120%. Aby bylo Z0 \u2264 \u00b15%, mus\u00ed b\u00fdt tolerance \u0161\u00ed\u0159ky \u2264 \u00b110%.<\/p>

          To vysv\u011btluje, pro\u010d n\u011bkter\u00e9 desky plo\u0161n\u00fdch spoj\u016f z PTFE a n\u011bkter\u00e9 desky plo\u0161n\u00fdch spoj\u016f z fr4 vy\u017eaduj\u00ed toleranci \u0161\u00ed\u0159ky \u00b10,02 mm. D\u016fvodem je kontrola Z0.<\/p>

          \u0158\u00edzen\u00ed procesu pro charakteristickou impedanci<\/h2>

          1. Kontrola a inspekce v\u00fdroby filmu<\/strong>
            Udr\u017eujte konstantn\u00ed teplotu a vlhkost (21\u00b12\u00b0C, 55\u00b15%), udr\u017eujte \u010distou m\u00edstnost a prov\u00e1d\u011bjte kompenzaci \u0161\u00ed\u0159ky procesu.<\/p><\/li>

          2. Design panelu<\/strong>
            Okraje panel\u016f by nem\u011bly b\u00fdt p\u0159\u00edli\u0161 \u00fazk\u00e9. Zajist\u011bte rovnom\u011brn\u00e9 pokoven\u00ed. P\u0159i galvanick\u00e9m pokovov\u00e1n\u00ed pou\u017eijte pseudokatodu k rozd\u011blen\u00ed proudu. Na okraj panelu p\u0159idejte kup\u00f3n pro testov\u00e1n\u00ed Z0.<\/p><\/li>

          3. Lept\u00e1n\u00ed<\/strong>
            \u0158\u00edzen\u00ed procesn\u00edch parametr\u016f pro sn\u00ed\u017een\u00ed pod\u0159ez\u00e1n\u00ed. Prove\u010fte kontrolu prvn\u00edho pr\u016fchodu. Sni\u017ete zbytkovou m\u011b\u010f, m\u011bd\u011bn\u00e9 ot\u0159epy a m\u011bd\u011bn\u00e9 od\u0159ezky. Zkontrolujte \u0161\u00ed\u0159ku stopy a udr\u017eujte ji v po\u017eadovan\u00e9m rozsahu (\u00b110% nebo \u00b10,02 mm).<\/p><\/li>

          4. Kontrola AOI<\/strong>
            U vnit\u0159n\u00edch vrstev najd\u011bte mezery ve stop\u00e1ch a v\u00fdstupky. U vysokorychlostn\u00edch sign\u00e1l\u016f 2 GHz mus\u00ed i mezera 0,05 mm zp\u016fsobit vy\u0159azen\u00ed desky. Kontrola \u0161\u00ed\u0159ky vnit\u0159n\u00ed vrstvy a defekt\u016f je kl\u00ed\u010dov\u00e1.<\/p><\/li>

          5. Laminov\u00e1n\u00ed<\/strong>
            Pro sn\u00ed\u017een\u00ed tlaku a sn\u00ed\u017een\u00ed pr\u016ftoku prysky\u0159ice pou\u017eijte vakuovou laminaci. Uchov\u00e1vejte v\u00edce prysky\u0159ice, proto\u017ee prysky\u0159ice ovliv\u0148uje \u03b5r. V\u00edce prysky\u0159ice \u010dasto sni\u017euje \u03b5r. Kontrolujte toleranci tlou\u0161\u0165ky laminace. Pokud je tlou\u0161\u0165ka hotov\u00e9 desky nerovnom\u011brn\u00e1, m\u011bn\u00ed se tlou\u0161\u0165ka dielektrika a ovliv\u0148uje Z0.<\/p><\/li>

          6. V\u00fdb\u011br dobr\u00e9ho z\u00e1kladn\u00edho materi\u00e1lu<\/strong>
            P\u0159\u00edsn\u011b dodr\u017eujte model materi\u00e1lu z\u00e1kazn\u00edka. \u0160patn\u00fd model znamen\u00e1 \u0161patn\u00fd \u03b5r, \u0161patnou tlou\u0161\u0165ku. \u00dapln\u00fd proces proveden\u00fd s nespr\u00e1vn\u00fdm materi\u00e1lem m\u00e1 st\u00e1le za n\u00e1sledek zmetky, proto\u017ee Z0 siln\u011b z\u00e1vis\u00ed na \u03b5r.<\/p><\/li>

          7. P\u00e1jec\u00ed maska (coverlay)<\/strong>
            P\u00e1jec\u00ed maska na povrchu desky m\u016f\u017ee sn\u00ed\u017eit Z0 o 1-3 \u03a9. Teoreticky by tlou\u0161\u0165ka p\u00e1jec\u00ed masky nem\u011bla b\u00fdt p\u0159\u00edli\u0161 siln\u00e1. V praxi nen\u00ed efekt velk\u00fd. P\u0159ed p\u00e1jec\u00ed maskou se povrch vodi\u010de st\u00fdk\u00e1 se vzduchem (\u03b5r = 1), tak\u017ee nam\u011b\u0159en\u00e1 Z0 je vy\u0161\u0161\u00ed. Po p\u00e1jec\u00ed masce klesne Z0 o 1-3 \u03a9, proto\u017ee \u03b5r p\u00e1jec\u00ed masky je p\u0159ibli\u017en\u011b 4,0.<\/p><\/li>

          8. Absorpce vlhkosti<\/strong>
            Zabra\u0148te absorpci vlhkosti v hotov\u00fdch v\u00edcevrstv\u00fdch desk\u00e1ch. Voda m\u00e1 \u03b5r \u2248 75. Vlhkost zp\u016fsobuje velk\u00fd pokles Z0 a nestabilitu.<\/p><\/li><\/ol>

            Souhrn<\/h2>

            U v\u00edcevrstv\u00fdch p\u0159enosov\u00fdch veden\u00ed na desk\u00e1ch jsou b\u011b\u017en\u00e9 rozsahy regulace Z0:<\/p>

            • 50 \u03a9 \u00b110%<\/p><\/li>

            • 75 \u03a9 \u00b110%<\/p><\/li>

            • 28 \u03a9 \u00b110%<\/p><\/li><\/ul>

              Pro kontrolu variability vezm\u011bte v \u00favahu tyto \u010dty\u0159i hlavn\u00ed faktory:<\/p>

              1. \u0160\u00ed\u0159ka stopy W<\/p><\/li>

              2. Tlou\u0161\u0165ka stopy T<\/p><\/li>

              3. Tlou\u0161\u0165ka dielektrika H<\/p><\/li>

              4. Dielektrick\u00e1 konstanta \u03b5r<\/p><\/li><\/ol>

                Nejv\u011bt\u0161\u00ed vliv m\u00e1 dielektrick\u00e1 tlou\u0161\u0165ka H. N\u00e1sleduje dielektrick\u00e1 konstanta \u03b5r. D\u00e1le \u0161\u00ed\u0159ka stopy W. Nejmen\u0161\u00ed vliv m\u00e1 tlou\u0161\u0165ka stopy T. Po volb\u011b z\u00e1kladn\u00edho materi\u00e1lu je zm\u011bna \u03b5r mal\u00e1. H lze regulovat, ale st\u00e1le se m\u011bn\u00ed. T je snadn\u011bji kontrolovateln\u00e1. \u0158\u00edzen\u00ed \u0161\u00ed\u0159ky stopy W v rozmez\u00ed \u00b110% je obt\u00ed\u017en\u00e9. Z\u00e1le\u017e\u00ed tak\u00e9 na probl\u00e9mech se stopou, jako jsou d\u00edrky, mezery a prom\u00e1\u010dkliny. V mnoha ohledech je nejefektivn\u011bj\u0161\u00ed a nejd\u016fle\u017eit\u011bj\u0161\u00ed metodou \u0159\u00edzen\u00ed Z0 p\u0159esn\u00e9 \u0159\u00edzen\u00ed a nastaven\u00ed \u0161\u00ed\u0159ky stopy.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

                What is PCB Impedance Control? PCB impedance control means controlling the impedance of traces. This impedance is also called controlled […]<\/p>","protected":false},"author":1,"featured_media":0,"parent":1898,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"no-sidebar","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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                What is PCB Impedance Control?<\\\/h2>

                PCB impedance control means controlling the impedance of traces. This impedance is also called controlled impedance. Controlled impedance is the characteristic impedance of a transmission line formed by PCB traces and their reference planes. When high-frequency signals travel on PCB transmission lines, this matters. Controlled impedance is important to solve signal integrity problems. Signal integrity means the signal travels without distortion.<\\\/p>

                The circuit impedance is set by the PCB physical size and the dielectric material. It is measured in ohms (\\u03a9). Types of PCB transmission lines that need impedance control include single-ended microstrip, single-ended stripline, differential microstrip pair, differential stripline pair, embedded microstrip, and coplanar (single-ended and differential).<\\\/p>

                Common methods to achieve impedance control<\\\/h2>

                1. Use PCB layer structure<\\\/h3>

                PCB designers can use the board layer stack to control impedance. Put different signal layers at different positions to control capacitance and inductance between layers. Usually, inner layers use higher impedance choices and outer layers use lower impedance choices to reduce reflection and crosstalk.<\\\/p>

                2. Use differential signal lines<\\\/h3>

                Differential pairs give better noise rejection and lower crosstalk risk. A differential pair is two parallel conductors. Their voltages are equal in size and opposite in polarity. Differential pairs give better signal integrity and noise resistance. The impedance of a differential pair is controlled by the spacing, trace width, and the ground plane layout.<\\\/p>

                3. Control trace geometry<\\\/h3>

                Trace width, spacing, and layout geometry can also control impedance. For common microstrip, wider traces and larger spacing lower impedance. For coaxial type structures, a smaller inner conductor and a larger outer conductor radius raise impedance. Choose trace geometry based on target impedance and signal frequency.<\\\/p>

                4. Choose PCB materials<\\\/h3>

                The dielectric constant of the PCB material affects impedance. Picking materials with stable dielectric properties is part of impedance control. For high frequency and high speed use, common materials are fr4 (glass-epoxy), PTFE (Teflon), and RF laminates.<\\\/p>

                5. Use simulation and design tools<\\\/h3>

                Before final PCB layout, use simulation and design tools to check and optimize impedance. These tools simulate circuit behavior, signal loss, and electromagnetic interactions. They help find the best board parameters. Common tools include CST Studio Suite, HyperLynx, and ADS.<\\\/p>

                Effects of PCB manufacturing on impedance<\\\/h2>

                Trace width<\\\/h3>

                Trace width directly affects transmission line impedance and loss. Most good engineers give the PCB maker a trace width tolerance with Gerber files. For example, if a trace width is designed as 6.2 mil and its impedance is 50 ohm, manufacturing instability that changes the trace width will change impedance. From experience with many factories, trace width may vary about 10%. We can model trace width change as a Gaussian distribution with a standard deviation of 10%.<\\\/p>

                Copper foil \\\/ plated copper thickness<\\\/h3>

                In PCB products, copper thickness has two parts: base copper thickness and plated copper thickness. Base copper is relatively uniform, but plated copper uniformity depends on factory process. Plated copper may vary a lot between factories. Different plated copper thickness will change trace impedance and loss. Impedance may vary in a small range, for example between 49.5 and 51 ohm. Compared with trace width, copper thickness has a smaller effect on impedance.<\\\/p>

                Dielectric thickness<\\\/h3>

                In PCB manufacture, dielectric thickness changes come from raw material variation, lamination pressure, and glue filling. If dielectric thickness changes, impedance and loss will change. In severe cases, transmission lines will have large loss. Impedance may vary from about 44 ohm to 54 ohm. The range can be as wide as 10 ohm.<\\\/p>

                Etch factor<\\\/h3>

                Conductors have finite thickness. After etch, traces are not perfect rectangles. They look closer to a trapezoid. The trapezoid angle changes with copper thickness (including plating). When copper is thin, the sidewall angle approaches 90\\u00b0. The angle size affects impedance. For example, when the sidewall angle is 70\\u00b0, impedance is about 50 ohm. When the angle is 90\\u00b0, impedance is about 48.37 ohm.<\\\/p>

                The above tests change one factor at a time. In real production, multiple variables change at once. Impedance can vary from about 40 ohm to 56 ohm. This far exceeds a typical requirement such as 50\\u03a9 \\u00b110%. During production, many parameters cause impedance change. For high-speed or high-end products, the PCB design and manufacturing process must strictly control every material and step. Otherwise, the product can show unexpected problems.<\\\/p>

                Impedance and characteristic impedance<\\\/h2>

                1. Resistance<\\\/h3>

                When an alternating current flows in a conductor, the opposition it meets is called impedance (Impedance). Symbol is Z. Unit is still ohm (\\u03a9). This opposition differs from DC resistance. In AC, besides resistance (R), there are inductive reactance (XL) and capacitive reactance (XC).<\\\/p>

                To distinguish from DC resistance, call the AC opposition impedance (Z).<\\\/p>

                The formula:<\\\/p>

                \\u00a0<\\\/div><\\\/div><\\\/div>
                Z<\\\/span> = \\u221a(R\\u00b2 + (XL \\u2212 XC)\\u00b2)
                \\n<\\\/code><\\\/div><\\\/div>

                2. Impedance (Z)<\\\/h3>

                With higher IC integration and higher signal frequency and speed, signals on PCB traces can be affected by the PCB trace itself. When signal frequency reaches a limit, the trace causes serious signal distortion or loss. This shows PCB traces carry not just current but energy in the form of pulses or square wave signals.<\\\/p>

                3. Characteristic impedance control (Z0)<\\\/h3>

                The opposition a signal sees when it travels is called characteristic impedance. Symbol is Z0.<\\\/p>

                So, fixing only \\\"open\\\", \\\"short\\\", and connectivity is not enough. For high speed and high frequency transmission lines, quality must be stricter. Passing an open\\\/short test or having small defects is not enough. You must measure Z0 and keep it within tolerance. If not, the board must be scrapped. Do not rework.<\\\/p>

                Signal propagation and transmission lines<\\\/h2>

                1. Definition of a signal transmission line<\\\/h3>

                1. From electromagnetic theory, shorter wavelength (\\u03bb) means higher frequency (f). Their product equals light speed. That is:<\\\/p><\\\/li><\\\/ol>

                  \\u00a0<\\\/div><\\\/div><\\\/div>
                  C<\\\/span> = \\u03bb \\u00b7 f = 3<\\\/span> \\u00d7 10<\\\/span>^10<\\\/span> cm\\\/s
                  \\n<\\\/code><\\\/div><\\\/div>

                  1. Any device may have a high signal frequency. After the signal travels through a PCB trace, the signal may slow or be delayed.<\\\/p><\\\/li><\\\/ol>

                    So, shorter trace length is better.<\\\/p>

                    1. Increasing wiring density or reducing wire size helps. But when component frequency becomes higher or pulse periods shorten, trace length may approach a portion of the signal wavelength. Then the trace will show obvious distortion.<\\\/p><\\\/li>

                    2. IPC-2141 clause 3.4.4 says: when a trace length approaches 1\\\/7 of the signal wavelength, the trace is treated as a signal transmission line.<\\\/p><\\\/li>

                    3. Example:<\\\/p><\\\/li><\\\/ol>

                      A device has signal frequency f = 10 MHz. PCB trace length is 50 cm. Do we need characteristic impedance control?<\\\/p>

                      Compute:<\\\/p>

                      \\u00a0<\\\/div><\\\/div><\\\/div>
                      C = \\u03bb \\u00b7 f = 3 \\u00d7 10^10 cm\\\/s
                      \\n\\u03bb = C \\\/ f = (3 \\u00d7 10^10 cm\\\/s) \\\/ (1 \\u00d7 10^7 \\\/s) = 3000 cm
                      \\ntrace length \\\/ wavelength = 50 \\\/ 3000 = 1\\\/60
                      \\n<\\\/code><\\\/div><\\\/div>

                      Because 1\\\/60 is much less than 1\\\/7, this trace is a normal wire and does not need characteristic impedance control.<\\\/p>

                      Maxwell's equations tell us: the propagation speed VS of a sine wave in a medium relates to light speed C and dielectric constant \\u03b5r as:<\\\/p>

                      \\u00a0<\\\/div><\\\/div><\\\/div>
                      VS<\\\/span> = C \\\/ \\u221a\\u03b5r
                      \\n<\\\/code><\\\/div><\\\/div>

                      When \\u03b5r = 1, signal speed equals light speed = 3 \\u00d7 10^10 cm\\\/s.<\\\/p>

                      2. Transmission speed and dielectric constant<\\\/h3>

                      Signal speed at 30 MHz for different materials:<\\\/p>

                      Material \\\/ Substrate<\\\/th>Tg (\\u00b0C)<\\\/th>Dielectric constant \\u03b5r<\\\/th>Signal speed (m\\\/\\u03bcs)<\\\/th><\\\/tr><\\\/thead>
                      Vacuum<\\\/td>\\\/<\\\/td>1.0<\\\/td>300.00<\\\/td><\\\/tr>
                      PTFE (Teflon)<\\\/td>\\\/<\\\/td>2.2<\\\/td>202.26<\\\/td><\\\/tr>
                      Thermoset polyphenylene ether<\\\/td>210<\\\/td>2.5<\\\/td>189.74<\\\/td><\\\/tr>
                      Cyanate ester<\\\/td>225<\\\/td>3.0<\\\/td>173.21<\\\/td><\\\/tr>
                      PTFE + E-glass<\\\/td>\\\/<\\\/td>2.6<\\\/td>186.25<\\\/td><\\\/tr>
                      Cyanate ester + glass<\\\/td>225<\\\/td>3.7<\\\/td>155.96<\\\/td><\\\/tr>
                      Polyimide + glass<\\\/td>230<\\\/td>4.5<\\\/td>141.42<\\\/td><\\\/tr>
                      Quartz<\\\/td>\\\/<\\\/td>3.9<\\\/td>151.98<\\\/td><\\\/tr>
                      Epoxy glass (fr4)<\\\/td>130\\u00b15<\\\/td>4.7<\\\/td>138.38<\\\/td><\\\/tr>
                      Aluminum<\\\/td>\\\/<\\\/td>9.0<\\\/td>100.00<\\\/td><\\\/tr><\\\/tbody><\\\/table><\\\/div><\\\/div>

                      The table shows: as \\u03b5r increases, signal speed in the material decreases. To get higher signal speed, choose higher characteristic impedance. To get higher Z0, choose lower \\u03b5r material. PTFE has the smallest \\u03b5r, so it gives the fastest speed.<\\\/p>

                      fr4 board uses epoxy resin plus E-glass. Its \\u03b5r is about 4.7. Signal speed is 138 m\\\/\\u03bcs. Changing the resin system can change \\u03b5r.<\\\/p>

                      Reasons to control characteristic impedance<\\\/h2>

                      Reason 1<\\\/h3>

                      When electronic equipment (computer, communications) runs, the driver sends a signal to the receiver through PCB traces. The characteristic impedance Z0 of the trace must match the driver and receiver electronic impedance. If matched, the signal energy transmits completely.<\\\/p>

                      Reason 2<\\\/h3>

                      If PCB quality is bad and Z0 is out of tolerance, signals will reflect, dissipate, attenuate, or delay. In severe cases, signals can be wrong and the device can crash.<\\\/p>

                      Reason 3<\\\/h3>

                      Strict material selection and process control are needed so multilayer board Z0 meets customer specs. Higher electronic impedance components usually need higher PCB Z0 to match. A multilayer board with correct Z0 is a qualified high-speed or high-frequency product.<\\\/p>

                      Relationship of Z0 to material and process<\\\/h2>

                      The microstrip characteristic impedance Z0 formula:<\\\/p>

                      \\u00a0<\\\/div><\\\/div><\\\/div>
                      Z0<\\\/span> = 87<\\\/span> \\\/ \\u221a\\u03b5r + 1.41<\\\/span> \\u00b7 ln [ 5.98<\\\/span> H \\\/ (0.8<\\\/span> W + T) ]
                      \\n<\\\/code><\\\/div><\\\/div>

                      Where:<\\\/p>

                      • \\u03b5r \\u2014 dielectric constant<\\\/p><\\\/li>

                      • H \\u2014 dielectric thickness<\\\/p><\\\/li>

                      • W \\u2014 trace width<\\\/p><\\\/li>

                      • T \\u2014 trace thickness<\\\/p><\\\/li><\\\/ul>

                        Lower \\u03b5r makes it easier to raise Z0 to match high-speed components.<\\\/p>

                        1. Z0 and \\u03b5r<\\\/h3>

                        Z0 is inversely related to \\u03b5r. Z0 increases as H increases. For strict Z0 high-frequency lines, dielectric thickness tolerance must be strict. Usually dielectric thickness change must not exceed 10%.<\\\/p>

                        2. Dielectric thickness effect<\\\/h3>

                        With higher routing density, larger H leads to more electromagnetic interference. For high-frequency and high-speed digital lines, as conductor density rises, reduce dielectric thickness to lower EMI and crosstalk, or use materials with lower \\u03b5r.<\\\/p>

                        From the formula, copper thickness T is an important factor. Larger T lowers Z0, but the change is small.<\\\/p>

                        3. Copper thickness effect<\\\/h3>

                        Thinner copper gives higher Z0, but its effect on Z0 is small. Using thin copper helps make fine traces and this helps control Z0 more than the copper thickness value alone.<\\\/p>

                        From the formula:<\\\/p>

                        \\u00a0<\\\/div><\\\/div><\\\/div>
                        Z0<\\\/span> = 87<\\\/span> \\\/ \\u221a\\u03b5r + 1.41<\\\/span> \\u00b7 ln [ 5.98<\\\/span> H \\\/ (0.8<\\\/span> W + T) ]
                        \\n<\\\/code><\\\/div><\\\/div>

                        As W (trace width) decreases, Z0 increases. Changing width has a larger impact on Z0 than changing thickness.<\\\/p>

                        4. Trace width effect<\\\/h3>

                        Z0 increases sharply as width W narrows. To control Z0, control trace width tightly. Today most high-frequency and high-speed digital traces have widths like 0.10 mm or 0.13 mm. Traditionally, width tolerance was \\u00b120%. For non-transmission line traces (trace length << signal wavelength \\\/ 7), \\u00b120% may be fine. But for Z0 controlled traces, \\u00b120% width error cannot meet requirements. At that point Z0 error often exceeds \\u00b110%.<\\\/p>

                        Example:<\\\/p>

                        A PCB microstrip has width 100 \\u03bcm, thickness 20 \\u03bcm, dielectric thickness 100 \\u03bcm. Assume copper thickness is uniform. If width changes \\u00b120%, can Z0 meet \\u00b110%?<\\\/p>

                        By formula:<\\\/p>

                        Let W0 = 100 \\u03bcm, W1 = 80 \\u03bcm, W2 = 120 \\u03bcm, T = 20 \\u03bcm, H = 100 \\u03bcm. Then Z01 \\\/ Z02 = 1.20. So Z0 just reaches \\u00b110%, not within \\u00b110%. To get Z0 within \\u00b110%, width variation must be much smaller than \\u00b120%. To get Z0 \\u2264 \\u00b15%, width tolerance must be \\u2264 \\u00b110%.<\\\/p>

                        This explains why some PTFE PCBs and some fr4 PCBs require width tolerance \\u00b10.02 mm. The reason is to control Z0.<\\\/p>

                        Process controls for characteristic impedance<\\\/h2>

                        1. Film making control and inspection<\\\/strong>
                          Keep constant temperature and humidity (21\\u00b12\\u00b0C, 55\\u00b15%), keep a clean room, and do width process compensation.<\\\/p><\\\/li>

                        2. Panel design<\\\/strong>
                          Panel edges should not be too narrow. Make plating uniform. Use pseudo-cathode in electroplating to distribute current. Add a coupon on the panel edge to test Z0.<\\\/p><\\\/li>

                        3. Etching<\\\/strong>
                          Control process parameters to reduce undercut. Do first-pass inspection. Reduce residual copper, copper burrs, and copper scraps. Check trace width and keep it within required range (\\u00b110% or \\u00b10.02 mm).<\\\/p><\\\/li>

                        4. AOI inspection<\\\/strong>
                          For inner layers, find trace gaps and protrusions. For 2 GHz high-speed signals, even a 0.05 mm gap must cause board scrap. Controlling inner layer width and defects is key.<\\\/p><\\\/li>

                        5. Lamination<\\\/strong>
                          Use vacuum lamination to lower pressure and reduce resin flow. Keep more resin because resin affects \\u03b5r. More resin often lowers \\u03b5r. Control lamination thickness tolerance. If finished board thickness is uneven, dielectric thickness varies and affects Z0.<\\\/p><\\\/li>

                        6. Select good base material<\\\/strong>
                          Strictly follow customer material model. Wrong model means wrong \\u03b5r, wrong thickness. A full process done with wrong material still results in scrap because Z0 depends strongly on \\u03b5r.<\\\/p><\\\/li>

                        7. Solder mask (coverlay)<\\\/strong>
                          Solder mask on the board surface can lower Z0 by 1\\u20133 \\u03a9. In theory, solder mask thickness should not be too thick. In practice the effect is not huge. Before solder mask, the conductor surface interfaces with air (\\u03b5r = 1) so measured Z0 is higher. After solder mask, Z0 drops 1\\u20133 \\u03a9 because solder mask \\u03b5r is about 4.0.<\\\/p><\\\/li>

                        8. Moisture absorption<\\\/strong>
                          Avoid moisture absorption in finished multilayer boards. Water has \\u03b5r \\u2248 75. Moisture causes large Z0 drop and instability.<\\\/p><\\\/li><\\\/ol>

                          Summary<\\\/h2>

                          For multilayer board transmission lines, common Z0 control ranges are:<\\\/p>

                          • 50 \\u03a9 \\u00b110%<\\\/p><\\\/li>

                          • 75 \\u03a9 \\u00b110%<\\\/p><\\\/li>

                          • 28 \\u03a9 \\u00b110%<\\\/p><\\\/li><\\\/ul>

                            To control variation, consider these four main factors:<\\\/p>

                            1. Trace width W<\\\/p><\\\/li>

                            2. Trace thickness T<\\\/p><\\\/li>

                            3. Dielectric thickness H<\\\/p><\\\/li>

                            4. Dielectric constant \\u03b5r<\\\/p><\\\/li><\\\/ol>

                              The largest influence is dielectric thickness H. Next is dielectric constant \\u03b5r. Then trace width W. The smallest is trace thickness T. After choosing base material, \\u03b5r change is small. H can be controlled but still varies. T is easier to control. Controlling trace width W within \\u00b110% is hard. Trace issues like pinholes, gaps, and dents also matter. In many ways, the most effective and important method to control Z0 is to control and adjust trace width precisely.<\\\/p>\",\"display_condition_list\":[{\"display_condition_login_status\":\"subscriber\",\"_id\":\"ee6d0f7\"}]},\"elements\":[],\"widgetType\":\"text-editor\"}],\"isInner\":false}]"],"_elementor_conditions":["a:0:{}"],"_edit_last":["1"],"_astra_content_layout_flag":["disabled"],"ast-title-bar-display":["disabled"],"_elementor_version":["3.31.2"],"_elementor_pro_version":["3.31.2"],"_wp_page_template":["default"],"_elementor_page_settings":["a:1:{s:10:\"hide_title\";s:3:\"yes\";}"],"rank_math_internal_links_processed":["1"],"rank_math_news_sitemap_robots":["index"],"rank_math_robots":["a:1:{i:0;s:5:\"index\";}"],"rank_math_seo_score":["30"],"rank_math_focus_keyword":["Impedance Control"],"site-post-title":["disabled"],"_uag_page_assets":["a:9:{s:3:\"css\";s:30185:\".uag-blocks-common-selector{z-index:var(--z-index-desktop) !important}@media (max-width: 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ufacturing instability that changes the trace width will change impedance. From experience with many factories, trace width may vary about 10%. We can model trace width change as a Gaussian distribution with a standard deviation of 10%.<\/p><h3 data-start=\"3122\" data-end=\"3162\">Copper foil \/ plated copper thickness<\/h3><p data-start=\"3164\" data-end=\"3628\">In PCB products, copper thickness has two parts: base copper thickness and plated copper thickness. Base copper is relatively uniform, but plated copper uniformity depends on factory process. Plated copper may vary a lot between factories. Different plated copper thickness will change trace impedance and loss. Impedance may vary in a small range, for example between 49.5 and 51 ohm. Compared with trace width, copper thickness has a smaller effect on impedance.<\/p><h3 data-start=\"3630\" data-end=\"3653\">Dielectric thickness<\/h3><p data-start=\"3655\" data-end=\"3983\">In PCB manufacture, dielectric thickness changes come from raw material variation, lamination pressure, and glue filling. If dielectric thickness changes, impedance and loss will change. In severe cases, transmission lines will have large loss. Impedance may vary from about 44 ohm to 54 ohm. The range can be as wide as 10 ohm.<\/p><h3 data-start=\"3985\" data-end=\"3999\">Etch factor<\/h3><p data-start=\"4001\" data-end=\"4400\">Conductors have finite thickness. After etch, traces are not perfect rectangles. They look closer to a trapezoid. The trapezoid angle changes with copper thickness (including plating). When copper is thin, the sidewall angle approaches 90\u00b0. The angle size affects impedance. For example, when the sidewall angle is 70\u00b0, impedance is about 50 ohm. When the angle is 90\u00b0, impedance is about 48.37 ohm.<\/p><p data-start=\"4402\" data-end=\"4843\">The above tests change one factor at a time. In real production, multiple variables change at once. Impedance can vary from about 40 ohm to 56 ohm. This far exceeds a typical requirement such as 50\u03a9 \u00b110%. During production, many parameters cause impedance change. For high-speed or high-end products, the PCB design and manufacturing process must strictly control every material and step. Otherwise, the product can show unexpected problems.<\/p><hr data-start=\"4845\" data-end=\"4848\" \/><h2 data-start=\"4850\" data-end=\"4890\">Impedance and characteristic impedance<\/h2><h3 data-start=\"4892\" data-end=\"4908\">1. Resistance<\/h3><p data-start=\"4910\" data-end=\"5193\">When an alternating current flows in a conductor, the opposition it meets is called impedance (Impedance). Symbol is Z. Unit is still ohm (\u03a9). This opposition differs from DC resistance. In AC, besides resistance (R), there are inductive reactance (XL) and capacitive reactance (XC).<\/p><p data-start=\"5195\" data-end=\"5267\">To distinguish from DC resistance, call the AC opposition impedance (Z).<\/p><p data-start=\"5269\" data-end=\"5281\">The formula:<\/p><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">Z<\/span> = \u221a(R\u00b2 + (XL \u2212 XC)\u00b2)<br \/>\n<\/code><\/div><\/div><h3 data-start=\"5315\" data-end=\"5334\">2. Impedance (Z)<\/h3><p data-start=\"5336\" data-end=\"5657\">With higher IC integration and higher signal frequency and speed, signals on PCB traces can be affected by the PCB trace itself. When signal frequency reaches a limit, the trace causes serious signal distortion or loss. This shows PCB traces carry not just current but energy in the form of pulses or square wave signals.<\/p><h3 data-start=\"5659\" data-end=\"5702\">3. Characteristic impedance control (Z0)<\/h3><p data-start=\"5704\" data-end=\"5798\">The opposition a signal sees when it travels is called characteristic impedance. Symbol is Z0.<\/p><p data-start=\"5800\" data-end=\"6111\">So, fixing only \"open\", \"short\", and connectivity is not enough. For high speed and high frequency transmission lines, quality must be stricter. Passing an open\/short test or having small defects is not enough. You must measure Z0 and keep it within tolerance. If not, the board must be scrapped. Do not rework.<\/p><hr data-start=\"6113\" data-end=\"6116\" \/><h2 data-start=\"6118\" data-end=\"6161\">Signal propagation and transmission lines<\/h2><h3 data-start=\"6163\" data-end=\"6209\">1. Definition of a signal transmission line<\/h3><ol data-start=\"6211\" data-end=\"6336\"><li data-start=\"6211\" data-end=\"6336\"><p data-start=\"6214\" data-end=\"6336\">From electromagnetic theory, shorter wavelength (\u03bb) means higher frequency (f). Their product equals light speed. That is:<\/p><\/li><\/ol><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">C<\/span> = \u03bb \u00b7 f = <span class=\"hljs-number\">3<\/span> \u00d7 <span class=\"hljs-number\">10<\/span>^<span class=\"hljs-number\">10<\/span> cm\/s<br \/>\n<\/code><\/div><\/div><ol start=\"2\" data-start=\"6374\" data-end=\"6502\"><li data-start=\"6374\" data-end=\"6502\"><p data-start=\"6377\" data-end=\"6502\">Any device may have a high signal frequency. After the signal travels through a PCB trace, the signal may slow or be delayed.<\/p><\/li><\/ol><p data-start=\"6504\" data-end=\"6539\">So, shorter trace length is better.<\/p><ol start=\"3\" data-start=\"6541\" data-end=\"6933\"><li data-start=\"6541\" data-end=\"6775\"><p data-start=\"6544\" data-end=\"6775\">Increasing wiring density or reducing wire size helps. But when component frequency becomes higher or pulse periods shorten, trace length may approach a portion of the signal wavelength. Then the trace will show obvious distortion.<\/p><\/li><li data-start=\"6777\" data-end=\"6920\"><p data-start=\"6780\" data-end=\"6920\">IPC-2141 clause 3.4.4 says: when a trace length approaches 1\/7 of the signal wavelength, the trace is treated as a signal transmission line.<\/p><\/li><li data-start=\"6922\" data-end=\"6933\"><p data-start=\"6925\" data-end=\"6933\">Example:<\/p><\/li><\/ol><p data-start=\"6935\" data-end=\"7048\">A device has signal frequency f = 10 MHz. PCB trace length is 50 cm. Do we need characteristic impedance control?<\/p><p data-start=\"7050\" data-end=\"7058\">Compute:<\/p><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\">C = \u03bb \u00b7 f = 3 \u00d7 10^10 cm\/s<br \/>\n\u03bb = C \/ f = (3 \u00d7 10^10 cm\/s) \/ (1 \u00d7 10^7 \/s) = 3000 cm<br \/>\ntrace length \/ wavelength = 50 \/ 3000 = 1\/60<br \/>\n<\/code><\/div><\/div><p data-start=\"7196\" data-end=\"7311\">Because 1\/60 is much less than 1\/7, this trace is a normal wire and does not need characteristic impedance control.<\/p><p data-start=\"7313\" data-end=\"7449\">Maxwell's equations tell us: the propagation speed VS of a sine wave in a medium relates to light speed C and dielectric constant \u03b5r as:<\/p><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">VS<\/span> = C \/ \u221a\u03b5r<br \/>\n<\/code><\/div><\/div><p data-start=\"7473\" data-end=\"7535\">When \u03b5r = 1, signal speed equals light speed = 3 \u00d7 10^10 cm\/s.<\/p><h3 data-start=\"7537\" data-end=\"7585\">2. Transmission speed and dielectric constant<\/h3><p data-start=\"7587\" data-end=\"7634\">Signal speed at 30 MHz for different materials:<\/p><div class=\"_tableContainer_1rjym_1\"><div class=\"_tableWrapper_1rjym_13 group flex w-fit flex-col-reverse\" tabindex=\"-1\"><table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"7636\" data-end=\"8134\"><thead data-start=\"7636\" data-end=\"7717\"><tr data-start=\"7636\" data-end=\"7717\"><th data-start=\"7636\" data-end=\"7659\" data-col-size=\"sm\">Material \/ Substrate<\/th><th data-start=\"7659\" data-end=\"7669\" data-col-size=\"sm\">Tg (\u00b0C)<\/th><th data-start=\"7669\" data-end=\"7694\" data-col-size=\"sm\">Dielectric constant \u03b5r<\/th><th data-start=\"7694\" data-end=\"7717\" data-col-size=\"sm\">Signal speed (m\/\u03bcs)<\/th><\/tr><\/thead><tbody data-start=\"7739\" data-end=\"8134\"><tr data-start=\"7739\" data-end=\"7768\"><td data-start=\"7739\" data-end=\"7748\" data-col-size=\"sm\">Vacuum<\/td><td data-start=\"7748\" data-end=\"7752\" data-col-size=\"sm\">\/<\/td><td data-start=\"7752\" data-end=\"7758\" data-col-size=\"sm\">1.0<\/td><td data-start=\"7758\" data-end=\"7768\" data-col-size=\"sm\">300.00<\/td><\/tr><tr data-start=\"7769\" data-end=\"7805\"><td data-start=\"7769\" data-end=\"7785\" data-col-size=\"sm\">PTFE (Teflon)<\/td><td data-start=\"7785\" data-end=\"7789\" data-col-size=\"sm\">\/<\/td><td data-start=\"7789\" data-end=\"7795\" data-col-size=\"sm\">2.2<\/td><td data-start=\"7795\" data-end=\"7805\" data-col-size=\"sm\">202.26<\/td><\/tr><tr data-start=\"7806\" data-end=\"7860\"><td data-start=\"7806\" data-end=\"7838\" data-col-size=\"sm\">Thermoset polyphenylene ether<\/td><td data-start=\"7838\" data-end=\"7844\" data-col-size=\"sm\">210<\/td><td data-start=\"7844\" data-end=\"7850\" data-col-size=\"sm\">2.5<\/td><td data-start=\"7850\" data-end=\"7860\" data-col-size=\"sm\">189.74<\/td><\/tr><tr data-start=\"7861\" data-end=\"7899\"><td data-start=\"7861\" data-end=\"7877\" data-col-size=\"sm\">Cyanate ester<\/td><td data-start=\"7877\" data-end=\"7883\" data-col-size=\"sm\">225<\/td><td data-start=\"7883\" data-end=\"7889\" data-col-size=\"sm\">3.0<\/td><td data-start=\"7889\" data-end=\"7899\" data-col-size=\"sm\">173.21<\/td><\/tr><tr data-start=\"7900\" data-end=\"7937\"><td data-start=\"7900\" data-end=\"7917\" data-col-size=\"sm\">PTFE + E-glass<\/td><td data-start=\"7917\" data-end=\"7921\" data-col-size=\"sm\">\/<\/td><td data-start=\"7921\" data-end=\"7927\" data-col-size=\"sm\">2.6<\/td><td data-start=\"7927\" data-end=\"7937\" data-col-size=\"sm\">186.25<\/td><\/tr><tr data-start=\"7938\" data-end=\"7984\"><td data-start=\"7938\" data-end=\"7962\" data-col-size=\"sm\">Cyanate ester + glass<\/td><td data-start=\"7962\" data-end=\"7968\" data-col-size=\"sm\">225<\/td><td data-start=\"7968\" data-end=\"7974\" data-col-size=\"sm\">3.7<\/td><td data-start=\"7974\" data-end=\"7984\" data-col-size=\"sm\">155.96<\/td><\/tr><tr data-start=\"7985\" data-end=\"8027\"><td data-start=\"7985\" data-end=\"8005\" data-col-size=\"sm\">Polyimide + glass<\/td><td data-start=\"8005\" data-end=\"8011\" data-col-size=\"sm\">230<\/td><td data-start=\"8011\" data-end=\"8017\" data-col-size=\"sm\">4.5<\/td><td data-start=\"8017\" data-end=\"8027\" data-col-size=\"sm\">141.42<\/td><\/tr><tr data-start=\"8028\" data-end=\"8057\"><td data-start=\"8028\" data-end=\"8037\" data-col-size=\"sm\">Quartz<\/td><td data-start=\"8037\" data-end=\"8041\" data-col-size=\"sm\">\/<\/td><td data-start=\"8041\" data-end=\"8047\" data-col-size=\"sm\">3.9<\/td><td data-start=\"8047\" data-end=\"8057\" data-col-size=\"sm\">151.98<\/td><\/tr><tr data-start=\"8058\" data-end=\"8102\"><td data-start=\"8058\" data-end=\"8078\" data-col-size=\"sm\">Epoxy glass (fr4)<\/td><td data-start=\"8078\" data-end=\"8086\" data-col-size=\"sm\">130\u00b15<\/td><td data-start=\"8086\" data-end=\"8092\" data-col-size=\"sm\">4.7<\/td><td data-start=\"8092\" data-end=\"8102\" data-col-size=\"sm\">138.38<\/td><\/tr><tr data-start=\"8103\" data-end=\"8134\"><td data-start=\"8103\" data-end=\"8114\" data-col-size=\"sm\">Aluminum<\/td><td data-start=\"8114\" data-end=\"8118\" data-col-size=\"sm\">\/<\/td><td data-start=\"8118\" data-end=\"8124\" data-col-size=\"sm\">9.0<\/td><td data-start=\"8124\" data-end=\"8134\" data-col-size=\"sm\">100.00<\/td><\/tr><\/tbody><\/table><\/div><\/div><p data-start=\"8136\" data-end=\"8378\">The table shows: as \u03b5r increases, signal speed in the material decreases. To get higher signal speed, choose higher characteristic impedance. To get higher Z0, choose lower \u03b5r material. PTFE has the smallest \u03b5r, so it gives the fastest speed.<\/p><p data-start=\"8380\" data-end=\"8508\">fr4 board uses epoxy resin plus E-glass. Its \u03b5r is about 4.7. Signal speed is 138 m\/\u03bcs. Changing the resin system can change \u03b5r.<\/p><hr data-start=\"8510\" data-end=\"8513\" \/><h2 data-start=\"8515\" data-end=\"8560\">Reasons to control characteristic impedance<\/h2><h3 data-start=\"8562\" data-end=\"8573\">Reason 1<\/h3><p data-start=\"8575\" data-end=\"8849\">When electronic equipment (computer, communications) runs, the driver sends a signal to the receiver through PCB traces. The characteristic impedance Z0 of the trace must match the driver and receiver electronic impedance. If matched, the signal energy transmits completely.<\/p><h3 data-start=\"8851\" data-end=\"8862\">Reason 2<\/h3><p data-start=\"8864\" data-end=\"9031\">If PCB quality is bad and Z0 is out of tolerance, signals will reflect, dissipate, attenuate, or delay. In severe cases, signals can be wrong and the device can crash.<\/p><h3 data-start=\"9033\" data-end=\"9044\">Reason 3<\/h3><p data-start=\"9046\" data-end=\"9311\">Strict material selection and process control are needed so multilayer board Z0 meets customer specs. Higher electronic impedance components usually need higher PCB Z0 to match. A multilayer board with correct Z0 is a qualified high-speed or high-frequency product.<\/p><hr data-start=\"9313\" data-end=\"9316\" \/><h2 data-start=\"9318\" data-end=\"9362\">Relationship of Z0 to material and process<\/h2><p data-start=\"9364\" data-end=\"9415\">The microstrip characteristic impedance Z0 formula:<\/p><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">Z0<\/span> = <span class=\"hljs-number\">87<\/span> \/ \u221a\u03b5r + <span class=\"hljs-number\">1.41<\/span> \u00b7 ln [ <span class=\"hljs-number\">5.98<\/span> H \/ (<span class=\"hljs-number\">0.8<\/span> W + T) ]<br \/>\n<\/code><\/div><\/div><p data-start=\"9477\" data-end=\"9483\">Where:<\/p><ul data-start=\"9485\" data-end=\"9584\"><li data-start=\"9485\" data-end=\"9513\"><p data-start=\"9487\" data-end=\"9513\">\u03b5r \u2014 dielectric constant<\/p><\/li><li data-start=\"9514\" data-end=\"9542\"><p data-start=\"9516\" data-end=\"9542\">H \u2014 dielectric thickness<\/p><\/li><li data-start=\"9543\" data-end=\"9562\"><p data-start=\"9545\" data-end=\"9562\">W \u2014 trace width<\/p><\/li><li data-start=\"9563\" data-end=\"9584\"><p data-start=\"9565\" data-end=\"9584\">T \u2014 trace thickness<\/p><\/li><\/ul><p data-start=\"9586\" data-end=\"9654\">Lower \u03b5r makes it easier to raise Z0 to match high-speed components.<\/p><h3 data-start=\"9656\" data-end=\"9671\">1. Z0 and \u03b5r<\/h3><p data-start=\"9673\" data-end=\"9872\">Z0 is inversely related to \u03b5r. Z0 increases as H increases. For strict Z0 high-frequency lines, dielectric thickness tolerance must be strict. Usually dielectric thickness change must not exceed 10%.<\/p><h3 data-start=\"9874\" data-end=\"9907\">2. Dielectric thickness effect<\/h3><p data-start=\"9909\" data-end=\"10155\">With higher routing density, larger H leads to more electromagnetic interference. For high-frequency and high-speed digital lines, as conductor density rises, reduce dielectric thickness to lower EMI and crosstalk, or use materials with lower \u03b5r.<\/p><p data-start=\"10157\" data-end=\"10262\">From the formula, copper thickness T is an important factor. Larger T lowers Z0, but the change is small.<\/p><h3 data-start=\"10264\" data-end=\"10293\">3. Copper thickness effect<\/h3><p data-start=\"10295\" data-end=\"10468\">Thinner copper gives higher Z0, but its effect on Z0 is small. Using thin copper helps make fine traces and this helps control Z0 more than the copper thickness value alone.<\/p><p data-start=\"10470\" data-end=\"10487\">From the formula:<\/p><div class=\"contain-inline-size rounded-2xl relative bg-token-sidebar-surface-primary\"><div class=\"sticky top-9\"><div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\"><div class=\"bg-token-bg-elevated-secondary text-token-text-secondary flex items-center gap-4 rounded-sm px-2 font-sans text-xs\">\u00a0<\/div><\/div><\/div><div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">Z0<\/span> = <span class=\"hljs-number\">87<\/span> \/ \u221a\u03b5r + <span class=\"hljs-number\">1.41<\/span> \u00b7 ln [ <span class=\"hljs-number\">5.98<\/span> H \/ (<span class=\"hljs-number\">0.8<\/span> W + T) ]<br \/>\n<\/code><\/div><\/div><p data-start=\"10549\" data-end=\"10658\">As W (trace width) decreases, Z0 increases. Changing width has a larger impact on Z0 than changing thickness.<\/p><h3 data-start=\"10660\" data-end=\"10684\">4. Trace width effect<\/h3><p data-start=\"10686\" data-end=\"11112\">Z0 increases sharply as width W narrows. To control Z0, control trace width tightly. Today most high-frequency and high-speed digital traces have widths like 0.10 mm or 0.13 mm. Traditionally, width tolerance was \u00b120%. For non-transmission line traces (trace length &lt;&lt; sign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