{"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\/fi\/pcb-manufacturer\/impedance-control-pcb\/","title":{"rendered":"Impedanssi PCB - optimoi signaalin eheys"},"content":{"rendered":"
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Mik\u00e4 on PCB-impedanssin ohjaus?<\/h2>

PCB-impedanssin ohjaus tarkoittaa j\u00e4lkien impedanssin hallintaa. T\u00e4t\u00e4 impedanssia kutsutaan my\u00f6s ohjatuksi impedanssiksi. Ohjattu impedanssi on piirilevyn j\u00e4lkien ja niiden vertailutasojen muodostaman siirtolinjan ominaisimpedanssi. Kun suurtaajuussignaalit kulkevat piirilevyn siirtolinjoilla, t\u00e4ll\u00e4 on merkityst\u00e4. Hallittu impedanssi on t\u00e4rke\u00e4 signaalin eheysongelmien ratkaisemiseksi. Signaalin eheys tarkoittaa, ett\u00e4 signaali kulkee ilman v\u00e4\u00e4ristymi\u00e4.<\/p>

Piirin impedanssi m\u00e4\u00e4r\u00e4ytyy piirilevyn fyysisen koon ja dielektrisen materiaalin mukaan. Se mitataan ohmeina (\u03a9). Impedanssin s\u00e4\u00e4t\u00f6\u00e4 tarvitsevia piirilevyjen siirtojohtotyyppej\u00e4 ovat yksipuolinen mikroliuskajohto, yksipuolinen raideliuskajohto, differentiaalinen mikroliuskajohtopari, differentiaalinen raideliuskajohtopari, upotettu mikroliuskajohto ja koplanaarinen (yksipuolinen ja differentiaalinen).<\/p>

Yleiset menetelm\u00e4t impedanssin s\u00e4\u00e4t\u00f6\u00f6n<\/h2>

1. K\u00e4yt\u00e4 PCB-kerrosrakennetta<\/h3>

Piirilevysuunnittelijat voivat k\u00e4ytt\u00e4\u00e4 piirilevyn kerrospinoa impedanssin hallintaan. Aseta eri signaalikerrokset eri asentoihin kapasitanssin ja induktanssin hallitsemiseksi kerrosten v\u00e4lill\u00e4. Yleens\u00e4 sisemmiss\u00e4 kerroksissa k\u00e4ytet\u00e4\u00e4n korkeamman impedanssin valintoja ja ulommissa kerroksissa matalamman impedanssin valintoja heijastuksen ja ristikk\u00e4is\u00e4\u00e4nen v\u00e4hent\u00e4miseksi.<\/p>

2. K\u00e4yt\u00e4 differentiaalisia signaalijohtoja<\/h3>

Differentiaaliset parit antavat paremman h\u00e4iri\u00f6nsietokyvyn ja pienemm\u00e4n ristikk\u00e4is\u00e4\u00e4nen riskin. Differentiaalipari on kaksi rinnakkaista johdinta. Niiden j\u00e4nnitteet ovat yht\u00e4 suuret ja vastakkaiset napaisuudeltaan. Differentiaaliparit antavat paremman signaalin eheyden ja kohinansietokyvyn. Differentiaaliparin impedanssia s\u00e4\u00e4dell\u00e4\u00e4n v\u00e4lyksill\u00e4, johtimien leveydell\u00e4 ja maatason asettelulla.<\/p>

3. Ohjausj\u00e4ljen geometria<\/h3>

J\u00e4ljen leveys, v\u00e4li ja asettelugeometria voivat my\u00f6s vaikuttaa impedanssiin. Tavallisessa mikroliuskajohdossa leve\u00e4mm\u00e4t j\u00e4ljet ja suuremmat v\u00e4lykset alentavat impedanssia. Koaksiaalityyppisiss\u00e4 rakenteissa pienempi sis\u00e4johdin ja suurempi ulkojohtimen s\u00e4de nostavat impedanssia. Valitse j\u00e4lkigeometria tavoiteimpedanssin ja signaalitaajuuden perusteella.<\/p>

4. Valitse PCB-materiaalit<\/h3>

Piirilevymateriaalin dielektrisyysvakio vaikuttaa impedanssiin. Materiaalien valitseminen, joilla on vakaat dielektriset ominaisuudet, on osa impedanssin hallintaa. Korkeataajuiseen ja nopeaan k\u00e4ytt\u00f6\u00f6n yleisi\u00e4 materiaaleja ovat fr4 (lasi-epoksi), PTFE (teflon) ja RF-laminaatit.<\/p>

5. Simulointi- ja suunnitteluty\u00f6kalujen k\u00e4ytt\u00f6<\/h3>

Ennen lopullista piirilevyn asettelua k\u00e4yt\u00e4 simulointi- ja suunnitteluty\u00f6kaluja impedanssin tarkistamiseen ja optimointiin. N\u00e4m\u00e4 ty\u00f6kalut simuloivat piirin k\u00e4ytt\u00e4ytymist\u00e4, signaalih\u00e4vi\u00f6it\u00e4 ja s\u00e4hk\u00f6magneettisia vuorovaikutuksia. Ne auttavat l\u00f6yt\u00e4m\u00e4\u00e4n parhaat levyn parametrit. Yleisi\u00e4 ty\u00f6kaluja ovat CST Studio Suite, HyperLynx ja ADS.<\/p>

PCB-valmistuksen vaikutukset impedanssiin<\/h2>

J\u00e4ljen leveys<\/h3>

J\u00e4ljen leveys vaikuttaa suoraan siirtolinjan impedanssiin ja h\u00e4vi\u00f6\u00f6n. Useimmat hyv\u00e4t insin\u00f6\u00f6rit antavat piirilevyn valmistajalle Gerber-tiedostojen avulla j\u00e4ljen leveyden toleranssin. Jos esimerkiksi j\u00e4ljen leveydeksi on suunniteltu 6,2 millimetri\u00e4 ja sen impedanssi on 50 ohmia, j\u00e4ljen leveytt\u00e4 muuttava valmistuksen ep\u00e4vakaus muuttaa impedanssia. Monista tehtaista saadun kokemuksen mukaan j\u00e4ljen leveys voi vaihdella noin 10%. J\u00e4ljen leveyden muutos voidaan mallintaa Gaussin jakaumana, jonka keskihajonta on 10%.<\/p>

Kuparifolio \/ pinnoitettu kupari paksuus<\/h3>

PCB-tuotteissa kuparin paksuudella on kaksi osaa: peruskuparin paksuus ja p\u00e4\u00e4llystetty kuparin paksuus. Peruskupari on suhteellisen tasainen, mutta p\u00e4\u00e4llystetyn kuparin tasaisuus riippuu tehtaan prosessista. Pinnoitettu kupari voi vaihdella paljon tehtaiden v\u00e4lill\u00e4. Erilainen p\u00e4\u00e4llystetyn kuparin paksuus muuttaa j\u00e4lkiimpedanssia ja h\u00e4vi\u00f6t\u00e4. Impedanssi voi vaihdella pienell\u00e4 alueella, esimerkiksi 49,5 ja 51 ohmin v\u00e4lill\u00e4. Verrattuna j\u00e4ljen leveyteen kuparin paksuudella on pienempi vaikutus impedanssiin.<\/p>

Dielektrinen paksuus<\/h3>

Piirilevyjen valmistuksessa dielektrisen paksuuden muutokset johtuvat raaka-aineen vaihtelusta, laminointipaineesta ja liiman t\u00e4yt\u00f6st\u00e4. Jos dielektrinen paksuus muuttuu, impedanssi ja h\u00e4vi\u00f6t muuttuvat. Vaikeissa tapauksissa siirtojohdoissa on suuri h\u00e4vi\u00f6. Impedanssi voi vaihdella noin 44 ohmista 54 ohmiin. Vaihteluv\u00e4li voi olla jopa 10 ohmia.<\/p>

Sy\u00f6vytystekij\u00e4<\/h3>

Johtimien paksuus on rajallinen. Sy\u00f6vytyksen j\u00e4lkeen j\u00e4ljet eiv\u00e4t ole t\u00e4ydellisi\u00e4 suorakulmioita. Ne n\u00e4ytt\u00e4v\u00e4t enemm\u00e4nkin puolisuunnikkaalta. Puolisuunnikkaan kulma muuttuu kuparin paksuuden (my\u00f6s pinnoituksen) mukaan. Kun kupari on ohutta, sivukulma l\u00e4hestyy 90\u00b0. Kulman koko vaikuttaa impedanssiin. Esimerkiksi kun sivukulma on 70\u00b0, impedanssi on noin 50 ohmia. Kun kulma on 90\u00b0, impedanssi on noin 48,37 ohmia.<\/p>

Edell\u00e4 esitetyiss\u00e4 testeiss\u00e4 muutetaan yksi tekij\u00e4 kerrallaan. Todellisessa tuotannossa useat muuttujat muuttuvat samanaikaisesti. Impedanssi voi vaihdella noin 40 ohmista 56 ohmiin. T\u00e4m\u00e4 ylitt\u00e4\u00e4 huomattavasti tyypillisen vaatimuksen, kuten 50\u03a9 \u00b110%. Tuotannon aikana monet parametrit aiheuttavat impedanssin muutoksen. Nopeiden tai korkealaatuisten tuotteiden osalta piirilevysuunnittelu- ja valmistusprosessin on valvottava tiukasti jokaista materiaalia ja vaihetta. Muuten tuotteessa voi ilmet\u00e4 odottamattomia ongelmia.<\/p>

Impedanssi ja ominaisimpedanssi<\/h2>

1. Vastus<\/h3>

Kun vaihtovirta kulkee johtimessa, sen kohtaamaa vastusta kutsutaan impedanssiksi (impedanssi). Symboli on Z. Yksikk\u00f6 on edelleen ohmi (\u03a9). T\u00e4m\u00e4 vastus eroaa tasavirtaresistanssista. Vaihtovirrassa on resistanssin (R) lis\u00e4ksi induktiivinen reaktanssi (XL) ja kapasitiivinen reaktanssi (XC).<\/p>

Erottamiseksi tasavirtaresistanssista kutsutaan vaihtovirtavastuksen impedanssiksi (Z).<\/p>

Kaava:<\/p>

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

2. Impedanssi (Z)<\/h3>

Kun IC-integraatio on lis\u00e4\u00e4ntynyt ja signaalitaajuus ja -nopeus ovat korkeammat, PCB-j\u00e4ljet voivat vaikuttaa PCB-j\u00e4lkeen. Kun signaalitaajuus saavuttaa rajan, j\u00e4lki aiheuttaa vakavia signaalin v\u00e4\u00e4ristymi\u00e4 tai h\u00e4vi\u00f6it\u00e4. T\u00e4m\u00e4 osoittaa, ett\u00e4 piirilevyjen j\u00e4ljet eiv\u00e4t kuljeta vain virtaa vaan my\u00f6s energiaa pulssien tai neli\u00f6aaltosignaalien muodossa.<\/p>

3. Ominaisimpedanssin s\u00e4\u00e4t\u00f6 (Z0)<\/h3>

Signaalin kulkiessaan n\u00e4kem\u00e4\u00e4 vastusta kutsutaan ominaisimpedanssiksi. Symboli on Z0.<\/p>

Pelk\u00e4st\u00e4\u00e4n \u201cavoimen\u201d, \u201clyhyen\u201d ja liitett\u00e4vyyden korjaaminen ei siis riit\u00e4. Suurnopeus- ja suurtaajuussiirtolinjojen osalta laadun on oltava tiukempi. Aukko-\/lyhyttestin l\u00e4p\u00e4iseminen tai pienten vikojen esiintyminen ei riit\u00e4. Z0 on mitattava ja pidett\u00e4v\u00e4 toleranssin sis\u00e4ll\u00e4. Jos n\u00e4in ei tapahdu, levy on romutettava. \u00c4l\u00e4 tee uudelleenk\u00e4sittely\u00e4.<\/p>

Signaalin eteneminen ja siirtojohdot<\/h2>

1. Signaalin siirtolinjan m\u00e4\u00e4ritelm\u00e4<\/h3>

  1. S\u00e4hk\u00f6magneettisen teorian mukaan lyhyempi aallonpituus (\u03bb) tarkoittaa korkeampaa taajuutta (f). Niiden tulo vastaa valonnopeutta. Toisin sanoen:<\/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. Mill\u00e4 tahansa laitteella voi olla korkea signaalitaajuus. Kun signaali kulkee piirilevyn j\u00e4ljen l\u00e4pi, signaali voi hidastua tai viiv\u00e4sty\u00e4.<\/p><\/li><\/ol>

      Lyhyempi j\u00e4ljen pituus on siis parempi.<\/p>

      1. Johdotustiheyden lis\u00e4\u00e4minen tai johdinkoon pienent\u00e4minen auttaa. Mutta kun komponenttien taajuus kasvaa tai pulssijaksot lyhenev\u00e4t, j\u00e4ljen pituus voi l\u00e4hesty\u00e4 osaa signaalin aallonpituudesta. Silloin j\u00e4lki osoittaa selv\u00e4\u00e4 v\u00e4\u00e4ristym\u00e4\u00e4.<\/p><\/li>

      2. IPC-2141:n lausekkeessa 3.4.4 sanotaan, ett\u00e4 kun j\u00e4ljen pituus on l\u00e4hes 1\/7 signaalin aallonpituudesta, j\u00e4lke\u00e4 k\u00e4sitell\u00e4\u00e4n signaalin siirtojohtona.<\/p><\/li>

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

        Laitteen signaalitaajuus on f = 10 MHz. Piirilevyn j\u00e4ljen pituus on 50 cm. Tarvitaanko ominaisimpedanssin s\u00e4\u00e4t\u00f6\u00e4?<\/p>

        Laske:<\/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.
        \nj\u00e4ljen pituus \/ aallonpituus = 50 \/ 3000 = 1\/60
        \n<\/code><\/div><\/div>

        Koska 1\/60 on paljon pienempi kuin 1\/7, t\u00e4m\u00e4 johto on normaali johdin eik\u00e4 tarvitse ominaisimpedanssin s\u00e4\u00e4t\u00f6\u00e4.<\/p>

        Maxwellin yht\u00e4l\u00f6t kertovat meille: siniaallon etenemisnopeus VS v\u00e4liaineessa on suhteessa valon nopeuteen C ja dielektrisyysvakioon \u03b5r seuraavasti:<\/p>

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

        Kun \u03b5r = 1, signaalin nopeus vastaa valonnopeutta = 3 \u00d7 10^10 cm\/s.<\/p>

        2. Siirtonopeus ja dielektrisyysvakio<\/h3>

        Signaalin nopeus 30 MHz:n taajuudella eri materiaaleilla:<\/p>

        Materiaali\/alusta<\/th>Tg (\u00b0C)<\/th>Dielektrisyysvakio \u03b5r<\/th>Signaalin nopeus (m\/\u03bcs)<\/th><\/tr><\/thead>
        Tyhji\u00f6<\/td>\/<\/td>1.0<\/td>300.00<\/td><\/tr>
        PTFE (teflon)<\/td>\/<\/td>2.2<\/td>202.26<\/td><\/tr>
        L\u00e4mp\u00f6kovettuva polyfenyleenieetteri<\/td>210<\/td>2.5<\/td>189.74<\/td><\/tr>
        Syanaattiesteri<\/td>225<\/td>3.0<\/td>173.21<\/td><\/tr>
        PTFE + E-lasi<\/td>\/<\/td>2.6<\/td>186.25<\/td><\/tr>
        Syanaattiesteri + lasi<\/td>225<\/td>3.7<\/td>155.96<\/td><\/tr>
        Polyimidi + lasi<\/td>230<\/td>4.5<\/td>141.42<\/td><\/tr>
        Kvartsi<\/td>\/<\/td>3.9<\/td>151.98<\/td><\/tr>
        Epoksilasi (fr4)<\/td>130\u00b15<\/td>4.7<\/td>138.38<\/td><\/tr>
        Alumiini<\/td>\/<\/td>9.0<\/td>100.00<\/td><\/tr><\/tbody><\/table><\/div><\/div>

        Taulukosta k\u00e4y ilmi, ett\u00e4 kun \u03b5r kasvaa, signaalin nopeus materiaalissa pienenee. Suuremman signaalinopeuden saavuttamiseksi on valittava suurempi ominaisimpedanssi. Saadaksesi suuremman Z0:n, valitse pienempi \u03b5r-materiaali. PTFE:ll\u00e4 on pienin \u03b5r, joten se antaa nopeimman nopeuden.<\/p>

        fr4-levyss\u00e4 k\u00e4ytet\u00e4\u00e4n epoksihartsia ja E-lasia. Sen \u03b5r on noin 4,7. Signaalin nopeus on 138 m\/\u03bcs. Hartsij\u00e4rjestelm\u00e4n vaihtaminen voi muuttaa \u03b5r:\u00e4\u00e4.<\/p>

        Syyt ominaisimpedanssin s\u00e4\u00e4t\u00e4miseen<\/h2>

        Syy 1<\/h3>

        Kun elektroniset laitteet (tietokone, viestint\u00e4) toimivat, ohjain l\u00e4hett\u00e4\u00e4 signaalin vastaanottimeen piirilevyn j\u00e4lkien kautta. J\u00e4ljen ominaisimpedanssin Z0 on vastattava ohjaimen ja vastaanottimen elektronista impedanssia. Jos se on sovitettu, signaalienergia siirtyy t\u00e4ydellisesti.<\/p>

        Syy 2<\/h3>

        Jos piirilevyn laatu on huono ja Z0 on toleranssin ulkopuolella, signaalit heijastuvat, h\u00e4vi\u00e4v\u00e4t, vaimentuvat tai viiv\u00e4styv\u00e4t. Vakavissa tapauksissa signaalit voivat olla v\u00e4\u00e4ri\u00e4 ja laite voi kaatua.<\/p>

        Syy 3<\/h3>

        Tarvitaan tiukkoja materiaalivalintoja ja prosessinohjausta, jotta monikerroksinen levy Z0 t\u00e4ytt\u00e4\u00e4 asiakkaan vaatimukset. Korkeamman elektronisen impedanssin komponentit tarvitsevat yleens\u00e4 korkeamman piirilevyn Z0:n. Monikerroksinen levy, jossa on oikea Z0, on p\u00e4tev\u00e4 suurnopeus- tai suurtaajuustuote.<\/p>

        Z0:n suhde materiaaliin ja prosessiin<\/h2>

        Mikroliuskaimpedanssin ominaisimpedanssi Z0 kaava:<\/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>

        Miss\u00e4:<\/p>

        • \u03b5r - dielektrisyysvakio<\/p><\/li>

        • H - dielektrinen paksuus<\/p><\/li>

        • W - j\u00e4ljen leveys<\/p><\/li>

        • T - j\u00e4ljen paksuus<\/p><\/li><\/ul>

          Pienempi \u03b5r helpottaa Z0:n nostamista nopeiden komponenttien mukaiseksi.<\/p>

          1. Z0 ja \u03b5r<\/h3>

          Z0 on k\u00e4\u00e4nt\u00e4en verrannollinen \u03b5r:\u00e4\u00e4n. Z0 kasvaa, kun H kasvaa. Tiukan Z0:n korkeataajuusjohtojen osalta dielektrisen paksuuden toleranssin on oltava tiukka. Yleens\u00e4 dielektrisen paksuuden muutos ei saa ylitt\u00e4\u00e4 10%.<\/p>

          2. Dielektrisen paksuuden vaikutus<\/h3>

          Kun reititystiheys on suurempi, suurempi H aiheuttaa enemm\u00e4n s\u00e4hk\u00f6magneettisia h\u00e4iri\u00f6it\u00e4. Suurtaajuisten ja nopeiden digitaalisten linjojen kohdalla johtotiheyden kasvaessa pienenn\u00e4 dielektrisen paksuutta EMI:n ja ristikk\u00e4isviestinn\u00e4n v\u00e4hent\u00e4miseksi tai k\u00e4yt\u00e4 materiaaleja, joiden \u03b5r on pienempi.<\/p>

          Kaavan mukaan kuparin paksuus T on t\u00e4rke\u00e4 tekij\u00e4. Suurempi T pienent\u00e4\u00e4 Z0:ta, mutta muutos on pieni.<\/p>

          3. Kuparin paksuuden vaikutus<\/h3>

          Ohuempi kupari antaa suuremman Z0-arvon, mutta sen vaikutus Z0-arvoon on pieni. Ohuen kuparin k\u00e4ytt\u00f6 auttaa tekem\u00e4\u00e4n hienoja j\u00e4lki\u00e4, mik\u00e4 auttaa hallitsemaan Z0:ta enemm\u00e4n kuin pelkk\u00e4 kuparin paksuusarvo.<\/p>

          Kaavasta:<\/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>

          Kun W (j\u00e4ljen leveys) pienenee, Z0 kasvaa. Leveyden muuttamisella on suurempi vaikutus Z0:een kuin paksuuden muuttamisella.<\/p>

          4. J\u00e4ljen leveyden vaikutus<\/h3>

          Z0 kasvaa jyrk\u00e4sti leveyden W kaventuessa. Jos haluat hallita Z0:ta, s\u00e4\u00e4d\u00e4 j\u00e4ljen leveys tiukasti. Nyky\u00e4\u00e4n useimpien suurtaajuisten ja nopeiden digitaalisten j\u00e4lkien leveys on 0,10 mm tai 0,13 mm. Perinteisesti leveyden toleranssi oli \u00b120%. Muiden kuin siirtolinjan j\u00e4lkien osalta (j\u00e4ljen pituus << signaalin aallonpituus \/ 7) \u00b120% voi olla hyv\u00e4. Mutta Z0-ohjatuilla j\u00e4ljill\u00e4 \u00b120%:n leveysvirhe ei voi t\u00e4ytt\u00e4\u00e4 vaatimuksia. T\u00e4ll\u00f6in Z0-virhe ylitt\u00e4\u00e4 usein \u00b110%.<\/p>

          Esimerkki:<\/p>

          Piirilevyn mikroliuska on leveydelt\u00e4\u00e4n 100 \u03bcm, paksuudeltaan 20 \u03bcm ja dielektrisyydelt\u00e4\u00e4n 100 \u03bcm. Oletetaan, ett\u00e4 kuparin paksuus on tasainen. Jos leveys muuttuu \u00b120%, voiko Z0 t\u00e4ytt\u00e4\u00e4 \u00b110%?<\/p>

          Kaavalla:<\/p>

          Olkoon W0 = 100 \u03bcm, W1 = 80 \u03bcm, W2 = 120 \u03bcm, T = 20 \u03bcm, H = 100 \u03bcm. T\u00e4ll\u00f6in Z01 \/ Z02 = 1,20. Z0 saavuttaa siis juuri \u00b110%, ei \u00b110%:n sis\u00e4ll\u00e4. Jotta Z0 olisi \u00b110%:n sis\u00e4ll\u00e4, leveysvaihtelun on oltava paljon pienempi kuin \u00b120%. Jotta Z0 olisi \u2264 \u00b15%, leveyspoikkeaman on oltava \u2264 \u00b110%.<\/p>

          T\u00e4m\u00e4 selitt\u00e4\u00e4, miksi jotkut PTFE-piirilevyt ja jotkut fr4-piirilevyt vaativat leveystoleranssia \u00b1 0,02 mm. Syyn\u00e4 on Z0:n valvonta.<\/p>

          Ominaisimpedanssin prosessinohjaus<\/h2>

          1. Filmin valmistuksen valvonta ja tarkastus<\/strong>
            Pid\u00e4 l\u00e4mp\u00f6tila ja kosteus vakiona (21 \u00b1 2 \u00b0C, 55 \u00b1 5%), pid\u00e4 puhdas huone ja tee leveysprosessin kompensointi.<\/p><\/li>

          2. Paneelin rakenne<\/strong>
            Paneelin reunat eiv\u00e4t saa olla liian kapeat. Pinnoitus on teht\u00e4v\u00e4 tasaiseksi. K\u00e4yt\u00e4 pseudokatodia galvanoinnissa virran jakamiseksi. Lis\u00e4\u00e4 paneelin reunaan kuponki Z0:n testaamiseksi.<\/p><\/li>

          3. Etsaus<\/strong>
            Ohjaa prosessiparametreja alileikkauksen v\u00e4hent\u00e4miseksi. Suorita ensimm\u00e4isen l\u00e4piviennin tarkastus. V\u00e4henn\u00e4 kuparij\u00e4\u00e4mi\u00e4, kupariharjuja ja kuparij\u00e4tteit\u00e4. Tarkista j\u00e4ljen leveys ja pid\u00e4 se vaaditulla alueella (\u00b110% tai \u00b10,02 mm).<\/p><\/li>

          4. AOI-tarkastus<\/strong>
            Etsi sisempien kerrosten kohdalta j\u00e4lki\u00e4 ja ulokkeita. 2 GHz:n suurnopeussignaaleissa jopa 0,05 mm:n rako aiheuttaa levyn romuttumista. Sis\u00e4kerroksen leveyden ja vikojen hallinta on avainasemassa.<\/p><\/li>

          5. Laminointi<\/strong>
            K\u00e4yt\u00e4 tyhji\u00f6laminointia paineen alentamiseksi ja hartsin virtauksen v\u00e4hent\u00e4miseksi. S\u00e4ilyt\u00e4 enemm\u00e4n hartsia, koska hartsi vaikuttaa \u03b5r. Lis\u00e4\u00e4 hartsia usein alentaa \u03b5r:\u00e4\u00e4. Valvotaan laminoinnin paksuuden toleranssia. Jos valmiin levyn paksuus on ep\u00e4tasainen, dielektrinen paksuus vaihtelee ja vaikuttaa Z0:een.<\/p><\/li>

          6. Valitse hyv\u00e4 pohjamateriaali<\/strong>
            Noudata tiukasti asiakkaan materiaalimallia. V\u00e4\u00e4r\u00e4 malli tarkoittaa v\u00e4\u00e4r\u00e4\u00e4 \u03b5r, v\u00e4\u00e4r\u00e4\u00e4 paksuutta. V\u00e4\u00e4r\u00e4ll\u00e4 materiaalilla tehty t\u00e4ydellinen prosessi johtaa silti romuun, koska Z0 riippuu voimakkaasti \u03b5r:st\u00e4.<\/p><\/li>

          7. Juotosmaski (coverlay)<\/strong>
            Levyn pinnalla oleva juotosmaski voi alentaa Z0:ta 1-3 \u03a9. Teoriassa juotosmaskin paksuus ei saisi olla liian paksu. K\u00e4yt\u00e4nn\u00f6ss\u00e4 vaikutus ei ole valtava. Ennen juotosmaskia johtimen pinta on kosketuksissa ilman kanssa (\u03b5r = 1), joten mitattu Z0 on suurempi. Juotosmaskin j\u00e4lkeen Z0 laskee 1-3 \u03a9, koska juotosmaskin \u03b5r on noin 4,0.<\/p><\/li>

          8. Kosteuden imeytyminen<\/strong>
            V\u00e4lt\u00e4 kosteuden imeytymist\u00e4 valmiisiin monikerroslevyihin. Vesi on \u03b5r \u2248 75. Kosteus aiheuttaa suuren Z0-pudotuksen ja ep\u00e4vakautta.<\/p><\/li><\/ol>

            Yhteenveto<\/h2>

            Monikerroslevyjen siirtolinjojen yleiset Z0-ohjausalueet ovat:<\/p>

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

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

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

              Jos haluat hallita vaihtelua, ota huomioon n\u00e4m\u00e4 nelj\u00e4 p\u00e4\u00e4tekij\u00e4\u00e4:<\/p>

              1. J\u00e4ljen leveys W<\/p><\/li>

              2. J\u00e4ljen paksuus T<\/p><\/li>

              3. Dielektrinen paksuus H<\/p><\/li>

              4. Dielektrisyysvakio \u03b5r<\/p><\/li><\/ol>

                Suurin vaikutus on dielektrisell\u00e4 paksuudella H. Seuraavana on dielektrisyysvakio \u03b5r. Sen j\u00e4lkeen tulee j\u00e4ljen leveys W. Pienin vaikutus on j\u00e4ljen paksuus T. Kun perusmateriaali on valittu, \u03b5r:n muutos on pieni. H:ta voidaan hallita, mutta se vaihtelee edelleen. T on helpompi hallita. J\u00e4ljen leveyden W kontrollointi \u00b110%:n sis\u00e4ll\u00e4 on vaikeaa. J\u00e4lkiongelmilla, kuten rei'ill\u00e4, aukoilla ja kolhuilla, on my\u00f6s merkityst\u00e4. Monin tavoin tehokkain ja t\u00e4rkein menetelm\u00e4 Z0:n hallitsemiseksi on j\u00e4ljen leveyden tarkka hallinta ja s\u00e4\u00e4t\u00e4minen.<\/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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