{"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\/de_at\/pcb-manufacturer\/impedance-control-pcb\/","title":{"rendered":"Impedanz-PCBs - Optimieren Sie die Signalintegrit\u00e4t"},"content":{"rendered":"
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Was ist PCB Impedanzkontrolle?<\/h2>

Impedanzkontrolle auf Leiterplatten bedeutet die Kontrolle der Impedanz von Leiterbahnen. Diese Impedanz wird auch als kontrollierte Impedanz bezeichnet. Die kontrollierte Impedanz ist die charakteristische Impedanz einer \u00dcbertragungsleitung, die aus Leiterbahnen und ihren Bezugsebenen besteht. Wenn Hochfrequenzsignale auf PCB-\u00dcbertragungsleitungen \u00fcbertragen werden, ist dies von Bedeutung. Die kontrollierte Impedanz ist wichtig, um Probleme der Signalintegrit\u00e4t zu l\u00f6sen. Signalintegrit\u00e4t bedeutet, dass das Signal ohne Verzerrung \u00fcbertragen wird.<\/p>

Die Schaltungsimpedanz wird durch die physische Gr\u00f6\u00dfe der Leiterplatte und das dielektrische Material bestimmt. Sie wird in Ohm (\u03a9) gemessen. Zu den Arten von PCB-\u00dcbertragungsleitungen, die eine Impedanzkontrolle ben\u00f6tigen, geh\u00f6ren Single-Ended-Mikrostreifen, Single-Ended-Streifenleitungen, differentielle Mikrostreifenpaare, differentielle Streifenleitungspaare, eingebettete Mikrostreifen und koplanare Leitungen (Single-Ended und differentiell).<\/p>

Gemeinsame Methoden zur Impedanzkontrolle<\/h2>

1. PCB-Lagenstruktur verwenden<\/h3>

Leiterplattendesigner k\u00f6nnen den Leiterplattenlagenstapel zur Impedanzkontrolle verwenden. Bringen Sie verschiedene Signallagen an unterschiedlichen Positionen an, um die Kapazit\u00e4t und Induktivit\u00e4t zwischen den Lagen zu steuern. Normalerweise werden f\u00fcr die inneren Lagen h\u00f6here Impedanzen und f\u00fcr die \u00e4u\u00dferen Lagen niedrigere Impedanzen gew\u00e4hlt, um Reflexionen und \u00dcbersprechen zu verringern.<\/p>

2. Differenzielle Signalleitungen verwenden<\/h3>

Differenzialpaare bieten eine bessere Rauschunterdr\u00fcckung und ein geringeres Risiko des \u00dcbersprechens. Ein differentielles Paar besteht aus zwei parallelen Leitern. Ihre Spannungen sind gleich gro\u00df und von entgegengesetzter Polarit\u00e4t. Differenzialpaare bieten eine bessere Signalintegrit\u00e4t und Rauschunterdr\u00fcckung. Die Impedanz eines differentiellen Paares wird durch den Abstand, die Leiterbahnbreite und das Layout der Massefl\u00e4che gesteuert.<\/p>

3. Geometrie der Kontrollspur<\/h3>

Leiterbahnbreite, Abst\u00e4nde und Layout-Geometrie k\u00f6nnen ebenfalls die Impedanz beeinflussen. Bei herk\u00f6mmlichen Mikrostreifenleitungen senken breitere Leiterbahnen und gr\u00f6\u00dfere Abst\u00e4nde die Impedanz. Bei koaxialen Strukturen erh\u00f6hen ein kleinerer Innenleiter und ein gr\u00f6\u00dferer Au\u00dfenleiterradius die Impedanz. W\u00e4hlen Sie die Leiterbahngeometrie entsprechend der Zielimpedanz und der Signalfrequenz.<\/p>

4. PCB-Materialien ausw\u00e4hlen<\/h3>

Die Dielektrizit\u00e4tskonstante des Leiterplattenmaterials beeinflusst die Impedanz. Die Auswahl von Materialien mit stabilen dielektrischen Eigenschaften ist Teil der Impedanzkontrolle. F\u00fcr Hochfrequenz- und Hochgeschwindigkeitsanwendungen werden h\u00e4ufig fr4 (Glas-Epoxid), PTFE (Teflon) und RF-Laminate verwendet.<\/p>

5. Verwendung von Simulations- und Entwurfswerkzeugen<\/h3>

Verwenden Sie vor dem endg\u00fcltigen PCB-Layout Simulations- und Design-Tools, um die Impedanz zu pr\u00fcfen und zu optimieren. Diese Tools simulieren das Schaltungsverhalten, Signalverluste und elektromagnetische Wechselwirkungen. Sie helfen dabei, die besten Leiterplattenparameter zu finden. Zu den g\u00e4ngigen Tools geh\u00f6ren CST Studio Suite, HyperLynx und ADS.<\/p>

Auswirkungen der Leiterplattenherstellung auf die Impedanz<\/h2>

Spurbreite<\/h3>

Die Leiterbahnbreite wirkt sich direkt auf die Impedanz und den Verlust der \u00dcbertragungsleitung aus. Die meisten guten Ingenieure geben dem Leiterplattenhersteller mit den Gerber-Dateien eine Toleranz f\u00fcr die Leiterbahnbreite vor. Wenn beispielsweise eine Leiterbahnbreite von 6,2 mil entworfen wurde und die Impedanz 50 Ohm betr\u00e4gt, f\u00fchrt eine Fertigungsinstabilit\u00e4t, die die Leiterbahnbreite ver\u00e4ndert, zu einer Ver\u00e4nderung der Impedanz. Aus Erfahrung mit vielen Fabriken kann die Leiterbahnbreite um 10% variieren. Wir k\u00f6nnen die \u00c4nderung der Leiterbahnbreite als eine Gau\u00dfsche Verteilung mit einer Standardabweichung von 10% modellieren.<\/p>

Kupferfolie \/ plattiertes Kupfer Dicke<\/h3>

Bei Leiterplattenprodukten besteht die Kupferdicke aus zwei Teilen: der Dicke des Basiskupfers und der Dicke des plattierten Kupfers. Das Basiskupfer ist relativ gleichm\u00e4\u00dfig, aber die Gleichm\u00e4\u00dfigkeit des plattierten Kupfers h\u00e4ngt vom Herstellungsverfahren ab. Die Dicke des plattierten Kupfers kann von Fabrik zu Fabrik stark variieren. Unterschiedliche Kupferdicken ver\u00e4ndern die Impedanz und den Verlust von Leiterbahnen. Die Impedanz kann in einem kleinen Bereich variieren, zum Beispiel zwischen 49,5 und 51 Ohm. Im Vergleich zur Leiterbahnbreite hat die Kupferdicke einen geringeren Einfluss auf die Impedanz.<\/p>

Dielektrische Dicke<\/h3>

Bei der Leiterplattenherstellung ergeben sich \u00c4nderungen der dielektrischen Dicke aus Schwankungen des Rohmaterials, des Laminierdrucks und der Klebstofff\u00fcllung. Wenn sich die dielektrische Dicke \u00e4ndert, \u00e4ndern sich Impedanz und Verlust. In schwerwiegenden F\u00e4llen haben die \u00dcbertragungsleitungen einen hohen Verlust. Die Impedanz kann von etwa 44 Ohm bis 54 Ohm variieren. Die Spanne kann bis zu 10 Ohm betragen.<\/p>

\u00c4tzfaktor<\/h3>

Leiterbahnen haben eine endliche Dicke. Nach dem \u00c4tzen sind die Leiterbahnen keine perfekten Rechtecke. Sie sehen eher wie ein Trapez aus. Der Trapezwinkel \u00e4ndert sich mit der Kupferdicke (einschlie\u00dflich der Beschichtung). Wenn das Kupfer d\u00fcnn ist, n\u00e4hert sich der Seitenwandwinkel 90\u00b0. Die Gr\u00f6\u00dfe des Winkels beeinflusst die Impedanz. Wenn der Seitenwandwinkel z. B. 70\u00b0 betr\u00e4gt, liegt die Impedanz bei etwa 50 Ohm. Wenn der Winkel 90\u00b0 betr\u00e4gt, liegt die Impedanz bei 48,37 Ohm.<\/p>

Bei den obigen Tests wird jeweils ein Faktor ge\u00e4ndert. In der realen Produktion \u00e4ndern sich mehrere Variablen auf einmal. Die Impedanz kann von etwa 40 Ohm bis 56 Ohm variieren. Dies \u00fcbersteigt bei weitem eine typische Anforderung wie 50\u03a9 \u00b110%. W\u00e4hrend der Produktion f\u00fchren viele Parameter zu Impedanz\u00e4nderungen. Bei Hochgeschwindigkeits- oder High-End-Produkten muss das PCB-Design und der Herstellungsprozess jedes Material und jeden Schritt streng kontrollieren. Andernfalls kann das Produkt unerwartete Probleme aufweisen.<\/p>

Impedanz und Wellenwiderstand<\/h2>

1. Widerstand<\/h3>

Wenn ein Wechselstrom in einem Leiter flie\u00dft, wird der Widerstand, auf den er trifft, als Impedanz (Scheinwiderstand) bezeichnet. Das Symbol ist Z. Die Einheit ist immer noch Ohm (\u03a9). Dieser Widerstand unterscheidet sich vom Gleichstromwiderstand. Bei Wechselstrom gibt es neben dem Widerstand (R) auch den induktiven Blindwiderstand (XL) und den kapazitiven Blindwiderstand (XC).<\/p>

Zur Unterscheidung vom Gleichstromwiderstand wird der Wechselstromwiderstand als Impedanz (Z) bezeichnet.<\/p>

Die Formel:<\/p>

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

2. Impedanz (Z)<\/h3>

Bei h\u00f6herer IC-Integration und h\u00f6herer Signalfrequenz und -geschwindigkeit k\u00f6nnen Signale auf Leiterbahnen durch die Leiterbahn selbst beeinflusst werden. Wenn die Signalfrequenz einen Grenzwert erreicht, verursacht die Leiterbahn ernsthafte Signalverzerrungen oder -verluste. Dies zeigt, dass Leiterbahnen nicht nur Strom, sondern auch Energie in Form von Impulsen oder Rechtecksignalen \u00fcbertragen.<\/p>

3. Kontrolle der charakteristischen Impedanz (Z0)<\/h3>

Der Widerstand, den ein Signal auf seinem Weg erf\u00e4hrt, wird als Wellenwiderstand bezeichnet. Das Symbol ist Z0.<\/p>

Es reicht also nicht aus, nur \u201coffen\u201d, \u201ckurz\u201d und \"Anschluss\" zu reparieren. Bei Hochgeschwindigkeits- und Hochfrequenz\u00fcbertragungsleitungen muss die Qualit\u00e4t noch strenger sein. Es reicht nicht aus, einen Unterbrechungs-\/Kurzschlusstest zu bestehen oder kleine Defekte zu haben. Sie m\u00fcssen Z0 messen und innerhalb der Toleranz halten. Ist dies nicht der Fall, muss die Leiterplatte verschrottet werden. Keine Nacharbeit.<\/p>

Signalausbreitung und \u00dcbertragungsleitungen<\/h2>

1. Definition einer Signal\u00fcbertragungsleitung<\/h3>

  1. Nach der elektromagnetischen Theorie bedeutet eine k\u00fcrzere Wellenl\u00e4nge (\u03bb) eine h\u00f6here Frequenz (f). Ihr Produkt entspricht der Lichtgeschwindigkeit. Das hei\u00dft:<\/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. Jedes Ger\u00e4t kann eine hohe Signalfrequenz haben. Nachdem das Signal eine Leiterbahn durchlaufen hat, kann es langsamer oder verz\u00f6gert werden.<\/p><\/li><\/ol>

      Eine k\u00fcrzere Leiterbahnl\u00e4nge ist also besser.<\/p>

      1. Eine Erh\u00f6hung der Verdrahtungsdichte oder eine Verringerung der Drahtgr\u00f6\u00dfe ist hilfreich. Wenn jedoch die Bauteilfrequenz h\u00f6her wird oder sich die Impulsperioden verk\u00fcrzen, kann sich die Leiterbahnl\u00e4nge einem Teil der Signalwellenl\u00e4nge n\u00e4hern. Dann weist die Leiterbahn eine deutliche Verzerrung auf.<\/p><\/li>

      2. IPC-2141 Abschnitt 3.4.4 besagt: Wenn eine Leiterbahnl\u00e4nge 1\/7 der Signalwellenl\u00e4nge erreicht, wird die Leiterbahn als Signal\u00fcbertragungsleitung behandelt.<\/p><\/li>

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

        Ein Ger\u00e4t hat eine Signalfrequenz f = 10 MHz. Die Leiterbahnl\u00e4nge betr\u00e4gt 50 cm. Ist eine Kontrolle des Wellenwiderstandes erforderlich?<\/p>

        Berechnen:<\/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
        \nLeiterbahnl\u00e4nge \/ Wellenl\u00e4nge = 50 \/ 3000 = 1\/60
        \n<\/code><\/div><\/div>

        Da 1\/60 viel kleiner ist als 1\/7, ist diese Leiterbahn eine normale Leitung und ben\u00f6tigt keine Impedanzkontrolle.<\/p>

        Die Maxwell-Gleichungen besagen, dass die Ausbreitungsgeschwindigkeit VS einer Sinuswelle in einem Medium mit der Lichtgeschwindigkeit C und der Dielektrizit\u00e4tskonstante \u03b5r in Beziehung steht:<\/p>

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

        Wenn \u03b5r = 1 ist, entspricht die Signalgeschwindigkeit der Lichtgeschwindigkeit = 3 \u00d7 10^10 cm\/s.<\/p>

        2. \u00dcbertragungsgeschwindigkeit und Dielektrizit\u00e4tskonstante<\/h3>

        Signalgeschwindigkeit bei 30 MHz f\u00fcr verschiedene Materialien:<\/p>

        Material\/Substrat<\/th>Tg (\u00b0C)<\/th>Dielektrizit\u00e4tskonstante \u03b5r<\/th>Signalgeschwindigkeit (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>
        Duroplastischer Polyphenylenether<\/td>210<\/td>2.5<\/td>189.74<\/td><\/tr>
        Cyanat-Ester<\/td>225<\/td>3.0<\/td>173.21<\/td><\/tr>
        PTFE + E-Glas<\/td>\/<\/td>2.6<\/td>186.25<\/td><\/tr>
        Cyanat-Ester + Glas<\/td>225<\/td>3.7<\/td>155.96<\/td><\/tr>
        Polyimid + Glas<\/td>230<\/td>4.5<\/td>141.42<\/td><\/tr>
        Quarz<\/td>\/<\/td>3.9<\/td>151.98<\/td><\/tr>
        Epoxidglas (fr4)<\/td>130\u00b15<\/td>4.7<\/td>138.38<\/td><\/tr>
        Aluminium<\/td>\/<\/td>9.0<\/td>100.00<\/td><\/tr><\/tbody><\/table><\/div><\/div>

        Die Tabelle zeigt: Mit zunehmendem \u03b5r nimmt die Signalgeschwindigkeit im Material ab. Um eine h\u00f6here Signalgeschwindigkeit zu erreichen, w\u00e4hlen Sie einen h\u00f6heren Wellenwiderstand. Um einen h\u00f6heren Z0 zu erhalten, w\u00e4hlen Sie ein Material mit niedrigerem \u03b5r. PTFE hat das kleinste \u03b5r und bietet daher die h\u00f6chste Geschwindigkeit.<\/p>

        Die fr4-Platte verwendet Epoxidharz und E-Glas. Ihr \u03b5r betr\u00e4gt etwa 4,7. Die Signalgeschwindigkeit betr\u00e4gt 138 m\/\u03bcs. Ein Wechsel des Harzsystems kann \u03b5r ver\u00e4ndern.<\/p>

        Gr\u00fcnde f\u00fcr die Kontrolle des Wellenwiderstandes<\/h2>

        Grund 1<\/h3>

        Wenn ein elektronisches Ger\u00e4t (Computer, Kommunikationsger\u00e4t) l\u00e4uft, sendet der Treiber ein Signal \u00fcber Leiterbahnen an den Empf\u00e4nger. Die charakteristische Impedanz Z0 der Leiterbahn muss mit der elektronischen Impedanz von Treiber und Empf\u00e4nger \u00fcbereinstimmen. Wenn sie \u00fcbereinstimmen, wird die Signalenergie vollst\u00e4ndig \u00fcbertragen.<\/p>

        Grund 2<\/h3>

        Wenn die Qualit\u00e4t der Leiterplatte schlecht ist und Z0 au\u00dferhalb der Toleranz liegt, werden die Signale reflektiert, gestreut, ged\u00e4mpft oder verz\u00f6gert. In schweren F\u00e4llen k\u00f6nnen die Signale falsch sein und das Ger\u00e4t kann abst\u00fcrzen.<\/p>

        Grund 3<\/h3>

        Strenge Materialauswahl und Prozesskontrolle sind erforderlich, damit der Z0 der Mehrlagenleiterplatte den Kundenspezifikationen entspricht. Komponenten mit h\u00f6herer elektronischer Impedanz erfordern in der Regel einen h\u00f6heren Z0 der Leiterplatte, um sie anzupassen. Eine mehrlagige Leiterplatte mit korrektem Z0 ist ein qualifiziertes Hochgeschwindigkeits- oder Hochfrequenzprodukt.<\/p>

        Beziehung von Z0 zu Material und Prozess<\/h2>

        Die Formel f\u00fcr den Mikrostreifenwellenwiderstand 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>

        Wo:<\/p>

        • \u03b5r - Dielektrizit\u00e4tskonstante<\/p><\/li>

        • H - dielektrische Dicke<\/p><\/li>

        • W - Leiterbahnbreite<\/p><\/li>

        • T - Dicke der Leiterbahn<\/p><\/li><\/ul>

          Ein niedrigeres \u03b5r macht es einfacher, Z0 zu erh\u00f6hen, um es an Hochgeschwindigkeitskomponenten anzupassen.<\/p>

          1. Z0 und \u03b5r<\/h3>

          Z0 steht in umgekehrter Beziehung zu \u03b5r. Z0 steigt mit zunehmendem H. F\u00fcr strenge Z0-Hochfrequenzleitungen muss die Toleranz der dielektrischen Dicke streng sein. Normalerweise darf die \u00c4nderung der dielektrischen Dicke 10% nicht \u00fcberschreiten.<\/p>

          2. Effekt der dielektrischen Dicke<\/h3>

          Bei h\u00f6herer Leitungsdichte f\u00fchrt ein gr\u00f6\u00dferes H zu mehr elektromagnetischen St\u00f6rungen. Bei Hochfrequenz- und Hochgeschwindigkeits-Digitalleitungen sollte mit zunehmender Leitungsdichte die dielektrische Dicke reduziert werden, um EMI und \u00dcbersprechen zu verringern, oder Materialien mit geringerem \u03b5r verwendet werden.<\/p>

          Aus der Formel geht hervor, dass die Kupferdicke T ein wichtiger Faktor ist. Ein gr\u00f6\u00dferes T senkt Z0, aber die \u00c4nderung ist gering.<\/p>

          3. Effekt der Kupferdicke<\/h3>

          D\u00fcnneres Kupfer ergibt einen h\u00f6heren Z0-Wert, aber die Auswirkungen auf Z0 sind gering. Die Verwendung von d\u00fcnnem Kupfer hilft bei der Herstellung feiner Leiterbahnen, was die Kontrolle von Z0 st\u00e4rker unterst\u00fctzt als der Wert der Kupferdicke allein.<\/p>

          Aus der Formel:<\/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>

          Wenn W (Leiterbahnbreite) abnimmt, nimmt Z0 zu. Eine \u00c4nderung der Breite hat einen gr\u00f6\u00dferen Einfluss auf Z0 als eine \u00c4nderung der Dicke.<\/p>

          4. Effekt der Leiterbahnbreite<\/h3>

          Z0 steigt stark an, wenn die Breite W kleiner wird. Um Z0 zu kontrollieren, muss die Leiterbahnbreite engmaschig kontrolliert werden. Heutzutage haben die meisten digitalen Hochfrequenz- und Hochgeschwindigkeitsbahnen eine Breite von 0,10 mm oder 0,13 mm. Traditionell betrug die Breitentoleranz \u00b120%. F\u00fcr nicht \u00fcbertragungsgebundene Leiterbahnen (Leiterbahnl\u00e4nge << Signalwellenl\u00e4nge \/ 7) mag \u00b120% in Ordnung sein. Aber bei Z0-gesteuerten Leiterbahnen kann der Breitenfehler von \u00b120% die Anforderungen nicht erf\u00fcllen. In diesem Fall \u00fcbersteigt der Z0-Fehler oft \u00b110%.<\/p>

          Beispiel:<\/p>

          Eine Mikrostreifenleiterplatte hat eine Breite von 100 \u03bcm, eine Dicke von 20 \u03bcm und eine dielektrische Dicke von 100 \u03bcm. Es wird angenommen, dass die Kupferdicke gleichm\u00e4\u00dfig ist. Wenn sich die Breite um \u00b120% \u00e4ndert, kann Z0 dann \u00b110% entsprechen?<\/p>

          Nach der Formel:<\/p>

          Es sei W0 = 100 \u03bcm, W1 = 80 \u03bcm, W2 = 120 \u03bcm, T = 20 \u03bcm, H = 100 \u03bcm. Dann ist Z01 \/ Z02 = 1,20. Z0 erreicht also gerade \u00b110%, liegt aber nicht innerhalb von \u00b110%. Um Z0 innerhalb von \u00b110% zu erhalten, muss die Breitenvariation viel kleiner als \u00b120% sein. Um Z0 \u2264 \u00b15% zu erhalten, muss die Breitentoleranz \u2264 \u00b110% sein.<\/p>

          Dies erkl\u00e4rt, warum einige PTFE-Leiterplatten und einige fr4-Leiterplatten eine Breitentoleranz von \u00b10,02 mm erfordern. Der Grund ist die Kontrolle von Z0.<\/p>

          Prozesskontrollen f\u00fcr charakteristische Impedanz<\/h2>

          1. Kontrolle und Inspektion der Filmherstellung<\/strong>
            Halten Sie die Temperatur und Luftfeuchtigkeit konstant (21\u00b12\u00b0C, 55\u00b15%), halten Sie einen sauberen Raum und f\u00fchren Sie einen Breitenausgleich durch.<\/p><\/li>

          2. Gestaltung des Panels<\/strong>
            Die Kanten der Platten sollten nicht zu schmal sein. Die Beschichtung sollte gleichm\u00e4\u00dfig sein. Verwenden Sie beim Galvanisieren eine Pseudokathode, um den Strom zu verteilen. F\u00fcgen Sie einen Coupon an der Plattenkante hinzu, um Z0 zu testen.<\/p><\/li>

          3. \u00c4tzen<\/strong>
            Kontrollieren Sie die Prozessparameter, um Hinterschnitte zu reduzieren. F\u00fchren Sie eine First-Pass-Inspektion durch. Reduzieren Sie Restkupfer, Kupfergrate und Kupferabf\u00e4lle. Pr\u00fcfen Sie die Leiterbahnbreite und halten Sie sie innerhalb des erforderlichen Bereichs (\u00b110% oder \u00b10,02 mm).<\/p><\/li>

          4. AOI-Inspektion<\/strong>
            Suchen Sie bei Innenlagen nach Leiterbahnl\u00fccken und \u00dcberst\u00e4nden. Bei 2-GHz-Hochgeschwindigkeitssignalen muss schon eine L\u00fccke von 0,05 mm zu Leiterplattenausschuss f\u00fchren. Die Kontrolle der Innenlagenbreite und der Defekte ist entscheidend.<\/p><\/li>

          5. Kaschierung<\/strong>
            Verwenden Sie die Vakuumlaminierung, um den Druck zu senken und den Harzfluss zu reduzieren. Bewahren Sie mehr Harz auf, da Harz den \u03b5r beeinflusst. Mehr Harz senkt oft \u03b5r. Kontrollieren Sie die Toleranz bei der Laminatdicke. Wenn die Dicke der fertigen Platte ungleichm\u00e4\u00dfig ist, variiert die dielektrische Dicke und beeinflusst Z0.<\/p><\/li>

          6. Gutes Grundmaterial ausw\u00e4hlen<\/strong>
            Halten Sie sich strikt an das Materialmodell des Kunden. Falsches Modell bedeutet falsches \u03b5r, falsche Dicke. Ein vollst\u00e4ndiger Prozess mit falschem Material f\u00fchrt immer noch zu Ausschuss, da Z0 stark von \u03b5r abh\u00e4ngt.<\/p><\/li>

          7. L\u00f6tstoppmaske (Coverlay)<\/strong>
            Die L\u00f6tmaske auf der Leiterplattenoberfl\u00e4che kann Z0 um 1-3 \u03a9 verringern. In der Praxis ist der Effekt nicht sehr gro\u00df. Vor der L\u00f6tmaske hat die Leiteroberfl\u00e4che eine Grenzfl\u00e4che zur Luft (\u03b5r = 1), so dass der gemessene Z0 h\u00f6her ist. Nach der L\u00f6tmaske sinkt Z0 um 1-3 \u03a9, weil \u03b5r der L\u00f6tmaske etwa 4,0 betr\u00e4gt.<\/p><\/li>

          8. Feuchtigkeitsaufnahme<\/strong>
            Vermeiden Sie die Feuchtigkeitsaufnahme in fertigen Mehrschichtplatten. Wasser hat \u03b5r \u2248 75. Feuchtigkeit verursacht einen gro\u00dfen Z0-Abfall und Instabilit\u00e4t.<\/p><\/li><\/ol>

            Zusammenfassung<\/h2>

            F\u00fcr \u00dcbertragungsleitungen auf Mehrlagenplatten sind die \u00fcblichen Z0-Steuerungsbereiche:<\/p>

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

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

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

              Zur Kontrolle der Schwankungen sind diese vier Hauptfaktoren zu ber\u00fccksichtigen:<\/p>

              1. Spurbreite W<\/p><\/li>

              2. Spurendicke T<\/p><\/li>

              3. Dielektrische Dicke H<\/p><\/li>

              4. Dielektrizit\u00e4tskonstante \u03b5r<\/p><\/li><\/ol>

                Den gr\u00f6\u00dften Einfluss hat die dielektrische Dicke H. Danach folgt die Dielektrizit\u00e4tskonstante \u03b5r. Dann die Leiterbahnbreite W. Der kleinste Einfluss ist die Leiterbahndicke T. Nach der Wahl des Basismaterials ist die \u00c4nderung von \u03b5r gering. H kann kontrolliert werden, schwankt aber immer noch. T ist leichter zu steuern. Die Kontrolle der Leiterbahnbreite W innerhalb von \u00b110% ist schwierig. Probleme mit Leiterbahnen wie Nadell\u00f6cher, L\u00fccken und Dellen spielen ebenfalls eine Rolle. In vielerlei Hinsicht ist die wirksamste und wichtigste Methode zur Kontrolle von Z0 die pr\u00e4zise Kontrolle und Einstellung der Leiterbahnbreite.<\/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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tself. 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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