{"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\/bs\/pcb-manufacturer\/impedance-control-pcb\/","title":{"rendered":"Impedantne tiskane plo\u010dice \u2014 optimizirajte integritet signala"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"2428\" class=\"elementor elementor-2428\" data-elementor-post-type=\"page\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e3bf423 e-flex e-con-boxed e-con e-parent\" data-id=\"e3bf423\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2c73ff6 elementor-widget elementor-widget-text-editor\" data-id=\"2c73ff6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2 data-start=\"0\" data-end=\"32\">\u0160ta je kontrola impedanse PCB-a?<\/h2><p data-start=\"34\" data-end=\"483\">Kontrola impedanse na PCB-u zna\u010di kontrolu impedanse tragova. Ova impedansa se tako\u0111er naziva kontrolisana impedansa. Kontrolisana impedansa je karakteristi\u010dna impedansa prenosne linije formirane tragovima na PCB-u i njihovim referentnim ravninama. Kada visokofrekventni signali putuju na prenosnim linijama na PCB-u, to je va\u017eno. Kontrolisana impedansa je va\u017ena za rje\u0161avanje problema integriteta signala. Integritet signala zna\u010di da signal putuje bez izobli\u010denja.<\/p><p data-start=\"485\" data-end=\"838\">Impedansa kola odre\u0111ena je fizi\u010dkom veli\u010dinom \u0161tampane plo\u010dice i dielektri\u010dnim materijalom. Mjeri se u ohmima (\u03a9). Vrste prijenosnih linija na \u0161tampanoj plo\u010dici koje zahtijevaju kontrolu impedanse uklju\u010duju jednostrani mikrostrip, jednostranu striplinu, diferencijalni mikrostrip par, diferencijalni striplin par, ugra\u0111eni mikrostrip i koplanarne (jednostrane i diferencijalne).<\/p><hr data-start=\"840\" data-end=\"843\" \/><h2 data-start=\"845\" data-end=\"891\">Uobi\u010dajene metode za postizanje kontrole impedanse<\/h2><h3 data-start=\"893\" data-end=\"923\">1. Koristite strukturu slojeva PCB-a<\/h3><p data-start=\"925\" data-end=\"1227\">Dizajneri PCB-a mogu koristiti slojevitost plo\u010de za kontrolu impedanse. Postavljanjem razli\u010ditih signalnih slojova na razli\u010dite pozicije kontroliraju se kapacitivnost i indukativnost izme\u0111u slojeva. Obi\u010dno se za unutra\u0161nje slojeve koriste ve\u0107e impedanse, a za vanjske slojeve manje impedanse kako bi se smanjili odraz i preslu\u0161avanje.<\/p><h3 data-start=\"1229\" data-end=\"1265\">2. Koristite diferencijalne signalne linije<\/h3><p data-start=\"1267\" data-end=\"1625\">Diferencijalni parovi omogu\u0107avaju bolje odbijanje \u0161uma i manji rizik od me\u0111usobnog ometanja. Diferencijalni par je dva paralelna provodnika. Njihovi naponi su jednaki po veli\u010dini i suprotni po polaritetu. Diferencijalni parovi pru\u017eaju bolju integritet signala i otpornost na \u0161um. Impedancija diferencijalnog para kontrolira se razmakom, \u0161irinom staze i rasporedom zemljene ravnine.<\/p><h3 data-start=\"1627\" data-end=\"1656\">3. Kontrola geometrije traga<\/h3><p data-start=\"1658\" data-end=\"1977\">\u0160irina staze, razmak i geometrija rasporeda tako\u0111er mogu kontrolirati impedanciju. Kod uobi\u010dajenih mikrostrip struktura, \u0161ire staze i ve\u0107i razmak smanjuju impedanciju. Kod koaksijalnih struktura, manji unutra\u0161nji vodi\u010d i ve\u0107i radijus vanjskog vodi\u010da pove\u0107avaju impedanciju. Odaberite geometriju staze na osnovu ciljane impedancije i frekvencije signala.<\/p><h3 data-start=\"1979\" data-end=\"2006\">4. Odaberite materijale za PCB<\/h3><p data-start=\"2008\" data-end=\"2264\">Dielektri\u010dna konstanta materijala PCB-a utje\u010de na impedanciju. Odabir materijala sa stabilnim dielektri\u010dnim svojstvima dio je kontrole impedancije. Za visoke frekvencije i velike brzine uobi\u010dajeni materijali su FR4 (staklo-epoksid), PTFE (Teflon) i RF laminati.<\/p><h3 data-start=\"2266\" data-end=\"2304\">5. Koristite alate za simulaciju i dizajn<\/h3><p data-start=\"2306\" data-end=\"2582\">Prije kona\u010dnog rasporeda \u0161tampane plo\u010dice, koristite simulacijske i dizajnerske alate za provjeru i optimizaciju impedanse. Ovi alati simuliraju pona\u0161anje kola, gubitak signala i elektromagnetske interakcije. Poma\u017eu u pronala\u017eenju najboljih parametara plo\u010dice. Uobi\u010dajeni alati uklju\u010duju CST Studio Suite, HyperLynx i ADS.<\/p><hr data-start=\"2584\" data-end=\"2587\" \/><h2 data-start=\"2589\" data-end=\"2632\">Uticaj proizvodnje PCB-a na impedanciju<\/h2><h3 data-start=\"2634\" data-end=\"2648\">\u0160irina traga<\/h3><p data-start=\"2650\" data-end=\"3120\">\u0160irina trake direktno utje\u010de na impedanciju i gubitke transmisijske linije. Ve\u0107ina dobrih in\u017eenjera daje proizvo\u0111a\u010du PCB-a toleranciju \u0161irine trake uz Gerber datoteke. Na primjer, ako je \u0161irina trake projektovana na 6,2 mila i njena impedansa je 50 oma, nestabilnost u proizvodnji koja mijenja \u0161irinu trake promijenit \u0107e i impedansu. Prema iskustvu s mnogim fabrikama, \u0161irina trake mo\u017ee varirati za oko 10%. Promjenu \u0161irine trake mo\u017eemo modelirati kao Gaussovu raspodjelu sa standardnom devijacijom od 10%.<\/p><h3 data-start=\"3122\" data-end=\"3162\">Bakrena folija \/ debljina oblo\u017eenog bakra<\/h3><p data-start=\"3164\" data-end=\"3628\">U PCB proizvodima debljina bakra ima dva dijela: debljinu osnovnog bakra i debljinu oblo\u017eenog bakra. Osnovni bakar je relativno ujedna\u010den, ali ujedna\u010denost oblo\u017eenog bakra zavisi od procesa u fabrici. Debljina oblo\u017eenog bakra mo\u017ee znatno varirati me\u0111u fabrikama. Razli\u010dite debljine oblo\u017eenog bakra mijenjaju impedansu trake i gubitke. Impedansa mo\u017ee varirati u malom rasponu, na primjer izme\u0111u 49,5 i 51 oma. U pore\u0111enju sa \u0161irinom trake, debljina bakra ima manji utjecaj na impedansu.<\/p><h3 data-start=\"3630\" data-end=\"3653\">Debljina dielektrika<\/h3><p data-start=\"3655\" data-end=\"3983\">U proizvodnji tiskanih plo\u010dica promjene debljine dielektrika nastaju zbog varijacija u sirovinama, pritiska laminacije i punjenja ljepilom. Ako se promijeni debljina dielektrika, promijenit \u0107e se i impedansa i gubici. U te\u0161kim slu\u010dajevima transmisijske linije \u0107e imati velike gubitke. Impedansa mo\u017ee varirati od otprilike 44 oma do 54 oma. Raspon mo\u017ee biti \u0161irok i do 10 oma.<\/p><h3 data-start=\"3985\" data-end=\"3999\">Faktor \u017earenja<\/h3><p data-start=\"4001\" data-end=\"4400\">Provodnici imaju kona\u010dnu debljinu. Nakon graviranja, staze nisu savr\u0161eni pravougaonici. Vi\u0161e li\u010de na trapez. Ugao trapeza se mijenja s debljinom bakra (uklju\u010duju\u0107i i pozlatbu). Kada je bakar tanak, ugao bo\u010dnog zida se pribli\u017eava 90\u00b0. Veli\u010dina ugla utje\u010de na impedanciju. Na primjer, kada je ugao bo\u010dnog zida 70\u00b0, impedancija je oko 50 oma. Kada je ugao 90\u00b0, impedancija je oko 48,37 oma.<\/p><p data-start=\"4402\" data-end=\"4843\">Gore navedeni testovi mijenjaju jedan faktor odjednom. U stvarnoj proizvodnji vi\u0161e varijabli se mijenja istovremeno. Impedansa mo\u017ee varirati od otprilike 40 oma do 56 oma. Ovo daleko prema\u0161uje tipi\u010dni zahtjev kao \u0161to je 50 \u03a9 \u00b110 %. Tokom proizvodnje mnogi parametri uzrokuju promjenu impedanse. Za brze ili vrhunske proizvode, dizajn PCB-a i proces proizvodnje moraju strogo kontrolirati svaki materijal i svaki korak. U suprotnom, proizvod mo\u017ee pokazati neo\u010dekivane probleme.<\/p><hr data-start=\"4845\" data-end=\"4848\" \/><h2 data-start=\"4850\" data-end=\"4890\">Impedansa i karakteristi\u010dna impedansa<\/h2><h3 data-start=\"4892\" data-end=\"4908\">1. Otpor<\/h3><p data-start=\"4910\" data-end=\"5193\">Kada u provodniku te\u010de naizmjeni\u010dna struja, otpor koji ona nailazi naziva se impedansa (Impedance). Simbol je Z. Jedinica je i dalje om (\u03a9). Ovaj otpor se razlikuje od otpora istosmjerne struje. U naizmjeni\u010dnoj struji, osim otpora (R), postoje induktivna reaktansa (XL) i kapacitivna reaktansa (XC).<\/p><p data-start=\"5195\" data-end=\"5267\">Da bi se razlikovalo od otpora na istosmjernoj struji, naziva se impedansa za naizmjeni\u010dnu struju (Z).<\/p><p data-start=\"5269\" data-end=\"5281\">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. Impedansa (Z)<\/h3><p data-start=\"5336\" data-end=\"5657\">Uz ve\u0107u integraciju integriranih kola, ve\u0107u frekvenciju signala i ve\u0107u brzinu, signali na tragovima PCB-a mogu biti pod utjecajem samog traga. Kada frekvencija signala dostigne odre\u0111enu granicu, trag uzrokuje ozbiljno izobli\u010denje ili gubitak signala. To pokazuje da tragovi PCB-a ne prenose samo struju, ve\u0107 i energiju u obliku impulsa ili kvadratnih valnih signala.<\/p><h3 data-start=\"5659\" data-end=\"5702\">3. Kontrola karakteristi\u010dne impedanse (Z0)<\/h3><p data-start=\"5704\" data-end=\"5798\">Opozicija koju signal vidi dok putuje naziva se karakteristi\u010dna impedansa. Simbol je Z0.<\/p><p data-start=\"5800\" data-end=\"6111\">Dakle, otklanjanje samo otvorenih i kratkih spojeva i provjera povezanosti nije dovoljno. Za visokobrzinske i visokofrekventne prijenosne linije kvaliteta mora biti stro\u017ea. Prolazak testa otvorenog\/kratkog spoja ili prisustvo malih defekata nije dovoljno. Morate izmjeriti Z0 i odr\u017eavati ga unutar tolerancije. Ako ne, plo\u010du treba odbaciti. Ne popravljajte je.<\/p><hr data-start=\"6113\" data-end=\"6116\" \/><h2 data-start=\"6118\" data-end=\"6161\">Propagacija signala i prijenosne linije<\/h2><h3 data-start=\"6163\" data-end=\"6209\">1. Definicija signalnog prijenosnog voda<\/h3><ol data-start=\"6211\" data-end=\"6336\"><li data-start=\"6211\" data-end=\"6336\"><p data-start=\"6214\" data-end=\"6336\">Prema elektromagnetnoj teoriji, kra\u0107i talasni du\u017eina (\u03bb) zna\u010di ve\u0107u frekvenciju (f). Njihov proizvod je brzina svjetlosti. To jest:<\/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> zatvori <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\">Bilo koji ure\u0111aj mo\u017ee imati visoku frekvenciju signala. Nakon \u0161to signal pro\u0111e kroz trag na tiskanoj plo\u010dici, signal se mo\u017ee usporiti ili zakasniti.<\/p><\/li><\/ol><p data-start=\"6504\" data-end=\"6539\">Dakle, kra\u0107a du\u017eina traga je bolja.<\/p><ol start=\"3\" data-start=\"6541\" data-end=\"6933\"><li data-start=\"6541\" data-end=\"6775\"><p data-start=\"6544\" data-end=\"6775\">Pove\u0107anje gusto\u0107e o\u017ei\u010denja ili smanjenje promjera \u017eica poma\u017ee. Ali kada frekvencija komponente postane vi\u0161a ili se periodi impulsa skrate, du\u017eina staze mo\u017ee se pribli\u017eiti dijelu talasne du\u017eine signala. Tada \u0107e staza pokazati o\u010diglednu distorziju.<\/p><\/li><li data-start=\"6777\" data-end=\"6920\"><p data-start=\"6780\" data-end=\"6920\">IPC-2141 klauzula 3.4.4 ka\u017ee: kada du\u017eina traga pribli\u017eno dostigne 1\/7 talasne du\u017eine signala, trag se tretira kao signalna transmisijska linija.<\/p><\/li><li data-start=\"6922\" data-end=\"6933\"><p data-start=\"6925\" data-end=\"6933\">Primjer:<\/p><\/li><\/ol><p data-start=\"6935\" data-end=\"7048\">Ure\u0111aj ima signalnu frekvenciju f = 10 MHz. Du\u017eina staze na tiskanoj plo\u010dici je 50 cm. Da li je potrebna kontrola karakteristi\u010dne impedanse?<\/p><p data-start=\"7050\" data-end=\"7058\">Izra\u010dunaj:<\/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^-1) = 3000 cm<br \/>\ndu\u017eina traga \/ talasna du\u017eina = 50 \/ 3000 = 1\/60<br \/>\n<\/code><\/div><\/div><p data-start=\"7196\" data-end=\"7311\">Po\u0161to je 1\/60 mnogo manje od 1\/7, ovaj trag je obi\u010dni vod i ne zahtijeva kontrolu karakteristi\u010dne impedanse.<\/p><p data-start=\"7313\" data-end=\"7449\">Maxwellove jedna\u010dine nam govore: brzina propagacije VS sinusnog vala u mediju povezana je sa brzinom svjetlosti C i dielektri\u010dnom konstantom \u03b5r na sljede\u0107i na\u010din:<\/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\">protiv<\/span> = C \/ \u221a\u03b5r<br \/>\n<\/code><\/div><\/div><p data-start=\"7473\" data-end=\"7535\">Kada je \u03b5r = 1, brzina signala je jednaka brzini svjetlosti = 3 \u00d7 10^10 cm\/s.<\/p><h3 data-start=\"7537\" data-end=\"7585\">2. Brzina prijenosa i dielektri\u010dna konstanta<\/h3><p data-start=\"7587\" data-end=\"7634\">Brzina signala pri 30 MHz za razli\u010dite materijale:<\/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\">Materijal \/ Podloga<\/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\">Dielektri\u010dna konstanta \u03b5r<\/th><th data-start=\"7694\" data-end=\"7717\" data-col-size=\"sm\">Brzina signala (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\">Vakuum<\/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\">Termoreaktivni polifenilenski eter<\/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\">Cijanatni 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-staklo<\/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\">Cijanatni ester + staklo<\/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\">Poliamid + staklo<\/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\">Kvarc<\/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\">Epooksno staklo (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\">Aluminij<\/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\">Tabela pokazuje: kako se \u03b5r pove\u0107ava, brzina signala u materijalu opada. Da biste dobili ve\u0107u brzinu signala, odaberite vi\u0161i karakteristi\u010dni impedans. Da biste dobili ve\u0107i Z0, odaberite materijal s ni\u017eim \u03b5r. PTFE ima najmanji \u03b5r, pa omogu\u0107ava najve\u0107u brzinu.<\/p><p data-start=\"8380\" data-end=\"8508\">FR4 plo\u010da koristi epoksidnu smolu i E-staklo. Njen \u03b5r je oko 4,7. Brzina signala je 138 m\/\u03bcs. Promjena sistema smole mo\u017ee promijeniti \u03b5r.<\/p><hr data-start=\"8510\" data-end=\"8513\" \/><h2 data-start=\"8515\" data-end=\"8560\">Razlozi za kontrolu karakteristi\u010dne impedanse<\/h2><h3 data-start=\"8562\" data-end=\"8573\">Razlog 1<\/h3><p data-start=\"8575\" data-end=\"8849\">Kada elektroni\u010dka oprema (ra\u010dunar, komunikacije) radi, poja\u010dalo \u0161alje signal prijemniku putem tragova na tiskanoj plo\u010dici. Karakteristi\u010dni impedans Z0 traga mora odgovarati elektroni\u010dkom impedansu poja\u010dala i prijemnika. Ako su uskla\u0111eni, energija signala se prenosi u potpunosti.<\/p><h3 data-start=\"8851\" data-end=\"8862\">Razlog 2<\/h3><p data-start=\"8864\" data-end=\"9031\">Ako je kvalitet PCB-a lo\u0161 i Z0 je izvan tolerancije, signali \u0107e se reflektovati, rasipati, prigu\u0161iti ili ka\u0161njeti. U te\u0161kim slu\u010dajevima signali mogu biti pogre\u0161ni i ure\u0111aj se mo\u017ee sru\u0161iti.<\/p><h3 data-start=\"9033\" data-end=\"9044\">Razlog 3<\/h3><p data-start=\"9046\" data-end=\"9311\">Potrebna je stroga selekcija materijala i kontrola procesa kako bi vi\u0161eslojna plo\u010da Z0 zadovoljila specifikacije kupca. Komponente s vi\u0161om elektroni\u010dkom impedancijom obi\u010dno zahtijevaju vi\u0161i Z0 PCB-a da bi bile uskla\u0111ene. Vi\u0161eslojna plo\u010da s ispravnim Z0 je kvalificirani proizvod za visoke brzine ili visoke frekvencije.<\/p><hr data-start=\"9313\" data-end=\"9316\" \/><h2 data-start=\"9318\" data-end=\"9362\">Odnos Z0 prema materijalu i procesu<\/h2><p data-start=\"9364\" data-end=\"9415\">Formula za karakteristi\u010dnu impedanciju mikrostrip linije Z0:<\/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\">Gdje:<\/p><ul data-start=\"9485\" data-end=\"9584\"><li data-start=\"9485\" data-end=\"9513\"><p data-start=\"9487\" data-end=\"9513\">\u03b5r \u2014 dielektri\u010dna konstanta<\/p><\/li><li data-start=\"9514\" data-end=\"9542\"><p data-start=\"9516\" data-end=\"9542\">H \u2014 debljina dielektrika<\/p><\/li><li data-start=\"9543\" data-end=\"9562\"><p data-start=\"9545\" data-end=\"9562\">W \u2014 \u0161irina traga<\/p><\/li><li data-start=\"9563\" data-end=\"9584\"><p data-start=\"9565\" data-end=\"9584\">T \u2014 debljina traga<\/p><\/li><\/ul><p data-start=\"9586\" data-end=\"9654\">Manji \u03b5r olak\u0161ava podizanje Z0 kako bi odgovarao visokobrzim komponentama.<\/p><h3 data-start=\"9656\" data-end=\"9671\">1. Z0 i \u03b5r<\/h3><p data-start=\"9673\" data-end=\"9872\">Z0 je obrnuto proporcionalan \u03b5r. Z0 se pove\u0107ava s porastom H. Za strogo visokofrekventne linije Z0 tolerancija debljine dielektrika mora biti stroga. Obi\u010dno promjena debljine dielektrika ne smije prelaziti 10\u207b\u00b3.<\/p><h3 data-start=\"9874\" data-end=\"9907\">2. Utjecaj debljine dielektrika<\/h3><p data-start=\"9909\" data-end=\"10155\">Uz ve\u0107u gusto\u0107u ruta, ve\u0107i H dovodi do ve\u0107ih elektromagnetskih smetnji. Za visokofrekventne i visokobrzinske digitalne linije, kako se pove\u0107ava gusto\u0107a provodnika, smanjite debljinu dielektrika da biste smanjili EMI i preslu\u0161avanje, ili koristite materijale s ni\u017eim \u03b5r.<\/p><p data-start=\"10157\" data-end=\"10262\">Iz formule je debljina bakra T va\u017ean faktor. Ve\u0107i T smanjuje Z0, ali je promjena mala.<\/p><h3 data-start=\"10264\" data-end=\"10293\">3. Utjecaj debljine bakra<\/h3><p data-start=\"10295\" data-end=\"10468\">Tanje bakarno provodno jezgro daje ve\u0107u Z0, ali njegov utjecaj na Z0 je mali. Kori\u0161tenje tankog bakra poma\u017ee pri izradi tankih tragova, \u0161to vi\u0161e poma\u017ee u kontroli Z0 nego sama debljina bakra.<\/p><p data-start=\"10470\" data-end=\"10487\">Iz formule:<\/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\">Kako se smanjuje W (\u0161irina traga), Z0 se pove\u0107ava. Promjena \u0161irine ima ve\u0107i utjecaj na Z0 nego promjena debljine.<\/p><h3 data-start=\"10660\" data-end=\"10684\">4. Utjecaj \u0161irine traga<\/h3><p data-start=\"10686\" data-end=\"11112\">Z0 naglo raste kako se \u0161irina W su\u017eava. Da biste kontrolisali Z0, strogo kontrolisite \u0161irinu traga. Danas ve\u0107ina visokofrekventnih i visokobrzinskih digitalnih tragova ima \u0161irine poput 0,10 mm ili 0,13 mm. Tradicionalno je tolerancija \u0161irine bila \u00b120%. Za tragove koji nisu transmisijske linije (du\u017eina traga &lt;&lt; talasna du\u017eina signala \/ 7), \u00b120% mo\u017ee biti u redu. Ali za tragove kod kojih se kontrolira Z0, pogre\u0161ka u \u0161irini od \u00b120% ne mo\u017ee zadovoljiti zahtjeve. U tom slu\u010daju pogre\u0161ka Z0 \u010desto prelazi \u00b110%.<\/p><p data-start=\"11114\" data-end=\"11122\">Primjer:<\/p><p data-start=\"11124\" data-end=\"11281\">Mikrostrip na tiskanoj plo\u010di ima \u0161irinu 100 \u03bcm, debljinu 20 \u03bcm i dielektri\u010dnu debljinu 100 \u03bcm. Pretpostavimo da je debljina bakra jednoli\u010dna. Ako se \u0161irina promijeni za \u00b120%, mo\u017ee li Z0 ispuniti \u00b110%?<\/p><p data-start=\"11283\" data-end=\"11294\">Po formuli:<\/p><p data-start=\"11296\" data-end=\"11545\">Neka W0 = 100 \u03bcm, W1 = 80 \u03bcm, W2 = 120 \u03bcm, T = 20 \u03bcm, H = 100 \u03bcm. Onda je Z01 \/ Z02 = 1.20. Dakle, Z0 samo dose\u017ee \u00b110%, a ne unutar \u00b110%. Da bi Z0 bio unutar \u00b110%, varijacija \u0161irine mora biti mnogo manja od \u00b120%. Da bi Z0 \u2264 \u00b15%, tolerancija \u0161irine mora biti \u2264 \u00b110%.<\/p><p data-start=\"11547\" data-end=\"11660\">Ovo obja\u0161njava za\u0161to neki PTFE PCB-ovi i neki FR4 PCB-ovi zahtijevaju toleranciju \u0161irine od \u00b10,02 mm. Razlog je kontrola Z0.<\/p><hr data-start=\"11662\" data-end=\"11665\" \/><h2 data-start=\"11667\" data-end=\"11714\">Kontrole procesa za karakteristi\u010dnu impedanciju<\/h2><ol data-start=\"11716\" data-end=\"13499\"><li data-start=\"11716\" data-end=\"11872\"><p data-start=\"11719\" data-end=\"11872\"><strong data-start=\"11719\" data-end=\"11757\">Kontrola i inspekcija proizvodnje filmova<\/strong><br data-start=\"11757\" data-end=\"11760\" \/>Odr\u017eavajte stalnu temperaturu i vla\u017enost (21\u00b12 \u00b0C, 55\u00b15 %), odr\u017eavajte \u010distu prostoriju i vr\u0161ite kompenzaciju \u0161irine procesa.<\/p><\/li><li data-start=\"11874\" data-end=\"12061\"><p data-start=\"11877\" data-end=\"12061\"><strong data-start=\"11877\" data-end=\"11893\">Dizajn panela<\/strong><br data-start=\"11893\" data-end=\"11896\" \/>Rubovi panela ne bi trebali biti previ\u0161e uski. Osigurajte ujedna\u010denu oblogu. Koristite pseudo-katodu u elektrolitnom presvla\u010denju za raspodjelu struje. Dodajte kupon na rub panela za test Z0.<\/p><\/li><li data-start=\"12063\" data-end=\"12284\"><p data-start=\"12066\" data-end=\"12284\"><strong data-start=\"12066\" data-end=\"12077\">\u017diganje<\/strong><br data-start=\"12077\" data-end=\"12080\" \/>Kontrolirajte parametre procesa kako biste smanjili podrezivanje. Izvedite inspekciju prvog prolaza. Smanjite preostali bakar, bakrene \u017eljebove i bakrene otpatke. Provjerite \u0161irinu traga i odr\u017eavajte je unutar zahtjevanog raspona (\u00b110% ili \u00b10,02 mm).<\/p><\/li><li data-start=\"12286\" data-end=\"12486\"><p data-start=\"12289\" data-end=\"12486\"><strong data-start=\"12289\" data-end=\"12307\">Inspekcija AOI<\/strong><br data-start=\"12307\" data-end=\"12310\" \/>Za unutra\u0161nje slojeve prona\u0111ite praznine i izbo\u010dine na tragovima. Za brze signale od 2 GHz, \u010dak i praznina od 0,05 mm mo\u017ee uzrokovati odbacivanje plo\u010de. Kontrola \u0161irine unutra\u0161njih slojeva i nedostataka je klju\u010dna.<\/p><\/li><li data-start=\"12488\" data-end=\"12766\"><p data-start=\"12491\" data-end=\"12766\"><strong data-start=\"12491\" data-end=\"12505\">Laminacija<\/strong><br data-start=\"12505\" data-end=\"12508\" \/>Koristite vakuumsku laminaciju za smanjenje pritiska i protoka smole. Ostavite vi\u0161e smole jer smola utje\u010de na \u03b5r. Vi\u0161e smole \u010desto smanjuje \u03b5r. Kontrolirajte toleranciju debljine laminacije. Ako je debljina gotove plo\u010de neujedna\u010dena, debljina dielektrika varira i utje\u010de na Z0.<\/p><\/li><li data-start=\"12768\" data-end=\"12989\"><p data-start=\"12771\" data-end=\"12989\"><strong data-start=\"12771\" data-end=\"12800\">Odaberite dobar osnovni materijal.<\/strong><br data-start=\"12800\" data-end=\"12803\" \/>Strogo se pridr\u017eavajte modela materijala kupca. Pogre\u0161an model zna\u010di pogre\u0161an \u03b5r, pogre\u0161nu debljinu. Cijeli proces izveden s pogre\u0161nim materijalom i dalje rezultira otpadom jer Z0 uveliko ovisi o \u03b5r.<\/p><\/li><li data-start=\"12991\" data-end=\"13343\"><p data-start=\"12994\" data-end=\"13343\"><strong data-start=\"12994\" data-end=\"13020\">Solder maska (coverlay)<\/strong><br data-start=\"13020\" data-end=\"13023\" \/>Maska za lemljenje na povr\u0161ini plo\u010de mo\u017ee smanjiti Z0 za 1\u20133 \u03a9. U teoriji debljina maske za lemljenje ne bi trebala biti prevelika. U praksi je utjecaj nevelik. Prije maske za lemljenje povr\u0161ina provodnika je u kontaktu sa zrakom (\u03b5r = 1), pa je izmjereni Z0 vi\u0161i. Nakon maske za lemljenje Z0 se smanjuje za 1\u20133 \u03a9 jer je \u03b5r maske za lemljenje oko 4,0.<\/p><\/li><li data-start=\"13345\" data-end=\"13499\"><p data-start=\"13348\" data-end=\"13499\"><strong data-start=\"13348\" data-end=\"13371\">Upijanje vlage<\/strong><br data-start=\"13371\" data-end=\"13374\" \/>Izbjegavajte upijanje vlage u gotovim vi\u0161eslojnim plo\u010dama. Voda ima \u03b5r \u2248 75. Vla\u017enost uzrokuje veliki pad Z0 i nestabilnost.<\/p><\/li><\/ol><hr data-start=\"13501\" data-end=\"13504\" \/><h2 data-start=\"13506\" data-end=\"13515\">Sa\u017eetak<\/h2><p data-start=\"13517\" data-end=\"13587\">Za vi\u0161eslojne plo\u010de s prijenosnim vodovima, uobi\u010dajeni rasponi kontrole Z0 su:<\/p><ul data-start=\"13589\" data-end=\"13628\"><li data-start=\"13589\" data-end=\"13602\"><p data-start=\"13591\" data-end=\"13602\">50 \u03a9 \u00b110%<\/p><\/li><li data-start=\"13603\" data-end=\"13616\"><p data-start=\"13605\" data-end=\"13616\">75 \u03a9 \u00b110%<\/p><\/li><li data-start=\"13617\" data-end=\"13628\"><p data-start=\"13619\" data-end=\"13628\">28 \u03a9 \u00b110%<\/p><\/li><\/ul><p data-start=\"13630\" data-end=\"13685\">Da biste kontrolisali varijaciju, uzmite u obzir ove \u010detiri glavne faktore:<\/p><ol data-start=\"13687\" data-end=\"13782\"><li data-start=\"13687\" data-end=\"13705\"><p data-start=\"13690\" data-end=\"13705\">\u0160irina traga W<\/p><\/li><li data-start=\"13706\" data-end=\"13728\"><p data-start=\"13709\" data-end=\"13728\">Debljina traga T<\/p><\/li><li data-start=\"13729\" data-end=\"13756\"><p data-start=\"13732\" data-end=\"13756\">Debljina dielektrika H<\/p><\/li><li data-start=\"13757\" data-end=\"13782\"><p data-start=\"13760\" data-end=\"13782\">Dielektri\u010dna konstanta \u03b5r<\/p><\/li><\/ol><p data-start=\"13784\" data-end=\"14251\">Najve\u0107i utjecaj ima debljina dielektrika H. Zatim slijedi dielektri\u010dna konstanta \u03b5r. Zatim \u0161irina traga W. Najmanji utjecaj ima debljina traga T. Nakon odabira osnovnog materijala, promjena \u03b5r je mala. H se mo\u017ee kontrolirati, ali se i dalje mijenja. T je lak\u0161e kontrolirati. Kontrola \u0161irine traga W unutar \u00b110% je te\u0161ka. Problemi na tragu, poput rupica, praznina i udubljenja, tako\u0111er su va\u017eni. Na mnogo na\u010dina, naju\u010dinkovitija i najva\u017enija metoda za kontrolu Z0 je precizna kontrola i pode\u0161avanje \u0161irine traga.<\/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":"<p>What is PCB Impedance Control? PCB impedance control means controlling the impedance of traces. This impedance is also called controlled [&hellip;]<\/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":"","ast-disable-related-posts":"","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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center\";s:15:\"background-size\";s:4:\"auto\";s:21:\"background-attachment\";s:6:\"scroll\";s:15:\"background-type\";s:0:\"\";s:16:\"background-media\";s:0:\"\";s:12:\"overlay-type\";s:0:\"\";s:13:\"overlay-color\";s:0:\"\";s:15:\"overlay-opacity\";s:0:\"\";s:16:\"overlay-gradient\";s:0:\"\";}}"],"footnotes":[""],"_elementor_edit_mode":["builder"],"_elementor_template_type":["wp-page"],"_elementor_data":["[{\"id\":\"e3bf423\",\"elType\":\"container\",\"settings\":{\"display_condition_list\":[{\"display_condition_login_status\":\"subscriber\",\"_id\":\"7fd0735\"}]},\"elements\":[{\"id\":\"2c73ff6\",\"elType\":\"widget\",\"settings\":{\"editor\":\"<h2 data-start=\\\"0\\\" data-end=\\\"32\\\">What is PCB Impedance Control?<\\\/h2><p data-start=\\\"34\\\" data-end=\\\"483\\\">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><p data-start=\\\"485\\\" data-end=\\\"838\\\">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><hr data-start=\\\"840\\\" data-end=\\\"843\\\" \\\/><h2 data-start=\\\"845\\\" data-end=\\\"891\\\">Common methods to achieve impedance control<\\\/h2><h3 data-start=\\\"893\\\" data-end=\\\"923\\\">1. Use PCB layer structure<\\\/h3><p data-start=\\\"925\\\" data-end=\\\"1227\\\">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><h3 data-start=\\\"1229\\\" data-end=\\\"1265\\\">2. Use differential signal lines<\\\/h3><p data-start=\\\"1267\\\" data-end=\\\"1625\\\">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><h3 data-start=\\\"1627\\\" data-end=\\\"1656\\\">3. Control trace geometry<\\\/h3><p data-start=\\\"1658\\\" data-end=\\\"1977\\\">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><h3 data-start=\\\"1979\\\" data-end=\\\"2006\\\">4. Choose PCB materials<\\\/h3><p data-start=\\\"2008\\\" data-end=\\\"2264\\\">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><h3 data-start=\\\"2266\\\" data-end=\\\"2304\\\">5. Use simulation and design tools<\\\/h3><p data-start=\\\"2306\\\" data-end=\\\"2582\\\">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><hr data-start=\\\"2584\\\" data-end=\\\"2587\\\" \\\/><h2 data-start=\\\"2589\\\" data-end=\\\"2632\\\">Effects of PCB manufacturing on impedance<\\\/h2><h3 data-start=\\\"2634\\\" data-end=\\\"2648\\\">Trace width<\\\/h3><p data-start=\\\"2650\\\" data-end=\\\"3120\\\">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><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; 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><p data-start=\\\"11114\\\" data-end=\\\"11122\\\">Example:<\\\/p><p data-start=\\\"11124\\\" data-end=\\\"11281\\\">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><p data-start=\\\"11283\\\" data-end=\\\"11294\\\">By formula:<\\\/p><p data-start=\\\"11296\\\" data-end=\\\"11545\\\">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><p data-start=\\\"11547\\\" data-end=\\\"11660\\\">This explains why some PTFE PCBs and some fr4 PCBs require width tolerance \\u00b10.02 mm. The reason is to control Z0.<\\\/p><hr data-start=\\\"11662\\\" data-end=\\\"11665\\\" \\\/><h2 data-start=\\\"11667\\\" data-end=\\\"11714\\\">Process controls for characteristic impedance<\\\/h2><ol data-start=\\\"11716\\\" data-end=\\\"13499\\\"><li data-start=\\\"11716\\\" data-end=\\\"11872\\\"><p data-start=\\\"11719\\\" data-end=\\\"11872\\\"><strong data-start=\\\"11719\\\" data-end=\\\"11757\\\">Film making control and inspection<\\\/strong><br data-start=\\\"11757\\\" data-end=\\\"11760\\\" \\\/>Keep constant temperature and humidity (21\\u00b12\\u00b0C, 55\\u00b15%), keep a clean room, and do width process compensation.<\\\/p><\\\/li><li data-start=\\\"11874\\\" data-end=\\\"12061\\\"><p data-start=\\\"11877\\\" data-end=\\\"12061\\\"><strong data-start=\\\"11877\\\" data-end=\\\"11893\\\">Panel design<\\\/strong><br data-start=\\\"11893\\\" data-end=\\\"11896\\\" \\\/>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><li data-start=\\\"12063\\\" data-end=\\\"12284\\\"><p data-start=\\\"12066\\\" data-end=\\\"12284\\\"><strong data-start=\\\"12066\\\" data-end=\\\"12077\\\">Etching<\\\/strong><br data-start=\\\"12077\\\" data-end=\\\"12080\\\" \\\/>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><li data-start=\\\"12286\\\" data-end=\\\"12486\\\"><p data-start=\\\"12289\\\" data-end=\\\"12486\\\"><strong data-start=\\\"12289\\\" data-end=\\\"12307\\\">AOI inspection<\\\/strong><br data-start=\\\"12307\\\" data-end=\\\"12310\\\" \\\/>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><li data-start=\\\"12488\\\" data-end=\\\"12766\\\"><p data-start=\\\"12491\\\" data-end=\\\"12766\\\"><strong data-start=\\\"12491\\\" data-end=\\\"12505\\\">Lamination<\\\/strong><br data-start=\\\"12505\\\" data-end=\\\"12508\\\" \\\/>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><li data-start=\\\"12768\\\" data-end=\\\"12989\\\"><p data-start=\\\"12771\\\" data-end=\\\"12989\\\"><strong data-start=\\\"12771\\\" data-end=\\\"12800\\\">Select good base material<\\\/strong><br data-start=\\\"12800\\\" data-end=\\\"12803\\\" \\\/>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><li data-start=\\\"12991\\\" data-end=\\\"13343\\\"><p data-start=\\\"12994\\\" data-end=\\\"13343\\\"><strong data-start=\\\"12994\\\" data-end=\\\"13020\\\">Solder mask (coverlay)<\\\/strong><br data-start=\\\"13020\\\" data-end=\\\"13023\\\" \\\/>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><li data-start=\\\"13345\\\" data-end=\\\"13499\\\"><p data-start=\\\"13348\\\" data-end=\\\"13499\\\"><strong data-start=\\\"13348\\\" data-end=\\\"13371\\\">Moisture absorption<\\\/strong><br data-start=\\\"13371\\\" data-end=\\\"13374\\\" \\\/>Avoid moisture absorption in finished multilayer boards. Water has \\u03b5r \\u2248 75. Moisture causes large Z0 drop and instability.<\\\/p><\\\/li><\\\/ol><hr data-start=\\\"13501\\\" data-end=\\\"13504\\\" \\\/><h2 data-start=\\\"13506\\\" data-end=\\\"13515\\\">Summary<\\\/h2><p data-start=\\\"13517\\\" data-end=\\\"13587\\\">For multilayer board transmission lines, common Z0 control ranges are:<\\\/p><ul data-start=\\\"13589\\\" data-end=\\\"13628\\\"><li data-start=\\\"13589\\\" data-end=\\\"13602\\\"><p data-start=\\\"13591\\\" data-end=\\\"13602\\\">50 \\u03a9 \\u00b110%<\\\/p><\\\/li><li data-start=\\\"13603\\\" data-end=\\\"13616\\\"><p data-start=\\\"13605\\\" data-end=\\\"13616\\\">75 \\u03a9 \\u00b110%<\\\/p><\\\/li><li data-start=\\\"13617\\\" data-end=\\\"13628\\\"><p data-start=\\\"13619\\\" data-end=\\\"13628\\\">28 \\u03a9 \\u00b110%<\\\/p><\\\/li><\\\/ul><p data-start=\\\"13630\\\" data-end=\\\"13685\\\">To control variation, consider these four main factors:<\\\/p><ol data-start=\\\"13687\\\" data-end=\\\"13782\\\"><li data-start=\\\"13687\\\" data-end=\\\"13705\\\"><p data-start=\\\"13690\\\" data-end=\\\"13705\\\">Trace width W<\\\/p><\\\/li><li data-start=\\\"13706\\\" data-end=\\\"13728\\\"><p data-start=\\\"13709\\\" data-end=\\\"13728\\\">Trace thickness T<\\\/p><\\\/li><li data-start=\\\"13729\\\" data-end=\\\"13756\\\"><p data-start=\\\"13732\\\" data-end=\\\"13756\\\">Dielectric thickness H<\\\/p><\\\/li><li data-start=\\\"13757\\\" data-end=\\\"13782\\\"><p data-start=\\\"13760\\\" data-end=\\\"13782\\\">Dielectric constant \\u03b5r<\\\/p><\\\/li><\\\/ol><p data-start=\\\"13784\\\" data-end=\\\"14251\\\">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 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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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