[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-266549-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-266549-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","electronics-equations-semiconductor-bjt-mosfet","Electronics Equations - Semiconductor, BJT, MOSFET","","Equations and key semiconductor device relations cover physical constants, charge and carrier concentration links, mobility and drift-diffusion, and diode junction behavior. Core diode formulas include built-in voltage, junction capacitance, turn-on voltage, and DC/AC small-signal expressions such as transconductance and resistance. The guide continues with BJT parameter definitions for gains and on/saturation voltages, and extends to MOSFET operating-mode threshold conditions, saturation and tri-state currents, small-signal transconductance, drain current, early-effect output resistance, power, and amplifier gain relationships.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/electronics-equations-semiconductor-bjt-mosfet/266549/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/electronics-equations-semiconductor-bjt-mosfet/266549.png","ImageObject",300,407,{"name":42,"@type":43},"Quinn","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-20","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What foundational physical constants and voltages are used in the semiconductor equations?","Question",{"text":62,"@type":63},"The notes list Boltzmann’s constant, electron charge, electron volt conversion, thermal voltage VT, and related relationships used to derive current and voltage expressions.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Which formulas define diode behavior for both DC and AC small-signal operation?",{"text":67,"@type":63},"The document provides the DC diode current ID in terms of IS and thermal voltage, then gives AC small-signal forms including diode transconductance gd and diode resistance rd.",{"name":69,"@type":60,"acceptedAnswer":70},"How are BJT and MOSFET small-signal parameters and amplifier gains expressed?",{"text":71,"@type":63},"For BJT, it summarizes relationships for transconductance and resistance. For MOSFET, it provides AC transconductance gm, drain current expressions, early-effect output resistance ro, power PT, and amplifier gain formulas for different load conditions.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},266549,1789408845,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},6,50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":101,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":110},962075114765,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Equations in Electronics : Semicon, BJT, MOSFET  \nAndersen Ang  \nCreated: 2012 . Last update: 2017-Feb-1  \nSemiconductor  \n1. Boltzmann's Constant K = 8:6 􀀂 10􀀀5eVK  \n2. Electron Charge e = 􀀀1:6 􀀂 10􀀀19C  \n3. Electron Volt 1eV = 1:6 􀀂 10􀀀19J  \n4. Thermal Voltage VT = kTq t 26mV300K  \n5. Intrinsic Electron Concentration ni = BT ~~3~~2 exp EkTg  \n6. Hole-Electron Relationship np = n2i  \n7. Charge Carrier concentration with doping np = nN2~~i~~A pn = nN2~~i~~d  \n8. Simplified Constant BSi = 5:23 􀀂 1015 cm􀀀3K 􀀀3=2 BGe = 1:66 􀀂 1015 BGaAs = 2:1 􀀂 1014  \n9. Gap Energy Eg;Ge = 0:66eV Eg;GaAs = 1:4eV  \n10. Drift Velocity of Charge Carrier under external E-field vd;n = 􀀀􀀖E vd;p = 􀀖E  \n11. Dirft Current Density and Electrical Conductivity Jdrift = (en􀀖n + ep􀀖p) E = 􀀛E 􀀛 (S=cm)  \n12. Mobility of Charge Carrier 􀀖n : 1350cm2 =V 􀀀 s 􀀖p: 480cm2 =V 􀀀 s  \n13. Diffusion Current Density Jdiff;n = eDn dndx Jdiff;p = 􀀀eDp dpdx D (cm2 =s)  \n14. Einstein Relationship D􀀖pp = D􀀖nn = kTq = VT  \n15. Build-in Voltage VBi = VT ln 􀀒 NN2iA 􀀓  \n16. Junction Capacitance Cj =  Cjo r 1 + VemVbif  \n17. Turn on voltage V􀀍 (pn) = 0:7 V􀀍 (SB) = 0:3  \n18. DC Diode Current ID = IS 􀀒 e ~~ ~~VVDT 􀀀 1􀀓 IS = 10􀀀15 􀀘 10􀀀13A  \n19. AC Diode Current id = IDQVTvd  \n20. AC Diode Transconductance gd = IDQVT  \n21. AC Diode Resistance rd = g1  \nBJT  \n1. Common-Emitter Current Gain , Common-Base Current Gain 􀀌 =  􀀋  􀀋 =  􀀌   \n1 􀀀 􀀋 , 􀀌 + 1 , ic = 􀀌iB 􀀀 􀀋iE , iE = (􀀌 + 1) iB  \n2. Voltage : Turn on / Saturation VBE (on; Si) = 0:7 , VBE (on; Ge) = 0:3V , VBE (sat) = 0:8 , VBB > VBE (on) , VCE > VBE (on) , VCE (sat; Si) = 0:3V; VCE (sat; Ge) = 0:1V  \n3. AC Collector Current and Emitter Current iC = IS exp v~~ ~~Bv~~ ~~TE , ic = 􀀌iB , iE = (􀀌 + 1) iB  \n4. AC Transconductance and Resistance gm = ICQVT , r􀀙 = 􀀌g~~ ~~m = VTIBQ = 􀀌IVCTQ , re = 􀀋g~~ ~~m ,  VA  \nro = PT = IC VCE  \nICQ ,  \nMOSFET  \n1. Thershold Voltage of different opeartion mode VTN;DeMod \u003C 0 , VTN;EnMode > 0 , VT P;DeMode >  \n0 , VT P;EnMode \u003C 0  \n2. MOSFET Parameters Kn = k20~~ ~~ W~~n~~L , k0n = 􀀖ox Cox , Cox = 􀀏tooxx  \n3. Drain-Gate Voltage VDS (sat) = VGS 􀀀 VTN = VSG + VT P  \n4. Saturation Mode Current  \nIDS (sat) = KN (VGS 􀀀 VTN )2 = k20~~ ~~ W~~n~~L (VGS 􀀀 VTN )2 = KP (VSG + VT P )2 = kp20~~ ~~ WL (VSG + VT P )2 5. Tri-state Mode Current  \nIDS (tri) = Kn (2(VGS 􀀀 VTH )VDS 􀀀 V2DS ) = KP (2(VSG + VTH )VSD 􀀀 V2SD ) , VDS > VDS (sat)  \n6. MOSFET AC Transconductance gm = 2KN (VGSQ 􀀀 VTN ) = 2 pKN IDQ = ivdgs  \n7. MOSFET AC Drain Current id = 2Kn vgs (VGSQ 􀀀 VTN )  \n8. Early Effect Resistance ro = 􀀕I1DQ = VAIDQ  \n9. Power PT = IDVDS  \n10. Amplifier Gains     Av (with ench. load) = 􀀀gmD 􀀒 roD jj g1mL j jroL 􀀓 􀀙 􀀀g~~ ~~mg~~ ~~mLD = 􀀀 22p~~ ~~Kp~~ ~~KnnDIDQDLIDQL =  r ~~ ~~KKnDnL~~ ~~  = s ~~ ~~((WWLL))DL Av (with dept. load) = 􀀀gmD (roD j jroL ) 􀀙 􀀀g~~ ~~mg~~ ~~mLD = 􀀀 22p~~ ~~Kp~~ ~~KnnDIDQDLIDQL = r ~~ ~~KKnDnL = s ~~ ~~((WWLL))DL","cbCaidQT5ybU7TLf","https://ap.wps.com/l/cbCaidQT5ybU7TLf","pdf",177209,"English","# Semiconductor\n## Boltzmann and charge relations\n## Carrier concentration, drift/diffusion, and diode junction\n# BJT\n## Current gain, turn-on/saturation voltages\n## Small-signal collector/emitter relations\n# MOSFET\n## Threshold conditions and operating modes\n## Saturation/tri-state currents and small-signal parameters\n## Amplifier gains and output resistance","[{\"question\":\"What foundational physical constants and voltages are used in the semiconductor equations?\",\"answer\":\"The notes list Boltzmann’s constant, electron charge, electron volt conversion, thermal voltage VT, and related relationships used to derive current and voltage expressions.\"},{\"question\":\"Which formulas define diode behavior for both DC and AC small-signal operation?\",\"answer\":\"The document provides the DC diode current ID in terms of IS and thermal voltage, then gives AC small-signal forms including diode transconductance gd and diode resistance rd.\"},{\"question\":\"How are BJT and MOSFET small-signal parameters and amplifier gains expressed?\",\"answer\":\"For BJT, it summarizes relationships for transconductance and resistance. For MOSFET, it provides AC transconductance gm, drain current expressions, early-effect output resistance ro, power PT, and amplifier gain formulas for different load conditions.\"}]","Electronics Equations - Semiconductor, BJT, MOSFET | PDF"]