3.2 Terminal Characteristics of Junction Diodes (pp )

Transcription

1 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc /6 3. Termnal Characterstcs of Juncton odes (pp.47-53) A Juncton ode I.E., A real dode! Smlar to an deal dode, ts crcut symbol s: HO: The Juncton ode Cure HO: The Juncton ode Equaton A. The Forward Bas Regon Consder when nv T (.e, when 5mV ). Jm Stles The Un. of Kansas ept. of EECS

2 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc /6 Note then (when 5mV ) that e, so that a nvt forward based juncton dode approxmaton s: nvt = Is e nvt s for nvt I e An exponental cure! Example: I s =0 -, n= Volts A juncton dode n forward bas wth sgnfcant but plausble current always has a oltage between approxmately 0.5V and 0.8 V! Jm Stles The Un. of Kansas ept. of EECS

3 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc 3/6 I.E., 0 5. < < 0 8. (aprox.) when n f.b. Therfore, we often APPROXIMATE the forward based juncton dode oltage as smply: Note that ths approxmaton: a) b) HO: The Juncton ode Forward Bas Equaton HO: Example: A Juncton ode Crcut B. The Reerse Bas Regon Now consder when nv T (.e, when 5mV ). Jm Stles The Un. of Kansas ept. of EECS

4 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc 4/6 Note then that now e nvt, so that a reerse based juncton dode approxmaton s: nvt = Is e I for s nv T Therefore, a reerse based juncton dode has a tny, negate current. HO: Forward and Reerse Bas Approxmatons C. The Breakdown Regon If becomes too negate, then dode wll breakdown (b.d.)! * I.E., sgnfcant current wll flow from cathode to anode ( < 0!). Jm Stles The Un. of Kansas ept. of EECS

5 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc 5/6 * wll reman at approxmately -V ZK, regardless of. Therefore, breakdown s descrbe mathematcally as: Note that V ZK s a knee oltage (.e., alue s subjecte). Jm Stles The Un. of Kansas ept. of EECS

6 /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc 6/6. Power sspaton n Juncton odes Consder the power dsspated by a juncton dode (.e., P =V I) f.b. r.b. b.d. Thus, we typcally try to aod breakdown. In other words, we desre V ZK to be as bg as possble! Jm Stles The Un. of Kansas ept. of EECS

7 /9/008 The Juncton ode Cure.doc /3 The Juncton ode Cure In many ways, juncton dode (.e., real dode) behaor s smlar to that of deal dodes. Howeer, there are some mportant and profound dfferences! Frst, recall the deal dode current oltage cure: Ths cure s pece-wse lnear, wth two unambguous regons reerse bas (where < 0 and = 0), and forward bas (where > 0 and = 0). Now consder the behaor of a juncton dode: Jm Stles The Un. of Kansas ept. of EECS

8 /9/008 The Juncton ode Cure.doc /3 Please note that unlke the deal dode, the juncton dode cure: a) s contnuous (not pece-wse lnear). b) Has three apparent regons of operaton (not two). c) Has, therefore, ambguous boundares between regons (.e., contnuous transtons occur between regons the cure has two knees!). By comparson to the deal dode, we lkewse defne one regon of the juncton dode cure as the forward bas regon, and another as the reerse bas regon. The thrd regon has no smlarty wth deal dode behaor (.e., ths s a new regon). We call ths regon breakdown. Jm Stles The Un. of Kansas ept. of EECS

9 /9/008 The Juncton ode Cure.doc 3/3 Note that the breakdown regon occurs when the juncton dode oltage (from anode to cathode) s approxmately less than or equal to a oltage alue VZK. The alue V ZK s known as the zener breakdown oltage, and s a fundamental performance parameter of any juncton dode. As we shall see later, the behaor of a juncton dode n the forward and reerse bas regon s a predctable result of semconductor physcs! As such we can wrte an explct mathematcal expresson, smultaneously descrbng the behaor of a juncton dode n both the forward and reerse bas regons (but not n breakdown!): nvt I = s e for > V ZK Jm Stles The Un. of Kansas ept. of EECS

10 /9/008 PN Juncton ode Equaton.doc / The Juncton ode Equaton The relatonshp between the current through a juncton dode ( ) and the oltage across t ( ) s: nvt I = s e for > V ZK Note: ths equaton descrbes dode behaor n the forward and reerse based regon only (.e., not ald for breakdown). Q: Good golly! Just what do those dog-gone parameters n, I s and V T mean? A: Smlar to the resstance alue R of a resstor, or the capactance C of a capactor, these three parameters specfy the performance of a juncton dode. Specfcally, they are:. I s = Saturaton (or scale) Current. epends on dode materal, sze, and temperature. Typcal alues range from 0-8 to 0-5 A (.e., tny)! Jm Stles The Un. of Kansas ept. of EECS

11 /9/008 PN Juncton ode Equaton.doc /. V T = Thermal Voltage = kt q Where: k = Boltzman s Constant T = ode Temperature ( K ) q = Charge on an electron (coulombs) At 0 C, V T 5 mv IMPORTANT NOTE!: Unless otherwse stated, we wll assume that each and eery juncton dode s at room temperature (.e., T = 0 C ). Thus, we wll always assume that the thermal oltage V T of all juncton dodes s 5 mv (.e., V = 5 mv )! T 3. n = a constant called the dealty factor (.e. a fudge factor ). Typcally, n Jm Stles The Un. of Kansas ept. of EECS

12 /9/008 The Juncton ode Forward Bas Equaton.doc /6 The Juncton ode Forward Bas Equaton In forward bas, we hae learned that the dode current can be related to the dode oltage usng the followng approxmaton: nvt = I e I e S S nv T, proded that 5 mv. We can nert ths approxmaton to alternately express n terms of dode current : Ie S e nv T nv T = = I S = ln T IS nv = nvt ln I S Jm Stles The Un. of Kansas ept. of EECS

13 /9/008 The Juncton ode Forward Bas Equaton.doc /6 Now, say a oltage across some juncton dode results n a current. Lkewse, dfferent oltage across ths same dode a dode of course results n a dfferent current. We can defne the dfference between these two oltages as Δ =, and then usng the aboe equaton can express ths oltage dfference as: Δ = = nvt ln nvt ln IS IS I S = nvt ln IS Δ = nvt ln Ykes! Look at what ths equaton says: * The dfference n the two oltages s dependent on the rato of the two currents. * Ths oltage dfference s ndependent of scale current I s. We can lkewse nert the aboe equaton and express the rato of the two currents n terms of the dfference of the two oltages: Jm Stles The Un. of Kansas ept. of EECS

14 /9/008 The Juncton ode Forward Bas Equaton.doc 3/6 = nvt ln ( ) = VT ln n ( ) = exp nvt Agan, we fnd that ths expresson s ndependent of scale current I s. Q: Stop wastng my tme wth these pontless deratons! Are these expressons een remotely useful!?! A: These expressons are often ery useful! Frequently, nstead of explctly prodng dece parameters n and I s, a juncton dode s specfed by statng n, and then a statement of the specfc dode current resultng from a specfc dode oltage. For example, a juncton dode mght be specfed as: A juncton dode wth n = pulls ma of current at a oltage =0.6 V. Jm Stles The Un. of Kansas ept. of EECS

15 /9/008 The Juncton ode Forward Bas Equaton.doc 4/6 The aboe statement completely specfes the performance of ths partcular juncton dode we can now determne the current flowng through ths dode for any other alue of dode oltage. Lkewse, we can fnd the oltage across the dode for any other dode current alue. For example, say we wsh to fnd the current through the juncton dode specfed aboe when a potental dfference of =0.7 V s placed across t. We hae two optons for fndng ths current: Opton : We know that n = and that =ma when =0.6 V. Thus, we can use ths nformaton to sole for scale current I s : I e S S I e nv T S = = I = e x0 I S =. ma Now, we use the forward-based juncton dode equaton to determne the current through ths dece at the new oltage of =0.7 V: = I e = S nv T ( 755x0 ) = 09. ma e Jm Stles The Un. of Kansas ept. of EECS

16 /9/008 The Juncton ode Forward Bas Equaton.doc 5/6 Opton Here, we drectly determne the current at = 0.7 usng one of the expressons dered earler n ths handout! Usng = ma and =0.6 we can state the relaton shp between current as and oltage as: ( ) exp = nvt ( 06) = exp For =0.7 V we can therefore fnd current as: ( ). = exp 005. = 09. ma Opton (usng the equatons we dered n ths handout) s obously qucker and easer (note n opton we dd not hae to deal wth annoyng numbers lke 7.55 x 0 -!). Fnally, we should also note that juncton dodes are often specfed smply as a ma dode or a 0 ma dode or a 00 ma dode. These statement mplctly prode the dode current at the standard dode test oltage of =0.7 V. Jm Stles The Un. of Kansas ept. of EECS

17 /9/008 The Juncton ode Forward Bas Equaton.doc 6/6 Q: But what about the alue of juncton dode dealty factor n? A: If no alue of n s proded (and there s not suffcent nformaton gen to determne t), we typcally just assume that n =. For example, consder the followng problem: etermne the oltage across a 00 ma juncton dode when there s ma of current flowng through t. A 00 ma juncton dode smply means a juncton dode that wll hae a current of 00 ma flowng through t ( =00 ma) f the oltage across t s =0.7 V. We wll assume that n =, snce no other nformaton about that parameter was gen. Thus, usng =0.7, =00mA, and = ma, we can determne the alue of : = nvt ln 07. = ( 005. ) ln 00 = = 060. V EXCELENT! Jm Stles The Un. of Kansas ept. of EECS

18 /9/008 Example A Juncton ode Crcut.doc /3 Example: A Juncton ode Crcut Consder the followng crcut wth two juncton dodes: - V S 00 Ω 6.5 ma R The dodes are dentcal, wth n = and I S = 0-4 A. Q: If the current through the resstor s 6.5 ma, what s the oltage of source V S?? A: Ths s a dffcult problem to sole! Certanly, we cannot just wrte: = V S and then the answer. Instead, let s just determne what we can, and see what happens! Jm Stles The Un. of Kansas ept. of EECS

19 /9/008 Example A Juncton ode Crcut.doc /3 - V S 00 Ω 6.5 ma R ) If 6.5 ma flows through a 0. K resstor, the oltage across that resstor s: ( ) R = = 065. V ) If the oltage across the resstor s 0.65 V, then the oltage across the dode, whch s parallel to the resstor, s the same alue: = = 065. V R 3) If we know the oltage across a p-n juncton dode, then we also know ts current! = IS exp = 0 exp = 96. ma nv T ) If we know and the current through the resstor, we know (usng KCL) the current through : = 65. = = 846. ma Jm Stles The Un. of Kansas ept. of EECS

20 /9/008 Example A Juncton ode Crcut.doc /3 - V S 00 Ω 6.5 ma R ) If 6.5 ma flows through a 0. K resstor, the oltage across that resstor s: ( ) R = = 065. V ) If the oltage across the resstor s 0.65 V, then the oltage across the dode, whch s parallel to the resstor, s the same alue: = = 065. V R 3) If we know the oltage across a p-n juncton dode, then we also know ts current! = IS exp = 0 exp = 96. ma nv T ) If we know and the current through the resstor, we know (usng KCL) the current through : = 65. = = 846. ma Jm Stles The Un. of Kansas ept. of EECS

21 /9/008 Example A Juncton ode Crcut.doc 3/3 = 846. ma - V 00 Ω S R = 065. V 6.5 ma = 96. ma = 065. V 5) If we know the current through a juncton dode, then we can fnd the oltage across t: = nvt ln = 005. ln = 069. V 4 IS 0 6) Fnally, f we know and, we can fnd V S usng KVL: VS = = = 34. V = 069. V = 846mA. 00 Ω - = 065. V R V S =.34V 6.5 ma = 96. ma = 065. V Jm Stles The Un. of Kansas ept. of EECS

22 /9/008 Forward and Reerse Bas Approxmatons.doc /6 Forward and Reerse Bas Approxmatons Q: Man, am I eer befuddled! Is the behaor of a juncton dode n the forward based regon descrbed as ths: nvt = Is e? or as ths: or as ths s nvt = I e? > 0 and = 0 7. V??? A: Actually, all three of the aboe statements are true (or, at least, approxmately so)! Let s reew what we know about the juncton dode n forward and reered bas:. Frst, we know that f the dode s not n breakdown, the relatonshp between current and oltage can be precsely descrbed as: Jm Stles The Un. of Kansas ept. of EECS

23 /9/008 Forward and Reerse Bas Approxmatons.doc /6 nvt I = s e for > V ZK Q: Here s where I get confused. Is ths equaton ald for reerse bas, or s t ald for forward bas? A: The aboe expresson s ald for forward bas, and t s ald for reerse bas, and t s also ald for the transton regon between forward and reerse bas! In other words, the aboe equaton s a ery accurate descrpton of the juncton dode behaor wth the mportant excepton of when the juncton dode s n breakdown.. Now, lets smplfy the preous expresson further, separately examnng the cases when the juncton dode s n forward bas (.e., nv T ), and reerse bas (.e., -VZK < nvt ). For the forward bas case, we fnd that: nvt e f nv T Jm Stles The Un. of Kansas ept. of EECS

24 /9/008 Forward and Reerse Bas Approxmatons.doc 3/6 Therefore, we can approxmate the juncton dode behaor n forward bas mode as: nvt s T I e for nv (.e., forward based) Lkewse, for the reerse bas case, we fnd that: nvt e f nv T Therefore, we can approxmate the juncton dode behaor n reerse bas mode as: I for -V < nv (.e., reersed based) s ZK T Combnng, we can approxmate the expresson at the top of the preous page as: nvt Is e for nvt (.e., forward based) Is for -V ZK < nvt (.e., reersed based) 3. We can now smplfy these expressons een further! We rewrte the aboe approxmaton for forward bas so that the juncton dode oltage s a functon of juncton dode current: Jm Stles The Un. of Kansas ept. of EECS

25 /9/008 Forward and Reerse Bas Approxmatons.doc 4/6 Ie s e nv T nv T = I s = ln T Is nv = = nvt ln I s As a preous example demonstrated, as we ary the alue of dode current from mcroamps to kloamps, the dode oltage wll ary only a few hundred mllolts, from about 0.5 V to 0.9 V. Thus, we can assume that f any apprecable current s flowng from juncton dode anode to juncton dode cathode (.e., forward bas condton), the juncton dode oltage wll be approxmately (.e., wthn a few hundred mllolts) 0.7 V. Q: It looks to me that you are sayng a forward based juncton dode exhbts a dode oltage of =700mV, regardless of the dode current, rght? Jm Stles The Un. of Kansas ept. of EECS

26 /9/008 Forward and Reerse Bas Approxmatons.doc 5/6 A: NO! Ths s not what I am sayng! As s edent n the preous two equatons, the juncton dode current n forward bas s drectly dependent on dode current as the current ncreases, the oltage ncreases! For each possble dode current, there s a specfc (and dfferent) dode oltage. * Howeer, we fnd that ths ncrease s logarthmcally related to dode current, such that the oltage ncreases ery slowly wth ncreasng current t takes a bunch of addtonal juncton dode current to ncrease the juncton dode oltage een a small amount. * Thus, we are smply sayng that for all apprecable (and plausble) dode currents, the juncton dode oltage wll be wthn of few hundred mllolts of, say, 700 mv. * As a result, = 0.7 V s not a bad approxmaton for forward based juncton dodes! Now, we can lkewse smplfy further our approxmaton for a reerse based juncton dode. Recall that we now approxmate the reerse bas dode current as = I. s Howeer, recall that the dode saturaton current I s s a ery small alue, typcally 0-8 to 0-5 Amps! Q: A bllonth of an amp!? That s so tny t mght as well be zero! Jm Stles The Un. of Kansas ept. of EECS

27 /9/008 Forward and Reerse Bas Approxmatons.doc 6/6 A: Precsely! The reerse bas current alue = Is s so small that we can approxmate t as zero: 0 f V < nv (reerse bas) ZK T Thus, we arre at an een smpler (albet less accurate) approxmaton of juncton dode behaor n forward and reerse bas: 0 7. f > 0 (forward bas) 0 f V < < 0 (reerse bas) ZK Each of the three expressons examned n ths handout can be used to descrbe the behaor of juncton dodes n forward and/or reerse bas. The frst expresson we examned s the most accurate, but t s lkewse the most mathematcally complex. Conersely, the thrd expresson aboe s the smplest, but s lkewse the least accurate. We wll fnd that all three of the expressons are useful to us, dependng on what specfcally we are attemptng to determne, and how accurately we need to determne t! Jm Stles The Un. of Kansas ept. of EECS