4. Bipolar Junction Transistors. 4. Bipolar Junction Transistors TLT-8016 Basic Analog Circuits 2005/2007 1

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1 4. polar Juncton Transstors 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

2 4. asc Operaton of the npn polar Juncton Transstor npn JT conssts of thn p-type layer between two n-type layers; Layers: emtter, base, collector; Two nteractng pn junctons: emtter-base and base-collector; Emtter regon s doped ery healy, compared wth the base regon Fgure 4. The npn JT. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 2

3 asc Operaton n the Acte regon Fgure 4.2 An npn transstor wth arable basng sources (common-emtter confguraton). Shokley equaton for the emtter current E E I ES exp VT (4.) Fgure 4. urrent flow for an npn JT n the acte regon. I ES A saturaton current V T 26mV thermal oltage Most of the current s due to electrons mong from the emtter through the base to the collector. ase current conssts of holes crossng from the base nto the emtter and of holes that recombne wth electrons n the base. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

4 Frst - Order ommon - Emtter haracterstcs Fgure 4.4 ommon-emtter characterstcs of a typcal npn JT. Amplfcaton by the JT In Fgure 4.4: If 0µA, ma 00 tmes more β (4.2) β - common-emtter current gan. Typcally β Factors Affectng the urrent Gan Dopng of the emtter area compared wth the base area ase regon should be thn; Geometry of the dece 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4

5 Dece Equatons E (4.) ( α ) E (4.8) α - common-base current gan. Typcally α I s scale current α (4.4) E E α IES exp (4.5) VT I I α s I ES s exp V E T (4.6) (4.7) ( ) I exp E α ES (4.9) VT β β (4.) β α β α (4.0) α 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 5

6 Example 4. Usng Dece ures to Determne α and β Determne the alues of α and β for the transstor wth the characterstcs shown n Fgure 4.4. Soluton: For example: at E 4 V and 0 µa; ma; β ma 00 0 µ A β α β Fgure 4.4 ommon-emtter characterstcs of a typcal npn JT. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 6

7 Secondary Effects ase - Wdth Modulaton ase-wdth modulaton: the dependence of the base wdth from E. ase-wdth modulaton affects and. V A Early oltage ollector reakdown Aalanche breakdown n the depleton regon of the collector-base juncton Punch-through Leakage urrent I O reerse leakage current. Flows from collector to the base. Fgure 4.5 ommon-emtter characterstcs dsplayng exaggerated secondary effects. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 7

8 4.2 Load - Lne Analyss of a ommon - Emtter Amplfer Analyss of the Input urrent V n( t ) ( t ) E( t ) (4.) Analyss of the Output rcut Fgure 4.0 ommon-emtter amplfer. V E (4.4) Fgure 4. Load-lne analyss of the amplfer of Fgure polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 8

9 Example 4.2 Graphcal Determnaton of Q-pont and Peak Sgnal Swngs Suppose that the current of Fgure 4.0 has V 0 V, V.6 V, 40 kω and 2 kω. The nput sgnal s a 0.4 V peak, khz snusod gen by n (t)0.4sn(2000πt). The common-emtter characterstcs for the transstor are shown n Fgure 4.2a and b. Fnd the maxmum, mnmum and Q- pont alues for E. Soluton Fgure 4.2 Load-lne analyss for Example polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 9

10 Fgure 4. Voltage waeforms for the amplfer of Fgure 4.0. See Example 4.2. Gan n Example 4.2: Ampltude at the nput: 0.4V Ampltude at the output 7 5 2V A polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 0

11 Dstorton Fgure 4.4 Output of the amplfer of Example 4.2 for n (t).2 sn(2000πt) showng gross dstorton. utoff: E < 0.6V and 0 Saturaton regon: s large and s not proportonal to t. When transstor enters n cutoff or n saturaton, clppng of the output sgnal occurs. Fgure 4.5 Amplfcaton occurs n the acte regon. lppng occurs when the nstantaneous operatng pont enters saturaton or cutoff. In saturaton, E < 0.2 V. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

12 4. The pnp polar Juncton Transstor pnp transstor: thn n type semconductor layer between two p type semconductor layers asc charge carrers: holes All relatonshps between the currents and oltages n a pnp JT are the same as n npn JT. There are two basc dfferences: The currents flow n opposte drectons; The oltages hae opposte polartes. α E ( α ) E β E E E IES exp VT (4.5) (4.6) (4.7) (4.8) (4.9) Fgure 4.6 The pnp JT. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 2

13 Fgure 4.7 ommon-emtter characterstcs for a pnp JT. Pay attenton that the oltages are negate. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

14 4.4 Large - Sgnal D rcut Models Fgure 4.20 egons of operaton on the characterstcs of an npn JT. Acte regon: I > 0; V E > 0.2V Saturaton regon: I > 0; βi > I > 0 utoff regon: V E < 0.5V; V < 0.5V; 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4

15 Acte - egon Model Fgure 4.9a JT large-sgnal models. (Note: Values shown are approprate for typcal small-sgnal slcon deces at a temperature of 00K.) 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 5

16 Saturaton - egon Model Fgure 4.9b JT large-sgnal models. (Note: Values shown are approprate for typcal small-sgnal slcon deces at a temperature of 00K.) 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 6

17 utoff - egon Model Fgure 4.9c JT large-sgnal models. (Note: Values shown are approprate for typcal small-sgnal slcon deces at a temperature of 00K.) 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 7

18 Example 4. Determnaton of JT Operaton egon A gen transstor has β 00. Determne the regon of operaton f (a) I 50µA and I ma; (b) I 50µA and V E 5V; (c) V E -2V and V E -V. Soluton: (a) I 50µA > 0 acte or saturaton regon; βi mA > I saturaton regon. (b) I 50µA > 0 acte or saturaton regon; V E 5V > 0.2V acte regon. (c) V E -2V < 0.5V most probably cutoff; V E -V < 0.5V ths confrms cutoff regon. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 8

19 4.5 Large - Sgnal D Analyss of JT rcuts Step : Assume an operaton regon for the JT and replace t by the correspondng large sgnal equalent crcut. Step 2: Sole the crcut to fnd I, I, and V E. Step : heck to see f the alues found n Step 2 are consstent wth the assumed operatng state. If so the soluton s complete; otherwse return to Step. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 9

20 Example 4.4 The Fxed - ase as rcut The D bas crcut shown n Fgure 4.2a has 200 kω, kω and V 5 V. The transstor has β 00. Sole for I and V E. Soluton: Frst assumpton: utoff. The equalent crcut s n Fgure 4.2(b). I 0 thus the oltage drop across s zero. Thus V E V 5V > 0.5V. The assumpton s not ald. Fgure 4.2 as crcut of Examples 4.4 and polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

21 Second assumpton: Saturaton. The equalent crcut s n Fgure 4.2c. I I V V mA 7.5 µa βi mA < I The assumpton s not ald. Thrd assumpton: Acte regon. The equalent crcut s n Fgure 4.2d. I I V E V β I 7.5mA V I 7.5 µa I > 0; V E > 0.2V. The condtons are met. 7.85V Fgure 4.2 as crcut of Examples 4.4 and polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 2

22 Example 4.5 The Fxed - ase as rcut wth Hgher eta epeat example 4.4 wth β00. Soluton: Frst, we assume that the crcut operatng n the acte regon. V E V. I µ A I β I ma V I 6.45V < 0.2V One of the requrements for the acte regon V E >0.2 V s not met. Next we assume that the transstor s n saturaton. V. I ma βi V. I µ A mA > 4.8mA Fgure 4.2 as crcut of Examples 4.4 and polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

23 Analyss for the Four - esstor as rcut 2 / / (4.2) 2 V (4.22) 2 V 2 V I VE EIE (4.2) ( ) I I E β I V V E ( β ) E (4.24) VE V I EIE (4.25) Fgure 4.28 Four-resstor bas crcut. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 2

24 Dscrete as - rcut Desgn The prncpal goal of bas crcut desgn s to achee nearly dentcal operatng pont for the JTs, een though the JT parameters may ary sgnfcantly from unt to unt. In the desgn usually are gen the supply oltage V, the collector current I n the quescent pont and often V E n the quescent pont. The desgn steps are:. hoce of V E, f t s not specfed. A good choce s V V E 2. Determnng of the oltage drop V E across E and the oltage V V, whch s across. A good choce s V VE VE V V 2 5. Snce I E (β)i I V I 6. V V E V E V E V I 2 E ( V V ) ( I I2 ) ( V V ) I I 2 I E V I V V - E I 2 2 E E V I I E E V E - V E I - V. I I β 4. hoce of the current I 2 to be I 2 (0..20)I. Four-resstor bas crcut. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

25 How the crcut stablze the quescent pont? Assume that the emtter current I s ncreased, due to some reason. Then Emtter current I E s ncreased also, snce I E I. V E ncreases snce V E I E E I 2 s at least 0 tmes more than I. It s the basc part of the current through. Thus the both currents are stable and depend ery weak on the araton of the currents n the JT. The stable currents through and 2 defne a stable oltage V. V E V - V E and the ncreasng of V E decreases V E. Smaller V E means smaller base current I (see the nput characterstc n Fgure 4.4). I βi and the smaller base current returns the collector current to ts ntal alue. I 2 I V I 2 I I V E V 2 E V E - - V E I E Four-resstor bas crcut. - V 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

26 Problem D4.9. Four-resstor bas crcut desgn. Suppose that V 20V, kω, and a quescent pont of I Q 5mA s desred. The transstor has β rangng from 50 to 50. Desgn a four resstor bas crcut. Use standard 5%- tolerance resstors. Soluton: Snce s specfed we can determne the oltage drop across t and the oltage V V V V E V V V E I V Q V 5V V VE VE V To determne I, we take the smallest alue of β. In ths way we wll determne the largest alue of I and the largest alue of I 2. If β s hgher, the condton for I 2 wll be also satsfed. I I 2 I 0I β µA 6 ma ( 5 0 ) ( 0 ) ( V V ) ( I I ) 500Ω 8.2kΩ 6 ( ) ( ) 0.7kΩ 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/ E 2 V V E I I E 2 2 The 5%-tolerance standard alues for the resstors are E.5kΩ, 8.2kΩ, 2 kω. I 2 I V I 2 I 2 I V E V E - V E - V E I E Four-resstor bas crcut. - V

27 4.6 Small - Sgnal Equalent rcuts Small - Sgnal urrent - Voltage elatonshp () be ( ) IQ b t IQ E α IES exp (4.28) (4.4) V VT T V () ( t) EQ be( t ) t be b ( ) IQ b( t ) α IES exp (4.5) (4.29) r π VT V r T π (4.6) VEQ IQ ( ) be( t ) IQ b( t ) α IES exp exp (4.0) VT VT βvt rπ (4.7) IQ VEQ ( ) IQ α IES exp (4.) VT ( t) β ( t) (4.8) ( t) I ( ) be t Q b( t ) IQ exp (4.2) I ( t ) β I β ( t ) ( x ) x VT exp ( t) β ( t) Q (4.9) c c b Q (4.) (4.40) b 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

28 Small - Sgnal Equalent rcut for the JT c β rπ () t () t β be g m rπ IQ g m VT () t r () t and ( t) g ( t) be π b c m be (4.4) (4.42) Exercse 4.9 At room temperature, a certan transstor has β00. ompute the alues of g m and r π for I Q 0 ma. epeat for I Q ma Soluton: βvt β 00 At I 0mA : rπ 260Ω; g 85mS m I 0 0 r 260 Q βvt β 00 At I ma : rπ 2600Ω; g 8.5mS m I 0 r 2600 Q 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/ π π Fgure 4. Small-sgnal equalent crcuts for the JT.

29 4.7 The ommon - Emtter Amplfer, 2, and E E2 form the four resstor basng crcut; and 2 are couplng capactors; E s bypass capactor. For ac sgnal the supply oltage s short crcut. Fgure 4.4 ommon-emtter amplfer. If E 0 the nput sgnal s between the base and the emtter (ground); the output sgnal s between collector and the emtter (V, whch s ground for ac sgnal) common-emtter amplfer. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

30 The Small - Sgnal Equalent rcut s 2 s s - n - 2 E E2 E L E L o o s n - - The frst step n creatng the small-sgnal equalent crcut: the dc oltage sources are replaced by short crcuts The second step n creatng the small-sgnal equalent crcut for md-band regon: the couplng capactors and the bypass capactors are replaced by short crcuts Fgure 4.4 ommon-emtter amplfer. (b) Fnal small-sgnal md-band equalent crcut. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 0

31 Voltage Gan n r be π b e E E ( β ) b (4.45) o ' L β (4.46) b A o n rπ β ' L ( β ) E (4.47) Fgure 4.4 ommon-emtter amplfer. Smplfcatons: (4.4) / 2 / (4.44) / ' L L / L 2 If E 0: If (β) E >> r π : A A β r π ' L β ' L ' L ( β ) E E and the oltage gan doesn t depend on JT parameters. Open crcut oltage gan (when L ) A o o n rπ β ( β ) E (4.48) 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

32 Input Impedance urrent Gan and Power Gan o Z A n A (4.5) n L G A A (4.52) Fgure 4.4 ommon-emtter amplfer. Z n t rπ ( β ) E (4.49) Z n b n (4.50) / / Z n t 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 2

33 Output Impedance Fgure 4.4 ommon-emtter amplfer. b 0 and β b 0. Thus there s an open crcut between and E. Z o (4.5) 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007

34 Example 4.9 alculaton of ommon - Emtter Amplfer Performance a) Fnd A, A o, Z n, A, G, and Z o for the amplfer shown n Fgure 4.5. b) epeat part (a) f the emtter resstor E s splt n nto E 00 Ω and E2 900 Ω, wth bypass capactor n the parallel wth E2. β of the JT s 00 and from dc analyss s found that the quescent pont s I Q 4.2mA and V E 6.72V. Soluton: r π βvt Ω I Q. Ω k / / 2 ( 0 0 ) ( 5 0 ) ' L / / ( 2 0 ) ( 0 ) 667 L Ω Fgure 4.5 ommon-emtter amplfer of Example polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4

35 a) A Z A o n A G o n n n o n 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/ b) A o n r π β ' L E ( β ) ' 6.2 βl ( 00 ) 00 rπ 6 o β Ao β n rπ ( β ) E r π 9. 6 ( 00 ) 00 Z t r π 6Ω n Zt rπ ( β ) E 6 ( 00 ) kω b / / Z (. 0 ) o n A A A Z n L t 5 Ω ( 28.) ( 06) 2980 Z o kω Z 2. Ω / / Z k n t (. 0 ) ( ) 54 A G o n A A A Z n L ( 7.89) ( 6.2) Z o kω

36 4.8 The Emtter Follower, 2, and E are from the four resstor basng crcut. and 2 are couplng capactors. The nput sgnal s between the base and the ground (the collector, snce the supply oltage s short crcut for the ac sgnal); the output sgnal s between the emtter and the ground (the collector) common-collector amplfer. n be o Fgure 4.6 Emtter follower. Thus n > o and A <. Usually A emtter follower. Typcal applcaton as a buffer amplfer, snce t has hgh nput mpedance and small output mpedance. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 6

37 Small - Sgnal Equalent rcut s 2 s s - n 2 E o L s - n 2 E o L The frst step n creatng the small-sgnal equalent crcut: the dc oltage sources are replaced by short crcuts The second step n creatng the small-sgnal equalent crcut for md-band regon: the the couplng capactors and the bypass capactors are replaced by short crcuts Fgure 4.6 Emtter follower. (b) Fnal small-sgnal md-band equalent crcut. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 7

38 Voltage Gan Fgure 4.6 Emtter follower. Smplfcatons: (4.54) / 2 / (4.55) / ' L L E / L 2 E n A o ' L ( β ) (4.56) π b ( ) ' β r (4.57) r π ' ( β ) L ( β ) ' L L < (4.58) Snce usually (β) L >> r π A. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 8

39 Input Impedance Fgure 4.6 Emtter follower. Z Z t (4.59) / / Z b t n rπ ( β ) ' L (4.60) For small power JT L s n the range of kohms and β ~ 00. Thus the range of Z t s hundreds of kohms. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 9

40 Output Impedance Z o x x Fgure 4.6 Emtter follower. (4.6) Z o x x ( β )/( ' r ) ( / ) s π E (4.65) ' s rπ x Z b β b x (4.62) ot ( β ) (4.66) E rπ ' If s 0 Zot s ( β ) gm / / / (4.6) s 2 x ' rπ b sb 0 (4.64) For small power JT g m ~ ms. Thus the range of Z ot s Ohms or tens of Ohms. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

41 Example 4.0 alculaton of Emtter Follower Performance. ompute the oltage gan, nput mpedance, current gan, power gan, and output mpedance of the emtter-follower amplfer dsplayed n Fgure 4.7a. The dc analyss ges the followng quescent pont: I Q 4.2mA and V E.7V. Soluton Fgure 4.7 Emtter follower of Example 4.0. r π βvt Ω I Q Ω / / ( 0 ) ( 2 0 ) 667 L E 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/ ' L A r π ' ( β ) L ( β ) ' L 260 ( 200) ( 200) ' ( β ) 260 ( 200) 667 Ω Zt rπ L 5 k Z 6. Ω / / Z k t ( 50 0 ) ( 5 0 ) 5 Z ' s o / s / / 2 ( 0 0 ) ( 00 0 ) ( 00 0 ) ( β )/( ' r ) ( / ) s π ( 200) ( ) ( 2 0 ) E 8. kω 46.6 Ω 50kΩ Z A ; 8. / / 2 ( 00 0 ) ( 00 0 ) 0 8 A G A A L

42 4.9 The JT as a Dgtal Logc Swtch Fgure 4.4 TL nerter. Fgure 4.42b Load-lne analyss of TL nerter under noload condtons. The crcut n Fg. 4.4 s a modfcaton of common-emtter amplfer ntended for operaton n saturaton and n cut-off regon only. ut-off state: V n < 0.5 (logcal zero). JT s n cut-off and I 0. There s no oltage drop across and V o V (logcal one). Saturaton state: V n s hgh (logcal one), usually V n V. Vn 0.7 In saturaton V E < 0.2V. Ths V o V E < 0.2V (logcal zero). V 0.7 To hae saturaton regon, and must be desgned n such a way that β >. The output has logcally opposte oltage to the nput (zero-one; one-zero). The crcut s called logcal nerter. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/

43 TL NO Gate When at the three nputs are appled low oltages (logcal zeros) all JT are n cutoff, no current flows through and V o V (logcal one). When a hgh oltage s presentng at one or more of the nputs (logcal ones at these nputs) the correspondng JTs are n saturaton and V o < 0.2V (logcal zero). Fgure 4.45 Three-nput TL NO gate. 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:

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