# 6. BJT Small Signal

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BJT Small-Signal Analysis Contents Common-Emitter fixed-bias configuration Voltage divider bias CE Emitter bias Emitter-follower configuration Common-base configuration Collector-feedback configuration Hybrid equivalent circuit and model re transistor model employs a diode and controlled current source to duplicate the behavior of a transistor in the region of interest. The re and hybrid models will be used to analyze small-signal AC analysis of standard transistor network configurations. Ex: Common-base, common-emitter and common-collector configurations. The network analyzed represent the majority of those appearing in practice today. BJT Small Signal Analysis AC equivalent of a network is obtained by: 1. Setting all DC sources to zero 2. Replacing all capacitors by s/c equiv. 3. Redraw the network in more convenient and logical form Common-Emitter (CE) Fixed-Bias Configuration The input (Vi) is applied to the base and the output (Vo) is from the collector. The Common-Emitter is characterized as having high input impedance and low output impedance with a high voltage and current gain. Removing DC effects of VCC and Capacitors Common-Emitter (CE) Fixed-Bias Configuration re Model Determine |, re, and ro: | and ro: look in the specification sheet for the transistor or test the transistor using a curve tracer. re: calculate re using dc analysis: EeI26mVr =Common-Emitter (CE) Fixed-Bias Configuration Impedance Calculations Input Impedance: Output Impedance: e B ir || R Z | =e B e ir 10 Rr Z|| >~Or || R ZC o =c o10 roZRRc>~Common-Emitter (CE) Fixed-Bias Configuration Gain Calculations Voltage Gain (Av): Current Gain (Ai): Current Gain from Voltage Gain: eo Ciovr) r || (RVVA = =C oeCv10R rrRA> =) r )(R R (rr RIIAe B C oo Bioi||+ += =e B C oir 10 R , 10R rA|| > >~Civ iRZA A =Common-Emitter (CE) Fixed-Bias Configuration Voltage Gain eCv C oeo Ce bo C bve b io C b OiOvrRA 10R or r ifr) r || (R- r I) r || (R IAr I V) r || (R I VVVA = > O ==== ==Common-Emitter (CE) Fixed-Bias Configuration Current gain ( )( )( )( )Civ iB oB oioie B C oe B C oB oioie BBC ooibboioie BBibe Bi BbC ooboC ob ooRZA Aoo equation t this use can or weR rR rIIA, r 10 R and 10R r ifr R R rR rIIAr RRR r rIIIIIIA r RRII and r RI RIR r rII and R rI rIcircuits output and input the to rule divider - current the applying by determined is gain current The = = ~ = > > + += = ||.|

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\|= =+=+=+=+=Common-Emitter (CE) Fixed-Bias Configuration Phase Relationship The phase relationship between input and output is 180 degrees. The negative sign used in the voltage gain formulas indicates the inversion. Common-Emitter (CE) Fixed-Bias Configuration CE Voltage-Divider Bias Configuration re Model You still need to determine |, re, and ro. CE Voltage-Divider Bias Configuration Impedance Calculations Input Impedance: Output Impedance: 2 12 12 1R RR RR || R R+= ='e r || R Zi B'=o C r || R Zo=C C10R roR Zo>~CE Voltage-Divider Bias Configuration Gain Calculations Voltage Gain (Av): Current Gain (Ai): Current Gain from Voltage Gain: eo Ciovrr || RVVA = =C oeCiov10R rrRVVA> ~ =) r R )( R (rr RIIAe C ooioi||+'+ '= =C oe ioi10R rr RR IIA>+' '~ =|e C oioir 10 R , 10R rIIA|| > ' >~ =Civ iRZA A =CE Voltage-Divider Bias Configuration Voltage Gain eC v C oeo C vo Ceioeibo C b OrRA 10R or r ifr) r || (RA) r || (RrV VrVI) r || )(R I ( V= > O == ||.|

\| == =CE Voltage-Divider Bias Configuration Current gain ( )( )( )( )ee ooioiC oe C ooioiB 2 1r R'R' r R' rr R'IIA, R 10 r for r R' R rr R'IIAR R || R R'format. same the have gain will current for the equation the , R' thefor except ion, configurat bias - fixed emitter -common that similar to so is network the since+~+~ => + += == =CE Voltage-Divider Bias Configuration CiV iioiioieRZA Aoption an asIIAR'R'IIA, r 10 R' if And = ~ = = =>||CE Voltage-Divider Bias Configuration Phase Relationship A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias. CE Voltage-Divider Bias Configuration CE Emitter-Bias Configuration Unbypassed RE re Model Again you need to determine |, re. CE Emitter-Bias Configuration Impedance Calculations Input Impedance: Output Impedance: E e b1)R ( r Z + + = | |) R (r ZE e b + ~ |e E E br RR Z>>~ |b B iZ || R Z =C oR Z =CE Emitter-Bias Configuration Defining the input impedance of a transistor with an unbypassed emitter resistor E be EE e bE ebibE b e b iE e e b iR Z to reduced be can above eqn , r an greater th much is R sinceR r Z1, an greater th normally is sinceR ) 1 ( rIVZR I ) 1 ( r I VR I r I V: side input the to KVL Applying~ + ~ + + = = + + = + =CE Emitter-Bias Configuration Voltage Gain (Av): Current Gain (Ai): Current Gain from Voltage Gain: Gain Calculations bCiovZRVVA | = =) R (r ZR rRVVAE e bE eCiov+ =+ = = |E bECiovR ZRRVVA| ~ ~ =b BBioiZ RRIIA+= = |Civ iRZA A =or CE Emitter-Bias Configuration Voltage Gain ECioVE bE eCioVE e bbCioVCbiC b C o obibRRVVAR ion Z approximat for the andR rRVVAgives ) R (r Z ng substitutiZRVVARZV R I R I VZVI= = ~+= = + == = ||.|

\| = = ==CE Emitter-Bias Configuration Current Gain CRZA AZ RRIIIIIIAIII IZ RRIIZ RI RI: in result ll circuit wi input the to rule divider - current the Applying . I Iion approximat permit the to Z to close often too is R of magnitude Theiv ib BBibboioibob ob BBibb Bi Bbi bb B = += = = == +=+==|||CE Emitter-Bias Configuration Phase Relationship A CE amplifier configuration will always have a phase relationship between input and output is 180 degrees. This is independent of the DC bias. CE Emitter-Bias Configuration Bypassed RE This is the same circuit as the CE fixed-bias configuration and therefore can be solved using the same re model. CE Emitter-Bias Configuration Emitter-Follower Configuration You may recognize this as the Common-Collector configuration. Indeed they are the same circuit. Note the input is on the base and the output is from the emitter. re Model You still need to determine | and re. Emitter-Follower Configuration Impedance Calculations Input Impedance: b B iZ || R Z =E e b1)R ( r Z + + = | |) R (r ZE e b + ~ |E bR Z | ~Emitter-Follower Configuration Calculation for the current Ie E eieeeeEeiE eiebbib ebibR rVIrr1) (r and 1) ( but R1) (rV 1)R ( r1)V (Igives for Z g subtitutinZV1) ( 1)I ( IZVI+= = ~+~ ++((

+=+ + +=+ = + ==Emitter-Follower Configuration Impedance Calculations (contd) Output Impedance: e E or || R Z =e E e or Rr Z>>~E eieR rVIion configurat follower emitter for the impedence output the Defining+= Emitter-Follower Configuration Gain Calculations Voltage Gain (Av): Current Gain (Ai): Current Gain from Voltage Gain: e EEiovr RRVVA+= =E e E e EiovR r R , r R 1VVA~ + >>~ =b BBiZ RRA+ ~ |Eiv iRZA A =Emitter-Follower Configuration Voltage gain 1VVAR r R, r an greater th much usually Rr RRVVAr RV RViovE e Ee Ee EEiove Ei Eo~ = ~ ++= = +=Emitter-Follower Configuration Current Gain Eiv ib BBib BBibboioibob e ob BBibb Bi BbRZA A or Z RRA, ) 1 ( sinceZ RR) 1 (IIIIIIA) 1 (III ) 1 ( I IZ RRIIZ RI RI =+ ~ ~ + ++ = = =+ =+ = = +=+=| | ||||Emitter-Follower Configuration Phase Relationship A CC amplifier or Emitter Follower configuration has no phase shift between input and output. Vo Emitter-Follower Configuration Common-Base (CB) Configuration The input (Vi) is applied to the emitter and the output (Vo) is from the collector. The Common-Base is characterized as having low input impedance and high output impedance with a current gain less than 1 and a very high voltage gain. re Model You will need to determine o and re. Common-Base (CB) Configuration Impedance Calculations Input Impedance: Output Impedance: e E ir || R Z =C oR Z =Common-Base (CB) Configuration Gain Calculations Voltage Gain (Av): Current Gain (Ai): eCeCiovrRrRVVA ~ = = o1IIAioi ~ = = oCommon-Base (CB) Configuration Voltage & Current gain eCeCioVCeioeieC eC c C o orRrRVVARrV VrVIR I ) R I ( R I V~ = = ||.|

\|=== = =1IIAI I II Iioii e oi e = = = = ==oo oCommon-Base (CB) Configuration Phase Relationship A CB amplifier configuration has no phase shift between input and output. Vo Common-Base (CB) Configuration Collector DC Feedback Configuration The network has a dc feedback resistor for increased stability, yet the capacitor C3 will shift portions of the feedback resistance to the input and output sections of the network in the ac domain. The portion of RF shifted to the input or output side will be determined by the desired ac input and output resistance levels. Substituting the re equivalent circuit into the ac equivalent network er || R ZF1 i =o F2 C or || R || R Z =2|| F C o R R Z ~Collector DC Feedback Configuration Impedance Calculations Input Impedance: Output Impedance: Voltage Gain eC F2iovC oeC F2 oioveioeibb oC F2 orR || RVVA, 10R r for rR || R || rVVAR'rV VrVIR' I VR || R || r R' = = > = = == ==Collector DC Feedback Configuration Current Gain ( )( )( )CiVioiF2 oCioiC F2 o F1F2 o F1ioiF1 e F1 e F1e F1 CF1ioie FF1C ib ##### BJT Base Resistance and Small Signal smcgarry/ELEC3908/Slides/ELEC3908...BJT Base Resistance and Small Signal Modelling ELEC 3908, Physical Electronics, Lecture 19 ELEC 3908, Physical
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