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

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1 polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng resstor network made up of resstor 1 and 2 and the voltage supply V. 2. The couplng capactor The balance of the crcut wth the transstor and collector and emtter resstors. V 1 1 v o v 2 Fgure 1. ommon mtter Amplfer rcut The common emtter amplfer crcut s the most often used transstor amplfer confguraton. The procedure to follow for the analyss of any amplfer crcut s as follows: 1. Perform the D analyss and determne the condtons for the desred operatng pont (the Qpont) 2. Develop the A analyss of the crcut. Obtan the voltage gan /6.071 Sprng 2006, hanotaks and ory 1

2 D rcut Analyss The basng network ( 1 and 2 ) prodes the Qpont of the crcut. The D equvalent crcut s shown on Fgure 2. V I Q TH I Q V V 0Q V TH I Q The parameters I Q the Qpont Fgure 2. D equvalent crcut for the common emtter amplfer., I Q, Q I and correspond to the values at the D operatng pont V OQ We may further smplfy the crcut representaton by consderng the JT model under D condtons. Ths s shown on Fgure 3. We are assumng that the JT s properly based and t s operatng n the forward actve regon. The voltage corresponds to the forward drop of the dode juncton, the 0.7 volts. I Q V ( on ) β I Q I Q V (on) Fgure 3. D model of an npn JT /6.071 Sprng 2006, hanotaks and ory 2

3 For the juncton we are usng the offset model shown on Fgure 4. The resstance equal to s r V T e = (1.1) I kt Where VT s the thermal voltage, VT, whch at room temperature s V T = 26 mv q s n general a small resstance n the range of a few Ohms.. r e I 1/ V Fgure 4 y ncorporatng the JT D model (Fgure 3) the D equvalent crcut of the common emtter amplfer becomes V I Q β I Q V 0Q TH V V TH I Q V (on) I Q Fgure /6.071 Sprng 2006, hanotaks and ory 3

4 ecall that the transstor operates n the actve (lnear) regon and the Qpont s determned by applyng KVL to the and loops. The resultng epressons are: V I V I Loop: TH = Q TH ( on) Q (1.2) Loop: VQ = V IQ IQ (1.3) quatons (1.2) and (1.3) defne the Qpont A rcut Analyss If a small sgnal s supermposed on the nput of the crcut the output sgnal s now a superposton of the Qpont and the sgnal due to as shown on Fgure 6. V 1 I Q c I Q c V 0Q vo TH V I Q e V TH Fgure 6 Usng superposton, the voltage V s found by: 1. Set V TH = 0 and calculate the contrbuton due to ( V 1 ). In ths case the capactor 1 along wth resstor TH form a hgh pass flter and for a very hgh value of 1 the flter wll pass all values of and V 1 = 2. Set =0 and calculate the contrbuton due to ( ). In ths case the V And therefore superposton gves VTH V 2 2 = VT H V = V TH (1.4) /6.071 Sprng 2006, hanotaks and ory 4

5 The A equvalent crcut may now be obtaned by settng all D voltage sources to zero. The resultng crcut s shown on Fgure 7 (a) and (b). Net by consderng the A model of the JT (Fgure 8), the A equvalent crcut of the common emtter amplfer s shown on Fgure 9. c c o TH b v ce v be e vo TH b v ce v be v o e (b) (a) Fgure 7. A equvalent crcut of common emtter amplfer c β b b Fgure 8. A model of a npn JT (the T model) b c vo β b TH e Fgure 9. A equvalent crcut model of common emtter amplfer usng the npn JT A model /6.071 Sprng 2006, hanotaks and ory 5

6 The gan of the amplfer of the crcut on Fgure 9 s A v vo c β b β = = = = ( r ) (1 β) ( r ) β 1r e e b e e (1.5) For β >> 1 and re << the gan reduces to A v (1.6) Let s now consder the effect of remong the emtter resstor. Frst we see that the gan wll dramatcally ncrease snce n general s small (a few Ohms). Ths mght appear to be advantageous untl we realze the mportance of n generatng a stable Qpont. y elmnatng the Qpont s dependent solely on the small resstance whch fluctuates wth temperature resultng n an mprecse D operatng pont. It s possble wth a smple crcut modfcaton to address both of these ssues: ncrease the A gan of the amplfer by elmnatng n A and stablze the Qpont by ncorporatng when under D condtons. Ths soluton s mplemented by addng capactor 2 as shown on the crcut of Fgure 10. apactor 2 s called a bypass capactor. V 1 1 v o v 2 2 Fgure 10. ommonemtter amplfer wth bypass capactor 2 Under D condtons, capactor 2 acts as an open crcut and thus t does not affect the D analyss and behaor of the crcut. Under A condtons and for large values of 2, ts effectve resstance to A sgnals s neglgble and thus t presents a short to ground. Ths condton mples that the mpedance magntude of 2 s much less than the resstance for all frequences of nterest. 1 << (1.7) ω /6.071 Sprng 2006, hanotaks and ory 6

7 Input Impedance esdes the gan, the nput,, and the output, o, mpedance seen by the source and the load respectvely are the other two mportant parameters characterzng an amplfer. The general two port amplfer model s shown on Fgure 11. o v Av v o Fgure 11. General two port model of an amplfer For the common emtter amplfer the nput mpedance s calculated by calculatng the rato v = (1.8) Where the relevant parameters are shown on Fgure 12. c vo e /β β b TH e Fgure /6.071 Sprng 2006, hanotaks and ory 7

8 The nput resstance s gven by the parallel combnaton of TH and the resstance seen at the base of the JT whch s equal to (1 β )( r ) e = //(1 β )( r ) (1.9) TH e Output Impedance It s tral to see that the output mpedance of the amplfer s o = (1.10) /6.071 Sprng 2006, hanotaks and ory 8

9 ommon ollector Amplfer: (mtter Follower) The common collector amplfer crcut s shown on Fgure 13. Here the output s taken at the emtter node and t s measured between t and ground. V 1 1 v 2 v o Fgure 13. mtter Follower amplfer crcut verythng n ths crcut s the same as the one we used n the analyss of the common emtter amplfer (Fgure 1) ecept that n ths case the output s sampled at the emtter. The D Qpont analyss s the same as developed for the common emtter confguraton. The A model s shown on Fgure 14. The output voltage s gven by vo = r e And the gan becomes (1.11) A v v v r o = = e 1 (1.12) c β b b TH e v o Fgure /6.071 Sprng 2006, hanotaks and ory 9

10 The mportance of ths confguraton s not the tral voltage gan result obtaned above but rather the nput mpedance characterstcs of the dece. The mpedance lookng at the base of the transstor s = (1 β )( r ) (1.13) b e And the nput mpedance seen by the source s agan the parallel combnaton of b TH and = //(1 β )( r ) (1.14) TH e The output mpedance may also be calculated by consderng the crcut shown on Fgure 15. c b A β b TH loop v Fgure 15 We have smplfed the analyss by remong the emtter resstor n the crcut of Fgure 15. So frst we wll calculate the mpedance seen by and then the total output resstance wll be the parallel combnaton of and. s gven by KL at the node A gves And KVL around the loop gves v = (1.15) (1 ) = b β (1.16) b TH r e v = 0 (1.17) And by combnng quatons (1.15), (1.16) and (1.17) becomes /6.071 Sprng 2006, hanotaks and ory 10

11 v TH = = re β 1 (1.18) The total output mpedance seen across resstor s TH o = TH // re β 1 (1.19) /6.071 Sprng 2006, hanotaks and ory 11

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