Simple way of teaching transistor amplifiers

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1 ession 793 iple way of teaching tansisto aplifies ogdan M. Wilaowski Uniesity of Wyoing bstact Fo sall signal analysis a siple change fo coonly used tanconductance g to tansesistance /g leads to a significant siplification of all equations. Moeoe these equations ae uch easie to eoize since they hae a fo of esisto atio fo () and () configuations and the fo o esisto diide fo () configuation. With pesented appoach ost of students ae able to ead diagas and to undestand the effect of each eleent change on the cicuit pefoance. tudents ae not lost with essy equations, but they ae in contol of thei design and they know which paaetes they hae to change in ode to change behaioal chaacteistics.. ntoduction tudents usually hae significant difficulties in eoizing all the equations fo calculation of gain, input and put esistances fo tansisto aplifies [][][3][4]. They do elatiely well if a coon souce (eitte) is used, but they ae lost when othe configuations ae consideed. n the pape, a siple way fo analysis of tansisto aplifies is intoduced. t fist, appoxiate and accuate ethods fo cicuit biasing ae discussed including both JT and FT aplifies. ll tansisto cicuit analysis should be always pefoed in the following ode:. iasing point calculation. alculation of sall signal paaetes 3. ain, input and put esistance calculation This pape is also oganized in that way. i V X V - - X R. iasing calculation Fig. iasing calculation fo FT tansisto with seies of esisto R alculation of the biasing point fo bipola tansisto cicuits ae elatiely staightfowad and usually students do not hae a poble with that. f it would be possible one should

2 ecoended using a siplified appoach instead of using the full Theenin equialent cicuit. n the case of MO cicuits it is usually elatiely easy to figue all tansisto cuents. Thee is, howee one difficult exception in the MO cicuity. This is the case fo JFTs and MO tansistos, shown in Fig., whee a esisto is connected with the seies in the souce. Usually to find a biasing point a quadatic equation should be soled. t is howee uch easie to use the following appoach. Fo n-channel FT tansisto V [ R ( VX ) ] VTH R. () Fo n-channel FT tansisto V [ R ( VX ) ] VTH R () and the dain cuent is ( ) V (3) whee is tansconductance paaete, V TH is theshold oltage. The diect foula fo dain cuent is VX [ ± R ( VX ) ] R ± (4) R whee the inus sign should be used fo p-channel deices. xaple The cicuit of Fig. has V X V, R 0kΩ, V TH 0.8V, and 0.5/V. Find the tansisto cuent. olution R 5V Fo () V R R ( V V ) and fo (3) 0.5 V [ ] V [ 5( 0.8) ] 0.8. V X TH TH 5 5 ( ) ( ). all signal tansisto paaetes The usage of h paaetes is quite coon fo descibing the sall signal odel of tansistos. Unfotunately these paaetes confuse students. n the case of bipola tansisto only thee g, o, and β but not fou h paaetes ae needed. ince β changes ab % pe

3 o and thee is lage β spead between eleents the acceptable assuption is that β β and this leads to futhe siplification. The sall signal equialent odel of bipola tansisto is shown in Fig. and 3. n the pesented appoach sall signal odel of Fig. 3 will be used. i β i β o o - Fig.. all signal equialent odel of bipola tansisto. Fo sall signal analysis. assuing β β i o β Fig. 3. all signal equialent odel of bipola tansisto used in analysis. all signal paaetes fo bipola tansisto ae: h VT V V V, o, β h, and β g h h 0 (5) kt whee theal potential V T 5V and aly oltage V 50 00V q When substate effects ae neglected MO linea odel is descibed only by two paaetes g and o.quialent diagas of FT tansistos ae shown in Fig. 4 and 5. n the pesented appoach sall signal odel of Fig. 5 will be used. all signal paaetes fo FTs ae: V V V V V o λ (6) g (V V ) λ TH g - Fig. 4. all signal equialent odel of MO tansisto. Fo sall signal analysis o.

4 i o Fig. 5. all signal equialent odel of MO tansisto used in analysis. V. ain calculation Thee ae thee basic cicuit configuations fo single tansisto aplifie. Lage cicuits can be alost always consideed as a coposition of these single-tansisto aplifies. xaple 3 in the end of this pesentation illustates this type of appoach. Fo bipola tansistos thee ae coon collecto, coon eitte, and coon base configuations. Fo FTs thee ae coon dain, coon souce, and coon gate configuations. iagas fo all thee FT configuations ae shown in Fig. 6. R R R i o i o i o U U R R R U (a) (b) (c) Fig. 6. asic configuations of single tansisto aplifies with idealized tansisto odels: (a) coon dain (oltage followe), (b) coon souce, and (c) coon gate. n the case of the coon dain configuation shown in Fig. 6(a), the oltage gain can be found by inspecting the diaga and using esisto diide foula. Fo and o >> R R o oltage gain (7) R R R The input esistance is in and put esistance is R R

5 n the case of the coon souce configuation shown in Fig. 6(b) also we hae to note that the sall signal oltage on x node follows the gate oltage. Fo and o >> the dain cuent is: i R (8) and fo the ohs law the put oltage is: R R ir and the oltage gain R R (9) The inus sign in equation aboe coes fo the diffeent diections (in espect to gound) of cuents though esisto and R. The input esistance is and put esistance is R. Note that the esistance of idealized tansisto seen fo the dain side is equal to infinity and the esistance seen fo the souce side is equal to zeo. n the case of the coon gate configuation shown in Fig. 6(c) 0, assuing that the input oltage souce is ideal (has no seies esistance) the sall signal dain cuent is: in in i (0) and fo the ohs law the put oltage is: R R ir in and the oltage gain () in Thee is no inus sign in aboe equation because the sall signal cuent though is excited fo a diffeent diection. The input esistance is in R and put esistance is R. The pesented aboe appoach with idealized tansistos allows us a fast calculation of basic paaetes of tansisto aplifies. This siplified appoach is good enough fo students to undestand how each cicuit paaete affects the cicuits pefoance. They lean if the alue of esistance should incease o decease to obtain equied paaetes. in xaple Find oltage gain, input and put esistance fo the aplifie with PMO tansisto shown in the Fig 7, and in this poble do not ignoe o. ssue that 00 µ/v, λ0.03v -, 0µ, R MΩ, R 5MΩ, R 0.3MΩ, V R U R R Fig. 6. icuit of xaple

6 olution The sall signal paaetes o and of the PMO tansisto ust be found at fist. Using (6) 5.8k o 3.33 M g λ The sall signal diaga of the cicuit using equialent PMO odel with idealized is shown in Fig. 8. Note that both diagas on Fig. 8(a) and Fig. 8(b) ae identical, soehow dawn diffeently. n expeienced student can use the diaga fo Fig. 8(a), while a less expeienced one has to edaw the diaga to the fo shown in Fig. 8(b) R U i i M o RXW URXW U i M i RXW U RXW R R R R R o (a) (b) Fig.8. all signal equialent diagas of cicuit of Fig. 7. y inspecting diagas on Fig. 8(a) o Fig. 8(b) one can find that: in i and fo the ohs law the put oltage is: R o ir o in and the oltage gain: R o 0.3MΩ 3.33M 7.4 in 5.8k The input esistance is in R R 0.83MΩ and put esistance is R o 75kΩ f both R and o ae included in the tansisto odel coputations ae usually oe coplicated than in the xaple. Let us conside a ey ipotant case shown in Fig. 9. The esistance (assuing in 0) is: o o R () ffectie tansconductance (assue 0)

7 R R g o R (3) i RXW i RXW URXW o i i 6 R R (a) (b) Fig. 9. oon souce configuations of single tansisto aplifie: (a) cicuit diaga and (b) equialent sall signal odel with idealized tansisto including o paaete xaple 3 Find Q-points and the diffeential-ode oltage gain of the opap of in Figue 0 if V V 7.5V, RF 50µ, n 5µ/V, V TN 0.75V, λ n 0.07V -, p 0µ/V, λ p 0.07V -, and V TP -0.75V. M0 0 M3 50 M4 0 M M M8 RF M M5 00 M V M6 0 M V ss Fig. 0 iple opeational aplifie

8 olution (a) Find the biasing cuents fist. y cicuit inspection one ay find that: 0.5; ; 0.5; 0.5; 0.5; µ Note that at this point effect of channel length odulation was ignoed. (b) Find sall signal tansisto paaetes. Using (6) one ay find that o W λ L Note that an appoxiate foula with V was used and the sall signal paaetes ae calculated only when equied. o o 35kΩ; o3 o4 35kΩ; o5 58.7kΩ; o 58.7kΩ; kω; kΩ; (c) ain calculation. Fo the diffeential stage thee ae two signal paths M,M3, M4 and M,M. n the fist path M can be consideed as configuation (9) and M3 and M4 as a cuent io o o ; n the second path thee ae two stages: M can be consideed as configuation (7) and M as configuation (). o o ; Using the concept of supeposition the total gain of the fist stage is 58 The gain of the second stage coposed of tansistos M5 and M is (9) o o The last stage coposed of M6 and M7 woks as a oltage followe and has gain 3. Fo accuate calculation a alue of load esistance ust be specified. The total gain is 3,439 V/V V. onclusion Fo sall signal analysis we usually hae to calculate input and put esistance and gain (seldo input o put conductance). Theefoe, it is oe natual to use instead of g. Note that with the pesented appoach (use instead of g ) the gain of aplifies is expessed as a atio of esistances instead of the coonly used foulas with g.

9 Fo the coon eitte/souce the gain is the atio of two esistances RL grl V instead of V R gr When tansisto is dien by souce with esistance R N than RL grl V instead of V RN RN R gr g β β Fo coon collecto/dain configuation would athe see a esisto diide R gr V instead of V R gr ll equations fo fequency esponses sees to be oe coplicated if g is used instead With this appoach students ae able to find the pope solution fo basic single stage aplifies within a couple of inutes [5][6]. Fo exaple, ost of the ae able to analyze 0 diffeent cicuits duing a 50 inute exa. The descibed ethod has an een oe significant adantage duing the design of analog integated cicuits such as OPMP. Moe ipotantly the students ae able to ead diagas and to undestand the effect of each eleent change on the cicuit pefoance. tudents ae not lost with essy equations, but they ae in contol of thei design and they know which paaetes they hae to change in ode to change behaioal chaacteistics. With liited space of this pesentation only MO exaples wee used, but cicuits with bipola tansistos can be analyzed in a siila way. ibliogaphy. Jaege, R, Micoelectonic icuit esign, Mcaw Hill 997. eda.. and.. ith, Micoelectonic icuits, Oxfod Uniesity Pess 998, 4-th edition. 3. Johns.. and. Matin, nalog ntegated icuit esign, JohnWiley & ons Neaen. lectonic icuit nalysis and esign, win ON M. WLMOW ogdan M. Wilaowski ( Fellow) he is a Pofesso of lectical ngineeing at the Uniesity of Wyoing. He is the teasue of ndustial lectonics ociety, a ebe of the Neual Netwok ouncil, an associate edito of Tans. on Neual Netwoks and Tans. on ducation.. Wilaowski is the autho of 4 textbooks, oe than 00 efeeed publications, and 7 patents. He eceied his M in copute engineeing in 966, Ph in neual coputing in 970, and.c. in integated cicuit design in 977, all fo the Technical Uniesity of dansk, Poland.