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Page2 The power supply oltage V = +5 olts and the load resstor R = 1 k. For the range of collector bas currents, I = 0.5 ma, 1 ma, 2.5 ma, 4 ma and 4.5 ma, determne the correspondng collector-to-emtter oltages V E and oltage gans A for each of the collector currents. Place answers n the table below. For I = 0.5 ma, we caculate I R 0.5 A 19.23 VT 0.026 V V I R 5.0 0.5 4.5 V E Ths calculaton s repeated now for each current I. V V I (ma) V E (olts) A (V/V) 0.5 ma 4.5 V - 19.2 V/V 1 ma 4.0 V - 38.5 V/V 2.5 ma 2.5 V - 96.2 V/V 4 ma 1.0 V - 153.8 V/V 4.5 ma 0.5 V - 177.1 V/V Problem 3 Bpolar Transstor Operaton (10 ponts) The essence of transstor operaton s that for change n be, represent t by be, results n a change n collector current c, represented by c. The small-sgnal approxmaton means keepng be small enough to allow c to be lnearly related to be by the relatonshp, c = g m be. The parameter g m s the transconductance of
Page3 the transstor. When passng c through resstor R, a chanage n output oltage o s generated. (a) Usng the expresson, A = - [I /V T ]R, where V T s the thermal oltage kt/q = 0.026 olt (not MOSFET threshold oltage), dere a smple expresson for transconductance g m. A I R VT We also know R out A g R m BE Therefore, g m I BE / V T (b) alculate the alue of g m when I = 0.5 ma. 0.5 For I = 0.5 ma, we calculate g 19.3 ma m 0.026 V Problem 4 Usng Grahcal Analyss (20 ponts) You are presented wth the NPN bpolar transstor crcut shown below: In ths problem you are to construct a graphcal drawng of the E characterstc of the BJT, wth base current alues of B = 10 A, 20 A, 30 A, 40 A and 50 A, to estmate amplfer parameters. To smplfy the problem we gnore the Early effect ; meanng the output resstance s nfnte (.e., horzontal lnes on the E characterstc) and take the BJT s current gan = 100 at all current leels. Gen: V = +5 olts and R = 1 k; these two parameters allow you to construct and draw the load lne upon the BJT s E characterstc cure.
Page4 (a) Draw the collector current lnes on the graph and then draw the load lne establshed by the collector load resstor R. (b) Estmate the peak-to-peak collector oltage swng resultng from drng the base current B oer the range of 10 A (mnmum) to 40 A (maxmum). Use the drawng aboe to estmate ths peak-to-peak oltage swng. Peak-to-peak swng = 4 olts 1 olt = 3 olts (c) Assumng the BJT based at V E = ½V, fnd the alues of I and I B at ths Q-pont (.e., Q s the quesent bas pont). The best bas pont Q s mdway between the total oltage range of (that would oltage V. Thus, V E = ½ V correspondng to V E = 2.5 olts. From the aboe plot pont Q corresponds to I = 2.5 ma. Base current I B = 2.5 ma/ = 2.5 ma/100 = 25 A. (d) Assumng the currrent alue at bas pont Q from part (c), gen that V BE = 0.700 olt and R B = 100 k, fnd the requred alue of power supply V BB. V BB = I B R B + 0.700 = (0.000025)(100,000) + 0.7 = 2.5 + 0.7 = 3.2 olts
Yes, they agree. Page5
Page6 Problem 6 Usng the T-equalent Model (20 ponts) For the NMOS transtor embedded wthn the schematc crcut, you are to use the T- equalent model (but assume that = 0 whch means that the output resstance s nfnte and can be gnored) to dere equatons for ts small-sgnal oltage gan behaor. (a) Draw the crcut wth the T-equalent model substtuted for the MOSFET symbol and n the format to be used for performng a small-sgnal analyss. Label all elements. (b) Dere a oltage gan expresson for s /.
Page7 1 gm gs RS gm g R and d m gs D g R s m gs S, s RS gmrs 1 1 gmrs RS gm Note ( / ) s non-nertng and less than unty. s (c) Dere a oltage gan expresson for d /. 1 gm gs RS gm g R d m gs D, d RD gmrd 1 1 gmrs RS gm Note ( / ) s nertng and often greater than unty d (dependng upon the alue of R ). D