I. Common Base / Common Gate Amplifiers - Current Buffer A. Introduction • A current buffer takes the input current which may have a relatively small Norton resistance and replicates it at the output port, which has a high output resistance • Input signal is applied to the emitter, output is taken from the collector • Current gain is about unity • Input resistance is low • Output resistance is high. V+ V+ i SUP ISUP iOUT IOUT RL R is S IBIAS IBIAS V− V− (a) (b) B. Biasing = /α ≈ • IBIAS ISUP ISUP EECS 6.012 Spring 1998 Lecture 19 II. Small Signal Two Port Parameters A. Common Base Current Gain Ai • Small-signal circuit; apply test current and measure the short circuit output current ib iout + = β v r gmv oib r − o ve roc it • Analysis -- see Chapter 8, pp. 507-509. • Result: –β ---------------o ≅ Ai = β – 1 1 + o • Intuition: iout = ic = (- ie- ib ) = -it - ib and ib is small EECS 6.012 Spring 1998 Lecture 19 B. Common Base Input Resistance Ri • Apply test current, with load resistor RL present at the output + v r gmv r − o roc RL + vt i − t • See pages 509-510 and note that the transconductance generator dominates which yields 1 Ri = ------ gm µ • A typical transconductance is around 4 mS, with IC = 100 A • Typical input resistance is 250 Ω -- very small, as desired for a current amplifier • Ri can be designed arbitrarily small, at the price of current (power dissipation) EECS 6.012 Spring 1998 Lecture 19 C. Common-Base Output Resistance Ro • Apply test current with source resistance of input current source in place • Note roc as is in parallel with rest of circuit g v m ro + vt it r − oc − v r RS + • Analysis is on pp. 510-511 of Chapter 8, with the final result boiling down to: R ≈r ||r 1 +g r ||R out oc o mπ s • If the RS is much greater than rπ, then the output resistance is approximately: []β Rout =roc oro • Rout is limited to the small-signal resistance of the current source EECS 6.012 Spring 1998 Lecture 19 D. Common-Base Two-Port Model • The output resistance depends on the source resistance -- which means that the CB current buffer is not unilateral • The two-port formal model is not strictly valid • Error in using the model is small • Conceptual simplification for design is huge iin iout 1 − iin roc ro[1 + gm(r RS)] gm • Input resistance << CE Amplifier • Output resistance >> CE Amplifier EECS 6.012 Spring 1998 Lecture 19 III. Common-Gate Amplifier A. Circuit Configuration + V + V iSUP ISUP I iOUT OUT V − V − RL i RS I s BIAS IBIAS − V − V (a) (b) • It is sometimes possible to tie the backgate to the source which shorts the backgate transconductance generator in small signal model • It is obvious that the current gain for this amplifier must be unity, since the gate current for a MOSFET is zero • The circuit analysis leading to the two port model is very similar to the CB amplifier -- see pp. 513 - 518 of the text. EECS 6.012 Spring 1998 Lecture 19 B. Common-Gate Two-Port Model • The resulting two port model is shown below: iin iout 1 − iin roc (ro + gmroRS) gm + gmb • The input resistance is the same as for the CB for the case where source and backgate are shorted. • When this isn’t the case, the backgate generator is added in (which helps!): 1 1 Ri =or------ Ri= ----------------------- gm gm+ gmb • Ri can be designed to be arbitrarily small, at the price of area, by increasing (W/L) or current • The output resistance is similar to the CB result with rπ --> infinity R = r r + g r R o oc o m o S EECS 6.012 Spring 1998 Lecture 19 IV. Common Collector/Drain Amplifier - Voltage Buffer A. Introduction • A voltage buffer takes the input voltage which may have a relatively large Thevenin resistance and replicates the voltage at the output port, which has a low output reisistance • Input signal is applied to the base/gate, output is taken from the emitter/source • Voltage gain is about unity • Input resistance is high • Output resistance is low V + V + RS + vs + − + + VBIAS − + VOUT V vOUT BIAS RL I − − iSUP SUP − V − V − B. Biasing = • Set VOUT to “halfway” between power rails-->VBIAS -VBE VOUT I kT SUP V = ------ ln -------------- BE q I S ≈ • Output voltage maximum VCC /2 -VCE(sat) VCC /2 - 0.2 V • Output voltage minumum set by voltage requirement across ISUP EECS 6.012 Spring 1998 Lecture 19 V. Small-Signal Two Port Parameters A. Common Colletor small-signal model and procedure for finding Av + g v v r m ro + v − t − + r oc vout − • Circuit analysis: current through roc || ro is vπ / rπ + gmvπ --> v – v v t out ()out -------------------- +g m v t – v out = ----------------- rπ roc ro β • Multiplying by rπ and recognizing that gm rπ = ο, v β ()()β()out v t – v out +1o vt – vout ==+ovt– vout ----------------- r π roc ro • Solving for the open-circuit voltage gain: 1≈ Av= ------------------------------------------------- 1 rπ 1+ ---------------------------------------()β - roc ro o + 1 EECS 6.012 Spring 1998 Lecture 19 B. Common-Collector Input Resistance Ri • Procedure: apply pure test source, leave load resistor RL ib β i + r o b it vt − ro roc RL β • Note that current through roc || ro ||RL is it + o it --> R = r + ()β + 1 rr R in π o oc o L C. Common Collector Output Resistance • Apply pure test current source at the output, leaving source resistance attached + v r g m v − R S it ro roc + v t − 1 R R ≈ ------ + ------S out β gm o EECS 6.012 Spring 1998 Lecture 19 D. Common Collector Two-Port Model • Good voltage buffer • Non unilateral network / + /β 1 gm RS o + + + v r + β (r r R ) v v in o o oc S − in out − − E. Common Drain Amplifier V+ V+ RS + v s − + + + VBIAS V + − OUT V vOUT RL I − BIAS − iSUP SUP − V − V− • Analysis: much the same as for CC amplifier • If VSB isn’t zero, then the voltage gain is degraded from about 1 to 0.8-0.9 EECS 6.012 Spring 1998 Lecture 19 F. Common Drain Amplifier Two-Port Model 1 + (gm gmb) + + + gm vin + v vout − (gm gmb) in − − ≈ ≈ • If VSB = 0, then the voltage gain is Av 1 and Ro 1 / gm • The CD amplifier is a reasonable voltage buffer • Improve output resistance by increasing gm • Input loading is a non-issue, since the gate is open-circuited for MOSFETs. EECS 6.012 Spring 1998 Lecture 19 VI. Summary A. Single-Stage Building Blocks Table 1: Simplified Two-Port Parameters Amplifier Type Controlled Source Input Resistance Ri Output Resistance Ro Common Gm = gm rπ ro || roc Emitter Common Gm = gm infinity ro || roc Source Common Ai = -1 1 / gm roc ||ro [1+gm(rπ||RS) ] Base 1 / gm if vsb = 0, roc || (ro + gmroRS ), if vsb=0 Common Ai = -1 -otherwise- Gate 1 / (gm + gmb) -otherwise- roc ||[ro+(gm+gmb)roRS] β β Common Av = 1 rπ + ο (ro || roc|| RL) (1 / gm ) + RS / ο Collector Common Av = 1 if vsb = 0, 1 / gm if vsb = 0, Drain -otherwise- infinity -otherwise- gm / (gm + gmb) 1 / (gm + gmb) EECS 6.012 Spring 1998 Lecture 19 B. Ultra Simplified Two-Port Parameters • gmb = 0, common base used as a current buffer --> RS >> rπ Table 2: Ultra Simplified Two-Port Parameters Amplifier Type Controlled Source Input Resistance Ri Output Resistance Ro Common Gm = gm rπ ro || roc Emitter Common Gm = gm infinity ro || roc Source β Common Ai = -1 1 / gm roc || ( οro) Base Common Ai = -1 1 / gm roc ||(gm RS ro) Gate β β Common Av = 1 rπ + ο (ro || roc|| RL) (1 / gm ) + RS / ο Collector Common Av = 1 infinity 1 / gm Drain • This table is adequate for first-cut hand design EECS 6.012 Spring 1998 Lecture 19.