Università degli Studi di Roma Tor Vergata Dipartimento di Ingegneria Elettronica Analogue Electronics Paolo olantonio A.A. 2015-16
ias issues The D bias point is affected by thermal issue due to the active device parameter variations with temperature oth I O and V E vary with the temperature, thus resulting in a variation of I 2 26
ias issues To reduce thermal issue, a feedback solution could be adopted V R 1 R I 1 I + v i - R 2 R E I E If the bias current I is increasing, then the voltage drop across R E is increasing also onsequently the base emitter voltage V E is decreasing Accounting for the device input characteristics, the base current I will be reduced Thus the device output current (I =H FE I ) will be reduced However, as we will see later, the resistor R E will reduce the A gain, therefore typically it is short circuited by a parallel capacitance 3 26
Thermal compensationtechniques y adding in the circuit some element that is bias dependent, thus able to reproduce the same variation of V E, I 0 (and b), it is possible to compensate the I variation ompensation of I 0 I 0 is the diode reverse saturated current V R 1 R I Assuming I V >>V E >>1 + I 0 VE I E - 4 26
Thermal compensationtechniques In the integrated implementation, since the resistor RE requires a by pass capacitance to allow higher gain, and this capacitance could be very high, a different approach is adopted ompensation in integrated circuits V The transistor Q 1 resembles a diode, being V E1 =V E1 Its collector current I 1 is given by: R 1 R I I 2 v i I 1 I 2 Q 2 v o Assuming V >>V E1 and (I 1 +I 2 )<<I 1 I 1 V E2 Q 1 V E1 If the two transistors are similar, accounting for V E1 =V E2 and R 1 =R, then the bias current I 2 is constant 5 26
Thermal compensationtechniques ompensation in integrated circuits The addiction of the two resistors R 2 er 3 improves the circuit behavior In this case, in fact, are the biasing currents I 1 and I 2,insteadofV E1 and V E2,tocontrol the D behavior of Q 1 and Q 2 V If R 2 =R 3 then R 1 I v i I 2 R I I R 3 v o R 2 =R 3 I 1 V E2 Q 2 y a suitable selection of parameter, and accounting that Q 1 =Q 2, it is possible to obtain Q 1 V E1 Moreover, selecting R =1/2R 1 then 6 26
JT equivalent A model Assuming a generic two port a representation is made by assuming some electrical quantities as independent variables, while the remaining ones are dependent R g i 1 i 2 v g v 1 v 2 In particular, starting from the set of equation y a series expansion around the quiescent bias point (i.e. Taylor or McLaurin ) 7 26
If a first order approximation is considered JT equivalent A model Defining An hybrid representation can be obtained 8 26
JT equivalent A model In particular, referring to the ommon Emitter configuration R g i 1 i 2 v g v 1 v 2 Input resistance with the output short circuited (ohms). Voltage gain 1 with the input open (dimensionless). Forward current gain with the output short circuited (dimensionless). Output conductance with the input open (ohms 1 ) 9 26
The hybrid model The previous equation can be represented by an equivalent circuit model (hybrid model) 10 26
Physical meaning of model parameters orrente di base I,mA 0.6 0.4 V 1 V I V 2 V V V I V I V cos t cos t = V 2 -V1 ollector current I, ma 40 30 20 10 I =200μA 160 120 80 40 I V I I I V cos t cos t 0.2 0 2 4 8 6 10 12 0 0.4 0.6 0.8 ollector-emitter voltage V E, V ase voltage V E,V Typical values: h fe n 10 n 100 h re 10-3 10-4 h ie 10 3 10 4 Ω h oe 10-5 10-4 11 26
Simplified model Accounting for the h parameter values, the model can be further simplified, assuming: Accounting for the diode behavior of the base emitter junction, it is possible to define: Thus obtaining the following model (similar to FET): 12 26
Amplifier configuration The basic amplifier configuration are named according to the JT pin that is common to both input and output networks ommon Emitter (E) ommon ollector () + i i R S R L R S + v s i v E E v ce V + i v s v E E R L V o V V - ommon ase () R S E i R i R o + v s v i =v E v =v o R L V 13 26
Analysis Approaches For each configuration, the equivalent hybrid model can be used, by assuming for the [h] parameters the corresponding values, i.e. the second letter of the subscript represent the device configuration ommon Emitter (E) h ie,h fe,h re,h oe ommon ollector () h ic,h fc,h rc,h oc R s [h je ] R s [h jc ] E v s + R L v s + R L E R s ommon ase () h ib,h fb,h rb,h ob E v s + [h jb ] R L With this appraoch the [h] parameters assume different values, but the amplifier relationships (voltage gain, input and output resistance) have the same form 14 26
Analysis Approaches A different approach is based on the adoption of the same JT equivalent model (i.e. E [h] parameters h xe ) In this case the expressions are different ommon Emitter (E) ommon ollector () R s R s v s + E R L v s + E R L ommon ase () R s v s + E R L 15 26
Analysis Approaches v s R s 1 1' I 1 I 2 2 R s I L Two-port active network (transistor) V 1 V 2 2' Z L v s I 1 1 h I i 2 2 I L h f I 1 h o V 1 V 2 Z L 1' + hrv2 2' Z i Y 0 Z i Y 0 h Approximate conversion formulas for hybrid parameters h ic h ie h rc 1 1 h oc hoe fc h fe h h ib ob h ie 1 h fe hoe 1 h fe hie hoe h rb h 1 hfe hfe h fb 1 h 16 26 fe re
D analysis of a simple amplifier onsider the following circuit from which we want determine the quiescent collector current and the quiescent output voltage, given that the h FE of the transistor is 100 The base emitter voltage V E is approximately 0.7V 17 26
ommon Emitter Amplifier Small signal equivalent circuit 18 26
ommon ollector Amplifier Small signal equivalent circuit 19 26
ommon ase Amplifier Small signal equivalent circuit 20 26
Phase Splitter Small signal equivalent circuit If R E =R,thenA V,1 = A V,2 The output resistances are different!!! 21 26
Summary Out,2 E E (with R E ) A V -h fe R L /h ie 1 h fe R L /h ie - h fe R /[h ie +(1+h fe )R E ] Out,1 (with R ) (1+h fe )R E /[h ie +(1+h fe )R E ] R in h ie h ie +(1+h fe )R L h ie /(1+h fe ) h ie +(1+h fe )R E h ie +(1+h fe )R E R out h ie /(1+h fe ) h ie /(1+h fe ) A I -h fe 1+h fe 1 -h fe R /R E 1+h fe 22 26
The use of feedback resistor As we have seen the use of resistor RE in the E amplifier is useful to stabilize the device operating point. It is also useful to stabilize the gain behaviour, resulting in: With feedback, the voltage gain is fixed by the resistive components, that are two stable and well defined passive components. Without the feedback the gain is h fe R L /h ie, thus varying with the transistor s operating condition and its variability (for h ie and h fe ) 23 26
Use of a decoupling capacitor However, the use of RE drastically reduces the amplifier voltage gain Thus it is quite common to remove the A feedback by using a decoupling capacitor 24 26
Use of a decoupling capacitor The adoption of decoupling capacitor change the frequency response of amplifiers E without feedback E with feedback E with R E and decoupling capacitor 25 26
Use of split emitter resistors The total emitter resistance R E1 +R E2 can be tailored to suit the biasing requirements of the circuit Only part of this resistance can be decoupled (R E2 ) to produce the required small signal performance ( R /R E1 ) 26 26