# EE 330 Lecture 25. Amplifier Biasing (precursor) Two-Port Amplifier Model

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1 EE 330 Lecture 25 Amplifier Biasing (precursor) Two-Port Amplifier Model

2 Amplifier Biasing (precursor) V CC R 1 V out V in B C E V EE Not convenient to have multiple dc power supplies Q very sensitive to V EE

3 Amplifier Biasing (precursor) V CC R 1 R B =500K R 1 =2K V out V out V in B C E V in C 1 =1uF B C E V EE Not convenient to have multiple dc power supplies Q very sensitive to V EE Compare the small-signal equivalent circuits of these two structures

4 Amplifier Biasing (precursor) V CC R 1 V out R B =500K R 1 =2K V out V in B C E V in C 1 =1uF B C E V EE Compare the small-signal equivalent circuits of these two structures R 1 R 1 V IN V IN R B Since Thevenin equivalent circuit in red circle is V IN, both circuits have same voltage gain

5 Amplifier Characterization (an example) Determine Q, A V, R IN Determine and (t) if V IN =.002sin(400t) R B =500K R 1 =2K V out V in C 1 =1uF B C E In the following slides we will analyze this circuit

6 Amplifier Characterization (an example) Biasing Circuit R B =500K R 1 =2K C=1uF (biasing components: C, R B, V CC in this case, all disappear in small-signal gain circuit) Several different biasing circuits can be used

7 Amplifier Characterization (an example) Biasing Circuit R B =500K R 1 =2K C=1uF Determine Q and the SS voltage gain, assume β=100

8 Amplifier Characterization (an example) Determine Q R B =500K C=1uF R 1 =2K β=100 R B1 =500K 0.6V I B βi B Q R B1 =500K dc equivalent circuit 12V-0.6V I CQ = βi BQ = mA 500K V = 12V-I R =12V - 2.3mA 2K 7.4V OUTQ C I B simplified dc equivalent circuit

9 Amplifier Characterization (an example) Determine the SS voltage gain i B R B =500K R 1 =2K V IN R B g m V BE V BE g π R 1 C=1uF β=100 ss equivalent circuit V g V R OUT m BE 1 V IN R B ss equivalent circuit R 1 V A IN V BE R g V 1 m ICQR1 AV - Vt 2.3mA 2K AV mV This basic amplifier structure is widely used and repeated analysis serves no useful purpose Have seen this circuit before but will repeat for review purposes

10 Amplifier Characterization (an example) Determine R IN R B =500K R 1 =2K i IN i B C=1uF β=100 V IN R B g m V BE V BE g π R 1 R IN IN Rin V i IN V IN R B ss equivalent circuit R 1 Rin RB // r Usually R B >>r π Rin RB // r r R in r I CQ βv t

11 Examples Determine and (t) if V IN =.002sin(400t) R B =500K R 1 =2K V out V A V OUT V IN V 177 OUT.002sin(400 t ) 0.354sin(400 t ) V t V +A V OUT OUTQ V IN V in C 1 =1uF B C E V 7.4 V sin(400 t) OUT

12 Two-Port Representation of Amplifiers R B =500K R 1 =2K C=1uF R L R 1 V IN R B R L i B V IN R B g m V BE V BE g π R 1 R L Two-Port Network Two-port model representation of amplifiers useful for insight into operation and analysis Internal components to the two-port can be quite complicated but equivalent two-port model is quite simple

13 Two-port representation of amplifiers Amplifiers can be modeled as a two-port V 1 y 12 V 2 y 11 y 22 V 2 y 21 V 1 Amplifier often unilateral (signal propagates in only one direction: wlog y 12 =0) One terminal is often common V 1 y 11 y 22 V 2 y 21 V 1

14 Two-port representation of amplifiers V 1 y 11 y 22 V 2 y 21 V 1 Thevenin equivalent output port often more standard R IN, A V, and R OUT often used to characterize the two-port of amplifiers V 1 R OUT A V V 1 R IN V 2

15 Amplifier input impedance, output impedance and gain are usually of interest Example 1: Assume amplifier is unilateral R S Why? V IN Amplifier R L R S R OUT V IN V 1 A V V 1 R IN V 2 R L R L R V IN OUT RL RIN V OUT = A V V A IN VAMP = = A R L +ROUT R S +RIN VIN R L +ROUT R S +RIN Can get gain without recondsidering details about components internal to the Amplifier!!! Analysis more involved when not unilateral V

16 Amplifier input impedance, output impedance and gain are usually of interest Why? Example 2: Assume amplifiers are unilateral R S V IN Amplifier 1 Amplifier 2 Amplifier 3 R L R S R OUT1 R OUT2 R OUT3 V IN V 11 A V1 V 11 R IN1 V 21 V 12 A V2 V 12 R IN2 V 22 V 13 A V3 V 31 R IN3 V 23 R L R L RIN3 RIN2 RIN1 V = A A A V R L +ROUT3 R OUT2 +RIN3 R OUT1 +RIN2 R S +RIN1 OUT V3 V2 V1 IN V OUT RL RIN3 RIN2 RIN1 A VAMP = = AV3 AV2 AV1 VIN R L +ROUT3 R OUT2 +RIN3 R OUT1 +RIN2 R S +RIN1 Can get gain without recondsidering details about components internal to the Amplifier!!! Analysis more involved when not unilateral

17 Two-port representation of amplifiers Amplifier usually unilateral (signal propagates in only one direction: wlog y 12 =0) One terminal is often common Amplifier parameters often used I 1 I 2 R OUT V 1 y 11 y 22 V 2 y 21 V 1 y parameters R V IN 1 A V V 1 V 2 Two Port (Thevenin) Amplifier parameters Amplifier parameters can also be used if not unilateral One terminal is often common I 1 I 2 R IN R OUT V1 y 12 V 2 y 11 y 22 V 2 y 21 V 1 A V VR V 2 1 A V V 1 V 2 Two Port (Thevenin) y parameters Amplifier parameters

18 Determination of small-signal model parameters: y 12 V 2 y 11 y 22 V 2 y 21 V 1 I 1 I 2 R IN R OUT V1 V 1 V 2 A VR V 2 Two Port (Thevenin) A V V 1 In the past, we have determined small-signal model parameters from the nonlinear port characteristics V 1,V 2 V,V I f f V,V I 1 2 f y ij i 1 V j 2 V V Q Will now determine small-signal model parameters for two-port comprised of linear networks Results are identical but latter approach is often much easier

19 Two-Port Equivalents of Interconnected Two-ports Example: i 1 i 1A i 2A i 2 V 1A y 11A y 12A V 2A y 21A V 1A y 22A V 2A V 1 i 1B i 2B V 2 V 1B y 11B y 12B V 2B y 21B V 1B y 22B V 2B I 1 I 2 R IN R OUT A V VR V 2 1 A V V 1 V 2 Two Port (Thevenin) could obtain two-port in any form often obtain equivalent circuit w/o identifying independent variables Unilateral iff A VR =0 Thevenin-Norton transformations can be made on either or both ports

20 Two-Port Equivalents of Interconnected Two-ports Example: i 1 i 1A i 2A i 2 V 1A y 11A y 12A V 2A y 21A V 1A y 22A V 2A R XX I 1B I 2B V 1 R 1 V 1B V 2B R B g21bv2b g12bv1b g11b g22b V 2 Two Port (Norton) i 1C v 1C H-parameters (Hybrid Parameters) V h i h v 1C 11C 1C 12C 2C h 22 h i i1 v 2 21C C 2 C C C i 2C v 2C Linear Two Port I 1 I 2 R IN R OUT A V VR V 2 1 A V V 1 V 2 Two Port (Thevenin)

21 RB i1c v1c R1 H-parameters (Hybrid Parameters) V1 C h11 C i1 C h12 Cv2C i 2C h21 C i1 C h22 Cv 2C Linear Two Port i2c v2c I1B V1B g11b g21bv2b g12bv1b Two Port (Norton) RXX g22b I2B V2B Determination of two-port model parameters (One method will be discussed here) i1a y12av2a V1A y11a y21av1a y22a i2a V2A A method of obtaining R in V test i test i 1 V 1 R in i 2 A vrv2 R o A v0v1 V 2 Terminate the output in a short-circuit 1 AVR i1 V 1 + V2 Rin Rin AV0 1 i2 V1 V2 R0 R0 V i V V i test test R in V i test test

22 RB i1c v1c R1 H-parameters (Hybrid Parameters) V1 C h11 C i1 C h12 Cv2C i 2C h21 C i1 C h22 Cv 2C Linear Two Port i2c v2c I1B V1B g11b g21bv2b g12bv1b Two Port (Norton) RXX g22b I2B V2B Determination of two-port model parameters i1a V1A y11a y12av2a y21av1a y22a i2a V2A A method of obtaining A V0 V test i 1 V 1 R in i 2 A vrv2 R o A v0v1 V 2 V out-test Terminate the output in an open-circuit 1 AVR i1 V1 V2 Rin Rin AV0 1 i2 V1 V2 R0 R0 V V i V V test out-test A out-test V0 V V test

23 RB i1c v1c R1 H-parameters (Hybrid Parameters) V1 C h11 C i1 C h12 Cv2C i 2C h21 C i1 C h22 Cv 2C Linear Two Port i2c v2c I1B V1B g11b g21bv2b g12bv1b Two Port (Norton) RXX g22b I2B V2B i1a i2a V1A y11a y22a V2A Determination of two-port model parameters y12av2a y21av1a A method of obtaining R 0 i 1 V 1 R in R o A vrv2 A v0v1 V 2 i 2 i test V test Terminate the input in a short-circuit 1 AVR i1 V1 V2 Rin Rin AV0 1 i2 V1 V2 R0 R0 V1 0 R 0 V i test test

24 RB i1c v1c R1 H-parameters (Hybrid Parameters) V1 C h11 C i1 C h12 Cv2C i 2C h21 C i1 C h22 Cv 2C Linear Two Port i2c v2c I1B V1B g11b g21bv2b g12bv1b Two Port (Norton) RXX g22b I2B V2B Determination of two-port model parameters i1a i2a A method of obtaining A VR V1A y11a y12av2a y21av1a y22a V2A V out-test i 1 V 1 R in i 2 A vrv2 R o A v0v V 2 1 V test Terminate the input in an open-circuit 1 AVR i1 V1 V2 Rin Rin AV0 1 i2 V1 V2 R0 R0 i1 0 A out-test VR V V test

25 Determination of Amplifier Two-Port Parameters Input and output parameters are obtained in exactly the same way, only distinction is in the notation used for the ports. Methods given for obtaining amplifier parameters R in, R OUT and A V for unilateral networks are a special case of the non-unilateral analysis by observing that A VR =0. In some cases, other methods for obtaining the amplifier paramaters are easier than what was just discussed

26 Examples Biasing Circuit R B1 =50K C=1uF R B2 =10K R 1 =0.5K Determine Q and the SS voltage gain (A V ), assume β=100 (A V is one of the small-signal model parameters for this circuit)

27 Examples R B1 =50K R B1 =50K C=1uF C=1uF R B2 =10K R 1 =0.5K R B2 =10K R 1 =0.5K V IN R B 10K//50K R 1 0.5K R 2 2K Determine Q and the SS voltage gain (A V ), assume β=100 (A V is one of the small-signal model parameters for this circuit)

28 Examples Determine Q R B1 =50K I BB Q R B1 =50K C=1uF V B R B2 =10K I BB I B R 1 =0.5K β=100 V B 0.6V R B2 =10K R 1 =0.5K I B βi B dc equivalent circuit This circuit is most practical when I B <<I BB With this assumption, R B1 =50K V B R B2 =10K I Q BB I B simplified R 1 =0.5K dc equivalent circuit RB2 V B = R B1+R B2 12V V -0.6V 1.4V B I CQ = I EQ = = = 2.8mA R 1.5K OUTQ C V =12V-I R = 6.4V Note: This Q-point is nearly independent of the characteristics of the nonlinear BJT!

29 Examples Determine SS voltage gain R B1 =50K i B R 1 =0.5K C=1uF V B R B2 =10K I BB I B R 1 =0.5K β=100 i B V BE g π R B =10K//50K g m V BE 8.3K R 1 =0.5K This voltage gain is nearly independent of the characteristics of the nonlinear BJT! This is a fundamentally different amplifier structure It can be shown that this is slightly non-unilateral A V V V g V R OUT m BE 2 V V R V g +g IN BE 1 BE m R2gm VBE R2gm R g +g R g +g V 1 BE 1 BE m 1 m A V R g R g R R 2 m 2 1 m 1

30 Examples Biasing Circuit R B1 =50K C 1 =1uF R B2 =10K R 1 =0.5K C 2 =100uF Determine Q, R IN, R OUT,and the SS voltage gain, and A VR assume β=100

31 Examples R B1 =50K C 1 =1uF R B1 =50K C 1 =1uF R B2 =10K R 1 =0.5K C 2 =100uF V IN R B2 =10K R 1 C 2 0.5K 100uF R IN R OUT V IN A VR V 2 R 1 A V V 1 0.5K Two Port (Thevenin) Determine Q, R IN, R OUT,and the SS voltage gain, and A VR ; assume β=100 (A V, R IN, R OUT, and A VR are the small-signal model parameters for this circuit)

32 Examples Determine Q R B1 =50K This is the same as the previous circuit! C 1 =1uF V OUTQ = 6.4V R B2 =10K R 1 =0.5K C 2 =100uF 5.6V I CQ = 2.8mA 2K R B1 =50K I BB Q V B R B2 =10K I B R 1 =0.5K Note: This Q-point is nearly independent of the characteristics of the nonlinear BJT! The dc equivalent circuit

33 Examples Determine the SS voltage gain This is the same as the previous-previous circuit! R B1 =50K C 1 =1uF R B2 =10K R 1 =0.5K C 2 =100uF A -g R V m 2 I A - V R CQ 2 V t V IN R B1 //R B2 R 2 5.6V AV mV The SS equivalent circuit Note: This Gain is nearly independent of the characteristics of the nonlinear BJT!

34 Examples R B1 =50K C 1 =1uF R B2 =10K R 1 =0.5K Determination of R IN β=100 C 2 =100uF The SS equivalent circuit R B1 //R B2 R 2 V IN i IN i b i c V IN V be g π g m V be g o V ce R 2 R B1 //R B2 R R //R //r r IN B1 B2 π π -1 1 I CQ 2.8mA r π = 928 βvt mV RIN R B1//R B2 //rπ rπ 930

35 Examples Determination of R OUT R B1 =50K The SS equivalent circuit R B1 //R B2 C 1 =1uF R B2 =10K R 1 =0.5K β=100 C 2 =100uF V IN R 2 i b i c i TEST V be g π g m V be g o V ce R 2 V TEST R B1 //R B2 R TEST OUT =R 2//ro V i TEST 1 1 ICQ 2.8mA 1 ro 1.4E-5 71K VAF 200V R R //r R 2K OUT 2 o 2

36 Examples Determine A VR The SS equivalent circuit R B1 =50K R B1 //R B2 C 1 =1uF R B2 =10K R 1 =0.5K β=100 C 2 =100uF V IN R 2 i b i c TEST V be g π g m V be g o V ce R 2 V TEST R B1 //R B2 TEST =0 AVR 0

37 Determination of small-signal two-port representation R B1 =50K C 1 =1uF R B2 =10K R 1 =0.5K C 2 =100uF V 1 R OUT A V V 1 R IN V 2 AV 215 RIN rπ 930 ROUT R2 2 This is the same basic amplifier that was considered many times K

38 End of Lecture 29 End of Slide 30

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