IFB270 Advanced Electronic Circuits

Transcription

1 IFB270 Advanced Electronic Circuits Chapter 0: Ampliier requency response Pro. Manar Mohaisen Department o EEC Engineering

2 Review o the Precedent Lecture Reviewed o the JFET and MOSFET Explained and analyzed the operation o common-source, common-drain, and common-gate ampliiers Explained the structure o a cascade ampliier Discussed the operation o a class D ampliier Described how MOSFETs are used in analog switching applications Described how MOSFETs are used in digital switching applications 2

3 Review o FET Ampliiers Comparison Common-source Common-drain Common-gate Voltage gain A g R v m d A v g R m s gmrs A g R v m d Input R R in R G V I GS GSS R R V / I in G GS GSS R in g m 3

4 Review o the Class D Ampliier Basic class D audio ampliier Signal low in a class D ampliier 4

5 Lecture Objectives To introduce several concepts on capacitance in ampliiers To introduce the Miller s Theorem To discover the decibel as a unit to measure power or gain To investigate the low-requency ampliier response To investigate the high-requency ampliier response To analyze the requency response o the multistage ampliier Keywords 5

6 Eect o coupling capacitors Capacitive reactance: Basic Concepts X C 2 C Ideally, coupling capacitors should be replaced by short-circuits However, at low requencies The capacitive reactance is high (not negligible) Thus, there is a voltage drop at C and C 3 and the voltage gain is reduced 6

7 Basic Concepts contd. Eect o bypass capacitors Ideally, bypass capacitors should be replaced by short-circuits However, at low requencies The capacitive reactance is high (not negligible) Thus, C 2 is not short (i.e., R S or R E is not bypassed) The voltage gain is reduced and a phase shit is introduced RC R A C v A perect coupling ' v r imperect coupling r' Z e e e 7

8 Basic Concepts contd. Eect o internal transistor capacitors At high requencies, bypass and coupling capacitors act as short-circuits Internal junction capacitances have low values, usually a ew picoarads However, internal junction capacitances come into play at high requency and Reduce the gain and introduce phase shit BJT JFET C bc is the output capacitance (a.k.a. C ob ) C be is the input capacitance (a.k.a. C ib ) C gd is the output capacitance C gs is the input capacitance In datasheets» Input capacitance C iss and reverse transer capacitance C rss are given, rom which C gd and C gs can be calculated. 8

9 Basic Concepts contd. Eect o internal transistor capacitors contd. At high requency, X Cbe becomes small enough, A signiicant voltage is lost due to the voltage-divider between R s and X Cbe At high requency, X Cbc becomes small enough, A signiicant amount o output signal is ed back out o phase with the input 9

10 Basic Concepts contd. Miller s Theorem C is the capacitance Cbc in BJT or Cgd in JFET C eectively appears as two capacitances A capacitance rom input to ground equivalent to C(Av + ) A capacitance rom output to ground equivalent to C(Av + ) / Av C 0

11 Decibel The Decibel Logarithmic measurement o the ratio between one power to another or one voltage to another Power ratio: A 0log() p(db) 0 Ap Voltage ratio: A A 20log() v(db) 0 v 0 db reerence (normalized gain) Critical requency

12 Other decibel units The Decibel contd. Voltage gain (Av) Decibel value log(32) = 30 db 8 20 log(8) = 8 db 20 log() = 0 db log(0.707) = -3 db log(0.25) = -8 db Power (mw) dbm 32 0 log(32) = 5 dbm 8 0 log(8) = 9 dbm 0 log() = 0 dbm log(0.707) = -.5 dbm log(0.25) = -9 dbm dbm 0log dbw 0log 0 0 P W mw P W W 2

13 Low-requency BJT Ampliier Response Midrange gain The maximum gain that occurs or the range o requencies between the upper and lower critical requencies Ideally, capacitors appear as short-circuits (X C = 0) However! At lower requencies, X C reactance is not negligible! input RC circuit output RC circuit bypass RC circuit 3

14 Low-requency BJT Ampliier Response contd. The input RC circuit The input RC circuit Neglected source internal resistance V base R Considered source internal resistance V base The critical point Rin 2 2 in XC V in in 2 2 s C () R R X in R Occurs when V b = V in X C = R in + Rs V in R r R () ' in() base e E base Rin Rin 2 2 in 2 2 in in R 2 in XC Rin Rin V V V V Lower critical requency (X C = R in + Rs) X R R C s 2 C in cl() input () 2() R cl input in Rs C Critical requency 4

15 Low-requency BJT Ampliier Response contd. The input RC circuit Example 0-3 Find the lower critical requency. Solution Without Rs cl() input 282 Hz 2() R C2(5.63k)(0. F) in When Rs is considered cl() input s 2(6.23k)(0. F) Hz 2() X 2()(0. C F) R R C in 5

16 Low-requency BJT Ampliier Response contd. The input RC circuit Voltage gain roll-o at low requencies In linear scale In db scale V Attenuation base R in Vin R X V Attenuation 20log db V base 2 2 in C Bode plot A ten-times change in requency is called a decade in 6

17 Low-requency BJT Ampliier Response contd. The input RC circuit Phase shit in the input RC circuit The output (V base ) leads the input (V in ) by the angle V C X tan C Rin Vin V R Examples: When XC = 0 = 0 When XC = Rin = 45 o V R Vin V C 7

18 Low-requency BJT Ampliier Response contd. The output RC circuit The lower critical requency o the circuit First, the circuit is thevenized and then, cl() output 2() R R C L C 3 Phase shit in the output RC circuit X tan C3 RC RL 8

19 Low-requency BJT Ampliier Response contd. The output RC circuit Example 0-5 Calculate the lower critical requency due to the output RC circuit. cl() output 50.8Hz 2() R 2(3.9k R C 5.6k)(0.33 F) L C 3 9

20 Low-requency BJT Ampliier Response contd. The bypass RC circuit The bypass RC circuit Aects the response (gain) at low requencies A v R r c ' e A v Rc r R ' e e 20

21 Low-requency BJT Ampliier Response contd. The bypass RC circuit Thevenin Theorem (looking at the base) R R R Rs th 2 In the emitter circuit R th is seen as R th ac This resistance is seen in series with r e, and the combination is in parallel with R E, thereore R R R r R th ' in() emitter E e ac I R E is swamped E R R R r R R in() emitter th ' E2 e E E2 ac 2

22 Low-requency BJT Ampliier Response contd. The bypass RC circuit The lower critical requency is Example 0-6 cl() bypass 2() R R C in() emitter E2 2 2( R/) r R R C th ' ac e E E2 2 R R R r R R in() emitter th ' E2 e E E2 ac 68k 22k k k = 44.6 cl() bypass 2( R R ) C in() emitter E Hz 22

23 Low-requency FET Ampliier Response contd. The input RC circuit Zero-biased D-MOSFET ampliier The input resistance (corrected!) R R R in G in() gate with R in() gate V I GS DSS The lower critical requency Occurs when V g = V in. Thereore, X C = R in, and cl() input 2 R C The gate voltage (V g ) leads the input by X in tan C Rin 23

24 Low-requency FET Ampliier Response contd. The output RC circuit Equivalent circuit Again, the FET is seen as a current source in parallel with R D The lower critical requency is given by cl() output The phase angle is given by 2() R D R C X tan C2 RD RL L 2 24

25 Total Low-requency Response Overall low-requency response o an ampliier BJT as an example cl() input 2() R in R C s cl() output 2() R R C L C 3 cl() bypass 2( R/) ' ac r th e RE R E2 C 2 25

26 Total Low-requency Response contd. Example 0-9 Midband gain (ideal case) A R R R v 54.0 r R r R ' e c C L ' E e E Critical requencies cl() input 2 () R in R C s 282Hz cl() output 2( R R ) C L C Hz cl() bypass 2( R/) ' ac r th e RE R E2 C Hz 26

27 Equivalence o C bc High-requency BJT Ampliier Response Miller s Theorem C C A in() Miller bc v C out() Miller C bc Av A v 27

28 High-requency BJT Ampliier Response contd. The input RC circuit The input critical requency Capacitive reactance = total resistance X R R R r R R R r Ctot ' ' s 2 ac e s 2 2 ac e C cu( input) tot 2( R R R ) r C cu( input) ' s 2 ac e tot 28

29 High-requency BJT Ampliier Response contd. The input RC circuit Example 0- β ac = 25, C be = 20 pf, and C bc = 2.4 pf, Find cu(input) First ind r e (DC analysis) V V B R E B R 2 R 2 V CC V V.76V r' e 25mV 25mV. I V / R E E E Second ind A v(midband) RL R A R C v 99 r r c ' e ' e Apply Miller s Theorem C C ( A ) 240pF in()() miller bc v midband C C C 260 pf in()() tot in Miller be Find the input resistance R R R R r ' () s 2 ac e 378 in tot Finally 2( R R R ) r C cu() input ' s 2 ac e tot.62mhz 29

30 High-requency BJT Ampliier Response contd. The input RC circuit Phase shit o the input RC circuit The output is taken across the capacitor, so the output o the circuit lags the input by tan s 2 XC tot ' ac e R R R r 30

31 High-requency BJT Ampliier Response contd. The output RC circuit The output critical requency cu() output 2( R ) R C C L out() Miller tan RL R X C Cout () Miller 3

32 High-requency FET Ampliier Response Analysis Exactly the same as that or the BJT with a small dierence The existence o C ds 32

33 High-requency Ampliier Response Total response At high-requencies The ampliier s requency response acts as a low-pass ilter This means that the output is taken across the capacitor 33

34 Total Ampliier Frequency Response The dominant requencies At these requencies, the ampliier gain is 3 db below the midband gain These requencies are reerred to as hal-power requencies cl(dominant) cu(dominant) 34

35 Total Ampliier Frequency Response contd. Bandwidth BW = cu(dom) cl(dom) cu(dom) Unit-gain Frequency T = A v(mid) BW For example: T = 00 MHz means that the transistor is capable o producing a voltage gain o, up to 00 MHz, or a gain o 0, up to 0 MHz, etc. 35

36 Frequency Response o Multistage Ampliiers Equal critical requencies I n ampliiers with equal dominant requencies are connected in series, then The multistage lower critical requency is given by ' cl() dom () cl dom / n 2 The multistage upper critical requency is given by 2 ()() ' / n cu dom cu dom Example cu(dom) = 80 khz and cl(dom) = 500 Hz, n = 4 ' 500 () 49.5 Hz cl dom 2/4 ' (80kHz) 2/4 34.8kHz cu() dom 36

37 Keywords Coupling capacitor Bypass capacitor Internal capacitance o a transistor Decibel Decade Bode plot Midband/midrange gain Bandwidth Lower and upper critical requencies Keywords Multistage ampliiers and its requency response Phase lead or phase lag High-pass and low-pass ilters Dominant lower/upper requencies Miller s theorem 37

38 Lecture Summary Introduced several concepts on capacitance in ampliiers Introduced the Miller s Theorem Discovered the decibel as a unit to measure power or gain Investigated the low-requency ampliier response Investigated the high-requency ampliier response Analyzed the requency response o the multistage ampliier Keywords 38

39 Quiz Based on the Figure, Find the gain o the ampliier Derive the expression o cl(input) and ind its value 39

40 In-class Assignment In the Figure, C, C2, C3, and the resistances are chosen so that cl(input) = 00 Hz, cl(output) = 00 Hz, and cl(bypass) = 0 Hz cu(input) = 00 khz, cu(output) = 00 khz A v(midband) = 00 Plot the Bode plot o this ampliier showing the exact slopes o the curves and the critical requencies on the requency axis. Find the range o requencies over which the ampliier has a constant gain 40