ELEN 3312
advertisement
ELEN 3312 Electronics II Chapter 7 Frequency Response Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 In this chapter, we will: Discuss the general frequency response characteristics of amplifiers. Derive the system transfer functions Develop the Bode diagrams of the magnitude and phase of the transfer functions. Analyze the frequency response of transistor circuits with capacitors. Determine the Miller effect and Miller capacitance. Determine the high- and low- frequency response of basic transistor circuit configurations. Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 1 Amplifier Gain Versus Frequency Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Transfer Functions of the Complex Frequency Name of Function Expression Voltage Transfer Function T(s) = Vo(s)/Vi(s) Current Transfer Function Io(s)/Ii(s) Transresistance Function Vo(s)/Ii(s) Transconductance Function Io(s)/Vi(s) Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 2 Series Coupling Capacitor Circuit sτ T (s) = K 2 ( ) 1 + sτ τ = ( RS + RP )CS K2 = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Rp R p + Rs Chapter 7 Parallel Load Capacitor Circuit 1 T ( s ) = K1 ( ) 1 + sτ τ = ( RS RP )C P K1 = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Rp R p + Rs Chapter 7 3 Bode Plot of Voltage Transfer Function Magnitude: Series Coupling Capacitor Circuit Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Bode Plot of Voltage Transfer Function Magnitude: Parallel Load Capacitor Circuit Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 4 Circuit with Series Coupling and Parallel Load Capacitor τ S = ( RS + RP )C S τ P = ( RS RP )C P fL = fH = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill 1 2πτ S 1 2πτ P Chapter 7 Bode Plot of Magnitude of Voltage Transfer Function: Series Coupling and Parallel Load Capacitor Example 7.2 Page 484 Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 5 Steady-State Output Response Coupling Capacitor Prof. Rubén Flores Donald A. Neamen Load Capacitor Microelectronics McGraw-Hill Chapter 7 Common Emitter with Coupling Capacitor fL = 1 2π ( RSi + Ri )CC Ri = RB [rπ + (β + 1)RE ] Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 6 Common Source with Output Coupling Capacitor fL = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill 1 2π ( RD + RC )CC Chapter 7 Emitter Follower with Output Coupling Capacitor fL = 1 2π ( Ro + RL )CC 2 R' + r Ro =r o RE s π β +1 Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 7 Problem-Solving Technique: Bode Plot of Gain Magnitude 1. Determine whether capacitor is producing a low-pass or high-pass circuit. a. Sketch general shape of Bode plot 2. Corner frequency is f = 1/(2πτ) where τ = ReqC a. Req is resistance seen by capacitor 3. Maximum gain magnitude is midband gain. a. Coupling and bypass capacitors act as shorts b. Load capacitors act as opens Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Common Source with Load Capacitor fH = 1 2π ( Ro RL )C L Ro = rd RD Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 8 Coupling and Parallel Load Capacitors Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Small-Signal Equivalent Circuit: Coupling and Parallel Load Capacitor fL = 1 2π [ RS + ( R1 R2 Ri )]CC fH = Ri = RB [rπ + (β + 1)RE ] Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill 1 2π ( RC RL )C L Chapter 7 9 Emitter Bypass Capacitor Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Bode Plot of Voltage Gain Magnitude: Emitter Bypass Capacitor A v ω →0 = g m rπ RC RS + rπ + (1 + β ) RE Av ω →∞ = fA = 1 2π ⋅τ A g m rπ RC RS + rπ fB = 1 2π ⋅τ B τ A = RE C E τB = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill RE C E (RS + rπ ) RS + rπ + RE (β + 1) Chapter 7 10 Two Coupling Capacitors and a Emitter Bypass Capacitor Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 PSpice Results for Two Coupling Capacitors and a Emitter Bypass Capacitor Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 11 Estimation of the Lower Cutoff Frequency Coupling and Bypass Capacitors Each capacitor affects the overall lower cutoff frequency. To determine the exact lower cutoff frequency is necessary to determine the amplifier’s transfer function and plot the Bode diagram. To estimate the lower frequency we have to: Determine the individual cutoff frequency of each capacitor and use the following formula f L ≈ f c (Cc1 ) + f c (Cc 2 ) + f c (C E ) Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Estimation of the Lower Cutoff Frequency To determine the cutoff frequency of each capacitor assume that all capacitor behaves as a short circuit (C=∞) except the one you are analyzing. For previous example To determine the cutoff frequency of Cc1, replace capacitors Cc2 and CE with a short. To determine the cutoff frequency of Cc2, replace capacitors Cc1 and CE with a short. To determine the cutoff frequency of CE, replace capacitors Cc1 and Cc2 with a short. Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 12 High Frequency Model for BJT Transistors rb,rc and rex are very small rµ is very large (MΩ) rb,rc,rex and rµ can be neglected. Prof. Rubén Flores Donald A. Neamen Expanded Hybrid π Equivalent Circuit Microelectronics McGraw-Hill Chapter 7 High Frequency Parameters rb, rc and rex are the base, collector and emitter series resistances and usually are very small and can be neglected. rµ is the reverse-biased diffusion resistance and usually is in order of MΩ and can be neglected. Cµ is the reverse-biased diffusion capacitance. Cπ is the forward-biased junction capacitance. CS is the junction capacitance of the reversebiased collector-substrate junction, usually can be neglected. Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 13 Simplified High Frequency Model for BJT Transistors Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Short-Circuit Current Gain To understand the frequency effects of the BJT transistor we have to determine the shortcircuit current gain. This analysis help us to determine at what frequency the transistor stops amplifying. Using the simplified hybrid- π model neglecting all series, diffusion resistances and Cs junction capacitance. Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 14 Short-Circuit Current Gain: Analysis of Frequency Response of BJT Ai = h fe (ω ) = Prof. Rubén Flores Donald A. Neamen IC = h fe (ω ) IB g m rπ β0 = 1 + jωrπ (Cπ + Cµ ) 1 + jωrπ (Cπ + Cµ ) Microelectronics McGraw-Hill Chapter 7 Bode Plot: Short-Circuit Current Gain fβ = 1 2π rπ (Cπ + Cµ ) Prof. Rubén Flores Donald A. Neamen fT = β o f β fT = gain-bandwidth product Microelectronics McGraw-Hill Chapter 7 15 Unity-Gain Bandwidth Product (fT) fT is a function of the DC collector current. The cutoff frequency (fT) is lower at low collector currents levels. However the cutoff frequency also decreases at high currents levels in the same way that β decreases at large currents. The fT is usually specified on the transistor data sheets. Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 The Miller Effect Z in , Miller = Zf 1 − AV Z out ,Miller = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Z f AV Av − 1 Chapter 7 16 Bypassed Common Emitter Small-Signal Equivalent Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Small-Signal Equivalent Circuit with Miller Capacitance: Bypassed Common Emitter CM = Cµ [1 + g m ( RC RL )] fH = Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill 1 2π [rπ RB (CM + Cπ )] Chapter 7 17 Common-Base Amplifier Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 High-Frequency Equivalent Circuit: Common Base f Hπ = 1 f Hµ = r 2π π RE RS Cπ 1 + β Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill 1 2π ( RC RL )C µ Chapter 7 18 Emitter-Follower Circuit Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 High-Frequency Equivalent Circuit: Emitter Follower 1 fH ≅ 2π [ RS RB (1 + g m RL' )rπ ](C µ + Prof. Rubén Flores Donald A. Neamen Cπ ) 1 + g m RL' Microelectronics McGraw-Hill Chapter 7 19 Equivalent Circuit for n-Channel Common Source MOSFET Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Unity-Gain Bandwidth fT = Prof. Rubén Flores Donald A. Neamen gm 2π (C gs + C gd ) Microelectronics McGraw-Hill Chapter 7 20 Small-Signal Equivalent Circuit with Miller Capacitance: MOSFET C M = C gd [1 + g m RL ] Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 4 Equivalent 2-port Networks Voltage Amplifier Current Amplifier Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 21 4 Equivalent 2-port Networks Transconductance Amplifier Transresistance Amplifier Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 Frequency Response of Multistage Amplifiers Prof. Rubén Flores Donald A. Neamen Microelectronics McGraw-Hill Chapter 7 22
