Chapter 6 frequency effects in amplifiers

CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.77 CHAPTER 6: FREQUENCY EFFECTS IN AMPLIFIERS Table of Contents 6.1. INTRODUCTION 79 6.2. BODE PLOTS AND FREQUENCY RESPONSE 80 6.3. LOW-FREQUENCY EFFECT OF BYPASS AND COUPLING CAPACITORS 83 6.3.1. Low-frequency effect of bypass capacitor 84 6.3.2. Low-frequency effect of coupling capacitor 87 6.4. HIGH FREQUENCY HYBRID-  BJT MODEL 90 6.5. HIGH-FREQUENCY FET MODELS 92 Table of Figures Fig. 6-1 Frequency response and transfer function 80 Fig. 6-2 Bode plots of Ex. 6.1 82 Fig. 6-3 CE amplifier 84 Fig. 6-4 Small-signal equivalent circuit 85 Fig. 6-5 Low- and mid-frequency asymptotic Bode plot 87 Fig. 6-6 Low frequency effect of coupling capacitor 88 Fig. 6-7 Bode plot of low frequency effect of coupling capacitor 90 CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.78 Fig. 6-8 High frequency hybrid-  bjt model 91 Fig. 6-9(a) Mid-frequency small-signal current-source FET model 92 Fig. 6-9(b) High-frequency small-signal current-source FET model 92 CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.79 CHAPTER 6: FREQUENCY EFFECTS IN AMPLIFIERS 6.1. INTRODUCTION In the previous chapters on amplifiers, the coupling and bypass capacitors were considered to be ideal shorts and the internal transistor capacitances were considered to be ideal opens. This treatment is valid when the frequency is in an amplifier’s midrange. As you know, capacitive reactance decreases with increasing frequency and vice versa. When the frequency is low enough, the coupling and bypass capacitors can no longer be considered as shorts because their reactances are large enough to have a significant effect. Also, when the frequency is high enough, the internal transistor capacitances can no longer be considered as opens because their reactances become small enough to have a significant effect on the amplifier operation. In this chapter, you will study the frequency effects on amplifier gain and phase shift. CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.80 6.2. BODE PLOTS AND FREQUENCY RESPONSE Fig. 6-1 Frequency response and transfer function       / T s N s D s  is the Laplace-domain transfer function. In amplifier analysis, transfer functions are the current-gain ratio     i T s A s  and voltage-gain ratio     v T s A s  . For convenience, with   s j , we make the following definitions: 1. Call    A j , the frequency transfer function. 2. Define     M A j , the gain ratio CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.81 3. Define      20log 20 log db M M A j , the amplitude ratio, measured in decibels (db). The graph of db M (simultaneously with  if desired) versus the logarithm of the input signal frequency (positives values only) is called a Bode plot. Example 6.1. A simple first-order network has Laplace-domain transfer function and frequency transfer function    1 ( ) 1 A s s and        1 ( ) 1 A j j Where  is the system time constant. (a) Determine the network phase angle  and the amplitude ratio db M . (b) Construct the Bode plot for the network. Solution (a) In polar form, the given frequency transfer function is                             1 2 1 2 1 1 tan 1 1 1 tan 1 A j Hence,        1 tan                  2 2 1 20 log 20log 10log 1 1 db M A j (b) If values of db M and  are calculated and plotted for various values of  , then a Bode plot is generated. This is done in Fig. 6-2, CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.82 where  is given in terms of time constants  rather than, say, hertz. This particular system is called a lag network because its phase angle  is negative for all  . Fig. 6-2 Bode plots of Ex. 6.1 Example 6.2 A simple first-order network has Laplace-domain transfer function and frequency transfer function      1 A s s and     ( ) 1 A j j . Determine the network phase angle  and the amplitude ratio db M , and discuss the nature of the Bode plot. Solution After    A j is converted to polar form, it becomes apparent that       1 tan CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.83 And                 2 2 20 log 20log 1 10 log 1 db M A j Thus, the complete Bode plot consists of the mirror images about zero of db M and  of Fig. 6-2. Since here the phase angle  is everywhere positive, this network is called a lead network. A break frequency, cutoff frequency or corner frequency is the frequency  1/ . For a simple lag or lead network, it is the frequency at which     2 2 M A j has changed by 50 percent from its value at   0 . Corner frequencies serve as key points in the construction of Bode plots. 6.3. LOW-FREQUENCY EFFECT OF BYPASS AND COUPLING CAPACITORS As the frequency of the input signal to an amplifier decreases below the midfrequency range, the voltage (or current) gain ratio decreases in magnitude. The low-frequency cutoff point L  is the frequency at which the gain ratio equals 1/ 2 ( 0.707)  times its midfrequency value, or at which db M has decreased by exactly 3 db from its midfrequency value. Low-frequency amplifier performance (attenuation, really) is a consequence of the use of bypass and coupling capacitors to fashion the dc bias characteristics. When viewed from the low-frequency region, such amplifier response is analogous to that of a high-pass filter. CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.84 6.3.1. Low-frequency effect of bypass capacitor Example 6.3. For the amplifier of Fig.6-3 , assume that C C   but that the bypass capacitor E C cannot be neglected. Also, let 0 re oe h h   and 0 i R  . (a) Find an expression that is valid for small signals and that gives the voltage-gain ratio   v A s at any frequency. (b) find the voltage-gain ratio at low frequencies. (c) the voltage-gain ratio at higher frequencies (d) the low-frequency cutoff point. (e) Sketch the asymptotic Bode plot for the amplifier (amplitude ratio only) Fig. 6-3 CE amplifier CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.85 Solution (a) The small-signal low-frequency equivalent circuit (with the approximation implemented) is displayed in Fig. 6-4. In the Laplace domain, we have     1/ 1 || 1/ 1 E E E E E E E E E E R sC R Z R sC R sC sR C      Fig. 6-4 Small-signal equivalent circuit Note that   1 e fe b i h i   Using KVL:   1 i ie b E e ie fe E b v h i Z i h h Z i          By Ohm’s law:     || fe C L L fe b C L b C L h R R v h i R R i R R         1 1 fe C L L E E v i C L E E ie ie fe E h R R v sR C A s v R R sR C h h h R         CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.86 (b) The low-frequency voltage-gain ratio is obtained by letting  0 s :                  0 0 lim 1 fe C L L v s i C L ie fe E h R R v A v R R h h R (c) The higher-frequency (midfrequency) voltage-gain ratio is obtained by letting   s :                                   1/ lim lim 1 / fe C L L E E v s s i C L E E ie ie fe E fe C L ie C L h R R v R C s A v R R R C h h h R s h R R h R R (d)   v A s can be rearranged to give:                          1 1 1 1 fe C L E E v E E ie C L ie fe E ie fe E h R R sR C A s R C h R R h h R s h h R Which clearly is of the form        1 2 1 1 v v s A s k s With     1 1 1 1 E E C R         1 2 1 1 ie fe E E E ie h h R R C h Typically,  1 fe h and  fe E ie h R h , so a reasonable approximation of  2 is [...].. .CHAPTER 6: Frequency Effects in Amplifiers 2  1 C E hie / h fe With RE  hie / h fe , 2 is an order of magnitude greater than 1 (e) The low- and midfrequency asymptotic Bode plot is depicted in Fig 6- 5 Fig 6- 5 Low- and mid -frequency asymptotic Bode plot 6. 3.2 Low -frequency effect of coupling capacitor Example 6. 4 In the circuit of Fig 6- 6(a), the impedance of the coupling capacitor... negligibly small (a) Find an expression for the voltage-gain ratio M  Av  j   vo / vS (b) Determine the midfrequency gain of this amplifier (c) Determine the low -frequency cutoff point L , and sketch an asymptotic Bode plot Val de Loire Program p.87 CHAPTER 6: Frequency Effects in Amplifiers (a) (b) Fig 6- 6 Low frequency effect of coupling capacitor Solution (a) The small-signal low -frequency equivalent... midfrequency gain follows from letting s  j   We have: Amid  h feRC RB RB  hie RS  hie || RB  (c) Cutoff frequency: L  1/   1 RB  hie   C  RS  hie || RB  C RS  RB  hie   hieRB    The asymptotic Bode plot is sketched in Fig 6- 7 Val de Loire Program p.89 CHAPTER 6: Frequency Effects in Amplifiers Fig 6- 7 Bode plot of low frequency effect of coupling capacitor 6. 4 HIGH FREQUENCY. .. Because of capacitance that is inherent within the transistor, amplifier current- and voltage-gain ratios decrease in magnitude as the frequency of the input signal increases beyond the midfrequency range The high -frequency cutoff point H is the frequency at which the gain ratio equals 1 / 2 times its midfrequency value, or at which M db has decreased by 3 db from its midfrequency value The range of... value is a function of I EQ Fig 6- 8 High frequency hybrid-  bjt model Val de Loire Program p.91 CHAPTER 6: Frequency Effects in Amplifiers 6. 5 HIGH -FREQUENCY FET MODELS The small-signal high -frequency model for the FET is an extension of the midfrequency model Three capacitors are added: C gs between gate and source, C gd between gate and drain, and C ds between drain and source They are all of the... called the high -frequency region Like L , H is a break frequency The most useful high -frequency model for the BJT is called the hybrid-  equivalent circuit In this model, the reverse voltage ratio hre Val de Loire Program p.90 CHAPTER 6: Frequency Effects in Amplifiers and output admittance hoe are assumed negligible The base ohmic resistance rbb , assumde to be located between terminal B and the... Amplifiers (a) (b) Fig 6- 6 Low frequency effect of coupling capacitor Solution (a) The small-signal low -frequency equivalent circuit is shown in Fig 6- 6(b) By Ohm’s law: IS  Val de Loire Program VS RS  hie || RB  1/ sC p.88 CHAPTER 6: Frequency Effects in Amplifiers Then current division gives: Ib  RB RBVS IS  RB  hie RB  hie RS  hie || RB  1/ sC  But Ohm’s law requires that Vo   h feRC... gs between gate and source, C gd between gate and drain, and C ds between drain and source They are all of the same order of magnitude - typically 1 to 10 pF Fig 6- 9(a) Mid -frequency small-signal current-source FET model Fig 6- 9(b) High -frequency small-signal current-source FET model Val de Loire Program p.92 . CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.79 CHAPTER 6: FREQUENCY EFFECTS IN AMPLIFIERS 6. 1. INTRODUCTION In the previous chapters on amplifiers, the coupling. CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.77 CHAPTER 6: FREQUENCY EFFECTS IN AMPLIFIERS Table of Contents 6. 1. INTRODUCTION 79 6. 2. BODE PLOTS AND FREQUENCY. operation. In this chapter, you will study the frequency effects on amplifier gain and phase shift. CHAPTER 6: Frequency Effects in Amplifiers Val de Loire Program p.80 6. 2. BODE PLOTS AND FREQUENCY