554 © Awpurite FREQUENCY RESPONSE sv 45 mV pesk inp signal 6 What would be the approximate rms amplitude of the output waveform at 300 Hz? Based on the oscilloscope measurement in Figure 10-5: at 5 kHe in dB Based on the oscilloscope measurement in Figure 10- at 60 He in dB express the voltage gain express the voltage gain sv ene gel] Oupat at 60 Hz FIGURE 10-55 Frequency tet of new preamp board using an oscilloscope. SUMMARY Section 10-1 @ The coupling and bypass capacitors of an amplifier alfect the low-frequency response. ‘The internal transistor capacitances affect the high-frequency response. Section 10-2 @ The decibel i a logarithmic unit of measurement for power gain and voltage gai, ‘A decrease in voltage gain to 70.7% of midrange value isa reduction of 3 6B {A alving of the voltage gain corresponds to reduction of 6 dB. The dim is a unit for measuring power levels referenced to 1 mW,Section 10-3 Section 10-4 Section 10-5 Section 10-6 Section 10-7 Key Formutas ¢ 555 © Critical frequencies are values of frequency at which the RC circuits reduce the voltage gain to 70.7% of its midrange value © Bach RC circuit eauses the gain to drop ata rate of 20 dBidceade For the low-frequency RC cieuit, the highest critical frequency isthe dominant critical frequency. © A decade of frequency change isa ten-times change (increase or decrease) An octave of frequeney change isa two-times change (increase or decrease) © For the high-frequency RC circuits, the lowes critical frequency isthe dominant critical frequency. ‘© ‘The bandwidth ofan amplifier is the range of frequencies between the dominant lower ertial frequency and the dominant upper critical frequency. ‘© The gain-bandwidth product is a transistor parameter that is constant and equal o the unity-gain frequency. © The dominant crtieal frequencies of a multistage amplifier establish the bandwidth © Two frequency response sasurement methods ae frequency/amplitude and step. Key terms and other bold terms in the chapter are defined inthe end-ol-book glossary. Bandwidth ‘The characteristic of certain types of electron circuits that specifies the usable range of frequencies that pass from input to output. Bode plot An idealized graph of the gain in 4B versus frequency used to graphically illustrate the response of an amplifier or file. Critical frequency The frequency at which the response ofan amplifier or filter is 3 dB less than at midrange. Decade A ten-times increase or deerease in the value of a quantity such as frequency. Decibel A logarithmic measure ofthe ratio of one power to another or one voltage to another. Midrange gain The gain thal ooeus for the range of frequencies between the lower and upper eit- eal frequencies. Roll-off The rate of decrease inthe guin of an amplifier above or below the critical frequencies, Tem er dine 20+ iat tee 102 Cam (8) geen te steve moe Dane Woe BJT Amplifier Low-Frequency Response WO-S Avimidy = 7 ‘Midrange voltage gain 106 fans = Fea, Lower ential fequeney input RC circuit a os w(% Ped ng 10-8 fatoupas = Lower ential frequency, output RC cect ale + RCsAMPLIFIER FREQUENCY RESPONSE 10-9 @ = tan 10-0 10M fetta) = 3505+ Ra Bad ReICe FET Amplifier Low-Frequency Response 1 10-12 Stiga = 2a (Re ll Rinigates)Cr =f Xen sos 0 uwi(32 1 1014 Set (Ry + Ry)C2 (_Xea seas = wo) BJT Amplifier High-Frequency Response — te FeR TR DRT Bar OCoe tana SEN Put) 1 10-16 feainguy 4170 FET Amplifier High-Frequency Response 10-20 Cus 10-21 10-22 10-23 10-24 10-25 faioupun = SE 28 aan = Fea vie 026 0 ) Total Response 1027 BW = fafa 1028 fy = Aria Maltstage Response atoms 10-29 Firm) = Vir 1 Phase angle, output RC circuit Resistance looking in a emitter Lower critical frequency, bypass RC circuit Lower ertieal frequency, input RC circuit Phase angle, input RC eireuit Lower critical frequency, output RC circuit Phase angle, output RC circuit Upper critical frequency, input RC circuit Phase angle, input RC circuit Upper erticalsrequeney, output RC cireuit Phase angle, output RC circuit Gat Gate-to-source cupacitance rain-to-souree capacitance ‘o-drain capacitance Upper critical frequency, input RC circuit Phase angle, input RC circuit Upper critical frequency, output RC circuit Phase angle, output RC circuit Bandwidth Unity-gain bandwidth ‘Overall dominant lower crtieal frequency for case of equal dominant critialfre- ‘quenciesCincurt-Action Quiz * 557 10-30 Seat) ‘Overall dominant upper erica requency for case of equal dominant critical frequencies ‘Measurement Techniques a ae re p= Lome ne 7 Answers can be found at www.pearsonhighered.com/Moyd. . Coupling capacitors in an amplifier determine the low-frequency response, . Bypass capacitors in an amplifier determine the high-frequency response. . Internal transistor capacitance has no effect on an ampliie’s frequency response J. Miller's theorem states that both gain and internal capacitances influence high-frequency response 5. The midrange gain is between the upper and lower eritical frequencies. 3. The eritical frequency is where the gain is 6 UB less than the midrange gain, 7, dBm isa unit for measuring power levels, & A ten-times change in frequency is called a decade 19. An octave corresponds toa doubling or halving ofthe frequency. 10, The input and output RC circuits have no effect on the frequency response |. A Bode plot shows the voltage guin versus frequency on a logarithmic sea. 12, Phase shift is part of an amplifies frequency response. Answers cant be found at ww. pearsonhighered.com Moy 1. IF the valu of Rin Figure 10-8 is increased, the signal voltage atthe base will (a) increase (b) decrease (€) not change 2. Ihe value of C; in Figure 10-27 is decreased, the critical frequency assoeiated with the input circuit will, (a) increase (b) decrease) not change 43. Ite value of R, in Figure 10-27 is increased, the voltage gain will (a) increase (b) decrease (€) not change 4. Ifthe value of Re in Figure 10-27 is deerease, the voltage gain will (a) increase (b) decrease) not change 5. If Voc in Figure 10-34 is inereased, the de emitter voltage will (@) increase (b) decrease (@) not change 6. Ihe transistor in Figure 10-34 is replaced with one having a higher Ba, the exitcal frequency will (a) increase (b) decrease (@) not change 7. I the tansistor in Figure 10-34 i replaced with one having a lower Bux, the midrange voltage sain will (a) increase (b) decrease (€) not change 8. Ihe value of Rp in Figure 10-42 isineeased, the voltage gui wil (@) increase () decrease (@) not change 9. Ifthe valu of Rin Figure 10-42 s increased the ertcal re (a) increase (b) decrease (@) not change 10, Ifthe FE in Figure 10-42 is replaced with one having a higher gq the ertcl frequency will (@) increase (b) decree (€)notchange rency will558 ¢ Ampurice FREQUENCY RESPONSE Section 10-1 Section 10-2 Section 10-3 Section 10-4 Section 10-5 Answers can be found at www-pearsonhighered.comvfloyd. 1. The low-froqueney response ofan amplifier is determined in par by (a) the voltage gain (b) the type of wansistor () the supply voltage (€) the coupling capacitors 2. The high-frequency response of an amplifier is determined in part by (a) the gain-baadwidih product () the bypass capacitor (©) the internal transistor capacitances (@) the roll-off 3 The Miller input capacitance of an amplifier is dependent, in part, on (a) the input coupling capacitor (b) the voltage gain (© the bypass capacitor (2) none of these 44. The decibel is used to express (a) power gain (b) voltage gain) attenuation _(@) all of these 5. When the voltage gain is 70.7% of its midrange valu, i is said to be (a) atenusted —(b) down dB (@) down 34B_—(@) down 1 4B 6. In an amplifier, the gain that occurs between the lower and upper critical frequencies is called the (a) critical gain (b) midrange gain (€) bandwidth gain (4) decibel gain 7. A certain amplifier has a voltage gain of 100 at midrange. Ifthe gain decreases by 6 dB, itis equal co (50 @) 707 -@O @ 20 8. The gain of a certin amplifier decreases by 6 dB when the frequency is reduced from 1 KHz to 10 He, The roll ofis, (a) ~3dBidecade (0) ~64dBidecade —_(€) —3.dBloctave__(@) —6UBloctave 19. The gain of a particular amplifier ata given frequency decreases by 6 dB when the frequency is doubled. The ollofT is (a) ~12dBidecade (0) —20dBidecade —_(€) 6 dBloctave__(@) answers (b) and (e) 10, The lower exitcal frequency ofa drect-coupled amplifier with no bypass capacitor is (@) variable (b) OH? —_(e) dependent on the bias (@) none ofthese 11. tthe upper critical frequency, the peak output voltage ofa certain amplifier is 10 V. The peak ‘voltage in the midrange of the amplifier is (@ 70TV (6) 637V_ @ M4I4V @) IOV 12. The high-frequency response of an amplifier is determined by the (@) coupling capacitors —__(b) bias cireuit (©) transistor capacitances (d) all ofthese 13, The Miller input and output capacitances for a BIT inverting amplifier depend on (@) CeO) Bac A, A) answers (@) and ©) 14, The bandwidth of an amplifier is determined by (a) the midrange gain (b) the ertical frequencies (©) therolloftrate (the input capacitance 18. An amplifier has the following critical frequencies: 1.2 kHz, 950 Hz, 8 kHz, and 8.5 kl¥z. The bandwidth is (@) 7550 Hz (b) 7300Hz —(@) 6800Hz—(@) 7050 Hz 16, Ideally, the midrange gain of an amplifier (a) increases with frequency (b) decreases with frequency (remain constant with frequency (@) depends on the coupling capacitorsProsiems * 559 117. The frequency at which an amplifier’s gain is {is called the (a) unity-gain frequency (b) midrange frequency (©) comer frequency (a) break frequency 18, When the voltage gain ofan amplifier is increased, the bandwidth (a) isnot affected —(b) increases (@) decreases (@) becomes distorted 19, If the fof the transistor used in a certain amplifier is 75 MHz and the bandwidth is 10 Mz, the voltage gin must be (750) 75 10 I 20, Inthe midrange of an amplifier’s bandwidth, the peak output voltage is 6 V. At the lower eriti- cal frequeney, the peak output voltage is (@)3V )382V |) 8A8V @) A24V Section 10-6 21. ‘The dominant lower critical frequency of a multistage amplifier is the Section 10-7. 23, In the step response of an Section 10-1 > FIGURE 10-56 “Multis file circuits are identified with a logo and are in the Problems folder on the companion website. Filenames correspond to figure numbers (eg, F106) (a) lowest fy 0) highest fy (@) average ofall the," (€) none of these 22. When the eritcal frequencies ofall ofthe stages are the same, the dominant eitical requeney i (@) higher than any individual f(b) lower than any individual fy (© equal tothe individual's (@) dhe sum of al individual fs inverting amplifier, a longer ise time means (a) anarower bandwidth (b) alower fy (6) aigher fy (@) answers (a) and (6) Answers to all odd-numbered problems are at the end ofthe book. BASIC PROBLEMS Basic Concepts 1. In acapacitively coupled amplifier, the input coupling capacitor and the output coupling capac itor form two ofthe circuits (along with the respective resistances) that determine the low fre- {quency response. Assuming thatthe input and output impedances are the same and neglecting the bypass circuit, which circuit wil first eause the gain to drop from its midrange value as the frequency is lowered? 2. Explain why the coupling capacitors do not havea significant effect on gain a suficienly high-signal frequencies. 13. List the capacitances that affect high-frequency gain in both BIT and FET amplifiers. 4. In the amplifier of Figure 10-6, lst the capacitances that affect the low-frequency response of the amplifier and those that affect the high-frequency response.560 AMPLIFIER FREQUENCY RESPONSE Section 10-2 Section 10-3 5. Determine the Miller input capacitance in Figure 10-56. 6, Determine the Miller output capacitance in Figure 10-56, 7. Determine the Miller input and output capacitances forthe amplifier in Figure 10-57. ov C210 pe Iggs=18 8A @ Vog=-10V Vesa) =-8V pgp = 10 mA oR AFIGURED ‘The Decibel 8. A certain amplifier exhibits an output power of § W with an input power of 0.5 W. What isthe power gain in dB? 9. Ifthe output voltage of an amplifier is 1.2 V rms and its voltage gain is $0, what isthe ms ‘input voltage? What is the gain in dB? 10, The midrange voltage gain of a certain amplifier is 65. Ata certain frequency beyond ‘midrange, the gain drops to 25. What is the gain reduetion in dB? 111, What are the dBm values corresponding tothe following power values? @2mW @ImW (© 4mW @) 025m 12, Express the midrange voltage gain ofthe amplifier in Figure 10-S6 in decibels. Also express the voltage gain in dB forthe critical frequencies. Low Frequency Amplifier Response 13, Determine the ertieal frequencies of each RC circuit in Figure 10-58. sur our 114, Determine the critical frequencies associated with the low-frequency response of the BIT amplifier in Figure 10-59. Which is the dominant critical frequency? Sketch the Bode plot A FIGURE 10-58 15, Determine the voltage gain ofthe amplifier in Figure 10-59 at one-tenth of the dominant critical frequency, atthe dominant critical frequency, and a ten times the dominant eitcal Frequency for the low-frequency response. 16. Determine the phase shift at each of the frequencies used in Problem 15,Proniems © 561 > FIGURE 10-59 17. Determine the critical frequencies associated with the low. frequency response ofthe FET am plier in Figure 10-60. Indicate the dominant critical frequency and draw the Bode plot. 418, Find the voltage gain ofthe amplifier in Figure 10-60 atthe following frequencies: 0.1 and 10f, where fis the dominant critical frequency. av Cug=10 oF Cad oF Ry fous =50 5A @ Vog=-10V 56090 2005 HF Yc = 6 ya 15s 0s we & x vox, eon 2 A FIGURE 10-60 Section 10-4 High Frequency Amplifier Response 19, Determine the critical frequencies associated with the high-frequency response of the amplifier in Figure 10-59. Identify the dominant critical frequency and sketch the Bode plot. 20, Determine the voltage gain ofthe amplifier in Figure 10-59 atthe following frequencies: 0.1, 4 10 and 10, where fis the dominant critical frequency in the high-frequency response. 21. ‘The datasheet for the FET in Figure 1060 gives C,.,= 4 pF and Ciy,= 10 pP. Determine the critical frequencies associated with the high-frequency response of the amplifier, and indicate the dominant frequency, 22, Determine the voltage gain in dB and the phase shift at each ofthe following multiples of the dom- inant erica frequency in Figure 10-60 forthe high-frequency response: 01 f Of and 100. Section 10-5 Total Amplifier Frequency Response 23. A panicular amplifier has the following low critical frequencies: 25 Hy, 42 Hy, and 136 Hz. It ‘also has high critical frequencies of 8 kHz and 20 kHz. Determine the upper and lower critical Frequencies, 24, Determine the bandwidth of the amplifier in Figure 10-59, 25, fy =200 MHz taken from the datasheet ofa transistor used in a certain amplifier. I the ‘midrange gain is determined to be 38 and if fs low enough to be neglected compared to fae ‘what bandwidth would you expeet? What value of f., would you expect?562 ¢ AmPurieR FREQUENCY RESPONSE > FIGURE 10-61 Section 10-6 Section 10-7 26. I the midrange gain of a given amplifier is 50 dB and therefore 47 dB at fy how much gain is there at 2,9 AL Af? At 10? Frequency Response of Multistage Amplifiers 27. Ina cenain two-stage amplifier, the first stage has critical frequencies of 230 Hz and 1.2 MHz. “The second stage has critical frequencies of 195 Hz and 2 MHz. What are the dominant critical frequencies? 28, What isthe bandwidth of the two-stage amplifier in Problem 27 29, Determine the bandwidth of a two-stage amplifier in which each stage has a lower critical frequency of 400 He and an upper ertical frequency of 800 ki. 30, What is the dominant lower critical frequency of a three-stage amplifier in which = 0 Hz foreach stage 31. Ina certain two-stage amplifier, the lower crtial lrequencies are f) 125 He, and the upper ertical frequencies are fq = 3 MEVz and fy the bandwidth Frequency Response Measurements 32, Ina step-response test ofa certain amplifier, 10 ns and ry= 1 ms, Determine 3d foe 33, Suppose you are measuring the frequency response of an amplifier witha signal source and aa ‘oscilloscope, Assume that the signal level and frequency are set such thatthe oscilloscope indi- cates an outpat voltage level of 5 V rms in the midrange ofthe ampliier's response. Ifyou ‘wish to determine the upper eritieal frequency, indicate what you would do and what scope in- ication you would look for. 34, Determine the approximate bandwidth of an amplifier from the indicated results ofthe step- response test in Figure 10-61 APPLICATION ACTIVITY PROBLEMS 3. Determine the dominant lower critical frequency forthe amplifier in Figure 10-S2 if the cou- pling capacitors are changed to | iF, Assume Ri, = 29 k®2and Bye = 100, 36. Does the change in Problem 35 significantly affect the overall bandwidth? 37. How does a change from 29k to 100k in load resistance on the final output of the ampli- fier in Figure 10-82 affect the dominant lower critical frequency? ‘38. I he transistors inthe modified preamp in the Application Activily have a By. of 300, deter- ‘mine the effect on the dominant lower eritial frequency DATASHEET PROBLEMS 39. Referring tothe paral datasheet fora 2N390s in Figure 10~62, determine the total input ex pactance for an amplifier ifthe voltage gain i 25 40, A contain amplifir uses a 2N3904 and has a midrange voltage gain of 50. Referring to the paral dataset in Figure 10~62, determine its minimum bandwith 41, The datasheet fora 2N435I MOSFET specifies the maximum values of itera capacitances as follows: C.=5 BF, Cys 1.3 pF, and Cag) =5 PE Determine Coys Cy aR CyProntems © 563, Electrical Characteristics _s-2ccussoownnns ‘Symbol Parameter Test Conditions | Min | Max | Unite OFF CHARACTERISTICS ‘ON CHARACTERISTICS" = 3 Caren Gar Te z t wo | 300 t @ EC itOmA vere ta so Vann | CE WEISS Le TOMA b= TOA a ESsimak=s0mA fs |v Tas | STRESS WER [ES TOTA b= DA we ‘SMALL SIGNAL CHARACTERISTICS Ca 7 SWITCHING CHARACTERISTICS Partial dataset forthe 203908. Copyright Fach Semicondutr Corporation, Used by persion. ADVANCED PROBLEMS 42. ‘Two single-stage capacitively coupled amplifiers like the one in Figure 10-56 are connected as ‘two-stage amplifier (R, is removed from the fst stage), Determine whether o¢ not this con ‘guration will operate as a linear amplifier with an input voltage of 10 mV rms. If na, modify the design to achieve maximum gain without distortion, 43, Two stages ofthe amplifier in Figure 10-60 ae connected in cascade. Determine the overall bandwidth 44, Redesign the amplifier in Figure 10-52 for an adjustable voltage gain of $0 to $00 and a lower critical frequeney of I kHz, MULTISIM TROUBLESHOOTING PROBLEMS ‘These file circuits are in the Troubleshooting Problems folder on the companion website 4. Open file TSP10-45 and determine the fault. 46. Open file TSP10-46 and determine the fault. 47. Open file TSP10-47 and determine the fault. 48, Open file TSP10-48 and determine the fault,