ࡱ> IKHRSTUVUM +bjbj== )~WW&lnnnnnnn8La7: "6666666$8 :~6-n60/nn70/0/0/rnn60/60/0/6nn6 I2$-.N'66170a769;(<60/nnnnCHAPTER 11 Solutions for Exercises E11.1 (a) A noninverting amplifier has positive gain. Thus  EMBED Equation.3  (b) An inverting amplifier has negative gain. Thus  EMBED Equation.3  E11.2  EMBED PBrush   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.3 Recall that to maximize the power delivered to a load from a source with fixed internal resistance, we make the load resistance equal to the internal (or Thvenin) resistance. Thus we make  EMBED Equation.3  Repeating the calculations of Exercise 11.2 with the new value of RL, we have  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.4  EMBED PBrush  By inspection,  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.5 Switching the order of the amplifiers of Exercise 11.4 to 3-2-1, we have  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.6  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.7 The input resistance and output resistance are the same for all of the amplifier models. Only the circuit configuration and the gain parameter are different. Thus we have  EMBED Equation.3 and we need to find the open-circuit voltage gain. The current amplifier with an open-circuit load is:   EMBED Equation.3  E11.8 For a transconductance-amplifier model, we need to find the short-circuit transconductance gain. The current-amplifier model with a short-circuit load is:   EMBED Equation.3  The impedances are the same for all of the amplifier models, so we have  EMBED Equation.3  E11.9 For a transresistance-amplifier model, we need to find the open-circuit transresistance gain. The transconductance-amplifier model with an open-circuit load is:   EMBED Equation.3  The impedances are the same for all of the amplifier models, so we have  EMBED Equation.3  E11.10 The amplifier has  EMBED Equation.3  (a) We have  EMBED Equation.3  which is much less than  EMBED Equation.3 , and we also have  EMBED Equation.3  which is much larger than  EMBED Equation.3 . Therefore for this source and load, the amplifier is approximately an ideal voltage amplifier. (b) We have  EMBED Equation.3  which is much greater than  EMBED Equation.3 , and we also have  EMBED Equation.3  which is much smaller than  EMBED Equation.3 . Therefore for this source and load, the amplifier is approximately an ideal current amplifier. (c) We have  EMBED Equation.3  which is much less than  EMBED Equation.3 , and we also have  EMBED Equation.3  which is much smaller than  EMBED Equation.3 . Therefore for this source and load, the amplifier is approximately an ideal transconductance amplifier. (d) We have  EMBED Equation.3  which is much larger than  EMBED Equation.3 , and we also have  EMBED Equation.3  which is much larger than  EMBED Equation.3 . Therefore for this source and load, the amplifier is approximately an ideal transresistance amplifier. (e) Because we have  EMBED Equation.3 , the amplifier does not approximate any type of ideal amplifier. E11.11 We want the amplifier to respond to the short-circuit current of the source. Therefore, we need to have  EMBED Equation.3 . Because the amplifier should deliver a voltage to the load that is independent of the load resistance, the output resistance  EMBED Equation.3  should be very small compared to the smallest load resistance. These facts ( EMBED Equation.3 very small and  EMBED Equation.3  very small) indicate that we need a nearly ideal transresistance amplifier. E11.12 The gain magnitude should be constant for all components of the input signal, and the phase should by proportional to the frequency of each component. The input signal has components with frequencies of 500 Hz, 1000 Hz and 1500 Hz, respectively. The gain is  EMBED Equation.3  at a frequency of 1000 Hz. Therefore the gain should be  EMBED Equation.3  at 500 Hz, and  EMBED Equation.3  at 1500 Hz. E11.13 We have  EMBED Equation.3   EMBED Equation.3  The corresponding phasors are  EMBED Equation.3  and  EMBED Equation.3 . Thus the complex gain is  EMBED Equation.3  E11.14  EMBED Equation.3  E11.15 Equation 11.13 states Percentage tilt  EMBED Equation.3  Solving for fL and substituting values, we obtain  EMBED Equation.3  as the upper limit for the lower half-power frequency. E11.16 (a)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  The desired term has an amplitude of V1 = 100 and a second-harmonic distortion term with an amplitude of V2 = 0.5. There are no higher order distortion terms so we have  EMBED Equation.3  or 0.5%.  EMBED Equation.3  (b)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  The desired term has an amplitude of V1 = 500 and a second-harmonic distortion term with an amplitude of V2 = 12.5. There are no higher order distortion terms so we have  EMBED Equation.3  or 2.5%.  EMBED Equation.3  E11.17 With the input terminals tied together and a 1-V signal applied, the differential signal is zero and the common-mode signal is 1 V. The common-mode gain is EMBED Equation.3  which is equivalent to -20 dB. Then we have  EMBED Equation.3  E11.18 (a)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Thus  EMBED Equation.3 . (b)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Thus  EMBED Equation.3 . (c)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  E11.19 Except for numerical values this Exercise is the same as Example 11.13 in the book. With equal resistances at the input terminals, the bias currents make no contribution to the output voltage. The extreme contributions to the output due to the offset voltage are  EMBED Equation.3  The extreme contributions to the output voltage due to the offset current are  EMBED Equation.3  Thus, the extreme output voltages due to all sources are  EMBED Equation.3  V. E11.20 This Exercise is similar to Example 11.13 in the book with  EMBED Equation.3 = 50 k and  EMBED Equation.3 = 0. With unequal resistances at the input terminals, the bias currents make a contribution to the output voltage given by  EMBED Equation.3  The extreme contributions to the output due to the offset voltage are  EMBED Equation.3  The extreme contributions to the output voltage due to the offset current are  EMBED Equation.3  Thus, the extreme output voltages due to all sources are a minimum of 2.5 V and a maximum of 10.83 V. Answers for Selected Problems P11.4*  EMBED Equation.3   EMBED Equation.3  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.5*  EMBED Equation.3   EMBED Equation.3  P11.10*  EMBED Equation.3 (. P11.15*  EMBED Equation.3  P11.20*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  EMBED Equation.3  P11.22* Five amplifiers must be cascaded to attain a voltage gain in excess of 1000. P11.25*  EMBED Equation.3  P11.32*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.33*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.38* The voltage-amplifier model is:  The transconductance-amplifier model is:  P11.40*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.41*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.52*  EMBED Equation.3  P11.55* To sense the open-circuit voltage of a sensor, we need an amplifier with very high input resistance (compared to the Thvenin resistance of the sensor). To avoid loading effects by the variable load resistance, we need an amplifier with very low output resistance (compared to the smallest load resistance). Thus, we need a nearly ideal voltage amplifier with a gain of 1000. P11.56* The input resistance is that of the ideal transresistance amplifier which is zero. The output resistance of the cascade is the output resistance of the ideal transconductance amplifier which is infinite. An amplifier having zero input resistance and infinite output resistance is an ideal current amplifier. Also, we have  EMBED Equation.3 . P11.61* We need a nearly ideal transconductance amplifier.  EMBED Equation.3   EMBED Equation.3  P11.67* The complex gain for the 1000-Hz component is  EMBED Equation.3  The complex gain for the 2000-Hz component is  EMBED Equation.3  P11.68* The signal to be amplified is the short-circuit current of an electrochemical cell (or battery). This signal is dc and therefore a dc-coupled amplifier is needed. P11.70*  EMBED Equation.3  P11.75* The gain at 2000 Hz must be  EMBED Equation.3 . The output signal is  EMBED Equation.3  The plots are:  P11.82*  EMBED Equation.3   EMBED Equation.3  P11.83* (a)  (b)  (c)  P11.86*  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  P11.93*  EMBED Equation.3  P11.98* The extreme values of the output voltage are:  EMBED Equation.3  If the resistors are exactly equal, then the output voltage is zero. P11.99* The output voltage can range from -3.333 to +3.333 V. 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