Repeat P11.53 if the input impedance is 1 M, the output

Explain how an inverting amplifier differs from a noninverting amplifier.

Draw the voltage-amplifier model and label its elements.

What are two causes of loading effects" in an amplifier circuit?

A signal source with an open-circuit voltage of Vs = 2 mV rms and an internal resistance of 50 k is connected to the input terminals of an amplifier having an open-circuit voltage gain of 100, an input resistance of 100 k, and an output resistance of 4.A 4-load is connected to the output terminals. Find the voltage gains Avs = Vo/Vs and Av = Vo/Vi. Also, find the power gain and current gain. *P

A certain amplifier operating with a 100- load has a voltage gain of 50 and a power gain of 5000. Determine the current gain and input resistance of the amplifier.

The current gain of an amplifier is 500, the load resistance is 100 , and the input resistance of the amplifier is 1 M. Determine the voltage gain and power gain under these conditions.

An amplifier having Ri = 1 M, Ro = 1 k, and Avoc = 104 is operated with a 1-k load. A source having a Thvenin resistance of 2 M and an open-circuit voltage of 3 cos(200t) mV is connected to the input terminals. Determine the output voltage as a function of time and the power gain. P1

A certain amplifier has an open-circuit voltage gain of unity, an input resistance of 1 M, and an output resistance of 100 . The signal source has an internal voltage of 5V rms and an internal resistance of 100 k. The load resistance is 50 . If the signal source is connected to the amplifier input terminals and the load is connected to the output terminals, find the voltage across the load and the power delivered to the load. Next, consider connecting the load directly across the signal source without the ampli- fier, and again find the load voltage and power. Compare the results. What do you conclude about the usefulness of a unitygain amplifier in delivering signal power to a load? P1

An amplifier with Ri = 12 k, Ro = 1 k, and Avoc = 10 is operated with a 1-k load. A source having a Thvenin resistance of 4 k and a short-circuit current of 2 cos(200t) mA is connected to the input terminals. Determine the output voltage as a function of time and the power gain. *P

An ideal ac current source is applied to the input terminals of an amplifier, and the amplifier output voltage is 2 V rms. Then, a 2-k resistance is placed in parallel with the current source and the amplifier input terminals, and the output voltage is 1.5 V rms. Determine the input resistance of the amplifier.

An amplifier has an open-circuit voltage gain of 100. With a 10-k load connected, the voltage gain is found to be only 80. Find the output resistance of the amplifier.

Suppose we have a resistive load that varies from 5 k to 10 k. We connect this load to an amplifier, and we need the voltage across the load to vary by less than 1 percent with variations in the load resistance. Denotes that answers are contained in the Student Solutions files. See Appendix E for more information about accessing the Student Solutions. Problems 555 What parameter of the amplifier is important in this situation? What range of values is allowed for the parameter?

A certain amplifier operates with a resistive load. The current gain and the voltage gain are equal. What can you say about the input resistance and the load resistance?

An amplifier has an open-circuit voltage gain of 1000, an input resistance of 20 k, and an output resistance of 2 . A signal source with an internal resistance of 10 k is connected to the input terminals of the amplifier. An 8- load is connected to the output terminals. Find the voltage gains Avs = Vo/Vs and Av = Vo/Vi. Also, find the power gain and current gain. *P

The output voltage vo of the circuit of Figure P11.15 is 100 mV with the switch closed. With the switch open, the output voltage is 50 mV. Find the input resistance of the amplifier. + 1 M vs + Rin Amplifier vo 10 k Figure P11.15

A certain amplifier has a voltage gain of 0.1. However, the power gain is 10. How is this possible? What is the value of the current gain? How does the load resistance compare with the input resistance of the amplifier?

Suppose we have a sensor, with a Thvenin resistance that varies from zero to 10 k, connected to the input of an amplifier. We want the output voltage of the amplifier to vary by less than 2 percent with changes in the Thvenin resistance of the sensor. What parameter of the amplifier is important in this situation? What range of values is allowed for the parameter?

Draw the cascade connection of two amplifiers. Write an expression for the open-circuit voltage gain of the cascade connection in terms of the open-circuit voltage gains and impedances of the individual amplifiers

Given that the amplifiers having the characteristics shown in Table P11.19 are cascaded in the order AB, find the input impedance, output impedance, and open-circuit voltage gain of the cascade. Repeat when the order is B A. Table P11.19. Amplifier Characteristics Open-Circuit Input Output Amplifier Voltage Gain Resistance Resistance ............................................................... A 100 3 k 400 B 500 1 M 2 k *P

Three amplifiers with the following characteristics are cascaded in Amplifier 1: Avoc1 = 100, Ri1 = 2 k, Ro1 = 1 k Amplifier 2: Avoc2 = 200, Ri2 = 4 k, Ro2 = 2 k Amplifier 3: Avoc3 = 300, Ri3 = 6 k, Ro3 = 3 k Find the parameters for the simplified model of the cascaded amplifier. P11.

Repeat Problem P11.20 with the amplifiers cascaded in the order 3, 2, 1.

Amplifiers having Avoc = 10, Ri = 2 k, and Ro = 2 k are available. How many of these amplifiers must be cascaded to attain a voltage gain of at least 1000 when operating with a 1-k load? P

Three identical amplifiers having Avoc = 25, Ri = 2 k, and Ro = 3 k are cascaded. Determine the input resistance, the open-circuit voltage gain, and the output resistance of the cascade.

Define the efficiency of a power amplifier. What is dissipated power in an amplifier? What form does dissipated power take?

Find the net power delivered to the ampli- fier by the three dc supply voltages shown in Figure P11.25. vin Amplifier + + + Rs 2 A vs + 15 V + + vo RL 5 V 1 A 15 V 1 A Figure P11.25

A certain amplifier has an input voltage of 100 mV rms, an input resistance of 100 k, and produces an output of 10V rms across an 8- load resistance. The power supply has a voltage of 15 V and delivers an average current of 2 A. Find the power dissipated in the amplifier and the efficiency of the amplifier.

An amplifier operates from a 12-V power supply that supplies a current of 1.5 A. The input signal current is 1 A rms, and the input resistance is 100 k. The amplifier delivers 10 V rms to a 10- load. Determine the power dissipated in the amplifier and the efficiency of the amplifier.

Under high-signal test conditions, a certain audio amplifier supplies a 24 V rms 1-kHz sinusoidal voltage to an 8- load. The power supply delivers 4 A at a voltage of 50 V to the amplifier. The signal power supplied by the input source is negligible. Determine the efficiency and the power dissipated in the amplifier.

Two amplifiers are cascaded. The first has supply power of 2 W, an input resistance of 1 M, and an input voltage of 2 mV rms. The second has a supply power of 22 W, a load resistance of 8 , and output voltage of 12 V rms. Determine the overall power gain, dissipated power, and efficiency.

Draw a voltage-amplifier model. Is the gain parameter measured under open-circuit or short-circuit conditions? Repeat for a current amplifier model, a transresistanceamplifier model, and a transconductanceamplifier model.

a. Which amplifier model contains a current-controlled voltage source? b. A current-controlled current source? c. A voltage- controlled current source?

An amplifier has an input resistance of 20 , an output resistance of 10 , and a short-circuit current gain of 3000. The signal source has an internal voltage of 100 mV rms and an internal impedance of 200 . The load is a 5- resistance. Find the current gain, voltage gain, and power gain of the amplifier. If the power supply has a voltage of 12 V and supplies an average current of 2 A, find the power dissipated in the amplifier and the efficiency. *

An amplifier has Ri = 100 , Ro = 1 k, and Rmoc = 10 k. Determine the values (including units) of Avoc, Gmsc, and Aisc for this amplifier.

An amplifier has Ri = 10 k, Ro = 100 , and Gmsc = 0.5 S. Determine the values (including units) of Avoc, Rmoc, and Aisc for this amplifier.

An amplifier has an input resistance of 100 , an output resistance of 10 , and a short-circuit current gain of 500. Draw the voltage amplifier model for the amplifier, including numerical values for all parameters. Repeat for the transresistance and transconductance models.

An amplifier has a short-circuit current gain of 10. When operated with a 50- load, the current gain is 8. Find the output resistance of the amplifier.

An amplifier has Ri = 2 k,Ro = 300, and Aisc = 200. Determine the values (including units) of Avoc, Rmoc, and Gmsc for this amplifier.

Amplifier A has an input resistance of 1 M, an output resistance of 200 , and an open-circuit transresistance gain of 100 M. Amplifier B has an input resistance of 50 , an output impedance of 500 k, and a short-circuit current gain of 100. Find the voltage amplifier model for the cascade of A followed by B. Then, determine the corresponding transconductance amplifier model. P11

Repeat Problem P11.38 if the order of the cascade is changed to B A.

An amplifier has an input resistance of 1 k, an output resistance of 200 , and a short-circuit transconductance gain of 0.5 S. Determine the open-circuit voltage gain, the short-circuit current gain, and the opencircuit transresistance gain.

An amplifier has an input resistance of 10 k, an output resistance of 2 k, and an open-circuit transresistance gain of 200 k. Determine the open-circuit voltage gain, the short-circuit current gain, and the shortcircuit transconductance gain. P

An amplifier has an open-circuit voltage gain of 100, a short-circuit transconductance gain of 0.2 S,and a short-circuit current gain of 50. Determine the input resistance, the output resistance, and the open-circuit transresistance gain.

An amplifier has an open-circuit transresistance gain of 200 , a short-circuit transconductance gain of 0.5 S, and a short-circuit current gain of 50. Determine the input resistance, the output resistance, and the open-circuit voltage gain.

An amplifier with Ri = 2 k, Ro = 500 , and Rmoc = 107 is operated with a 1-k load.A source having aThvenin resistance of 1 k and an open-circuit voltage of 2 cos(200t) mV is connected to the input terminals. Determine the output voltage as a function of time and the power gain. Sec

Describe an application in which an ampli- fier with very high input impedance is needed.

Give an application in which an amplifier with very low input impedance is needed.

We need an amplifier to supply a constant signal to each of a variable number of loads connected in parallel. What output impedance is needed in this situation?Why? What if the loads are connected in series?

Suppose we have a voltage source v(t) = Vdc + Vm cos(t) connected to the input terminals of an amplifier. The load is a nonlinear device such as an LED. a.What output impedance is needed for the amplifier if we need the current through the load to be proportional to v(t)? b. If we need the voltage across the load to be proportional to v(t)?

Give an example of a situation in which a specific input impedance is needed for an amplifier.

Give the input and output impedances for an ideal-voltage amplifier. Repeat for each of the other ideal amplifier types

An ideal transconductance amplifier having a short-circuit transconductance gain of 0.1 S is connected as shown in Figure P11.51. Find the resistance Rx = vx/ix seen from the input terminals. Amplifier + vx Rx vo + vin ix x x' + Figure P11.51

Repeat Problem P11.51, assuming that the amplifier has an input resistance of 1000 , an output impedance of 20 , and an opencircuit transresistance gain of 10 k. P

An amplifier has an input resistance of 1 , an output resistance of 1 , and an opencircuit voltage gain of 10. Classify this ampli- fier as an approximate ideal type and find the corresponding gain parameter. In deciding on an amplifier classification, assume that the source and load impedances are on the order of 1 k.

Repeat Problem P11.53 if the input impedance is 1 M, the output impedance is 1 M, and the open-circuit voltage gain is 100.

In instrumenting a physics experiment, we need to record the open-circuit voltage of a certain sensor. The voltage needs to be amplified by a factor of 1000 and applied to a variable load resistance. What type of ideal amplifier is needed? Justify your answer.

The output terminals of an ideal transresistance amplifier are connected to the input terminals of an ideal transconductance amplifier.What type of ideal amplifier results? Determine its gain parameter in terms of the gain parameters of the separate stages.

In recording automotive emissions, we need to sense the short-circuit current of a chemical sensor that has a variable Thvenin impedance. A voltage that is proportional to the current must be applied to the input of a data-acquisition module. What type of ideal amplifier is needed? Justify your answer.

What type of ideal amplifier is needed if we need to sense the short-circuit current of a sensor and drive a proportional current through a variable load? Explain your answer.

The output terminals of an ideal voltage amplifier are connected to the input terminals of an ideal transconductance amplifier. What type of ideal amplifier results? Determine its gain parameter in terms of the gain parameters of the separate stages.

Suppose we have a two-stage cascaded amplifier with an ideal transconductance amplifier as the first stage and an ideal transresistance amplifier as the second stage. What type of amplifier results and what is its gain in terms of the gains of the two stages? Repeat for the amplifiers cascaded in the opposite order

In a certain application, an amplifier is needed to sense the open-circuit voltage of a source and force current to flow through a load. The source resistance and load resistance are variable. The current delivered to the load is to be nearly independent of both the source resistance and load resistance. What type of ideal amplifier is needed? If the source resistance increases from 1 k to 2 k and it causes a 1 percent decrease in load current, what is the value of the input resistance? If the load resistance increases from 100 to 300 and this causes a 1 percent decrease in load current, what is the value of the output resistance? P

We need to design an amplifier for use in recording the short-circuit current of experimental electrochemical cells versus time. (For this purpose, a short circuit is any resistance less than 10 .) The amplifier output is to be applied to a strip-chart recorder that deflects 1 cm 1 percent for each volt applied. The input resistance of the recorder is unknown and likely to be variable, but it is greater than 10 k. A deflection of 1 cm per milliampere of cell current with an accuracy of about 3 percent is desired. What type of ideal amplifier is best suited for this application? Using your best judgment, find specifications for the amplifiers input impedance, output impedance, and gain parameter.

An amplifier is needed as a part of a system for documentation of voltages in the earth created by an electrical power distribution system. Voltage waveforms occurring between probes to be placed in the earth are to be amplified before being applied to the analog-to-digital converter (ADC) inputs of laptop computers. The internal impedance of the probe can be as high as 10 k in dry sand or as low as 10 in muck. Because several different models of ADCs are to be used in the project, the load impedance for the amplifier varies from 10 k to 1 M. Nominally, the voltage applied to the ADC is required to be 1000 times the open-circuit voltage of the probe 3 percent. What type of ideal amplifier is best suited for this application? Using your best judgment, find the specifications for the impedances and gain parameter of this amplifier.

Repeat Problem P11.63 if, instead of an ADC, a strip-chart recorder having an unknown impedance of less than 100 is used. The strip-chart recorder deflects 1 cm 1 percent per milliampere of applied current. It is desired that the amplifier be designed so that the recorder deflects 1 cm for each 0.1 V of probe voltage.

Sketch the gain magnitude of a typical dccoupled amplifier versus frequency. Repeat for an ac-coupled amplifier.

How is a wideband amplifier different from a narrowband amplifier?

The input to a certain amplifier is vin(t) = 0.1 cos(2000t) + 0.2 cos(4000t + 30) and the corresponding output voltage is vo(t) = 10 cos(2000t 20) + 15 cos(4000t + 20) Determine the values of the complex gain at f = 1000 Hz and at f = 2000 Hz.

Consider the amplifier of Problem P11.62. Should this amplifier be ac coupled or dc coupled? Explain your answer.

The output signal produced by a certain electret microphone consists of a 2-V dc term plus an ac audio signal that has an rms value of 10 mV. The frequencies of the components of the audio signal range from 20 Hz to 10 kHz. We need to amplify the audio signal to 10 V rms, which is to be applied to a loudspeaker. Should this ampli- fier be ac coupled or dc coupled? Explain your answer. What midband voltage gain is needed? What values are appropriate for the half-power frequencies?

The gain of an amplifier is given by A = 1000 [1 + j(f /fB)]2 Determine the upper half-power frequency in terms of fB.

Consider Figure P11.71, in which block A is an ideal transconductance amplifier and block B is an ideal voltage ampli- fier. The capacitance is initially uncharged. a. Derive an expression for vo(t) for t 0 in terms of the amplifier gains, vin(t), and the capacitance C. b. Derive an expression for the overall voltage gain of the system as a function of frequency. [Hint: Assume that vin(t) = Vm cos(2ft), determine the expression for vo(t), and then determine the complex voltage gain by taking the ratio of the phasors for the input and output.] c. Given Gmsc = 106 S, Avoc = 200, and C = 1 F, sketch Bode plots of the voltagegain magnitude and phase to scale for the range from 1 Hz to 1 kHz. vin(t) + vo(t) + A B C Figure P11.71

Consider Figure P11.72, in which block A is an ideal voltage amplifier and block B is an ideal transresistance amplifier. a. Derive an expression for vo(t) in terms of the amplifier gains, vin(t), and the capacitance C. b. Derive an expression for the overall voltage gain of the system as a function of frequency. [Hint: Assume that vin(t) = Vm cos(2ft), determine the expression for vo(t), and then determine the complex voltage gain by taking the ratio of the phasors for the input and output.] c. Given Rmoc = 103 , Avoc = 50/, and C = 1 F, sketch Bode plots of the voltage-gain magnitude and phase to scale for the range from 1 Hz to 1 kHz. vin(t) + vo(t) + A B C Figure P11.72

What are the requirements for the gain magnitude and phase of an amplifier so that linear distortion does not occur?

The input signal to an amplifier is vi(t) = 0.01 cos(2000t) + 0.02 cos(4000t). The gain of the amplifier as a function of frequency is given by A = 100 1 + j(f /1000) Find an expression for the output signal of the amplifier as a function of time

The input signal to an amplifier is vin(t) = 0.01 cos(2000t) + 0.02 cos(4000t). The complex gain of the amplifier at 1000 Hz is 100 45 . What complex value must the gain have at 2000 Hz for distortionless amplification? Sketch or write a computer program to plot the input and output waveforms to scale versus time

The output of an amplifier used to create special effects for audio signals is given by vo(t) = vin(t) + Kvin(t td) in which K and td are constants. a. Is this amplifier linear? Explain carefully. b. Determine the complex voltage gain as a function of frequency. [Hint: Assume that vin(t) = Vm cos(2ft), determine the corresponding output, and divide the phasor output by the phasor input.] c. Given K = 0.5 and td = 1 ms, use a computer to plot the gain magnitude and phase versus frequency for 0 f 10 kHz. d. Does this ampli- fier produce amplitude distortion? Phase distortion? Explain carefully.

Repeat Problem P11.76 for vo(t) = vin(t) + K d dt vin(t) For part (c), assume K = 1/(2000 ).

The output of a certain amplifier in terms of the input is vo(t) = Kvin(t td). a. Is this amplifier linear? Explain carefully. b. Determine the complex voltage gain as a function of frequency. [Hint: Assume that vin(t) = Vm cos(2ft), determine the corresponding output, and divide the phasor output by the phasor input.] c. Given K = 100 and td = 0.1 ms, plot the gain magnitude and phase versus frequency for 0 f 10 kHz. d. Does this amplifier produce amplitude distortion? Phase distortion? Explain carefully.

Sketch the pulse response of an amplifier, showing the rise time, overshoot, ringing, and tilt. Give an approximate relationship between rise time and the upper half-power frequency of a broadband amplifier. Give an approximate relationship between percentage tilt and the lower half-power frequency.

Consider the simple lowpass filter shown in Figure P11.80. a. Find the complex gain A = V2/V1 as a function of frequency.What are the magnitudes of A at dc and at very high frequencies? Find the half-power bandwidth B of the circuit in terms of R and C. b. Consider the case for which the capacitor is initially uncharged and v1(t) is a unit-step function. Find v2(t) and an expression for the rise time tr of the circuit in terms of R and C. c. Combine the results found in parts (a) and (b) to obtain a relationship between bandwidth and rise time for this circuit. Compare your result with Equation 11.11 on page 539. + + C R V1 V2 Figure P11.80

Consider the simple highpass filter shown in Figure P11.81(a). a. Find the complex gain A = V2/V1 as a function of frequency. b. What is the magnitude of the gain at dc? At very high frequencies? Find the halfpower frequency in terms of R and C. c. Consider the input pulse shown in Figure P11.81(b). Assuming that the capacitor Problems 561 is initially uncharged, find an expression for the output voltage v2(t)fort between 0 and T. Assuming that RC is much greater than T, find an approximate expression for percentage tilt. d. Combine the results of parts (b) and (c) to find a relationship between percentage tilt and the half-power frequency. (a) + + C V1 R V2 (b) v1(t) (V) 1 T t Figure P11.81

An audio amplifier is specified to have halfpower frequencies of 15 Hz and 15 kHz. The amplifier is to be used to amplify the pulse shown in Figure P11.81(b). Estimate the rise time and tilt of the amplifier output. The pulse width T is 2 ms

The gain magnitudes of several ampli- fiers are shown versus frequency in Figure P11.83. If the input to the amplifiers is the pulse shown in the figure, sketch the (a) 100.0 70.7 100k f (Hz) A( f ) Figure P11.83 (b) (c) (d) 100 100k f (Hz) 200 A( f ) 10 1 t (ms) vin(t) (mV) 200.0 141.4 20 50k f (Hz) A( f ) Figure P11.83 (Cont.) output of each amplifier versus time. Give quantitative estimates of as many features on each waveform sketch as you can.

The input signal and corresponding output signals are shown for several amplifiers in Figure P11.84. Sketch the gain magnitude of (a) 10 1.0 t (ms) vin(t) (mV) Figure P11.84

What is harmonic distortion? What causes it?

The input to an amplifier is vin(t) = 0.1 cos(2000t) and the corresponding output is vo(t) = 10 cos(2000t) + 0.2 cos(4000t) + 0.1 cos(6000t) Determine the distortion factors D2,D3, and D4. Also, determine the percentage of total harmonic distortion

The transfer characteristic of an amplifier is described by the equation vo(t) = 10vin(t) + 0.6v2 in(t) + 0.4v3 in(t) For the input vin(t) = 2 cos(200t), determine the distortion factors D2, D3, and D4. Also, compute the total harmonic distortion. You may find the following trigonometric identities useful: cos2(A) = 1 2 + 1 2 cos(2A) cos3(A) = 3 4 cos(A) + 1 4 cos(3A)

The transfer characteristic of an amplifier is described by the equation vo(t) = vin(t) + 0.1v2 in(t) For the input vin(t) = cos(1t) + cos(2t), determine the frequency and amplitude of each component of the output. You may find the following trigonometric identities useful: cos2(A) = 1 2 + 1 2 cos(2A) cos(A) cos(B) = 1 2 cos(A B) + 1 2 cos(A + B)

What is a differential amplifier? Define the differential input voltage and the common-mode input voltage. Write an expression for the output in terms of the Problems 563 differential and common-mode input components.

Define the common-mode rejection ratio of a differential amplifier.

In your own words, describe a situation in which a small differential signal is of interest and a large common-mode signal is also present.

The input signals vi1 and vi2 shown in Figure P11.92 are the inputs to a differential ampli- fier with a gain of Ad = 10. (Assume that the common-mode gain is zero.) Sketch the output of the amplifier to scale versus time. Sketch the common-mode input signal to scale versus time. vi1 (V) 1 0 23 1 t (ms) vi2 (V) 1 0 23 1 t (ms) Figure P11.92

A certain amplifier has a differential gain of 500. If the two input terminals are tied together and a 10-mV-rms input signal is applied, the output signal is 20 mV rms. Find the CMRR for this amplifier.

In a certain instrumentation amplifier, the input signal consists of a 20-mV-rms differential signal and a 5-V-rms 60-Hz interfering common-mode signal. It is desired that the common-mode contribution to the output signal be at least 60 dB lower than the contribution from the differential signal. What is the minimum CMRR allowed for the amplifier in decibels?

The output of a certain instrumentation amplifier in terms of the inputs is vo(t) = 1000vi1(t) 1001vi2(t). Determine the CMRR of this amplifier in decibels.

Draw the differential amplifier symbol and show sources for the offset voltage, bias current, and offset current.What effect do these sources have on the output signal of the amplifier?

Sketch the circuit diagram of a balancing circuit for a differential amplifier.

A differential amplifier has a differential gain of 500 and negligible common-mode gain. The input terminals are tied to ground through 1-k resistors having tolerances of 5 percent. What are the extreme values of the output voltage caused by a bias current of 100 nA? What is the output voltage if the resistors are exactly equal?

A differential amplifier has a bias current of 100 nA, a maximum offset current of 20 nA, a maximum offset voltage of 2 mV, an input resistance of 1 M, and a differential gain of 1000. The input terminals are tied to ground through (exactly equal) 100- k resistors. Find the extreme values of the output voltage if the common-mode gain is assumed to be zero.

Repeat Problem P11.99 if the CMRR of the amplifier is 60 dB. By what percentage is the extreme output voltage increased in this case, compared with zero common-mode gain?

A differential amplifier, including sources to model its dc imperfections, is shown under three different test conditions in Figure P11.101. The amplifier has a differential voltage gain of 100, a common-mode voltage gain of zero, and infinite input impedance. Determine the values of Voff, IB, and Ioff.