For the signal-source representations shown in Figs. 1.1(a) and 1.1(b), what are the open-circuit output voltages that would be observed? If, for each, the output terminals are short-circuited (i.e., wired together), what current would flow? For the representations to be equivalent, what must the relationship be between vs , is , and Rs ?
Ohm’s law relates V, I, and R for a resistor. For each of the situations following, find the missing item:
(a) R = 1 kΩ, V = 10 V
(b) V = 10 V, I = 1 mA
(c) R = 10 kΩ, I = 10 mA
(d) R = 100 Ω, V = 10 V
A signal source has an open-circuit voltage of 10 mV and a short-circuit current of 10 ?A. What is the source resistance?
Measurements taken on various resistors are shown below. For each, calculate the power dissipated in the resistor and the power rating necessary for safe operation using standard components with power ratings of 1/8 W, 1/4 W, 1/2 W, 1 W, or 2 W: (a) 1 k? conducting 30 mA (b) 1 k? conducting 40 mA (c) 10 k? conducting 3 mA (d) 10 k? conducting 4 mA (e) 1 k? dropping 20 V (f) 1 k? dropping 11 V
A signal source that is most conveniently represented by its Th
Ohm’s law and the power law for a resistor relate V, I, R, and P, making only two variables independent. For each pair identified below, find the other two:
(a) R = 1 kΩ, I = 10 mA
(b) V = 10 V, I = 1 mA
(c) V = 10 V, P = 1 W
(d) I = 10 mA, P = 0.1 W
(e) R = 1 kΩ, P = 1 W
A signal source that is most conveniently represented by its Norton equivalent form has is = 10 ?A and Rs = 100 k?. If the source feeds a load resistance RL, find the current io that flows through the load for RL = 1 k?, 10 k?, 100 k?, and 1 M?. Also, find the largest permissible value of RL for which the load current is at least 80% of the source current.
You are given three resistors whose values are 10 k?, 20 k?, and 40 k?. How many different resistances can you create using series and parallel combinations of these three? List them in value order, lowest first. Be thorough and organized. (Hint: In your search, first consider all parallel combinations, then consider series combinations, and then consider series-parallel combinations, of which there are two kinds).
Find the frequencies f and ? of a sine-wave signal with a period of 1 ms.
In the analysis and test of electronic circuits, it is often useful to connect one resistor in parallel with another to obtain a nonstandard value, one which is smaller than the smaller of the two resistors. Often, particularly during circuit testing, one resistor is already installed, in which case the second, when connected in parallel, is said to
What is the period T of sine waveforms characterized by frequencies of (a) f = 60 Hz? (b) f = 10?3 Hz?
Figure P1.6(a) shows a two-resistor voltage divider. Its function is to generate a voltage VO (smaller than the power-supply voltage VDD) at its output node X. The circuit looking back at node X is equivalent to that shown in Fig. P1.6(b). Observe that this is the Th
The UHF (ultra high frequency) television broadcast band begins with channel 14 and extends from 470 MHz to 806 MHz. If 6 MHz is allocated for each channel, how many channels can this band accommodate?
A two-resistor voltage divider employing a 3.3-k? and a 6.8-k? resistor is connected to a 9-V ground-referenced power supply to provide a relatively low voltage (close to 3V). Sketch the circuit. Assuming exact-valued resistors, what output voltage (measured to ground) and equivalent output resistance result? If the resistors used are not ideal but have a
When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied to a resistor, the total power dissipated may be calculated directly using the relationship or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 +
You are given three resistors, each of 10 k?, and a 9-V battery whose negative terminal is connected to ground. With a voltage divider using some or all of your resistors, how many positive-voltage sources of magnitude less than 9 V can you design? List them in order, smallest first. What is the output resistance (i.e., the Th
Consider a 4-bit digital word D = b3b2b1b0 (see Eq. 1.3) used to represent an analog signal vA that varies between 0 V and +15 V. (a) Give D corresponding to vA = 0 V, 1 V, 2 V, and 15 V. (b) What change in vA causes a change from 0 to 1 in (i) b0, (ii) b1, (iii) b2, and (iv) b3? (c) If vA = 5.2 V, what do you expect D to be? What is the resulting error in representation?
Two resistors, with nominal values of 4.7 k? and 10 k?, are used in a voltage divider with a +15-V supply to create a nominal +10-V output. Assuming the resistor values to be exact, what is the actual output voltage produced? Which resistor must be shunted (paralleled) by what third resistor to create a voltage-divider output of 10.00 V? If an output resistance of exactly 3.33 k? is also required, what do you suggest? What should be done if the original 4.7-k? and 10-k? resistors are used but the requirement is 10.00 V and 3.00 k??
An amplifier has a voltage gain of 100 V/V and a current gain of 1000 A/A. Express the voltage and current gains in decibels and find the power gain.
Current dividers play an important role in circuit design. Therefore it is important to develop a facility for dealing with current dividers in circuit analysis. Figure P1.10 shows a tworesistor current divider fed with an ideal current source I. Show that and find the voltage V that develops across the current divider
An amplifier operating from a single 15-V supply provides a 12-V peak-to-peak sine-wave signal to a 1-k? load and draws negligible input current from the signal source. The dc current drawn from the 15-V supply is 8 mA. What is the power dissipated in the amplifier, and what is the amplifier efficiency?
Design a simple current divider that will reduce the current provided to a 1-k? load to 20% of that available from the source
A transducer characterized by a voltage of 1 V rms and a resistance of 1 M? is available to drive a 10-? load. If connected directly, what voltage and power levels result at the load? If a unity-gain (i.e., ) buffer amplifier with 1-M? input resistance and 10-? output resistance is interposed between source and load, what do the output voltage and power levels become? For the new arrangement, find the voltage gain from source to load, and the power gain (both expressed in decibels).
A designer searches for a simple circuit to provide one-third of a signal current I to a load resistance R. Suggest a solution using one resistor. What must its value be? What is the input resistance of the resulting current divider? For a particular value R, the designer discovers that the otherwise-best-available resistor is 10% too high. Suggest two circuit topologies using one additional resistor that will solve this problem. What is the value of the resistor required? What is the input resistance of the current divider in each case?
The output voltage of a voltage amplifier has been found to decrease by 20% when a load resistance of 1 k? is connected. What is the value of the amplifier output resistance?
A particular electronic signal source generates currents in the range 0 mA to 1 mA under the condition that its load voltage not exceed 1 V. For loads causing more than 1 V to appear across the generator, the output current is no longer assured but will be reduced by some unknown amount. This circuit limitation, occurring, for example, at the peak of a sinewave signal, will lead to undesirable signal distortion that must be avoided. If a 10-k? load is to be connected, what must be done? What is the name of the circuit you must use? How many resistors are needed? What is (are) the(ir) value(s)?
An amplifier with a voltage gain of +40 dB, an input resistance of 10 k?, and an output resistance of 1 k? is used to drive a 1-k? load. What is the value of ? Find the value of the power gain in decibels
For the circuit in Fig. P1.14, find the Th
What would the overall voltage gain of the cascade amplifier in Example 1.3 be without stage 3?
Through repeated application of Th
For the cascade amplifier of Example 1.3, let vs be 1 mV. Find vi1, vi2, vi3, and vL.
For the circuit shown in Fig. P1.16, find the current in all resistors and the voltage (with respect to ground) at their common node using two methods: (a) Current: Define branch currents I1 and I2 in R1 and R2, respectively; identify two equations; and solve them. (b) Voltage: Define the node voltage V at the common node; identify a single equation; and solve it. Which method do you prefer? Why?
(a) Model the three-stage amplifier of Example 1.3 (without the source and load), using the voltage amplifier model. What are the values of Ri , Av o, and Ro? (b) If RL varies in the range 10 ? to 1000 ?, find the corresponding range of the overall voltage gain, vo/vs .
The circuit shown in Fig. P1.17 represents the equivalent circuit of an unbalanced bridge. It is required to calculate the current in the detector branch (R5) and the voltage across it. Although this can be done by using loop and node equations, a much easier approach is possible: Find the Th
Consider a current amplifier having the model shown in the second row of Table 1.1. Let the amplifier be fed with a signal current-source is having a resistance Rs , and let the output be connected to a load resistance RL. Show that the overall current gain is given by
For the circuit in Fig. P1.18, find the equivalent resistance to ground, Req. To do this, apply a voltage Vx between terminal X and ground and find the current drawn from Vx . Note that you can use particular special properties of the circuit to get the result directly! Now, if R4 is raised to 1.2 k?, what does Req become?
Consider the transconductance amplifier whose model is shown in the third row of Table 1.1. Let a voltage signal source vs with a source resistance Rs be connected to the input and a load resistance RL be connected to the output. Show that the overall voltage-gain is given by
The periodicity of recurrent waveforms, such as sine waves or square waves, can be completely specified using only one of three possible parameters: radian frequency, ?, in radians per second (rad/s); (conventional) frequency, f, in hertz (Hz); or period T, in seconds (s). As well, each of the parameters can be specified numerically in one of several ways: using letter prefixes associated with the basic units, using scientific notation, or using some combination of both. Thus, for example, a particular period may be specified as 100 ns, 0.1 ?s, 10
Consider a transresistance amplifier having the model shown in the fourth row of Table 1.1. Let the amplifier be fed with a signal current-source is having a resistance Rs , and let the output be connected to a load resistance RL. Show that the overall gain is given by
Find the complex impedance, Z, of each of the following basic circuit elements at 60 Hz, 100 kHz, and 1 GHz: (a) R = 1 k? (b) C = 10 nF (c) C = 2 pF (d) L = 10 mH (e) L = 1 nH
Find the input resistance between terminals B and G in the circuit shown in Fig. E1.21. The voltage vx is a test voltage with the input resistance Rin defined as Rin ? vx / ix.
Find the complex impedance at 10 kHz of the following networks: (a) 1 k? in series with 10 nF (b) 1 k? in parallel with 0.01 ?F (c) 100 k? in parallel with 100 pF (d) 100 ? in series with 10 mH
Consider a voltage amplifier having a frequency response of the low-pass STC type with a dc gain of 60 dB and a 3-dB frequency of 1000 Hz. Find the gain in dB at f = 10 Hz, 10 kHz, 100 kHz, and 1 MHz
Any given signal source provides an open-circuit voltage, voc, and a short-circuit current isc. For the following sources, calculate the internal resistance, Rs ; the Norton current, is ; and the Th
Consider a transconductance amplifier having the model shown in Table 1.1 with Ri = 5 k?, Ro = 50 k?, and Gm = 10 mA/V. If the amplifier load consists of a resistance RL in parallel with a capacitance CL, convince yourself that the voltage transfer function realized, Vo/Vi , is of the low-pass STC type. What is the lowest value that RL can have while a dc gain of at least 40 dB is obtained? With this value of RL connected, find the highest value that CL can have while a 3-dB bandwidth of at least 100 kHz is obtained.
A particular signal source produces an output of 30 mV when loaded by a 100-k? resistor and 10 mV when loaded by a 10-k? resistor. Calculate the Th
Consider the situation illustrated in Fig. 1.27. Let the output resistance of the first voltage amplifier be 1 k? and the input resistance of the second voltage amplifier (including the resistor shown) be 9 k?. The resulting equivalent circuit is shown in Fig. E1.24 where Vs and Rs are the output voltage and output resistance of the first amplifier, C is a coupling capacitor, and Ri is the input resistance of the second amplifier. Convince yourself that V2/Vs is a high-pass STC function. What is the smallest value for C that will ensure that the 3-dB frequency is not higher than 100 Hz?
A temperature sensor is specified to provide 2 mV/
A temperature sensor is specified to provide 2 mV/
The connection of a signal source to an associated signal processor or amplifier generally involves some degree of signal loss as measured at the processor or amplifier input. Considering the two signal-source representations shown in Fig. 1.1, provide two sketches showing each signal-source representation connected to the input terminals (and corresponding input resistance) of a signal processor. What signal-processor input resistance will result in 90% of the open-circuit voltage being delivered to the processor? What input resistance will result in 90% of the short-circuit signal current entering the processor?
To familiarize yourself with typical values of angular frequency ?, conventional frequency f, and period T, complete the entries in the following table:
For the following peak or rms values of some important sine waves, calculate the corresponding other value: (a) 117 V rms, a household-power voltage in North America (b) 33.9 V peak, a somewhat common peak voltage in rectifier circuits (c) 220 V rms, a household-power voltage in parts of Europe (d) 220 kV rms, a high-voltage transmission-line voltage in North America
Give expressions for the sine-wave voltage signals having: (a) 10-V peak amplitude and 10-kHz frequency (b) 120-V rms and 60-Hz frequency (c) 0.2-V peak-to-peak and 1000-rad/s frequency (d) 100-mV peak and 1-ms period
Using the information provided by Eq. (1.2) in association with Fig. 1.5, characterize the signal represented by v(t) = 1/2 + 2/? (sin 2000? t + sin 6000?t + sin 10,000? t + ...). Sketch the waveform. What is its average value? Its peak-topeak value? Its lowest value? Its highest value? Its frequency? Its period?
Measurements taken of a square-wave signal using a frequency-selective voltmeter (called a spectrum analyzer) show its spectrum to contain adjacent components (spectral lines) at 98 kHz and 126 kHz of amplitudes 63 mV and 49 mV, respectively. For this signal, what would direct measurement of the fundamental show its frequency and amplitude to be? What is the rms value of the fundamental? What are the peak-to-peak amplitude and period of the originating square wave?
What is the fundamental frequency of the highestfrequency square wave for which the fifth harmonic is barely audible by a relatively young listener? What is the fundamental frequency of the lowest-frequency square wave for which the fifth and some of the higher harmonics are directly heard? (Note that the psychoacoustic properties of human hearing allow a listener to sense the lower harmonics as well.)
Find the amplitude of a symmetrical square wave of period T that provides the same power as a sine wave of peak amplitude and the same frequency. Does this result depend on equality of the frequencies of the two waveforms?
Give the binary representation of the following decimal numbers: 0, 5, 8, 25, and 57.
Consider a 4-bit digital word b3b2b1b0 in a format called signed-magnitude, in which the most significant bit, b3, is interpreted as a sign bit
Consider an N-bit ADC whose analog input varies between 0 and VFS (where the subscript FS denotes
Figure P1.37 shows the circuit of an N-bit digital-toanalog converter (DAC). Each of the N bits of the digital word to be converted controls one of the switches. When the bit is 0, the switch is in the position labeled 0; when the bit is 1, the switch is in the position labeled 1. The analog output is the current iO. Vref is a constant reference voltage. (a) Show that (b) Which bit is the LSB? Which is the MSB? (c) For Vref = 10 V, R = 5 k?, and N = 6, find the maximum value of iO obtained. What is the change in iO resulting from the LSB changing from 0 to 1?
In compact-disc (CD) audio technology, the audio signal is sampled at 44.1 kHz. Each sample is represented by 16 bits. What is the speed of this system in bits per second?
Various amplifier and load combinations are measured as listed below using rms values. For each, find the voltage, current, and power gains (Av, Ai , and Ap, respectively) both as ratios and in dB: (a) vI = 100 mV, iI = 100 ?A, vO = 10 V, RL = 100 ? (b) v = 10 ?V, iI = 100 nA, vO = 2 V, RL = 10 k? (c) vI = 1 V, iI = 1 mA, vO = 10 V, RL = 10 ?
An amplifier operating from
An amplifier using balanced power supplies is known to saturate for signals extending within 1.2 V of either supply. For linear operation, its gain is 500 V/V. What is the rms value of the largest undistorted sine-wave output available, and input needed, with
Symmetrically saturating amplifiers, operating in the so-called clipping mode, can be used to convert sine waves to pseudo-square waves. For an amplifier with a small-signal gain of 1000 and clipping levels of
Consider the voltage-amplifier circuit model shown in Fig. 1.16(b), in which Av o = 10 V/V under the following conditions: (a) Ri = 10Rs , RL = 10Ro (b) Ri = Rs , RL = Ro (c) Ri = Rs/10, RL = Ro /10 Calculate the overall voltage gain vo/vs in each case, expressed both directly and in decibels.
An amplifier with 40 dB of small-signal, open-circuit voltage gain, an input resistance of 1 M?, and an output resistance of 10 ?, drives a load of 100 ?. What voltage and power gains (expressed in dB) would you expect with the load connected? If the amplifier has a peak output-current limitation of 100 mA, what is the rms value of the largest sine-wave input for which an undistorted output is possible? What is the corresponding output power available?
A 10-mV signal source having an internal resistance of 100 k? is connected to an amplifier for which the input resistance is 10 k?, the open-circuit voltage gain is 1000 V/V, and the output resistance is 1 k?. The amplifier is connected in turn to a 100-? load. What overall voltage gain results as measured from the source internal voltage to the load? Where did all the gain go? What would the gain be if the source was connected directly to the load? What is the ratio of these two gains? This ratio is a useful measure of the benefit the amplifier brings.
A buffer amplifier with a gain of 1 V/V has an input resistance of 1 M? and an output resistance of 10 ?. It is connected between a 1-V, 100-k? source and a 100-? load. What load voltage results? What are the corresponding voltage, current, and power gains (in dB)?
Consider the cascade amplifier of Example 1.3. Find the overall voltage gain vo/vs obtained when the first and second stages are interchanged. Compare this value with the result in Example 1.3, and comment.
You are given two amplifiers, A and B, to connect in cascade between a 10-mV, 100-k? source and a 100-? load. The amplifiers have voltage gain, input resistance, and output resistance as follows: for A, 100 V/V, 10 k?, 10 k?, respectively; for B, 1 V/V, 100 k?, 100 ?, respectively. Your problem is to decide how the amplifiers should be connected. To proceed, evaluate the two possible connections between source S and load L, namely, SABL and SBAL. Find the voltage gain for each both as a ratio and in decibels. Which amplifier arrangement is best?
A designer has available voltage amplifiers with an input resistance of 10 k?, an output resistance of 1 k?, and an open-circuit voltage gain of 10. The signal source has a 10- k? resistance and provides a 10-mV rms signal, and it is required to provide a signal of at least 2 V rms to a 1-k? load. How many amplifier stages are required? What is the output voltage actually obtained.
Design an amplifier that provides 0.5 W of signal power to a 100-? load resistance. The signal source provides a 30-mV rms signal and has a resistance of 0.5 M?. Three types of voltage-amplifier stages are available: (a) A high-input-resistance type with Ri = 1 M?, Avo = 10, and Ro = 10 k? (b) A high-gain type with Ri = 10 k?, Avo = 100, and Ro = 1 k? (c) A low-output-resistance type with Ri = 10 k?, Av o = 1, and Ro = 20 ? Design a suitable amplifier using a combination of these stages. Your design should utilize the minimum number of stages and should ensure that the signal level is not reduced below 10 mV at any point in the amplifier chain. Find the load voltage and power output realized.
It is required to design a voltage amplifier to be driven from a signal source having a 10-mV peak amplitude and a source resistance of 10 k? to supply a peak output of 3 V across a 1-k? load. (a) What is the required voltage gain from the source to the load? (b) If the peak current available from the source is 0.1 ?A, what is the smallest input resistance allowed? For the design with this value of Ri , find the overall current gain and power gain. (c) If the amplifier power supply limits the peak value of the output open-circuit voltage to 5 V, what is the largest output resistance allowed? (d) For the design with Ri as in (b) and Ro as in (c), what is the required value of open-circuit voltage gain of the amplifier? (e) If, as a possible design option, you are able to increase Ri to the nearest value of the form 1
A voltage amplifier with an input resistance of 10 k?, an output resistance of 200 ?, and a gain of 1000 V/V is connected between a 100-k? source with an open-circuit voltage of 10 mV and a 100-? load. For this situation: (a) What output voltage results? (b) What is the voltage gain from source to load? (c) What is the voltage gain from the amplifier input to the load? (d) If the output voltage across the load is twice that needed and there are signs of internal amplifier overload, suggest the location and value of a single resistor that would produce the desired output. Choose an arrangement that would cause minimum disruption to an operating circuit. (Hint: Use parallel rather than series connections.)
A current amplifier for which Ri = 1 k?, Ro = 10 k?, and Ais = 100 A/A is to be connected between a 100-mV source with a resistance of 100 k? and a load of 1 k?. What are the values of current gain io /ii , of voltage gain vo /vs , and of power gain expressed directly and in decibels?
A transconductance amplifier with Ri = 2 k?, Gm = 40 mA/V, and Ro = 20 k? is fed with a voltage source having a source resistance of 2 k? and is loaded with a 1-k? resistance. Find the voltage gain realized.
A designer is required to provide, across a 10-k? load, the weighted sum, vO = 10v1 + 20v2, of input signals v1 and v2, each having a source resistance of 10 k?. She has a number of transconductance amplifiers for which the input and output resistances are both 10 k? and Gm = 20 mA/V, together with a selection of suitable resistors. Sketch an appropriate amplifier topology with additional resistors selected to provide the desired result. (Hint: In your design, arrange to add currents.)
Figure P1.56 shows a transconductance amplifier whose output is fed back to its input. Find the input resistance Rin of the resulting one-port network. (Hint: Apply a test voltage vx between the two input terminals, and find the current ix drawn from the source. Then,
It is required to design an amplifier to sense the open-circuit output voltage of a transducer and to provide a proportional voltage across a load resistor. The equivalent source resistance of the transducer is specified to vary in the range of 1 k? to 10 k?. Also, the load resistance varies in the range of 1 k? to 10 k?. The change in load voltage corresponding to the specified change in Rs should be 10% at most. Similarly, the change in load voltage corresponding to the specified change in RL should be limited to 10%. Also, corresponding to a 10-mV transducer open-circuit output voltage, the amplifier should provide a minimum of 1 V across the load. What type of amplifier is required? Sketch its circuit model, and specify the values of its parameters. Specify appropriate values for Ri and Ro of the form 1
It is required to design an amplifier to sense the short-circuit output current of a transducer and to provide a proportional current through a load resistor. The equivalent source resistance of the transducer is specified to vary in the range of 1 k? to 10 k?. Similarly, the load resistance is known to vary over the range of 1 k? to 10 k?. The change in load current corresponding to the specified change in Rs is required to be limited to 10%. Similarly, the change in load current corresponding to the specified change in RL should be 10% at most. Also, for a nominal short-circuit output current of the transducer of 10 ?A, the amplifier is required to provide a minimum of 1 mA through the load. What type of amplifier is required? Sketch the circuit model of the amplifier, and specify values for its parameters. Select appropriate values for Ri and Ro in the form 1
It is required to design an amplifier to sense the open-circuit output voltage of a transducer and to provide a proportional current through a load resistor. The equivalent source resistance of the transducer is specified to vary in the range of 1 k? to 10 k?. Also, the load resistance is known to vary in the range of 1 k? to 10 k?. The change in the current supplied to the load corresponding to the specified change in Rs is to be 10% at most. Similarly, the change in load current corresponding to the specified change in RL is to be 10% at most. Also, for a nominal transducer open-circuit output voltage of 10 mV, the amplifier is required to provide a minimum of 1 mA current through the load. What type of amplifier is required? Sketch the amplifier circuit model, and specify values for its parameters. For Ri and Ro, specify values in the form 1
It is required to design an amplifier to sense the short-circuit output current of a transducer and to provide a proportional voltage across a load resistor. The equivalent source resistance of the transducer is specified to vary in the range of 1 k? to 10 k?. Similarly, the load resistance is known to vary in the range of 1 k? to 10 k?. The change in load voltage corresponding to the specified change in Rs should be 10% at most. Similarly, the change in load voltage corresponding to the specified change in RL is to be limited to 10%. Also, for a nominal transducer short-circuit output current of 10 ?A, the amplifier is required to provide a minimum voltage across the load of 1 V. What type of amplifier is required? Sketch its circuit model, and specify the values of the model parameters. For Ri and Ro, specify appropriate values in the form 1
For the circuit in Fig. P1.61, show that
Any linear two-port network including linear amplifiers can be represented by one of four possible parameter sets, given in Appendix C. For the voltage amplifier, the most convenient representation is in terms of the g parameters. If the amplifier input port is labeled as port 1 and the output port as port 2, its g-parameter representation is described by the two equations: Figure P1.64 shows an equivalent circuit representation of these two equations. By comparing this equivalent circuit to that of the voltage amplifier in Fig. 1.16(a), identify corresponding currents and voltages as well as the correspondence between the parameters of the amplifier equivalent circuit and the g parameters. Hence give the g parameter that corresponds to each of Ri , Av o and Ro. Notice that there is an additional g parameter with no correspondence in the amplifier equivalent circuit. Which one? What does it signify? What assumption did we make about the amplifier that resulted in the absence of this particular g parameter from the equivalent circuit in Fig. 1.16(a)?
Use the voltage-divider rule to derive the transfer functions of the circuits shown in Fig. 1.22, and show that the transfer functions are of the form given at the top of Table 1.2.
Figure P1.66 shows a signal source connected to the input of an amplifier. Here Rs is the source resistance, and Ri and Ci are the input resistance and input capacitance, respectively, of the amplifier. Derive an expression for and show that it is of the low-pass STC type. Find the 3-dB frequency for the case Rs = 20 k?, Ri = 80 k?, and Ci = 5 pF.
For the circuit shown in Fig. P1.67, find the transfer function and arrange it in the appropriate standard form from Table 1.2. Is this a high-pass or a lowpass network? What is its transmission at very high frequencies? [Estimate this directly, as well as by letting in your expression for T(s).] What is the corner frequency ?0? For R1 = 10 k?, R2 = 40 k?, and C = 0.1 ?F, find f0. What is the value of
It is required to couple a voltage source Vs with a resistance Rs to a load RL via a capacitor C. Derive an expression for the transfer function from source to load (i.e., ), and show that it is of the high-pass STC type. For Rs = 5 k? and RL = 20 k?, find the smallest coupling capacitor that will result in a 3-dB frequency no greater than 10 Hz.
Measurement of the frequency response of an amplifier yields the data in the following table: Provide plausible approximate values for the missing entries. Also, sketch and clearly label the magnitude frequency response (i.e., provide a Bode plot) for this amplifier.
The unity-gain voltage amplifiers in the circuit of Fig. P1.71 have infinite input resistances and zero output resistances and thus function as perfect buffers. Convince yourself that the overall gain will drop by 3 dB below the value at dc at the frequency for which the gain of each RC circuit is 1.0 dB down. What is that frequency in terms of CR?
A manufacturing error causes an internal node of a high-frequency amplifier whose Th
A designer wishing to lower the overall upper 3-dB frequency of a three-stage amplifier to 10 kHz considers shunting one of two nodes: Node A, between the output of the first stage and the input of the second stage, and Node B, between the output of the second stage and the input of the third stage, to ground with a small capacitor. While measuring the overall frequency response of the amplifier, she connects a capacitor of 1 nF, first to node A and then to node B, lowering the 3-dB frequency from 2 MHz to 150 kHz and 15 kHz, respectively. If she knows that each amplifier stage has an input resistance of 100 k?, what output resistance must the driving stage have at node A? At node B? What capacitor value should she connect to which node to solve her design problem most economically?
An amplifier with an input resistance of 100 k? and an output resistance of 1 k? is to be capacitor-coupled to a 10-k? source and a 1-k? load. Available capacitors have values only of the form 1
A voltage amplifier has the transfer function Using the Bode plots for low-pass and high-pass STC networks (Figs. 1.23 and 1.24), sketch a Bode plot for |Av|. Give approximate values for the gain magnitude at f = 10 Hz, 102 Hz, 103Hz, 104Hz, 105Hz, 106Hz, and 107 Hz. Find the bandwidth of the amplifier (defined as the frequency range over which the gain remains within 3 dB of the maximum value).
For the circuit shown in Fig. P1.76 first, evaluate and the corresponding cutoff (corner) frequency. Second, evaluate and the corresponding cutoff frequency. Put each of the transfer functions in the standard form (see Table 1.2), and combine them to form the overall transfer function, Provide a Bode magnitude plot for What is the bandwidth between 3-dB cutoff points?
A transconductance amplifier having the equivalent circuit shown in Table 1.1 is fed with a voltage source Vs having a source resistance Rs , and its output is connected to a load consisting of a resistance RL in parallel with a capacitance CL. For given values of Rs , RL, and CL, it is required to specify the values of the amplifier parameters Ri , Gm, and Ro to meet the following design constraints: (a) At most, x% of the input signal is lost in coupling the signal source to the amplifier (b) The 3-dB frequency of the amplifier is equal to or greater than a specified value f3 dB. (c) The dc gain is equal to or greater than a specified value A0. Show that these constraints can be met by selecting Find Ri , Ro, and Gm for Rs = 10 k?, x = 20%, Ao = 80, RL = 10 k?, CL = 10 pF, and f3dB = 3 MHz.
Use the voltage-divider rule to find the transfer function of the circuit in Fig. P1.78. Show that the transfer function can be made independent of frequency if the condition C1R1 = C2 R2 applies. Under this condition the circuit is called a compensated attenuator and is frequently employed in the design of oscilloscope probes. Find the transmission of the compensated attenuator in terms of R1 and R2.
An amplifier with a frequency response of the type shown in Fig. 1.21 is specified to have a phase shift of magnitude no greater than 11.4
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