Ohms law and the power law for a resistor relate V, I, R,

Ohms law relates V, I, and R for a resistor. For each of the situations following, find the missing item: (a) R = 1 k, V = 10 V (b) V = 10 V, I = 1 mA (c) R = 10 k, I = 10 mA (d) R = 100 , V = 10 V

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

Ohms 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 k, 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 k, P = 1 W

You are given three resistors whose values are 10 k, 20k, 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).

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 shunt the first. If the original resistor is 10 k, what is the value of the shunting resistor needed to reduce the combined value by 1%, 5%, 10%, and 50%? What is the result of shunting a 10-k resistor by 1 M? By 100 k? By 10 k?

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 Thvenin equivalent of the voltage divider circuit. Find expressions for VO and RO.

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 5% manufacturing tolerance, what are the extreme output voltages and resistances that can result?

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 Thvenin resistance) of each?

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 3.00k?

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

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 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?

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)?

For the circuit in Fig. P1.14, find the Thvenin equivalent circuit between terminals (a) 1 and 2, (b) 2 and 3, and (c) 1 and 3.

Through repeated application of Thvenins theorem, find the Thvenin equivalent of the circuit in Fig. P1.15 between node 4 and ground, and hence find the current that flows through a load resistance of 1.5 k connected between node 4 and ground.

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?

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 Thvenin equivalent of the circuit to the left of node 1 and the Thvenin equivalent of the circuit to the right of node 2. Then solve the resulting simplified circuit.

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?

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, 101 s, 105 ps, or 1 107 s. (For the definition of the various prefixes used in electronics, see Appendix H) For each of the measures listed below, express the trio of terms in scientific notation associated with the basic unit (e.g., 107 s rather than 101 s). (a) T = 104 ms (b) f = 1 GHz (c) = 6.28 102 rad/s (d) T = 10 s (e) f = 60 Hz (f) = 1 krad/s (g) f = 1900 MHz

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 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

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 Thvenin voltage, vs: (a) voc = 10 V, isc = 100 A (b) voc = 0.1 V, isc = 10 A

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 Thvenin voltage, Norton current, and source resistance.

A temperature sensor is specified to provide 2 mV/C. When connected to a load resistance of 10 k, the output voltage was measured to change by 10 mV, corresponding to a change in temperature of 10C. What is the source resistance of the sensor?

Refer to the Thvenin and Norton representations of the signal source (Fig. 1.1). If the current supplied by the source is denoted io and the voltage appearing between the source output terminals is denoted vo, sketch and clearly label vo versus io for 0 io is.

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.)

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.)

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 bit0 for positive and 1 for negative values. List the values that can be represented by this scheme. What is peculiar about the representation of zero? For a particular analog-to-digital converter (ADC), each change in b0 corresponds to a 0.5-V change in the analog input. What is the full range of the analog signal that can be represented? What signed-magnitude digital code results for an input of +2.5 V? For 3.0 V? For +2.7 V? For 2.8 V?

Consider an N-bit ADC whose analog input varies between 0 and VFS (where the subscript FS denotes full scale). (a) Show that the least significant bit (LSB) corresponds to a change in the analog signal of This is the resolution of the converter. (b) Convince yourself that the maximum error in the conversion (called the quantization error) is half the resolution; that is, the quantization error = (c) For VFS = 10 V, how many bits are required to obtain a resolution of 5 mV or better? What is the actual resolution obtained? What is the resulting quantization error?

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 3-V supplies provides a 2.2-V peak sine wave across a 100- load when provided with a 0.2-V peak input from which 1.0 mA peak is drawn. The average current in each supply is measured to be 20 mA. Find the voltage gain, current gain, and power gain expressed as ratios and in decibels as well as the supply power, amplifier dissipation, and amplifier efficiency

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 5-V supplies? With 10-V supplies? With 15-V supplies?

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 9 V, what peak value of input sinusoid is needed to produce an output whose extremes are just at the edge of clipping? Clipped 90% of the time? Clipped 99% of the time?

Consider the voltage-amplifier circuit model shown in Fig. 1.16(b), in which Avo = 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 10k 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, Avo = 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 10n and to decrease Ro to the nearest value of the form 1 10m , find (i) the input resistance achievable; (ii) the output resistance achievable; and (iii) the open-circuit voltage gain now required to meet the specifications.

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, D

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 10m .

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 10m .

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 10m .

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 10m .

For the circuit in Fig. P1.61, show that

An amplifier with an input resistance of 10 k, when driven by a current source of 1 A and a source resistance of 100 k, has a short-circuit output current of 10 mA and an open-circuit output voltage of 10 V. The device is driving a 4-k load. Give the values of the voltage gain, current gain, and power gain expressed as ratios and in decibels?

voltage gain, current gain, and power gain expressed as ratios and in decibels?

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, Avo 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.

Measurement of the frequency response of an amplifier yields the data in the following table: Provide approximate plausible values for the missing table entries. Also, sketch and clearly label the magnitude frequency response (Bode plot) of 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 Thvenin-equivalent node resistance is 100 k to be accidentally shunted to ground by a capacitor (i.e., the node is connected to ground through a capacitor). If the measured 3-dB bandwidth of the amplifier is reduced from the expected 6 MHz to 120 kHz, estimate the value of the shunting capacitor. If the original cutoff frequency can be attributed to a small parasitic capacitor at the same internal node (i.e., between the node and ground), what would you estimate it to be?

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 10n F. What are the values of the smallest capacitors needed to ensure that the corner frequency associated with each is less than 100 Hz? What actual corner frequencies result? For the situation in which the basic amplifier has an open-circuit voltage gain of 100 V/V, find an expression for

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, 103 Hz, 104 Hz, 105 Hz, 106 Hz, 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 f3dB. (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 = C2R2 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 over the amplifier bandwidth, which extends from 100 Hz to 1 kHz. It has been found that the gain falloff at the low-frequency end is determined by the response of a high-pass STC circuit and that at the highfrequency end it is determined by a low-pass STC circuit. What do you expect the corner frequencies of these two circuits to be? What is the drop in gain in decibels (relative to the maximum gain) at the two frequencies that define the amplifier bandwidth? What are the frequencies at which the drop in gain is 3 dB?