2 A resistor, denoted as is connected in series with the

a) Find the cutoff frequency in hertz for the RL filter shown in Fig. P14.1. b) Calculate H(jv) at v 0.125v, c and 8v c) If vi = 20 cos vt V write the steady-state expression for vo when v = 0.125vc v and v = 8vc .Figure P14.1

a) Find the cutoff frequency (in hertz) of the lowpass filter shown in Fig. P14.2. b) Calculate at and 10vcc) If write the steady-state expression for when and Figure P14.2 160  vi 5 mF vo 10vc 0.1v . c v

A resistor, denoted as is added in series with the inductor in the circuit in Fig. 14.4(a). The new lowpass filter circuit is shown in Fig. P14.3. a) Derive the expression for where H(s) = Vo>Vi b) At what frequency will the magnitude of be maximum? c) What is the maximum value of the magnitude of H(jv? d) At what frequency will the magnitude of H(jv equal its maximum value divided by 12? e) Assume a resistance of is added in series with the 50 mH inductor in the circuit in Fig. P14.1. FindH(j0.2vc H(jv ), c v H

A resistor denoted as RL is connected in parallel with the capacitor in the circuit in Fig. 14.7. The loaded low-pass filter circuit is shown in Fig. P14.7.a) Derive the expression for the voltage transfer function Vo/Vi .b) At what frequency will the magnitude of be maximum? c) What is the maximum value of the magnitude of?d) At what frequency will the magnitude of equal its maximum value divided by e) Assume a resistance of is added in parallel with the capacitor in the circuit in Fig. P14.4. Find and v H(j0)

Study the circuit shown in Fig. P14.5 (without the load resistor). a) As 0, the inductor behaves like what circuit component? What value will the output voltage have? b) As , the inductor behaves like what circuit component? What value will the output voltage v0 have? c) Based on parts (a) and (b), what type of filtering does this circuit exhibit? d) What is the transfer function of the unloaded filter? e) If R = 330 L = 10 mH and what is the cutoff frequency of the filter in rad/s?

Suppose we wish to add a load resistor in parallel with the resistor in the circuit shown in Fig. P14.5. a) What is the transfer function of the loaded filter? b) Compare the transfer function of the unloaded filter (part (d) of Problem 14.5) and the transfer function of the loaded filter (part (a) of Problem 14.6). Are the cutoff frequencies different? Are the passband gains different? c) What is the smallest value of load resistance that can be used with the filter from Problem 14.5(e) such that the cutoff frequency of the resulting filter is no more than 5% different from the unloaded filter?

Use a 1 mH inductor to design a low-pass, RL, passive filter with a cutoff frequency of 5 kHz. a) Specify the value of the resistor. b) A load having a resistance of is connected across the output terminals of the filter. What is the corner, or cutoff, frequency of the loaded filter in hertz? c) If you must use a single resistor from Appendix H for part (a), what resistor should you use? What is the resulting cutoff frequency of the filter?

8 Use a 10 mH inductor to design a low-pass passive filter with a cutoff frequency of 1600 . a) Specify the cutoff frequency in hertz. b) Specify the value of the filter resistor. c) Assume the cutoff frequency cannot decrease by more than 10%. What is the smallest value of load resistance that can be connected across the output terminals of the filter? d) If the resistor found in (c) is connected across the output terminals, what is the magnitude of H(jv) when = 0?

Design a passive RC low pass filter (see Fig. 14.7) with a cutoff frequency of 100 Hz using a 4.7 mF capacitor. a) What is the cutoff frequency in b) What is the value of the resistor? c) Draw your circuit, labeling the component values and output voltage. d) What is the transfer function of the filter in part (c)? e) If the filter in part (c) is loaded with a resistor whose value is the same as the resistor part (b), what is the transfer function of this loaded filter? f) What is the cutoff frequency of the loaded filter from part (e)? g) What is the gain in the pass band of the loaded filter from part (e)?

Use a 500 nF capacitor to design a low-pass passive filter with a cutoff frequency of . a) Specify the cutoff frequency in hertz. b) Specify the value of the filter resistor.c) Assume the cutoff frequency cannot increase by more than 5%. What is the smallest value of load resistance that can be connected across the output terminals of the filter? d) If the resistor found in (c) is connected across the output terminals, what is the magnitude of H(j) when = 0 ?

a) Find the cutoff frequency (in hertz) for the highpass filter shown in Fig. P14.11. b) Find H(j)at , 0.125 and 8 c) If vi = 75 cos t write the steady-state expression for vo when = c , = 0.125 and = 8c

2 A resistor, denoted as is connected in series with the capacitor in the circuit in Fig. 14.11(a). The new high-pass filter circuit is shown in Fig. P14.12. a) Derive the expression for where b) At what frequency will the magnitude of be maximum? c) What is the maximum value of the magnitude of ? d) At what frequency will the magnitude of equal its maximum value divided by ? e) Assume a resistance of is connected in series with the 80 F capacitor in the circuit in Fig. P14.11. Calculate

Using a 100 nF capacitor, design a high-pass passive filter with a cutoff frequency of 300 Hz. a) Specify the value of R in kilohms. b) A 47 resistor is connected across the output terminals of the filter. What is the cutoff frequency, in hertz, of the loaded filter?

Consider the circuit shown in Fig. P14.14. a) With the input and output voltages shown in the figure, this circuit behaves like what type of filter? b) What is the transfer function H(s) = Vo(s)>Vi(s),, of this filter? c) What is the cutoff frequency of this filter? d) What is the magnitude of the filters transfer function at ?

Suppose a 150 load resistor is attached to the filter in Fig. P14.14. a) What is the transfer function, H(s) = Vo(s)>Vi(s), of this filter? b) What is the cutoff frequency of this filter? c) How does the cutoff frequency of the loaded filter compare with the cutoff frequency of the unloaded filter in Fig. P14.14? d) What else is different for these two filters?

Design a passive RC high pass filter (see Fig. 14.10[a]) with a cutoff frequency 1500 krad/s. of 500 Hz using a 220 pF capacitor. a) What is the cutoff frequency in rad/s? b) What is the value of the resistor? c) Draw your circuit, labeling the component values and output voltage. d) What is the transfer function of the filter in part (c)? e) If the filter in part (c) is loaded with a resistor whose value is the same as the resistor in (b), what is the transfer function of this loaded filter? f) What is the cutoff frequency of the loaded filter from part (e)? g) What is the gain in the pass band of the loaded filter from part (e)?

Using a inductor, design a high-pass, RL, passive filter with a cutoff frequency of 1500 krad>s. a) Specify the value of the resistance, selecting from the components in Appendix H. b) Assume the filter is connected to a pure resistive load. The cutoff frequency is not to drop below 1200 krad/s. What is the smallest load resistor from Appendix H that can be connected across the output terminals of the filter?

For the bandpass filter shown in Fig. P14.18, find (a) o (b) fo (c) Q, (d) c1 (e) fe1 (f) c2 (g) fc2 and (h) Figure P14.18

Calculate the center frequency, the bandwidth, and the quality factor of a bandpass filter that has an upper cutoff frequency of and a lower cutoff frequency of 100 krad/s

A bandpass filter has a center, or resonant, frequency of and a quality factor of 4. Find the bandwidth, the upper cutoff frequency, and the lower cutoff frequency. Express all answers in kilohertz

Design a series RLC bandpass filter (see Fig. 14.19[a]) with a quality of 8 and a center frequency of 50 krad/s using a 0.01 F capacitor. a) Draw your circuit, labeling the component values and output voltage. b) For the filter in part (a), calculate the bandwidth and the values of the two cutoff frequencies.

The input to the series RLC bandpass filter designed in Problem 14.21 is 5cos t. Find the voltage drop across the resistor when (a) v = vo;(b) v= ; (c) v = v ; vc1 c2; (d) v = 0.1vo v = 10vo

The input to the series RLC bandpass filter designed in Problem 14.21 is 5cos t V. Find the voltage drop across the series combination of the inductor and capacitor when (a) = o; (b) = c1; (c) =c2 ; (d) = 0.1 o; (e)=10o .

4 Show that the alternative forms for the cutoff frequencies of a bandpass filter, given in Eqs. 14.36 and 14.37, can be derived from Eqs. 14.34 and 14.35.

Using a 50 nF capacitor in the bandpass circuit shown in Fig. 14.22, design a filter with a quality factor of 5 and a center frequency of 20 krad/s. a) Specify the numerical values of R and L. b) Calculate the upper and lower cutoff frequencies in kilohertz. c) Calculate the bandwidth in hertz.

Design a series RLC bandpass filter using only three components from Appendix H that comes closest to meeting the filter specifications in Problem 14.25. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filters center frequency and quality factor when compared to the values specified in Problem 14.25

Use a 5 nF capacitor to design a series RLC bandpass filter, as shown at the top of Fig. 14.27.The center frequency of the filter is 8 kHz, and the quality factor is 2. a) Specify the values of R and L. b) What is the lower cutoff frequency in kilohertz? c) What is the upper cutoff frequency in kilohertz? d) What is the bandwidth of the filter in kilohertz?

Design a series RLC bandpass filter using only three components from Appendix H that comes closest to meeting the filter specifications in Problem 14.27. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filters center frequency and quality factor when compared to the values specified in Problem 14.27.

For the bandpass filter shown in Fig. P14.29, calculate the following: (a) fo (b)Q; (c)fc1 (d)fc2 and (e) Figure P14.2

The input voltage in the circuit in Fig. P14.29 is 10 cos vt VCalculate the output voltage when (a) v = v ; o(b) v = v . c1and (c v = vc2

Consider the circuit shown in Fig. P14.31. a) Find o b) Find c) Find Q. d) Find the steady-state expression for when vi = 250 cos vot mV. e) Show that if is expressed in kilohms the Q of the circuit in Fig. P14.31 is Q = 20 1 + 100>RL f) Plot Q versus RL for 20 k RL 2 M Figure P14.31

A block diagram of a system consisting of a sinusoidal voltage source, an RLC series bandpass filter, and a load is shown in Fig. P14.32. The internal impedance of the sinusoidal source is 80 + j0 and the impedance of the load is 480 + j0 .The RLC series bandpass filter has a 20 nF capacitor, a center frequency of and a quality factor of 6.25. a) Draw a circuit diagram of the system. b) Specify the numerical values of L and R for the filter section of the system. c) What is the quality factor of the interconnected system? d) What is the bandwidth (in hertz) of the interconnected system? Figure P14.32

The purpose of this problem is to investigate how a resistive load connected across the output terminals of the bandpass filter shown in Fig. 14.19 affects the quality factor and hence the bandwidth of the filtering system. The loaded filter circuit is shown in Fig. P14.33. a) Calculate the transfer function for Vo/Vi the circuit shown in Fig. P14.33. b) What is the expression for the bandwidth of the system? c) What is the expression for the loaded bandwidth (L) as a function of the unloaded bandwidth ( (U)? d) What is the expression for the quality factor of the system? e) What is the expression for the loaded quality factor ( QL) as a function of the unloaded quality factor (QU )? f) What are the expressions for the cutoff frequencies wc1and wc2?

The parameters in the circuit in Fig. P14.33 are R = 2.4 k, C = 50 pF and L = 2 mH The quality factor of the circuit is not to drop below 7.5. What is the smallest permissible value of the load resistor RL?

For the bandreject filter in Fig. P14.35, calculate (a) (b) (c) Q; (d) in hertz; (e) (f) (g) and (h) . Figure P14.35

For the bandreject filter in Fig. P14.35, a) Find at and b) If , write the steady-state expression for vo when v = v , o v = v , c1v = vc2 v = 0.1v . o, v = 10vo

a) Show (via a qualitative analysis) that the circuit in Fig. P14.37 is a bandreject filter. b) Support the qualitative analysis of (a) by finding the voltage transfer function of the filter. c) Derive the expression for the center frequency of the filter. d) Derive the expressions for the cutoff frequencies wc1 and wc2 e) What is the expression for the bandwidth of the filter? f) What is the expression for the quality factor of the circuit

For the bandreject filter in Fig. P14.38, calculate (a) (b) (c) Q; (d) (e) (f) (g) and (h) in kilohertz

Design an RLC bandreject filter (see Fig. 14.28[a]) with a quality of 2.5 and a center frequency of 25 krad/s using a 200 nF capacitor. a) Draw your circuit, labeling the component values and output voltage. b) For the filter in part (a), calculate the bandwidth and the values of the two cutoff frequencies

The input to the RLC bandreject filter designed in Problem 14.39 is 10cos . Find the voltage drop across the series combination of the inductor and capacitor when (a)w = vo ; (b)w = wo ; (c)w = wc2 ; (d)w = 0.125wo ; (e) v = 8vo.

The input to the RLC bandreject filter designed in Problem 14.39 is 10cos . Find the voltage drop across the resistor when (a) w = wo ; (b) w = wc1 ; (c) w = wc2; (d) w = 0.125wo ; (e w = 8wo

Use a 500 nF capacitor to design a bandreject filter, as shown in Fig. P14.42. The filter has a center frequency of 4 kHz and a quality factor of 5. a) Specify the numerical values of R and L. b) Calculate the upper and lower corner, or cutoff, frequencies in kilohertz. c) Calculate the filter bandwidth in kilohertz

Assume the bandreject filter in Problem 14.42 is loaded with a 1 k resistor. a) What is the quality factor of the loaded circuit? b) What is the bandwidth (in kilohertz) of the loaded circuit? c) What is the upper cutoff frequency in kilohertz? d) What is the lower cutoff frequency in kilohertz?

Design a series RLC bandreject filter using only three components from Appendix H that comes closest to meeting the filter specifications in Problem 14.42. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filters center frequency and quality factor when compared to the values specified in Problem 14.42.

The purpose of this problem is to investigate how a resistive load connected across the output terminals of the bandreject filter shown in Fig. 14.28(a) affects the behavior of the filter. The loaded filter circuit is shown in Fig. P14.45. a) Find the voltage transfer function b) What is the expression for the center frequency? c) What is the expression for the bandwidth? d) What is the expression for the quality factor? e) Evaluate H(jwo). f) Evaluate H(j0) g) Evaluate H(j)h) What are the expressions for the corner frequencies wc1and wc2 ?

The parameters in the circuit in Fig. P14.45 are and RL = 150 a) Find wo (in kilohertz), and Q. b) Find and c) Find and d) Show that if is expressed in ohms the Q of the circuit is e) Plot Q versus for 10 RL RL 300 .

The load in the bandreject filter circuit shown in Fig. P14.42 is The center frequency of the filter is and the capacitor is 25 nF. At very low and very high frequencies, the amplitude of the sinusoidal output voltage should be at least 90% of the amplitude of the sinusoidal input voltage. a) Specify the numerical values of R and L. b) What is the quality factor of the circuit?

Given the following voltage transfer function:* 106s2 + 1000s + 25 * 106 . H a) At what frequencies (in radians per second) is the magnitude of the transfer function equal to unity? b) At what frequency is the magnitude of the transfer function maximum? c) What is the maximum value of the transfer function magnitude?

Consider the series RLC circuit shown in Fig. P14.49. When the output is the voltage across the resistor, we know this circuit is a bandpass filter. When the output is the voltage across the series combination of the inductor and capacitor, we know this circuit is a bandreject filter. This problem investigates the behavior of this circuit when the output is across the inductor. a) Find the transfer function, H(s ) = Vo(s)>Vi(s) when is the voltage across the inductor. b) Find the magnitude of the transfer function in part (a) for very low frequencies. c) Find the magnitude of the transfer function in part (a) for very high frequencies. d) Based on your answers in parts (b) and (c), what type of filter is this? e) Suppose R = 600 , L = 400 mH, C = 2.5 mFCalculate the cutoff frequency of this filter, that is, the frequency at which the magnitude of the transfer function is . 1>12

Repeat parts (a) (d) from Problem 14.49 for the circuit shown in Fig. P14.50. Note that the output voltage is now the voltage across the capacitor.

Design a series RLC bandpass filter (see Fig. 14.27) for detecting the low-frequency tone generated by pushing a telephone button as shown in Fig. 14.32. a) Calculate the values of L and C that place the cutoff frequencies at the edges of the DTMF low-frequency band. Note that the resistance in standard telephone circuits is always R = 600. b) What is the output amplitude of this circuit at each of the low-band frequencies, relative to the peak amplitude of the bandpass filter? c) What is the output amplitude of this circuit at the lowest of the high-band frequencies?

Design a DTMF high-band bandpass filter similar to the low-band filter design in Problem 14.51. Be sure to include the fourth high-frequency tone, 1633 Hz, in your design.What is the response amplitude of your filter to the highest of the lowfrequency DTMF tones?

The 20 Hz signal that rings a telephones bell has to have a very large amplitude to produce a loud enough bell signal. How much larger can the ringing signal amplitude be, relative to the low-bank DTMF signal, so that the response of the filter in Problem 14.51 is no more than half as large as the largest of the DTMF tones?