Solved: Using a 50 nF capacitor in the bandpass circuit shown in Fig. 14.22, design a

A series RC low-pass filter requires a cutoff frequency of 8 kHz. Use R = 10 kfl and compute the value of C required.

A series RL low-pass filter with a cutoff frequency of 2 kHz is needed. Using R = 5 kft, compute (a) L; (b) \H(joi)\ at 50 kHz; and (c) 8(ja>) at 50 kHz.

A series RL high-pass filter has R = 5 kfl and L = 3.5 mH. What is (oc for this filter?

A series RC high-pass filter has C = 1 /xF. Compute the cutoff frequency for the following values of R: (a) 100 H; (b) 5 kH; and (c) 30 kO.

Compute the transfer function of a series RC low-pass filter that has a load resistor RL in parallel with its capacitor.

Using the circuit in Fig. 14.19(a), compute the values of R and L to give a bandpass filter with a center frequency of 12 kHz and a quality factor of 6. Use a 0.1 fxF capacitor.

Using the circuit in Fig. 14.22, compute the values of L and C to give a bandpass filter with a center frequency of 2 kHz and a bandwidth of 500 Hz. Use a 250 Cl resistor.

Recalculate the component values for the circuit in Example 14.6(d) so that the frequency response of the resulting circuit is unchanged using a 0.2 ^tF capacitor.

Recalculate the component values for the circuit in Example 14.6(d) so that the quality factor of the resulting circuit is unchanged but the center frequency has been moved to 2 kHz. Use a 0.2 /xF capacitor.

Design the component values for the series RLC bandreject filter shown in Fig. 14.28(a) so that the center frequency is 4 kHz and the quality factor is 5. Use a 500 nF capacitor.

Recompute the component values for Assessment Problem 14.10 to achieve a bandreject filter with a center frequency of 20 kHz. The filter has a 100 fi resistor. The quality factor remains at 5.

Design a passive RC high pass filter (see Fig. 14.10[a]) with a cutoff frequency 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 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 kfl resistor is connected across the output terminals of the filter. What is the cutoff frequency, in hertz, of the loaded filter?

Using a 100 juH 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?

Consider the circuit shown in Fig. P14.15. 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) = 1/,,(^)/^:(^), of this filter? c) What is the cutoff frequency of this filter? d) What is the magnitude of the filter's transfer function at s jcojl

Suppose a 150 ft load resistor is attached to the filter in Fig. P14.15. a) What is the transfer function, H(s) = V( ,(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. P14.15? d) What else is different for these two filters?

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.

Calculate the center frequency, the bandwidth, and the quality factor of a bandpass filter that has an upper cutoff frequency of 121 krad/s and a lower cutoff frequency of 100 krad/s.

A bandpass filter has a center, or resonant, frequency of 50 krad/s and a quality factor of 4. Find the bandwidth, the upper cutoff frequency, and the lower cutoff frequency. Express all answers in kilohertz.

Use a 5 nF capacitor to design a series RLC bandPMBLEM Pa s s filter ' a s snow n a t tn e t0P o f Fig-14.27. The cen " PSPFCE ter frequency of the filter is 8 kHz, and the quality MumsiM 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 Ff that comes closest to meeting the filter specifications in Problem 14.20. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filter's center frequency and quality factor when compared to the values specified in Problem 14.20.

For the bandpass filter shown in Fig. P14.22, find "SPICE (a) coa, (b) fm (c) Q, (d) At (e) fch (f) coc2, (g) /c2, MULT,5IM and(h)iS. Figure P14.22 + 8kfi T~ llOmH ^ -A i ~10nF

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 14.23. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filter's center frequency and quality factor when compared to the values specified in Problem 14.23.

For the bandpass filter shown in Fig. P14.25, calculate -SPICE the following: (a) f0; (b) Q; (c) / c l ; (d) fc2; and (e) 0. MULTISIM Figure P14.25 20 H 40 mH 40 . " F -AW ^nrv> 1 ^ 180 n

The input voltage in the circuit in Fig. PI 4.25 is 500 cos cot mV. Calculate the output voltage when (a) co = co0; (b) co = coci; and (c) co = coc2.

Design a series RLC bandpass filter (see Fig. 14.19[aJ) with a quality of 8 and a center frequency of 50 krad/s, using a 0.01 /xF 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 14.27 is 50costttf mV. Find the voltage drop across the resistor when (a) co = eo(); (b) eo= (ocl; (c) co = o)c2\ (d) co = 0.2wo; (e) co = 5co()

The input to the series RLC bandpass filter designed in Problem 14.27 is 50coswt mV. Find the voltage drop across the series combination of the inductor and capacitor when (a) eo = coa; (b) to = o><;1; (c) co = coc2\ (d) co = 0.2ooo; (e) oo = 5c

A block diagram of a system consisting of a sinusoidal voltage source, an RLC series bandpass filter, and a load is shown in Fig. P14.30. The internal impedance of the sinusoidal source is 80 + ;0 fl, and the impedance of the load is 480 + /0 11. The RLC series bandpass filter has a 20 nF capacitor, a center frequency of 50 krad/s, 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?

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. PI 4.31. a) Calculate the transfer function VJV-, for the circuit shown in Fig. P14.31. b) What is the expression for the bandwidth of the system? c) What is the expression for the loaded bandwidth (/3{J as a function of the unloaded bandwidth (ft/)? d) What is the expression for the quality factor of the system? e) What is the expression for the loaded quality factor (Qi) as a function of the unloaded quality factor (0j) ? f) What are the expressions for the cutoff frequencies a)cl and ft>c2

Consider the circuit shown in Fig. P14.32. a) Find co(>. PSPICE MULTISIM b) Find (3. c) FmdQ. d) Find the steady-state expression for v when Vi = 250 cos a)0t mV. e) Show that if RL is expressed in kilohms the Q of the circuit in Fig. PI4.32 is Q = 20 1 + 100//?L f) Plot Q versus RL for 20 kfl

The parameters in the circuit in Fig. P14.31 are R = 2.4 kO, C = 50 pF, and L = 2 fiH. The quality factor of the circuit is not to drop below 7.5. What is the smallest permissible value of the load resistor /?L?

a) Show (via a qualitative analysis) that the circuit in Fig. P14.34 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 avi an d o>C2- e) What is the expression for the bandwidth of the filter? f) What is the expression for the quality factor of the circuit? Figure P14.34 C It- R

For the bandreject filter in Fig. PI4.35, calculate PSPICE (a) (oa; (b) fa; (c) Q; (d) mcl; (e) / c l ; (f) a>c2; (g) /, 2 ; HULTC,M and (h) j8 in kilohertz. Figure P14.35 50 fiH 20 nF 750 a

Use a 500 nF capacitor to design a bandreject filter, as shown in Fig. P14.36. 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 14.36 is PSPICE loaded with a 1 kft resistor. MULTISIM 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 14.36. a) Draw your filter, labeling all component values and the input and output voltages. b) Calculate the percent error in this new filter's center frequency and quality factor when compared to the values specified in Problem 14.36.

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 250cos&tf mV. Find the voltage drop across the series combination of the inductor and capacitor when (a) co = co(;, (b) co = toi; (c) co =

The input to the RLC bandreject filter designed in Problem 14.39 is 250coswf mV. Find the voltage drop across the resistor when (a) co = toa; (b) co = coc]; (c) co coc2; (d) o> = 02coa\ (e) co = 5con.

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. PI4.42. a) Find the voltage transfer function VjVi. 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{jcoa). f) Evaluate //(/0). g) Evaluate //(/co). h) What are the expressions for the corner frequencies coci and coc2

The parameters in the circuit in Fig. PI4.42 PSPICE are R = 30 ft, L = 1/JLH. C = 4 pF, and MULTISIM Rh=m a a) Find a( /3 (in kilohertz), and Q. b) Find //(/0) and //(/oo). c) Find fc2 and /c1. d) Show that if RL is expressed in ohms the Q of the circuit is Q = y [1 + (30/KOJ. e) Plot Q versus Rh for 10 ft < RL < 300 O.

The load in the bandreject filter circuit shown in Fig. PI4.42 is 500 ft. The center frequency of the filter is 25 krad/s, 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: Ys. 1010 10* H{s) s 2 + 50,000* + 10 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?

Design a series RLC bandpass filter (see Fig. 14.27) PERSPECTIVE *-or detecting the low-frequency tone generated by DEBST pushing a telephone button as shown in Fig. 14.32. PROBLEM 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 ft. 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 r!E!S?. t o tn e low-band filter design in Problem 14.46. Be PERSPECTIVE DESIGN" 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 telephone's bell has to PRSPECTIVE nav e a ver y l a rg e amplitude to produce a loud DESIGN"" 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 14.46 is no more than half as large as the largest of the DTMF tones?