Section 9-1

1. Identify each type of filter response in Figure 9-32.

A)Band-pass B)High-pass C)Low-pass D)Band-stop

2. A certain low-pass filter has a critical frequency of 800 Hz. What is its bandwidth?

For this low-pass filter with fc of 800 Hz, the bandwidth is 800Hz.

3. A single-pole high-pass filter has a frequency-selective network with R=2.2 kΩ and C=0.0015µF. What is the critical frequency?

fc=1/2πRC=1/(2π(2200Ω)(.0000000015F))= 48.2kHz

Can you determine the bandwidth from the available information? No.

4. What is the roll-off rate of the filter described in Problem 3?

As a single-pole filter it has a roll-off rate of -20 dB\decade.

5. What is the bandwidth of a band-pass filter whose critical frequencies are 3.2 kHz and 3.9 kHz?

BW=fc2-fc1=3.9kHz-3.2kHz=700Hz

What is the Q of this filter?

Q=fo/BW= √fc1fc2/700Hz= √(3.2×3.9)/700=5.05

6. What is the center frequency of a filter with a Q of 15 and a bandwidth of 1 kHz?

Q=fo/BW 15= fo/1kHz=15kHz

Section 9-2

7. What is the damping factor in each active filter shown in Figure 9-33?

DF=2-R1/R2 a)2- 1.2/1.2=1 b)2- 560/1000=1.44 c)both stage 1&2: 2- 330/1000=1.67

Which filters are approximately optimized for a Butterworth response characteristic?

b)2- 560/1000=1.44

8. For the filters in Figure 9-33 that do not have a Butterworth response, specify the changes necessary to convert them to Butterworth responses.

To get the Butterworth response the filter needs a ratio that is equivalent to 0.586. (R1/R2=0.586)=(R1=0.586R2) a)2- 1.2/1.2=1 R1=0.586(1200)=703.2Ω c)both stage 1&2: 2- 330/1000=1.67 R1=0.586(1000)=586Ω

9. Response curves for second-order filters are shown in Figure 9-34. Identify each as Butterworth, Chebyshev, or Bessel.

(a) Chebyshev (b) Butterworth (c) Bessel (d) Butterworth

Section 9-3

10. Is the four-pole filter in Figure 9-35 approximately optimized for a Butterworth response? No

What is the roll-off rate?

-80dB\decade

11. Determine the critical frequency in Figure 9-35.

Stage 1 math fc=1/(2π√(R_1 R_2 C_1 C_2 ))=1/(2π√(4700×6800×0.0000001×0.00000022))=189.8=190Hz

12. Without changing the response curve, adjust the component values in the filter of Figure 9-35 to make it an equal-value filter.

13. Modify the filter in Figure 9-35 to increase the roll-off rate to -120 dB\decade while maintaining an approximate Butterworth response.

14. Using a block diagram format, show how to implement the following roll-off rates using single-pole and two-pole low-pass filters with Butterworth responses.
(a) -40 dB\decade (b) -20 dB\decade (c) -60 dB\decade
(d) -100 dB\decade (e) -120 dB\decade

Section 9-4

15. Convert the equal-value filter from Problem 12 to a high-pass with the same critical frequency and response characteristic.

All that is needed to be done is switch the positions of the resistors and the capacitors.

16. Make the necessary circuit modification to reduce by half the critical frequency in Problem 15.

17. For the filter in Figure 9-36, (a) How would you increase the critical frequency?

Decrease resistor's 1&2 or decrease capacitor's 1&2.

(b) How would you increase the gain?

Decrease R4 or increase R3.

Section 9-5

18. Identify each band-pass filter configuration in Figure 9-37.

(a) two-pole high-pass and two-pole low-pass Cascading band-pass filter (b) Multiple-feedback band-pass filter (c) state-variable band-pass filter

19. Determine the center frequency and bandwidth for each filter in Figure 9-37.

(a) fo=4.95kHz BW=3.84kHz (b) fo=1/2πC √((R1+R3)/R1R2R3)=1/(2π.000000022) √((47000+1800)/(47000×1800×150000))=448.6=449Hz BW=fo/Q=449/4.65=96.5Hz (c) fo=1/2πR4C1=1/2πR7C2=1/(2π×10000×.000000001)=15.9kHz BW=fo/Q=15900/19=836.8=837Hz

20. Optimize the state-variable filter in Figure 9-38 for Q=50. What bandwidth is achieved?

BW=fo/Q=15900/50=318Hz

Section 9-6

21. Show how to make a notch (band-stop) filter using the basic circuit in Figure 9-38.

Using an Adder take the outputs from the low-pass and high-pass outputs.

22. Modify the band-stop filter in Problem 21 for a center frequency of 120 Hz.