Question & Answer

a. Filter Design

Filter Topology:

For this design, we will use the Multiple Feedback (MFB) topology for the band-pass filter. The MFB topology is commonly used for band-pass filters because it offers better performance in terms of component sensitivity compared to the Sallen-Key topology, especially at high frequencies like 1 MHz.

Design Equations:

Given the requirements:

• Center Frequency ($f_0$): 1 MHz
• Bandwidth ($BW$): 50 kHz
• Passband Gain ($A_v$): 20 dB
• Filter Order: Second-order

Design Equations for MFB Band-Pass Filter:

Summary:

• Center Frequency: 1 MHz
• Bandwidth: 50 kHz
• Passband Gain: 20 dB
• Filter Type: Second-order MFB Band-Pass
• Key Component Values:
  • $R_1 = R_2 = 1.59 \, \text{k}\Omega$
  • $C_1 = C_2 = 100 \, \text{pF}$
  • $R_3 = 1 \, \text{k}\Omega$, $R_4 = 10 \, \text{k}\Omega$

This design should meet the specified requirements for the communication system's band-pass filter.