GopalKrishna Advanced Rural Research Foundation

GARRF Virtual Engineering & Electronics Laboratory

KALAM ZERO RESEARCH FUNDING LAB

EXPERIMENT 24 ACTIVE BAND-PASS FILTER SIGNAL CONDITIONING PZT / SHM

๐Ÿ”ฌ Experiment 24 โ€” Active Band-Pass Filter

A band-pass filter combines the fundamental ideas of the high-pass filter and low-pass filter. Instead of passing everything above or below one frequency, it allows a selected range of frequencies to pass.

This is an important step toward real engineering signal-processing systems because many sensors do not require the complete frequency spectrum. Engineers often want to isolate the frequency range that contains useful information.

๐ŸŽฏ Experiment Objectives
  • Understand the principle of a band-pass filter.
  • Identify lower and upper cutoff frequencies.
  • Calculate bandwidth.
  • Calculate centre frequency.
  • Understand quality factor Q.
  • Observe attenuation outside the passband.
  • Study the effect of changing the two cutoff frequencies.
  • Understand the importance of band-pass filtering in PZT and SHM.
๐Ÿ’ก Think Before You Start
  • Why would an engineer want to reject both very low and very high frequencies?
  • What happens between the two cutoff frequencies?
  • What determines the bandwidth?
  • Why might a structural vibration measurement need a band-pass filter?

๐Ÿ“š 1. Theory โ€” What Is a Band-Pass Filter?

A band-pass filter allows a selected range of frequencies to pass while attenuating frequencies below and above that range.

It therefore has two important cutoff frequencies:

Bandwidth = fH โˆ’ fL
Centre Frequency = โˆš(fL ร— fH)
Q = Centre Frequency / Bandwidth

A higher Q means a narrower and more selective passband. A lower Q means a wider passband.

Engineering Concept

A practical band-pass filter can be constructed by combining high-pass and low-pass sections:

Input โ†’ High-Pass โ†’ Low-Pass โ†’ Amplifier โ†’ Output

The high-pass section establishes the lower cutoff. The low-pass section establishes the upper cutoff.

โš™๏ธ 2. Virtual Experiment Controls

๐ŸŸข Band-pass filter ready.

๐Ÿ”Œ 3. Virtual Band-Pass Filter Circuit

๐Ÿ“Š 4. Live Filter Results

Input Frequency 500 Hz
Lower Cutoff 100 Hz
Upper Cutoff 1000 Hz
Bandwidth 900 Hz
Centre Frequency 316.2 Hz
Q Factor 0.35
Filter Magnitude 0.93ร—
Output 1.86 V
Region PASSBAND

๐Ÿ“ˆ 5. Input and Filtered Output

The output amplitude depends on the frequency position relative to the lower and upper cutoff frequencies.

๐Ÿ“‰ 6. Band-Pass Frequency Response

The response rises after the lower cutoff, reaches the passband, and falls after the upper cutoff.

๐Ÿ“ 7. Mathematical Model

HHP = (f/fL) / โˆš[1 + (f/fL)ยฒ]
HLP = 1 / โˆš[1 + (f/fH)ยฒ]
|HBP| = |HHP| ร— |HLP|
Aout = Ain ร— Gain ร— |HBP|
Bandwidth = fH โˆ’ fL
f0 = โˆš(fLfH)
Q = f0/Bandwidth

๐Ÿ”ฌ 8. Current Engineering Analysis

๐Ÿงช 9. Perform the Experiment

  1. Start with the default values.
  2. Observe the lower and upper cutoff frequencies.
  3. Set the input frequency below fL.
  4. Observe strong attenuation.
  5. Move the frequency inside the passband.
  6. Observe the larger output.
  7. Move the frequency above fH.
  8. Observe the output falling again.
  9. Change fL and fH.
  10. Observe how the bandwidth changes.
  11. Try to create a narrow band-pass filter.
Research Challenge

Can you design a filter that passes approximately 400โ€“600 Hz while strongly rejecting frequencies below 100 Hz and above 2 kHz?

๐Ÿ”„ 10. Three Fundamental Filters

Experiment 22

Low-Pass
  • Passes low frequencies.
  • Rejects high frequencies.
  • Upper cutoff.

Experiment 23

High-Pass
  • Passes high frequencies.
  • Rejects low frequencies.
  • Lower cutoff.

Experiment 24

Band-Pass
  • Passes a frequency band.
  • Rejects low and high frequencies.
  • Two cutoff frequencies.

๐ŸŽฏ 11. Frequency Classification

Frequency Region Relationship Expected Behaviour
Below fL f < fL Strong attenuation
Near fL f โ‰ˆ fL Transition
Inside passband fL < f < fH Strong transmission
Near fH f โ‰ˆ fH Transition
Above fH f > fH Strong attenuation

๐Ÿง  12. Bandwidth & Q Investigation

fL fH Bandwidth Centre Frequency Q
100 Hz 1000 Hz 900 Hz 316 Hz 0.35
400 Hz 600 Hz 200 Hz 490 Hz 2.45
450 Hz 550 Hz 100 Hz 497 Hz 4.97
900 Hz 1100 Hz 200 Hz 995 Hz 4.97
Key Observation:

Narrowing the passband increases the Q factor. A high-Q filter is more selective.

๐Ÿ“ก 13. PZT & Structural Health Monitoring

Why is band-pass filtering important for SHM?

Structural systems can generate vibration over a wide range of frequencies. However, a particular structural mode, resonance or damage-sensitive feature may occupy only a limited frequency region.

A band-pass filter can isolate that region and reduce irrelevant components outside the target band.

PZT โ†’ Amplifier โ†’ High-Pass โ†’ Low-Pass โ†’ ADC โ†’ AI/ML โ†’ SHM

For example, if an engineering investigation is interested primarily in a vibration band around a particular structural resonance, filtering can reduce unwanted low-frequency drift and high-frequency noise before feature extraction.

Important Engineering Principle

Filtering must be designed from the physics of the measurement. An incorrectly selected passband can remove information that is actually important for detecting damage.

๐ŸŒ 14. Real-World Applications

โ“ 15. Student Quiz

Q1. A band-pass filter primarily:
Q2. A band-pass filter has:
Q3. Bandwidth is:
Q4. A higher Q generally means:
Q5. Band-pass filtering can be useful in SHM because it can:

๐Ÿค– CHITTI

GARRF Robotics & Engineering AI Mentor

Explore electronics, filters, sensors, robotics, signal processing and engineering applications with CHITTI.

๐Ÿ’ก Try asking:

"What is the difference between low-pass, high-pass and band-pass?"

"What is Q factor?"

"Why does a narrow band-pass filter have a high Q?"

"How can band-pass filtering help PZT SHM?"

"How would I select a passband for a structural vibration?"

โš ๏ธ 16. Physical Laboratory Safety

Important:

This is a virtual educational simulation. When constructing the physical circuit, verify op-amp supply voltage, component ratings, breadboard connections and measurement equipment.

Never connect experimental electronics directly to mains voltage.

๐ŸŽ“ 17. Experiment Conclusion

In this experiment we studied the operation of an active band-pass filter.

Unlike a low-pass or high-pass filter, the band-pass filter has both a lower and an upper cutoff frequency.

Bandwidth = fH โˆ’ fL
f0 = โˆš(fL ร— fH)
Q = f0 / Bandwidth

We also saw how a carefully selected frequency band can be used to extract useful information from a much more complicated signal.

This concept forms an important bridge between basic electronics, sensor instrumentation, vibration analysis, PZT systems and AI-assisted Structural Health Monitoring.

From filtering a signal to understanding a structure โ€” this is where electronics becomes intelligent engineering.