GopalKrishna Advanced Rural Research Foundation

GARRF Virtual Engineering & Electronics Laboratory

KALAM ZERO RESEARCH FUNDING LAB

EXPERIMENT 16 RC HIGH-PASS FILTER FREQUENCY RESPONSE SIGNAL PROCESSING

🔬 Experiment 16 — RC High-Pass Filter & Frequency Response

In Experiment 15, we studied the RC low-pass filter. Now we investigate its complementary circuit: the RC high-pass filter.

A high-pass filter attenuates low-frequency components while allowing higher-frequency components to pass. This simple circuit introduces students to another fundamental idea in electronic signal conditioning.

🎯 Experiment Objectives
  • Understand the operation of an RC high-pass filter.
  • Understand the concept of cutoff frequency.
  • Study attenuation of low-frequency signals.
  • Observe the effect of R and C on cutoff frequency.
  • Calculate the cutoff frequency.
  • Observe amplitude and phase response.
  • Study frequency-selective signal processing.
  • Connect basic filtering concepts with sensors and SHM.
👨‍🎓 Think Before You Start
  • Why does a capacitor allow high-frequency signals to pass?
  • Why is a low-frequency signal attenuated?
  • What happens if R increases?
  • What happens if C increases?
  • How is this circuit different from the low-pass filter?

🔄 From Experiment 15 to Experiment 16

Experiment 15 Experiment 16
RC Low-Pass RC High-Pass
Passes low frequencies Passes high frequencies
Attenuates high frequencies Attenuates low frequencies
Output across capacitor Output across resistor
💡 Engineering Insight

Together, the two experiments demonstrate one of the most important ideas in signal processing: different circuit arrangements can select different portions of the frequency spectrum.

📚 1. Theory

What is a High-Pass Filter?

A high-pass filter allows higher-frequency components of a signal to pass while reducing lower-frequency components.

RC High-Pass Circuit

The basic high-pass circuit contains a capacitor in series with the input and a resistor connected from the output node to ground. The output is measured across the resistor.

fc = 1 / (2πRC)

Transfer Function

|H(f)| = (f/fc) / √(1+(f/fc)²)

At frequencies much lower than the cutoff frequency, the output is strongly attenuated. As frequency increases, the output approaches the input amplitude.

Cutoff Frequency

At the cutoff frequency, the output magnitude is approximately 70.7% of the input magnitude, corresponding to approximately −3 dB.

🧩 2. Virtual Experiment Controls

🟢 RC high-pass filter ready. Adjust R, C and input frequency.

🔌 3. Virtual RC High-Pass Filter

📊 4. Live Results

Resistance 10.0 kΩ
Capacitance 0.10 µF
Cutoff Frequency 159.15 Hz
Input Frequency 100 Hz
Output Amplitude 0.532 V
Gain 53.2%
Attenuation −5.48 dB
Phase 57.86°

📈 5. Input and Output Waveforms

The output amplitude and phase change as the input frequency moves relative to the cutoff frequency.

📊 6. High-Pass Frequency Response

At low frequencies the gain is small. Above the cutoff frequency the gain approaches unity.

🔬 7. Engineering Analysis

📝 8. Student Observation Table

Trial R C fc Input f Output Gain Phase

🎓 9. Experiment Procedure

  1. Set R = 10 kΩ.
  2. Set C = 0.10 µF.
  3. Observe the calculated cutoff frequency.
  4. Set the input frequency well below the cutoff frequency.
  5. Observe the small output signal.
  6. Increase the frequency gradually.
  7. Observe the output amplitude increasing.
  8. Set the frequency equal to the cutoff frequency.
  9. Verify that the gain is approximately 70.7%.
  10. Increase the frequency above the cutoff frequency.
  11. Observe that the gain approaches 100%.
  12. Record at least five observations.
⭐ Engineering Challenge

Design a high-pass filter with a cutoff frequency close to 1 kHz.

Experiment with different combinations of R and C. Find at least three different R-C combinations that produce approximately the same cutoff frequency.

📐 10. Sample Calculation

For:

R = 10 kΩ
C = 0.10 µF

The cutoff frequency is:

fc = 1 / (2π × 10,000 × 0.1×10⁻⁶)
fc ≈ 159.15 Hz

At a frequency much higher than 159 Hz, the output approaches the input amplitude. At frequencies much lower than 159 Hz, the output is strongly attenuated.

🌍 11. Real-World Applications

🧠 12. Connection to PZT & Structural Health Monitoring

Many sensor systems contain unwanted low-frequency components, including slow drift, offsets and environmental variations. High-pass filtering provides a simple way of understanding how unwanted low-frequency components can be reduced.

🔬 Research Connection

In Structural Health Monitoring, engineers often analyse dynamic responses such as vibration, acoustic or electromechanical signals. Understanding high-pass filtering is an important foundation for designing signal-conditioning systems.

The same fundamental principle can later be implemented using active filters, digital filters and AI-based signal-processing systems.

❓ 13. Student Quiz

Q1. An RC high-pass filter primarily allows:
Q2. The cutoff frequency is:
Q3. At the cutoff frequency, the magnitude is approximately:
Q4. Increasing R or C generally:
Q5. A high-pass filter can be useful for reducing:

🤖 CHITTI

GARRF Robotics & Engineering AI Mentor

Students can use CHITTI to explore high-pass filters, frequency response, signal conditioning, sensors and robotics.

💡 Try asking:

“What is an RC high-pass filter?”

“Why does a capacitor pass high-frequency signals?”

“How do I calculate the cutoff frequency?”

“How can I design a 1 kHz high-pass filter?”

“How are high-pass filters useful in PZT SHM?”

⚠️ 14. Physical Laboratory Safety

Important:

This is a virtual experiment. If reproduced physically, use a current-limited laboratory supply and verify resistor, capacitor and instrument ratings before making connections.

🎓 15. Experiment Conclusion

The RC high-pass filter demonstrates how a simple resistor and capacitor can selectively control the frequency content of an electrical signal.
fc = 1/(2πRC)
At frequencies below the cutoff frequency, the signal is attenuated. At frequencies above the cutoff frequency, the output approaches the input. The experiment establishes a foundation for understanding signal-conditioning circuits used in electronics, robotics, instrumentation, sensors and Structural Health Monitoring. Simple components create powerful engineering concepts. The next step for the student is to ask: “What new system can I build using this principle?”