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RC Filter Frequency Response MicroSim

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Description

This MicroSim displays an interactive Bode plot — a graph of filter gain (in decibels) versus frequency (on a log scale) — for a first-order RC filter. Students can switch between low-pass and high-pass configurations, adjust component values, and watch the response curve, cutoff frequency marker, and \(-3 \text{ dB}\) reference line update instantly.

Key Concepts Demonstrated:

Quantity Formula Meaning
Cutoff frequency \(f_c = \dfrac{1}{2\pi RC}\) Frequency at which gain drops to \(-3 \text{ dB}\) (≈ 70.7% of passband)
Low-pass gain \(\|H(f)\| = \dfrac{1}{\sqrt{1+(f/f_c)^2}}\) Passes low frequencies, attenuates high
High-pass gain \(\|H(f)\| = \dfrac{f/f_c}{\sqrt{1+(f/f_c)^2}}\) Passes high frequencies, attenuates low
Roll-off rate \(-20 \text{ dB/decade}\) Gain drops 20 dB for each ×10 in frequency beyond \(f_c\)

Interactive Features:

  • Filter Type Buttons: Switch between Low-Pass and High-Pass instantly
  • R Slider: Adjust resistance from 100 Ω to 100 kΩ (log scale)
  • C Slider: Adjust capacitance from 1 nF to 10 μF (log scale)
  • Live \(f_c\) Display: Cutoff frequency updates in real time as you move sliders
  • Dashed Reference Lines: \(-3 \text{ dB}\) horizontal line and \(f_c\) vertical marker
  • Frequency Sweep: Animated orange cursor sweeps across the plot, showing gain at each frequency

How to Use

  1. Observe the initial state: 1 kΩ, 100 nF, \(f_c \approx 1.59 \text{ kHz}\), Low-Pass selected
  2. Move the R slider right — watch \(f_c\) drop and the curve shift left
  3. Move the C slider left — watch \(f_c\) rise and the curve shift right
  4. Click High-Pass — the curve flips; low frequencies are now attenuated
  5. Click Start Sweep to animate a cursor across the plot; the readout shows frequency and gain at each point
  6. Note where the cursor crosses the \(-3 \text{ dB}\) line — that is \(f_c\)
  7. Click Reset to return to default values

Lesson Plan

Learning Objectives

After completing this lesson, students will be able to:

  • Calculate the cutoff frequency \(f_c = \frac{1}{2\pi RC}\) for a given RC filter
  • Explain why the \(-3 \text{ dB}\) point is the standard definition of cutoff frequency
  • Predict how increasing R or C shifts the frequency response curve
  • Distinguish the behavior of low-pass and high-pass RC filters from their Bode plots
  • Describe the \(-20 \text{ dB/decade}\) roll-off rate of a first-order filter

Target Audience

  • College freshmen/sophomores in introductory circuits or signals courses
  • Prerequisites: Understanding of resistors, capacitors, and the concept of impedance

Activities

  1. Cutoff Frequency Prediction: Set R = 10 kΩ and C = 10 nF. Before moving sliders, calculate \(f_c\) by hand. Then check the display — does it match?

  2. Decade Comparison: Set R = 1 kΩ, C = 100 nF (\(f_c \approx 1.59 \text{ kHz}\)). Now multiply R by 10 (10 kΩ) — how does \(f_c\) change? Then restore R and multiply C by 10 — same result?

  3. Low-Pass vs High-Pass: With identical R and C values, toggle between the two filter types. What do you notice about the curves at \(f_c\)?

  4. Sweep Observation: Start the sweep and watch the gain readout. Pause mentally when the cursor is exactly at \(f_c\) — what is the gain in dB?

  5. Design Challenge: Design a low-pass filter with \(f_c = 10 \text{ kHz}\) using available component values. Use the sim to verify your design.

Assessment

Formative Questions:

  • If R = 4.7 kΩ and C = 33 nF, what is \(f_c\)?
  • At a frequency of \(10 f_c\), what is the approximate gain in dB for a low-pass filter?
  • Why do both low-pass and high-pass filters have the same gain (\(-3 \text{ dB}\)) at \(f_c\)?
  • If you need to shift \(f_c\) up by one decade, what change to R would achieve this?

Reflection Prompt:

Explain in your own words why the Bode plot x-axis uses a logarithmic frequency scale instead of a linear scale.

Technical Notes

The simulation implements the first-order RC filter transfer function:

Low-pass: [H_{LP}(f) = \frac{1}{1 + j(f/f_c)}, \quad |H_{LP}| = \frac{1}{\sqrt{1 + (f/f_c)^2}}]

High-pass: [H_{HP}(f) = \frac{j(f/f_c)}{1 + j(f/f_c)}, \quad |H_{HP}| = \frac{f/f_c}{\sqrt{1 + (f/f_c)^2}}]

Both are plotted as \(20 \log_{10}(|H|)\) in dB over 200 log-spaced frequency points from 1 Hz to 10 MHz. The chart uses Chart.js 4.x with a logarithmic x-axis. Component sliders use log mapping so each decade of R or C gets equal slider travel.

References