548  RC Filter Designer

Design and Analyze RC Filters for Signal Conditioning

548.1 RC Filter Designer Tool

This interactive tool helps you design RC filters for IoT signal conditioning applications. Calculate cutoff frequencies, visualize Bode plots, and get component recommendations with standard E24 value snapping.

NoteTool Overview

This filter designer provides:

  • Filter Type Selection: Low-pass, high-pass, band-pass, and band-stop configurations
  • Component Calculator: Enter R and C values to compute cutoff frequency
  • Reverse Calculator: Specify target frequency to get R/C suggestions
  • Bode Plot Visualization: Magnitude (dB) and phase response curves
  • Standard Value Snapping: E24 resistor and capacitor series
  • Transfer Function Display: Mathematical representation
TipHow to Use This Tool
  1. Select Filter Type: Choose LP, HP, BP, or BS from the dropdown
  2. Enter Components: Input resistance and capacitance values
  3. View Results: See cutoff frequency, Bode plots, and transfer function
  4. Use Suggester: Enter target frequency to get component recommendations
  5. Snap to E24: Click to use nearest standard component values

548.2 Understanding RC Filters

RC filters are fundamental building blocks in analog signal conditioning for IoT applications. They use passive components (resistors and capacitors) to shape the frequency response of signals.

548.2.1 Filter Types

Filter Type Passes Blocks Common Applications
Low-Pass Low frequencies High frequencies Noise removal, anti-aliasing
High-Pass High frequencies Low frequencies DC blocking, bass removal
Band-Pass Specific range Outside range Signal selection, tuning
Band-Stop Outside range Specific range Notch filters, 60Hz rejection

548.2.2 Cutoff Frequency Formula

The cutoff frequency (fc) is where the filter attenuates the signal by 3 dB (approximately 70.7% of the input):

\[f_c = \frac{1}{2\pi RC}\]

This is also called the -3dB point or half-power point.

548.2.3 Transfer Functions

NoteFirst-Order Filter Transfer Functions

Low-Pass: \[H(s) = \frac{\omega_c}{s + \omega_c}\]

High-Pass: \[H(s) = \frac{s}{s + \omega_c}\]

Where \(\omega_c = 2\pi f_c\) is the angular cutoff frequency.

548.3 Bode Plot Interpretation

Bode plots show how a filter responds across all frequencies:

548.3.1 Magnitude Response

  • Passband: Region where signals pass with minimal attenuation (near 0 dB)
  • Stopband: Region where signals are significantly attenuated
  • Roll-off: Rate of attenuation in the transition region
    • 1st order: -20 dB/decade
    • 2nd order: -40 dB/decade

548.3.2 Phase Response

  • First-order low-pass: 0 deg at DC, -45 deg at fc, approaches -90 deg at high frequencies
  • First-order high-pass: +90 deg at DC, +45 deg at fc, approaches 0 deg at high frequencies

548.4 E24 Standard Values

The E24 series provides 24 standard values per decade. Using standard values:

  • Reduces component cost
  • Improves availability
  • Maintains reasonable accuracy (5% tolerance)
TipE24 Value Selection Tips
  1. Always snap both R and C to E24 values
  2. Check the actual cutoff frequency after snapping
  3. Adjust the less critical component if needed
  4. Consider E96 (1%) values for precision applications

548.5 Practical Design Guidelines

548.5.1 Choosing Components

Application Typical fc R Range C Range
Temperature sensors 1-10 Hz 10k-100k 1-10 uF
Accelerometers 50-500 Hz 1k-10k 100nF-1uF
Audio signals 20 Hz-20 kHz 1k-47k 1nF-1uF
Anti-aliasing fs/2 1k-10k 10nF-100nF

548.5.2 Design Constraints

ImportantComponent Selection Constraints
  1. Resistance: Keep between 1k and 1M for most applications
    • Too low: Excessive current draw, loading effects
    • Too high: Noise pickup, bias current errors
  2. Capacitance: Consider size and availability
    • Electrolytic (1uF+): Polarized, larger, cheaper
    • Ceramic (< 1uF): Non-polarized, smaller, temperature dependent
    • Film: Stable, accurate, more expensive
  3. Source impedance: Filter R should be >> source impedance
  4. Load impedance: Load should be >> filter R

548.6 What’s Next

This interactive tool is implemented in approximately 800 lines of Observable JavaScript:

Key Features:

  1. Filter calculations: Accurate Butterworth response modeling for 1st and 2nd order filters
  2. Bode plot visualization: Logarithmic frequency axis, dB magnitude scale
  3. E24 value snapping: Automatic component value optimization
  4. Component suggester: Reverse calculator for target frequencies
  5. Interactive query: Real-time gain and phase at any frequency

IEEE Color Palette: - Navy (#2C3E50): Primary text, borders - Teal (#16A085): Magnitude response, positive values - Orange (#E67E22): Phase response, highlights - Purple (#9B59B6): Cutoff frequency markers - Red (#E74C3C): Query frequency marker - Gray (#7F8C8D): Axes, labels, secondary text

Mathematical Models: - Cutoff: fc = 1 / (2 * pi * R * C) - Low-pass magnitude: |H| = 1 / sqrt(1 + (f/fc)^(2n)) - Low-pass phase: phi = -n * atan(f/fc) - High-pass magnitude: |H| = 1 / sqrt(1 + (fc/f)^(2n))