How does an RC filter convert a microcontroller PWM pin to pure analog DC?

A PWM signal is a high-frequency square wave whose average voltage is proportional to duty cycle. Setting the RC filter cutoff frequency (fc) at least 10 to 20 times lower than the PWM frequency strips away the high-frequency switching harmonics, leaving an ultra-smooth DC analog voltage.

Why does an ADC input need an RC filter before the pin?

Microcontroller ADCs use an internal sample-and-hold capacitor that momentarily connects to the pin. An external RC filter serves two functions: it acts as an anti-aliasing filter to suppress high-frequency noise and acts as a charge reservoir to prevent ADC sample glitching.

What is the rolloff slope of a passive single-stage RC filter?

A single-pole RC filter attenuates at -20 dB per decade (-6 dB per octave) above cutoff. If steeper rolloff is needed, cascade two RC stages or design an active op-amp Sallen-Key 2nd-order filter (-40 dB/decade).

Free RC Low-Pass Filter Time Constant Calculator

⚡ Component Values & Signal Frequency

Resistance (R in kΩ) 10 kΩ = 10,000 Ohms

Capacitance (C in nF) 100 nF = 0.1 µF

Test Signal Freq (f in Hz) Frequency for attenuation & phase

Step Input Voltage (V_step) 3.3V or 5V logic step

📊 Time Domain & Frequency Response

Time Constant (τ = R·C) 1.00 ms Charges to 63.2% of step

Cutoff Frequency (-3dB fc) 159.2 Hz Attenuation: -3.01 dB

10% to 90% Rise Time (tr): 2.20 ms (2.2 × τ)

Settling Time to 99% (5τ): 5.00 ms

Gain @ Test Freq (500 Hz): -10.4 dB (0.30 V/V)

Phase Shift @ Test Freq: -72.3° (Phase lag)

✅ Smooth Response: Cutoff at 159 Hz provides strong 10 dB rejection against 500 Hz noise while preserving slow DC sensor changes.

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The Fundamental Physics of RC Low-Pass Filters

A simple resistor-capacitor (RC) network forms the most ubiquitous building block in analog and mixed-signal electronics. It functions simultaneously as a frequency-selective filter in the frequency domain and an integrator / delay in the time domain.

The Time Constant (( au = R imes C)) and Exponential Charging

When subjected to an instantaneous voltage step (V_{ ext{step}}), the capacitor charges according to an exponential curve:

V(t) = V_step × [ 1 - e^(-t / τ) ]

At (1 au): Voltage reaches 63.2% of the final value.
At (3 au): Voltage reaches 95.0%.
At (5 au): Voltage reaches 99.3% (considered fully settled for engineering purposes).
10% to 90% Rise Time: (t_r approx 2.197 imes au approx 2.2 au).

Frequency Domain: The -3dB Cutoff ((f_c))

The frequency where capacitive reactance equals resistance ((X_c = R)) is the cutoff frequency, where output signal power drops by exactly 50% (-3.01 dB) and phase lags by 45 degrees:

fc = 1 / (2 × π × R × C) = 1 / (2 × π × τ)