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Passive First Order RF Filters: Low Pass, High Pass, and Band Pass Workbench

Passive First Order RF Filters – Low Pass, High Pass & Band Pass Workbench

Interactive synthesis for first order RC low pass, CR high pass, and cascaded RC-CR band pass networks. Tune resistance, capacitance, or target cutoff frequency to inspect the live schematic, nearest E24 commercial values, and logarithmic dual Bode response.

Low Pass (1st-Order RC) Passes DC and low frequencies below fc = 1 / (2πRC) while attenuating high-frequency noise at -20 dB/decade (-6 dB/octave), with -45° phase shift at cutoff, E24 standard commercial component snapping, and 5-decade logarithmic dual Bode plots.
1st-Order RC Low Pass Two-Way Synthesis

Component & Cutoff Parameters

Adjust R or C to compute cutoff fc, or type a target fc to synthesize C automatically.

ZR = R
XC = 1 / (2πfC)
fc = 1 / (2πRC)

Typing a target fc synthesizes capacitance C for the selected resistance R.

Live Topology

Vector Circuit Schematic & Reactance

Animated gold dashes show passband AC signal flow from Vin to Vout.

IEC 60063 E24 Series

Standard Commercial Components (5% E24)

Nearest off-the-shelf E24 resistor and capacitor values and resulting cutoff accuracy.

Nearest E24 Resistor 1.0 kΩ
Nearest E24 Capacitor 10 nF
Realized Cutoff with E24 Parts 15.92 kHz (0.00% error)
5-Decade Logarithmic Sweep 159 Hz – 1.59 MHz

Frequency & Phase Response (Dual Bode Plot)

Gold solid curve shows gain in dB (left axis); charcoal dashed curve shows phase shift in degrees (right axis).

Probe Frequency (ftest)
Filter Metrics Exact Analytical Solution

Key Performance Characteristics

Frequency domain cutoff, phase angle, and time domain step response parameters.

Cutoff Frequency (fc) 15.92 kHz Half power point (−3.01 dB)
Angular Frequency (ωc) 100.0 krad/s ωc = 2π · fc
Time Constant (τ) 10.00 µs τ = R · C (63.2% step level)
Rise Time (10% to 90%) 21.97 µs tr = τ · ln(9) ≈ 0.35 / fc
Phase Shift at fc −45.0° Lagging phase (−90° max)
Stopband Roll-Off −20 dB/dec −6.02 dB per octave above fc

First Order Passive Filter Topologies at a Glance

Characteristic Low Pass (1st-Order RC) High Pass (1st-Order CR) Band Pass (Cascaded RC-CR)
Circuit Topology Series resistor R followed by shunt capacitor C to ground. Series DC-blocking capacitor C followed by shunt resistor R to ground. High-pass stage (C1, R1) cascaded into low-pass stage (R2, C2).
Transfer Function H(jω) 1 / (1 + j·f/fc) (j·f/fc) / (1 + j·f/fc) [(j·f/fL)/(1 + j·f/fL)] · [1/(1 + j·f/fH)]
Gain Magnitude |H(f)| 1 / √(1 + (f/fc)²) (f/fc) / √(1 + (f/fc)²) Peaks at geometric center f0 = √(fL·fH).
Phase Angle φ(f) −arctan(f / fc) (0° at DC, −45° at fc, −90° at ∞). +90° − arctan(f / fc) (+90° at DC, +45° at fc, 0° at ∞). +45° at fL, crosses 0° at f0, −45° at fH.
Physical Capacitor Action Open circuit at DC (passes low frequencies); shorts high-frequency noise to ground. Blocks DC bias and low-frequency hum; acts as a low-impedance bridge at high frequencies. C1 blocks DC/sub-band signals while C2 shunts out-of-band high frequencies.
Typical Engineering Uses ADC anti-aliasing, DAC reconstruction, PLL loop filters, power rail decoupling. AC coupling between amplifier stages, DC offset removal, baseline wander suppression. Wideband IF conditioning, sensor signal windowing, audio crossover pre-filtering.
Interactive first order passive RF and RC filter synthesis workbench. At the −3.01 dB cutoff frequency fc = 1/(2πRC), capacitive reactance |XC| equals resistance R, splitting input signal power equally.

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