An RLC notch filter is a passive circuit combining a resistor, inductor, and capacitor to severely attenuate one specific target frequency while letting all other frequencies pass through unaffected. In a real circuit, it changes the frequency response by carving out a deep, narrow "V-shaped" null (often 20dB to 40dB deep) at the resonant frequency, which is exactly what you need when a single interfering tone—like 60Hz mains hum or a specific switching noise spike—is ruining your signal. Beginners commonly confuse the RLC notch filter (band-stop) with an RLC bandpass filter; the difference is simply where you measure the output voltage: across the LC series combination for a notch, or across the resistor for a bandpass.
The Math and a Worked Numeric Example
To build a series-parallel RLC notch filter, the signal passes through a series resistor ($R_s$), and the output is taken across a parallel branch containing an inductor ($L$) and capacitor ($C$) wired in series with each other. At the resonant frequency, the inductive reactance ($X_L$) and capacitive reactance ($X_C$) are equal and opposite. They cancel out, causing the impedance of the LC branch to drop to near zero. This effectively shorts the target frequency to ground, while DC and other AC frequencies pass through $R_s$ to the output with minimal loss.
The target resonant frequency ($f_r$) is dictated by the Thomson formula:
$f_r = \frac{1}{2\pi\sqrt{LC}}$
Worked Example: Killing a 1 kHz PWM Whine
Suppose you are debugging an audio DAC board and your oscilloscope shows a persistent 1 kHz PWM artifact bleeding into the analog output. You need a passive notch filter to kill it without rolling off the 20 Hz - 20 kHz audio band.
- Pick the Capacitor: We choose a 10 µF polypropylene film capacitor (avoid ceramics here due to piezoelectric microphonics).
- Calculate the Inductor: Rearranging the formula for L: $L = \frac{1}{(2\pi \cdot 1000)^2 \cdot 10 \times 10^{-6}}$. This yields 2.53 mH.
- Select Standard Parts: We select a standard 2.5 mH shielded inductor. The actual resonant frequency shifts slightly to 1006 Hz, which is perfectly acceptable for a wide-enough notch.
- Set the Series Resistor ($R_s$): We use a 100 Ω metal film resistor. This value sets the Q-factor (bandwidth) and dictates the passband insertion loss. Assuming the LC branch has a residual resistance of 0.1 Ω at resonance, the notch depth will be roughly $20 \log_{10}(0.1 / 100)$, yielding an impressive -60 dB attenuation at exactly 1006 Hz.
Where You Meet This in Practice
You will rarely see a discrete RLC notch filter in modern consumer electronics, as digital signal processing (DSP) and switched-capacitor active filters have taken over. However, on the bench and in specialized hardware, passive RLC traps are irreplaceable:
- High-Voltage Power Electronics: When filtering switching node ringing on a 400V DC bus, you cannot use an op-amp-based active filter. A high-voltage-rated RLC notch safely absorbs the specific ringing frequency without exposing fragile silicon to common-mode spikes.
- RF Front-Ends and SDR: Software Defined Radios (SDRs) often suffer from front-end overload when a local FM broadcast tower (e.g., 98.1 MHz) is too close. A passive LC trap (an RLC notch with $R_s$ provided by the 50 Ω source impedance of the antenna) knocks out the specific station without adding the noise figure penalty of an active filter.
- Precision Instrumentation: In ECG or strain-gauge amplifiers, 50/60 Hz mains hum can saturate the high-gain first stage. While digital notch filters exist, they introduce latency. A passive RLC notch at the input prevents the interference from ever reaching the ADC.
Decision Tree: RLC Notch vs. The Alternatives
Choosing the right filter topology depends entirely on your frequency target, board space, and signal voltage. Use this decision matrix to lock in your approach.
| Scenario Constraint | Best Topology | Why It Wins |
|---|---|---|
| Target < 100 Hz, tight PCB space | Active Twin-T (Op-Amp) | Passive inductors for 60 Hz are physically massive and expensive. Op-amps simulate the inductor using capacitors and resistors. |
| Target > 10 MHz, minimal insertion loss | LC Trap / SAW Filter | At RF, the 50 Ω source impedance acts as $R_s$. Adding a physical resistor just burns signal power and adds thermal noise. |
| Target 100 Hz - 5 MHz, high voltage | Passive RLC Notch | Handles high voltage swings without clipping (unlike op-amps) and requires no power supply rails. |
| Need adjustable/variable frequency | Active State-Variable Filter | Tuning a passive RLC requires swapping physical inductors; active filters just need a potentiometer or digital pot. |
The Concrete Pick for Bench Audio/Sensor Work
If you are building a benchtop analyzer or sensor conditioner and need to kill mid-band noise (e.g., 1 kHz to 10 kHz), default to a passive RLC notch using these exact component classes:
- Inductor: Coilcraft DO3316P series (Shielded SMD power inductors offer low DCR and high saturation current).
- Capacitor: WIMA MKP10 or MKS2 series (Polypropylene/Polyester film. Never use X7R ceramics for audio notches; their capacitance drops with applied voltage and they generate piezoelectric noise).
- Resistor: Vishay MRS25 metal film (0.6W, 1% tolerance, low thermal noise).
Component Parasitics: Why Your Simulation Lies
If you simulate an RLC notch filter in LTspice, you will see a notch depth of -120 dB. When you build it on the bench, you might only see -30 dB. This discrepancy is caused by real-world parasitics, specifically the DC Resistance (DCR) of the inductor and the Equivalent Series Resistance (ESR) of the capacitor.
The depth of your notch is mathematically limited by the voltage divider formed by your series resistor ($R_s$) and the residual resistance of the LC branch ($R_{parasitic} = DCR + ESR$). If your inductor has a DCR of 2.0 Ω and your $R_s$ is 100 Ω, the absolute maximum attenuation you can achieve is $20 \log_{10}(2.0 / 100) = -34 \text{ dB}$. To get a deeper notch, you must either increase $R_s$ (which increases passband insertion loss) or buy a larger, lower-DCR inductor.
Bench Tip: Always measure your inductor's DCR with a 4-wire multimeter before soldering. Furthermore, check the inductor's Self-Resonant Frequency (SRF) on the datasheet. If your target notch frequency is above the inductor's SRF, the inductor's parasitic parallel capacitance takes over, and the component behaves like a capacitor. The filter will completely fail to notch the target frequency.
Frequently Asked Questions
Can I use an electrolytic capacitor for an RLC notch filter?
Technically yes, but practically no. Aluminum electrolytic capacitors have high ESR (often >1 Ω) and significant parasitic inductance (ESL). The high ESR will make your notch shallow and wide, while the ESL will create a secondary, unintended resonance at higher frequencies. Always use film capacitors (polypropylene, polyester, or polystyrene) for precision notch filters.
Does the physical order of L and C in the parallel branch matter?
Electrically, no. The LC branch is in series with itself, so $X_L + X_C$ is the same regardless of which component is closest to ground. However, from an EMI and layout perspective, it is often better to place the capacitor on the ground side. This keeps the high-impedance, noise-sensitive node of the inductor away from the ground plane, reducing parasitic capacitive coupling to adjacent traces.
How do I tune the filter if the components have 10% tolerance?
Inductors notoriously have 10% to 20% tolerances. To tune the filter on the bench, use a function generator and an oscilloscope. Wire a 10kΩ trimpot in series with a fixed resistor for $R_s$ to adjust the Q-factor (width) of the notch. To shift the center frequency, you will need to swap the capacitor; keep a kit of 5% tolerance film capacitors on hand to parallel them until you hit the exact null frequency.
