An RL high pass filter is a series resistor-inductor circuit that outputs the signal across the inductor, blocking low frequencies and DC while allowing high frequencies to pass. When you insert this topology into a signal path, it changes the circuit by stripping away low-frequency noise, ground loop hum, or DC bias voltages, leaving only the rapid AC transitions intact. Beginners frequently confuse this with an RL low pass filter (which takes the output across the resistor) or an RC high pass filter (which swaps the inductor for a capacitor and takes output across the resistor).
The Core Mechanics of an RL High Pass Filter
To understand how a high pass filter RL topology operates, you have to look at the inductor's frequency-dependent impedance. The impedance of an inductor is defined as ZL = j2πfL. At DC (0 Hz), the inductor's impedance is zero; it acts as a dead short. Because the output voltage is measured across the inductor, a short circuit yields 0V output. As the frequency increases, the inductor's reactance (XL) climbs linearly. Eventually, XL becomes so large relative to the series resistor that nearly all the input voltage drops across the inductor, passing the signal to the output.
The cutoff frequency (fc)—the point where the output power drops by half (-3 dB)—occurs when the inductive reactance exactly equals the resistance (XL = R). The formula to find this threshold is:
fc = R / (2πL)
Worked Numeric Example: Designing a 10 kHz Cutoff
Let's design a filter to block audio frequencies but pass ultrasonic sensor pulses, targeting a cutoff frequency of 10,000 Hz (10 kHz). We will select a standard 1 kΩ (1000 Ω) resistor for our series component.
First, we solve for the required inductance:
L = R / (2π × fc)
L = 1000 / (2 × 3.14159 × 10000)
L ≈ 0.0159 Henrys, or 15.9 mH
Below is the expected performance of this 1 kΩ / 15.9 mH high pass filter RL circuit across three test frequencies, assuming a 1V peak-to-peak input signal:
| Frequency | Inductive Reactance (XL) | Total Impedance (Z) | Vout / Vin | Attenuation |
|---|---|---|---|---|
| 1 kHz (Below fc) | 100 Ω | 1005 Ω | 0.099 V | -20.0 dB |
| 10 kHz (At fc) | 1000 Ω | 1414 Ω | 0.707 V | -3.0 dB |
| 100 kHz (Above fc) | 10000 Ω | 10050 Ω | 0.995 V | -0.04 dB |
Notice the roll-off rate. A first-order RL filter attenuates low frequencies at a rate of 20 dB per decade (or 6 dB per octave). At 1 kHz (one decade below our 10 kHz cutoff), the signal is crushed by exactly 20 dB, which aligns perfectly with first-order filter theory.
Where You Meet RL High Pass Filters in Practice
While RC filters dominate low-frequency audio work, RL filters carve out specific niches where capacitors fall short. Here is where you will actually wire these up on the bench:
- Rotary Encoder Signal Conditioning: Optical encoders on CNC machines output high-frequency square waves (often 50 kHz to 200 kHz) but act as antennas for 50/60 Hz mains hum. An RL high pass filter easily strips the low-frequency hum without introducing the phase-shift delays that large capacitors might cause in high-speed digital logic paths.
- RF Bias Tees and Chokes: In radio frequency (RF) amplifier design, you often need to inject a DC bias voltage into an RF signal line without letting the RF bleed back into your power supply. While the inductor is technically acting as a low-pass element for the DC supply, the overall network functions as an RL high pass filter for the RF signal path, forcing the high-frequency energy toward the antenna.
- Current Sensing in Motor Drives: When measuring high-frequency switching ripple across a shunt resistor in a brushless DC (BLDC) motor controller, an RL filter can be used to block the low-frequency fundamental motor drive waveform, allowing an oscilloscope to isolate and measure only the high-frequency switching noise.
In our 10 kHz example, we used a 15.9 mH inductor. In the real world, a 15 mH through-hole inductor has significant DC resistance (DCR) and parasitic parallel capacitance. This creates a self-resonant frequency (SRF). If your target high-pass frequency approaches the inductor's SRF, the component stops acting like an inductor and becomes a parallel LC tank circuit, completely ruining your filter response. For frequencies above 1 MHz, always switch to an RC or active filter topology.
RL vs. RC High Pass Filters: Component Selection
When should you reach for an inductor versus a capacitor? Use this decision matrix to choose the right topology for your BOM.
| Criteria | RL High Pass Filter | RC High Pass Filter |
|---|---|---|
| Cost & Size | High cost, physically bulky (especially >1 mH) | Very low cost, tiny SMD footprints available |
| Low-Frequency Cutoffs | Impractical (requires massive, expensive inductors) | Excellent (just increase the capacitor value) |
| High-Frequency Parasitics | Self-resonance ruins performance above a few MHz | Ceramic caps maintain stability well into the GHz range |
| Power Handling | Excellent; inductors handle high DC current without saturation if sized right | Poor; capacitors can suffer from microphonics or dielectric breakdown at high power |
The Verdict: Choose an RC filter for 95% of general-purpose audio, sensor, and microcontroller GPIO debouncing tasks. Choose an RL high pass filter when you are working in high-current environments, RF bias networks, or when you specifically need to avoid the dielectric absorption and microphonic noise inherent in large electrolytic or ceramic capacitors.
Frequently Asked Questions
What is the phase shift of an RL high pass filter at the cutoff frequency?
At the exact cutoff frequency (fc), the output voltage leads the input voltage by exactly +45 degrees. As the frequency drops further below the cutoff toward DC, the phase shift approaches +90 degrees. As the frequency rises well above the cutoff, the phase shift approaches 0 degrees (input and output are in phase). This phase lead is a critical consideration when designing feedback loops for op-amps or PLLs, as it can eat into your phase margin.
Can I use an RL high pass filter for audio speaker crossovers?
Technically yes, but it is rarely done in modern commercial speakers. To block bass frequencies (e.g., a 2 kHz crossover for a tweeter) using an RL topology, you would need a very large, heavy, and expensive inductor. Instead, audio engineers use a capacitor in series with the tweeter (which acts as an RC high pass filter where the tweeter's voice coil is the resistor). Inductors in speaker crossovers are almost exclusively used in low pass configurations for woofers.
Why does my RL high pass filter ring or oscillate on the oscilloscope?
If you are seeing high-frequency ringing on square waves passing through your filter, you are witnessing the effects of parasitic capacitance. Every physical inductor has a small amount of capacitance between its wire windings. Together with your resistor and the inductor's intended inductance, this creates an unintended RLC circuit. If the damping factor is too low, the circuit will resonate at its self-resonant frequency (SRF). To fix this, you can add a small snubber capacitor or a parallel damping resistor across the inductor to lower the Q-factor of the parasitic tank circuit.
How do I calculate the total impedance of an RL high pass filter?
Because the resistor and inductor are out of phase by 90 degrees, you cannot simply add their resistance values together. You must use vector addition. The total impedance (Z) is calculated using the Pythagorean theorem: Z = √(R² + XL²). For example, if R = 100 Ω and XL = 100 Ω, the total impedance is not 200 Ω, but rather √(10000 + 10000) = 141.4 Ω. This total impedance dictates how much current the filter will draw from your signal source.
