The RL High Pass Topology: Nodes and Behavior
An RL high pass filter allows high-frequency AC signals to pass while attenuating low frequencies and DC. Unlike the more common RC high pass filter (which uses a series capacitor), the RL topology relies on the frequency-dependent impedance of an inductor to shape the signal. The standard configuration places a resistor in series with the signal path and an inductor in parallel (shunt) to ground.
Node Labels & Signal Path:
- $V_{in}$: The input signal source (often a DC bus with superimposed AC ripple).
- $R_1$ (Series): Connects $V_{in}$ to Node A. Limits current and sets the filter's impedance baseline.
- Node A ($V_{out}$): The junction between $R_1$ and $L_1$. This is where you probe or route your filtered high-frequency signal.
- $L_1$ (Shunt): Connects Node A to Ground (GND). Acts as a low-impedance short for DC/low frequencies, and a high-impedance block for high frequencies.
| Parameter Changed | Effect on Cutoff Frequency ($f_c$) | Effect on DC Current Draw | Effect on High-Freq Output Amplitude |
|---|---|---|---|
| Increase $R_1$ | Increases (shifts right) | Decreases | Unchanged (approaches $V_{in}$) |
| Decrease $R_1$ | Decreases (shifts left) | Increases | Unchanged (approaches $V_{in}$) |
| Increase $L_1$ | Decreases (shifts left) | Unchanged (depends on DCR) | Unchanged |
| Decrease $L_1$ | Increases (shifts right) | Unchanged | Unchanged |
Why Choose RL Over the RC Alternative?
The default choice for AC coupling or high-pass filtering is usually an RC circuit (series capacitor, shunt resistor). So why bother with inductors, which are bulkier and more expensive? The decision comes down to DC bias handling, parasitics, and current capacity.
| Criteria | RL High Pass (Series R, Shunt L) | RC High Pass (Series C, Shunt R) |
|---|---|---|
| DC Path | Bleeds DC to ground via inductor DCR. | Blocks DC completely. |
| High DC Bus Extraction | Excellent. Shunt L safely passes DC to ground without burning massive heat, while extracting AC ripple at Node A. | Poor. Series C must be rated for the full DC bus voltage; MLCC capacitance drops severely under high DC bias. |
| Dielectric Absorption | None. Inductors store energy in a magnetic field. | Present in capacitors, causing signal "smearing" or ghosting in precision pulse circuits. |
| Microphonics | Negligible. | Ceramic capacitors (X7R/X5R) can act as microphones, injecting mechanical vibration noise into the signal. |
The Verdict: Choose the RL topology when you need to extract high-frequency AC signals (like switching ripple or RF carriers) from a high-voltage DC bus, or when you must avoid the voltage coefficient and microphonic artifacts inherent to ceramic capacitors. For standard audio AC-coupling where DC must be strictly blocked from the next stage, stick to RC.
Design Walkthrough: Extracting 100kHz Ripple from a 24V Bus
Let’s design a filter to extract the 100kHz switching ripple from a 24V DC power supply so we can feed it into an oscilloscope or an ADC for EMI analysis. We want a cutoff frequency ($f_c$) around 8kHz to ensure the 100kHz ripple passes with minimal attenuation, while lower-frequency line noise (50/60Hz) is heavily suppressed.
1. Select the Resistor ($R_1$):
We need to limit the DC current drawn from the 24V bus through the shunt inductor. Let’s target a power dissipation under 0.5W to use a standard 1W through-hole resistor safely.
$P = \frac{V^2}{R} \rightarrow R = \frac{24^2}{0.5W} = 1152\Omega$.
We will select the standard E24 value of 1.2 kΩ.
Actual power: $P = \frac{576}{1200} = 0.48W$.
Actual DC current: $I = \frac{24V}{1200\Omega} = 20mA$.
2. Calculate the Inductor ($L_1$):
Using our target $f_c \approx 8.7kHz$ and $R = 1200\Omega$:
$L = \frac{R}{2\pi f_c} = \frac{1200}{2 \pi (8700)} \approx 0.0219H$.
We will select a standard 22 mH inductor.
3. Pick Real Component Part Numbers:
- Resistor: Vishay PR01000101201JA100 (PR01 series, 1.2kΩ, 1W, 5% metal film). The 1W rating gives us a safe thermal margin for the 0.48W dissipation.
- Inductor: Bourns 82R-226K (22mH radial, 10% tolerance). Crucially, its saturation current ($I_{sat}$) is rated well above our 20mA DC bias, ensuring the core won't saturate and drop inductance at the operating point. Always verify the Bourns 82R series datasheet for exact saturation curves before ordering.
Failure Mode Contrast: What Breaks at the Extremes?
When debugging a board, knowing how a filter fails saves hours of tracing. Because this is a series-parallel network, open and short faults yield distinctly different symptoms at Node A. For a deeper theoretical breakdown of series/parallel fault analysis, refer to the component failure analysis guide on All About Circuits.
| Component | Fault Type | Symptom at Node A | Downstream Risk |
|---|---|---|---|
| $R_1$ (Series) | Open | $V_{out} = 0V$ (Floating/Dead) | None. Signal simply stops. |
| $R_1$ (Series) | Short | $V_{out} = V_{in}$ (24V DC + AC) | CRITICAL: Full DC bus voltage hits the ADC or scope input, likely destroying the downstream silicon. |
| $L_1$ (Shunt) | Open | $V_{out} = V_{in}$ (Filter defeated) | Downstream stage receives unfiltered 24V DC. High risk of overvoltage damage. |
| $L_1$ (Shunt) | Short (or core saturation) | $V_{out} = 0V$ (AC and DC both grounded) | $R_1$ must dissipate full short-circuit power. If $R_1$ is undersized, it will overheat and fail open. |
Step-by-Step Breadboard Testing
Do not apply the 24V DC bias until you have verified the AC frequency response. Follow this sequence to validate your design safely on the bench.
- Wire the Network: Insert the 1.2kΩ Vishay resistor and 22mH Bourns inductor into the breadboard. Connect one end of the resistor to your function generator output (this is $V_{in}$). Connect the other end of the resistor to Node A. Connect the inductor between Node A and the breadboard ground rail.
- Configure the Generator: Set your function generator to output a 1Vpp sine wave with 0V DC offset and a 50Ω output impedance. (We are testing the AC transfer function first).
- Probe the Input and Output: Connect Oscilloscope Channel 1 to $V_{in}$ and Channel 2 to Node A ($V_{out}$). Set both channels to AC coupling for clear viewing.
- Sweep for the -3dB Point: Start at 1kHz. Note the amplitude at Node A. Slowly increase the frequency. At approximately 8.7kHz, the amplitude at Node A should be 0.707V (which is $1Vpp \times 0.707$, or -3dB).
- Verify High-Frequency Pass: Push the frequency to 100kHz. The amplitude at Node A should be nearly identical to Channel 1 (~1Vpp), confirming the ripple will pass unattenuated.
- Apply DC Bias (Optional but recommended): If your lab power supply allows series injection, apply the 24V DC bias. Monitor the inductor temperature. It should remain cool to the touch, confirming the 20mA DC current is well below the core's saturation threshold.
The Final Decision Path
When deciding how to implement a high-pass filter for signal extraction or noise injection, use this decision matrix to lock in your topology and component class.
- IF the signal is audio-band (20Hz - 20kHz) AND must block DC completely from a sensitive op-amp input THEN use an RC High Pass with a film capacitor (e.g., WIMA MKS2) to avoid microphonics.
- IF the signal is an RF carrier (>10MHz) AND requires strict 50Ω impedance matching THEN use an LC Pi-network or distributed transmission line, as lumped RL elements will suffer from parasitic winding capacitance.
- IF you are extracting high-frequency switching ripple (10kHz - 500kHz) from a DC bus (12V - 48V) for measurement or feedback THEN use the RL High Pass topology described above.
