When you wire an inductor in series, the total inductance is the direct arithmetic sum of the individual components ($L_{total} = L_1 + L_2 + ... + L_n$), assuming zero mutual magnetic coupling. The current remains identical through every component in the chain, while the total DC resistance (DCR) and the AC impedance ($X_L$) both add up. This topology is the go-to configuration when you need to increase total inductance without relying on a single, physically massive core that might suffer from high parasitic capacitance or severe saturation limits.
Topology Description and Node Behavior
To analyze the circuit mathematically and practically, we define three primary nodes in a basic two-inductor series string:
- Node A (Input): The upstream connection point receiving the drive signal or DC rail.
- Node B (Junction): The physical and electrical bridge connecting the output terminal of $L_1$ to the input terminal of $L_2$.
- Node C (Output/Return): The downstream connection point feeding the load or returning to ground.
Because the same current ($I$) flows through Node A, Node B, and Node C sequentially, the voltage drop across the entire string is the sum of the individual drops ($V_{total} = V_{L1} + V_{L2}$). However, real-world behavior shifts dynamically based on frequency, core saturation, and fault conditions. The table below maps exactly what happens to the circuit parameters when a single variable changes.
| Parameter Changed | Effect on $L_{total}$ | Effect on $I_{total}$ (at fixed V) | Effect on Node B Voltage |
|---|---|---|---|
| AC Frequency Doubles | No change (Ideal) | Halves (due to $X_L = 2\pi fL$ doubling) | Phase shift increases; magnitude shifts based on load impedance |
| $L_1$ Value Increases 2x | Increases (New sum) | Decreases (Higher total reactance) | Increases (Larger voltage drop across $L_1$) |
| $L_1$ Core Saturates | Drops sharply (permeability $\mu$ falls) | Spikes (Reactance collapses) | Drops toward Node A potential |
| Mutual Coupling Added (Aiding) | Increases ($L_{total} = L_1 + L_2 + 2M$) | Decreases | Shifts based on coupled flux density |
| Temperature Rises (+40°C) | Slight drop (Core $\mu$ tempco) | Decreases slightly (Copper DCR increases) | Minor increase (Higher DCR drop at Node B) |
Series vs. Parallel: Why Choose Series and Failure Modes
Why wire inductors in series instead of parallel? The decision comes down to inductance targets, current handling, and fault tolerance. Wiring in series increases total inductance while forcing the full load current through every component. Wiring in parallel decreases total inductance and splits the current, but it introduces severe risks if the components are not perfectly matched.
According to fundamental circuit theory documented by resources like Electronics Tutorials, parallel inductors require identical values and DCR to share current evenly. If one parallel inductor has a slightly lower DCR, it hogs the current, heats up, drops in inductance due to thermal drift, and hogs even more current until it fails.
Failure Mode Contrast: What Breaks at the Extremes?
Understanding how the topology fails is critical for designing protective circuits. Here is the exact failure contrast between series and parallel configurations:
- Series Open (Wire breaks or internal winding snaps): The circuit is dead. Impedance becomes infinite, current drops to zero, and Node B floats or pulls to ground via the downstream load. It is a safe, fail-open condition.
- Series Short (Insulation melts, winding shorts to itself): The shorted inductor effectively becomes a piece of wire. $L_{total}$ drops to the value of the remaining inductor(s). The overall reactance plummets, causing a massive current spike that can saturate the remaining inductor or destroy downstream switching MOSFETs.
- Parallel Open: The remaining inductor is forced to carry 100% of the load current. If it was only sized for 50%, it will rapidly saturate and overheat.
- Parallel Short: A dead short across the power rail. Upstream fuses blow or traces vaporize.
Real-World Design Walkthrough: Picking Component Values
Let's design a series inductor string for a high-current DC-DC buck converter input filter. We need a total inductance of 22µH, and the circuit will see a continuous DC current of 4.0A. Instead of sourcing a single, expensive 22µH inductor rated for 5A+ (which would have a massive physical footprint), we can distribute the thermal load and BOM cost by using two smaller, readily available shielded SMD power inductors in series.
| Parameter | L1: Wurth 744043100 | L2: Bourns SRP1265A-120M | Combined Series Total |
|---|---|---|---|
| Inductance ($L$) | 10µH | 12µH | 22µH |
| DC Resistance (DCR) | 45mΩ (Max) | 24mΩ (Typ) | 69mΩ |
| Saturation Current ($I_{sat}$) | 2.8A | 6.5A | 2.8A (Bottleneck) |
| RMS Current ($I_{rms}$) | 2.3A | 5.5A | 2.3A (Bottleneck) |
Critical Design Catch: Look at the combined totals. While the inductance adds up perfectly to 22µH, the current rating of a series string is strictly limited by the weakest link. The Wurth inductor saturates at 2.8A and has an RMS thermal limit of 2.3A. Because the exact same 4.0A current must flow through both components, the Wurth inductor will violently saturate and overheat.
The Fix: We must select parts where both $I_{sat}$ and $I_{rms}$ exceed the maximum system current. For a 4.0A system, we need to swap L1 for a part like the Wurth 744355122 (2.2µH, 14A $I_{sat}$) and adjust L2 to a 20µH high-current variant, or simply use two 11µH inductors both rated for >5A. Never assume series wiring shares current like parallel resistors do; series current is absolute and unforgiving.
Breadboard Testing: Step-by-Step Verification
Before soldering your series inductor string to a custom PCB, you need to verify the total inductance and check for parasitic coupling on the breadboard. Follow this exact sequence using standard bench tools. As noted by practical guides on SparkFun's Inductor Tutorials, measuring inductance requires AC excitation, not just a DC multimeter.
- Physical Orientation (Decoupling): Plug the two inductors into the breadboard. Rotate one inductor 90 degrees relative to the other. If using unshielded radial leaded inductors, space them at least 2 inches apart. This minimizes mutual inductance ($M$) which would otherwise skew your $L_{total}$ reading.
- DCR Baseline Check: Set your multimeter (e.g., Fluke 87V) to the milliohm range. Zero the leads. Probe across the entire series string (Node A to Node C). Verify that the measured DCR matches the sum of the datasheet values (e.g., ~69mΩ + ~20mΩ for breadboard contact resistance). If it reads infinite, you have a broken winding or a bad breadboard contact.
- LCR Meter Verification: Connect your LCR meter (e.g., Keysight U1733C or UNI-T UT612) to Node A and Node C. Set the test frequency to 100kHz (standard for switching power supplies) and select the Series (Ls-Rs) measurement mode. Read the display. You should see the arithmetic sum (e.g., 22.1µH). If the reading is significantly higher or lower, your inductors are magnetically coupling; move them further apart or re-orient them.
- Scope Ring Test (Transient Response): Connect a function generator to Node A, outputting a 50kHz square wave (0V to 5V). Connect your oscilloscope probe to Node B (the junction). Trigger on the rising edge. You should see a damped sine wave (ringing). The frequency of this ringing ($f_r$) is dictated by the total series inductance and the parasitic capacitance of the breadboard and scope probe ($f_r = 1 / (2\pi\sqrt{L_{total}C_{parasitic}})$). If the ringing is heavily asymmetrical or clips early, one of the inductors is entering core saturation at the 5V step transient.
Mastering the inductor in series topology requires looking past the simple $L_1 + L_2$ formula. By respecting current bottlenecks, managing mutual coupling, and verifying transient behavior on the bench, you can reliably build custom magnetics that outperform off-the-shelf single-component solutions.
