Inductors in Series
When two or more inductors are connected in series, the same current flows through each inductor. In most practical circuits where the inductors are not magnetically coupled, their inductance values simply add together. Series-connected inductors are commonly used in power supplies, filter circuits, RF equipment and experimental circuits where a specific inductance value is required.
Series Connection
A series connection means the inductors are connected end-to-end so that there is only one path for current.
L1 ----- L2 ----- L3
The same current flows through every inductor in the series circuit.
Total Inductance (Uncoupled Inductors)
If the inductors are far enough apart that they do not influence each other's magnetic field, the total inductance is simply the sum of the individual inductances.
LT = L1 + L2 + L3 + ...
Example:
L1 = 10 µH L2 = 22 µH L3 = 68 µH LT = 10 + 22 + 68 = 100 µH
Voltage Distribution
Although the same current flows through every inductor, the voltage across each one depends on its inductance and the rate of change of current.
V = L × (dI / dt)
A larger inductance generally develops a larger voltage during changes in current.
Effect on Energy Storage
Connecting inductors in series increases the total inductance, allowing more magnetic energy to be stored for the same current.
Energy = ½ × L × I²
A larger total inductance stores more energy if the current remains the same.
Series Connection with Magnetic Coupling
If the inductors are mounted close together so that their magnetic fields interact, the total inductance is affected by mutual inductance (M).
| Connection | Total Inductance |
|---|---|
| Aiding (magnetic fields reinforce) | LT = L1 + L2 + 2M |
| Opposing (magnetic fields oppose) | LT = L1 + L2 − 2M |
In most ordinary electronic circuits, inductors are spaced far enough apart that mutual inductance can be ignored.
Advantages
- Easy way to obtain a larger inductance.
- Allows designers to combine standard inductor values.
- Can increase energy storage.
- Simple to analyse when inductors are uncoupled.
- Useful in prototypes and repairs.
Limitations
- Total DC resistance (DCR) also increases.
- Physical size becomes larger.
- Additional parasitic capacitance may reduce the self-resonant frequency.
- Mutual coupling can alter the expected inductance if components are placed too close together.
Typical Applications
| Application | Purpose |
|---|---|
| Power Supplies | Obtain a higher inductance. |
| RF Circuits | Tuning and matching. |
| Filters | Increase filter inductance. |
| Laboratory Experiments | Study inductance. |
| Prototype Circuits | Create non-standard inductance values. |
Worked Examples
| Inductors | Total Inductance |
|---|---|
| 10 µH + 10 µH | 20 µH |
| 22 µH + 47 µH | 69 µH |
| 100 µH + 220 µH | 320 µH |
| 1 mH + 2.2 mH | 3.2 mH |
Testing Series Inductors
- Measure the total inductance with an LCR meter.
- Check continuity through the complete series path.
- Measure the total DC resistance.
- Inspect for damaged windings or poor solder joints.
- Consider possible magnetic coupling if measurements differ from calculations.
Common Mistakes
- Ignoring mutual inductance when coils are close together.
- Assuming DCR remains unchanged.
- Overlooking the reduced self-resonant frequency of the combined inductors.
- Using inductors with different current ratings without considering the lowest-rated component.
- Ignoring polarity when intentionally using magnetically coupled inductors.
Interesting Facts
- Two identical inductors in series produce twice the inductance if they are not magnetically coupled.
- The total current rating of a series combination is limited by the lowest-rated inductor.
- Series-connected inductors are frequently used during circuit development when an exact value is unavailable.
- Magnetic coupling can either increase or decrease the total inductance depending on the winding orientation.
- Increasing inductance also increases the energy that can be stored at the same current.
Key Points
- For uncoupled inductors, the total inductance equals the sum of the individual inductances.
- The same current flows through every inductor in a series circuit.
- Series connections increase total inductance and energy storage.
- Mutual inductance affects the result when inductors are magnetically coupled.
- Always consider DCR, current rating and self-resonant frequency as well as inductance.