How do you solve a series-parallel inductor network?

Reduce it from the inside out: collapse the innermost parallel group with 1/Leq = 1/L1 + 1/L2 + …, add any series coils, and repeat until one value remains. The rules are the same as for resistors.

Do inductors follow the same rules as resistors?

Yes for the arithmetic — series adds and parallel takes reciprocals, exactly as with resistance. The difference is physical: inductors can couple magnetically, which no resistor network does, and coupling invalidates the reduction.

Which do you calculate first in a mixed inductor network?

The innermost group, meaning the one with nothing nested inside it. For a coil in series with a parallel pair, the pair is collapsed first and the series coil added to the result.

How does coupling affect a mixed inductor network?

It breaks the calculation. Coupling adds mutual inductance terms that step-by-step reduction does not model, and in a parallel branch it can also drive circulating current between the coils. Keep the parts apart, use shielded or toroidal types, or measure the assembly.

How do I know how much current each inductor carries?

Series elements all carry the full current. A parallel group splits it, but by DC resistance rather than by inductance, so the branch currents are not simply in the inductance ratio. Check each coil against its own saturation rating.

Mixed Series-Parallel Inductance Calculator

Mixed series-parallel inductor networks reduce from the inside out: collapse each parallel group with the reciprocal formula, add the series elements, and repeat — the same rules as resistors, provided no two coils couple.

How to Reduce a Series-Parallel Inductor Network

Inductors follow the resistor rules, which makes mixed inductor networks the most familiar of the three types: series adds, parallel takes reciprocals, and the reduction works from the innermost group outwards.

The two rules being applied

L_{s e r i e s} = L_{1} + L_{2} + \dots + L_{n}

\frac{1}{L_{p a r a l l e l}} = \frac{1}{L_{1}} + \frac{1}{L_{2}} + \dots + \frac{1}{L_{n}}

A coil in series with a parallel pair

For the commonest shape the two steps combine into one expression:

L_{e q} = L_{1} + \frac{L_{2} \times L_{3}}{L_{2} + L_{3}}

Collapse the parallel pair first, then add the series coil.

The order is not interchangeable, for the same reason as with resistors: the series coil is not across the same two nodes as the parallel pair, so it cannot be folded in until that pair has become a single value.

The assumption that does the most damage

Every step above assumes the coils are magnetically independent. That assumption is safe for resistors and capacitors and genuinely risky for inductors, because a mixed network usually means several coils in a small area. Where two of them couple, no amount of correct reduction gives the right answer — the network has to be treated as coupled, or the parts moved apart.

Worked example

Given

L1 = 4.7 µH in series with the bank
L2 = 10 µH ∥ L3 = 10 µH

Working

Step 1 — the parallel pair:
L2 ∥ L3 = 10 / 2 = 5 µH
Step 2 — add the series inductor:
Leq = 4.7 µH + 5 µH

Answer9.7 µH

Where Mixed Inductor Networks Appear

Multi-stage supply filtering

A pi filter — capacitor, series inductor, capacitor — repeated down a supply rail gives a chain of series inductances with the parallel resistance of the loads between them. Getting the total series inductance right sets the attenuation; getting the DC resistance right sets the voltage drop.

Paralleled chokes inside a filter

Where a single choke cannot carry the current, two in parallel take its place — and that parallel pair then sits in series with the rest of the filter. The network is mixed as soon as current forces the substitution.

Impedance matching networks

L and T matching networks combine series and shunt reactances by design. Their inductive parts reduce by these rules, though at RF the parasitic capacitance and self-resonance of each coil usually matter as much as the inductance.

Checking a Mixed Inductance Result

The same bounds that catch resistor errors work here, because the rules are the same:

The total must exceed any series coil taken on its own.
Every parallel group must have collapsed below its smallest member.
Removing a branch from a parallel group must raise the total.
Two equal coils in parallel must give exactly half of one.

The step-by-step derivation above shows each reduction, so a wrong intermediate value can be found at the step that produced it. What none of these checks can catch is coupling, which is why it deserves a measurement rather than a calculation when several coils sit close together.

Practical Limits in a Mixed Network

DC resistance follows the same topology as the inductance, so it has to be reduced separately — series resistances add, parallel ones combine reciprocally.
Saturation is per part, not per network. Work out the current in each branch and check every coil against its own rating.
A parallel pair splits current by resistance rather than by inductance, so the branch currents are not what the inductance ratio suggests.
Self-resonance limits the useful frequency of each coil individually. The network stops behaving as calculated above the lowest of them.

Common mistakes

Adding the series coil before collapsing the parallel group. The innermost group is reduced first.
Applying the capacitor rules by mistake. Inductors follow the resistor rules: series adds, parallel takes reciprocals.
Assuming no coupling in a network that packs several coils into a small area.
Reducing the inductances but not the DC resistances, and losing the voltage drop.
Checking saturation against the total current rather than the current in each branch.
Using the calculated inductance above the self-resonant frequency of the smallest coil, where it no longer behaves as an inductor at all.

Frequently asked questions

How do you solve a series-parallel inductor network?: Reduce it from the inside out: collapse the innermost parallel group with 1/Leq = 1/L1 + 1/L2 + …, add any series coils, and repeat until one value remains. The rules are the same as for resistors.
Do inductors follow the same rules as resistors?: Yes for the arithmetic — series adds and parallel takes reciprocals, exactly as with resistance. The difference is physical: inductors can couple magnetically, which no resistor network does, and coupling invalidates the reduction.
Which do you calculate first in a mixed inductor network?: The innermost group, meaning the one with nothing nested inside it. For a coil in series with a parallel pair, the pair is collapsed first and the series coil added to the result.
How does coupling affect a mixed inductor network?: It breaks the calculation. Coupling adds mutual inductance terms that step-by-step reduction does not model, and in a parallel branch it can also drive circulating current between the coils. Keep the parts apart, use shielded or toroidal types, or measure the assembly.
How do I know how much current each inductor carries?: Series elements all carry the full current. A parallel group splits it, but by DC resistance rather than by inductance, so the branch currents are not simply in the inductance ratio. Check each coil against its own saturation rating.

Assumptions and limitations for Mixed Series-Parallel Inductance Calculator are listed on the About page. Every worked example on this site is checked against the same solver the calculator uses.