The resonance frequency of a passive LC harmonic filter is set by the classic formula f_t = 1/(2π√(LC)), and the first design decision after picking L and C is how far to sit below the target harmonic order [S2][S7]. Industry guidance recommends a detuning margin of roughly 3% to 15% below the target harmonic to keep the filter from drifting into a parallel resonance with the source impedance [S1].
For a 50 Hz or 60 Hz system, that means the 5th harmonic sits at 250 Hz or 300 Hz, the 7th at 350 Hz or 420 Hz, and the 11th at 550 Hz or 660 Hz, and each filter is tuned slightly under those values, not on top of them [S2]. Component tolerance and ageing shift the LC product over time, so the detuning window also acts as a guard band for capacitor drift, reactor temperature rise, and frequency variation on weak networks [S4].
Worked 5th-Harmonic Example at 60 Hz
A typical 5th-harmonic filter uses a reactor of 40 mH in series with a capacitor of 8 µF, giving f_t = 1/(2π·√(40×10⁻³·8×10⁻⁶)) ≈ 281 Hz, or roughly harmonic order 4.69 on a 60 Hz base [S7]. That 6.2% detuning from the 300 Hz target (5th order) is right inside the 3-15% safe band recommended for low-voltage shunt filters [S1].
To hit the more conservative 4.7 tuning often seen on 5th-harmonic traps, the LC product must deliver f_t = 4.7·60 = 282 Hz; for a fixed C of 8 µF, that requires L ≈ 39.7 mH, which is consistent with the 40 mH value used in field installations [S4]. The same recipe at 50 Hz shifts the targets to 235 Hz (4.7·50) and 210 Hz (4.2·50), which is why European 5th-harmonic filters are commonly rated around 189-235 Hz [S1][S4].
Choosing the Detuning Order on a Real Bus
Plant practice splits into two camps: exact tuning to the harmonic order (5.0 or 7.0) and detuned filtering, which deliberately sits below the harmonic [S4]. Exact tuning gives the lowest impedance at the target frequency and the best absorption, but it carries higher engineering cost, larger reactors, and a sharper sensitivity to capacitance drift and source impedance changes [S4].
Detuned filters at 4.2, 4.7, or 6.7 are the default in commercial buildings and light industrial plants because they still drain 5th and 7th harmonic current while pushing the filter's series-resonance point away from any likely parallel resonance with the supply transformer and bus capacitance [S1][S4]. For capacitor banks that exist only for power factor correction and not for harmonic absorption, the reactor is usually sized for a tuning order of 3.8-4.3, a classic p=7% detuned reactor pattern that protects the bank from harmonic overvoltage [S5].
Why Source Impedance Changes the Answer
Parallel resonance is the failure mode that drives the detuning margin, and it is governed by the system short-circuit level, not just the filter components [S3]. Eaton's example uses 1500 kVA at 5% impedance to derive a parallel-resonance frequency of roughly the 50th harmonic on the unloaded bus, and once a capacitor bank is added that frequency collapses to the harmonic range where real damage happens [S3].
That is why a harmonic filter sized purely from its own LC product can still create a resonance problem on the bus: the bus capacitance and source inductance form a second resonant network that interacts with the filter. The standard fix is to model both networks, scan the impedance curve from the 2nd harmonic up, and confirm the filter's detuning point lands in a low-impedance trough while the system parallel-resonance peak misses every integer harmonic by at least 5-10% [S3][S5]. This is the same logic that shows up in VFD input-side filter design, where rectifier loads inject 5th, 7th, 11th, and 13th harmonics into a bus that already has capacitor banks for power factor correction.
Selection Criteria: Passive LC vs Active vs Detuned-Reactor
For a 5th-harmonic problem on a 400-690 V industrial bus, a passive single-tuned LC filter is the lowest-cost option at roughly 30-50% of the active alternative, but it is rigid: changing the load profile means re-sizing L and C [S1]. Quality factor Q is the design knob that sets the bandwidth and the losses; a typical Q of 30-60 gives a sharp notch and acceptable I²R losses, while a Q above 100 narrows the notch so much that capacitor drift pushes the filter off-tune within a few years [S4].
An active harmonic filter is the right call when the load mix is shifting (mixed VFD population, dynamic drives, arc furnaces) and the dominant harmonic order drifts over time, because it tracks the spectrum in real time instead of relying on a fixed LC trough [S1][S5]. A detuned reactor on a plain power-factor correction capacitor is the third option, used when harmonic absorption is not needed but resonance protection is; a p=7% reactor (tuning order ≈ 3.78) shifts the capacitor-bank resonance below the 5th harmonic and is the workhorse for commercial buildings with light non-linear load [S5].
Limitations, Constraints, and Common Mistakes
Three failure modes show up repeatedly in the field. First, tuning exactly to 5.00 or 7.00: capacitance tolerance of ±5% and inductance tolerance of ±3% are normal, so an "exactly tuned" filter can end up 200-400 Hz off its target within a few thermal cycles and excite the very parallel resonance it was meant to avoid [S4].
Second, ignoring the source impedance change after a transformer tap change or a new feeder: the parallel-resonance peak moves, and a previously safe detuning of 6% can land on the new peak [S3][S5]. Third, undersizing the reactor: minimum kVAr gives maximum L, which pushes the tuning order up toward the harmonic, exactly the opposite of what a detuned filter is supposed to do [S4]. The IEEE 519 THD limits and IEEE 1531-2020 filter-design guidance are the two reference points most engineers cite when sizing around these limits [S1]. For installations near large drives and rectifier loads, the same harmonic discipline shows up in adjacent harmonic reducer sizing as well, since both products sit on the same bus and see the same 5th, 7th, 11th, and 13th current spectrum.
Verification Steps Before Energising
Before a new filter is closed in, three checks are non-negotiable. Calculate f_t from the nameplate L and C of the as-installed components, not the design values, and confirm detuning is still inside the 3-15% band at both 50 Hz and 60 Hz base [S2]. Run an impedance scan from the 2nd to the 25th harmonic with the filter out, then with the filter in, and confirm no new parallel-resonance peak lands on an integer harmonic [S3][S5].
Trackable signals over the next quarter: revisions to IEEE 1531 around wide-bandgap-drive harmonic spectra, and the rollout of grid-forming inverter ride-through rules that will shift how active filters behave on weak networks.
For related coverage, see Strapping band sizing for heavy machinery export crates.