Short answer
The tuned damped filter transformer bus choice depends on the harmonic spectrum and how much the network changes. A single-tuned filter is a series inductor and capacitor with low resistance, so its quality factor is high and it absorbs a narrow band around its tuning frequency very effectively. A damped, or high-pass, filter adds a resistor, usually in parallel with the inductor, so it presents low impedance over a broad band above its tuning frequency and damps resonances, at the cost of resistor losses. For an illustrative series-RLC reference tuned at 235 Hz, f_t/Q gives 4.7 Hz at Q = 50 and 118 Hz at Q = 2. Those figures illustrate damping of the reference circuit; they do not define the bandwidth of a complete high-pass filter. Single-tuned designs suit a dominant harmonic on a stable network; damped designs suit wide spectra or changing network conditions. Both must be specified against stated spectra and network cases.
Two filter types
| Q | Bandwidth | Behaviour |
|---|---|---|
| 50 | ≈ 4.7 Hz | Sharp, drift-sensitive |
| 10 | ≈ 23.5 Hz | Moderate |
| 2 | ≈ 118 Hz | Broad, damped |
- Single-tuned: L and C in series, small R. Impedance minimum at f_t, rising sharply either side.
- Second-order damped (high-pass): C in series with L and R in parallel. Impedance falls toward R above f_t and stays low.
- Third-order and C-type: variations that reduce fundamental loss; see C-type harmonic filters.
Quality factor and bandwidth
Q = X_n / R, X_n = sqrt(L / C)
bandwidth ≈ f_t / Q
Illustrative example. Filter tuned at 235 Hz (4.7th on 50 Hz). Values chosen for demonstration.
| Q | Bandwidth | Behaviour |
|---|---|---|
| 50 | ≈ 4.7 Hz | Sharp absorption, sensitive to drift |
| 10 | ≈ 23.5 Hz | Moderate |
| 2 | ≈ 118 Hz | Broad, damped |
High-Q filters absorb a single harmonic strongly but lose effect quickly with tuning drift; see tolerance drift in tuned harmonic filters.
Resistor losses
In damped filters, fundamental and harmonic currents partly flow through the resistor. Losses can be a noticeable fraction of filter reactive rating and must be included in rating and cooling. C-type designs reduce fundamental loss.
Choosing
| Condition | Favours |
|---|---|
| One dominant harmonic, stable network | Single-tuned |
| Several harmonics above a frequency | Damped high-pass |
| Network impedance changes (transformer out, feeders switched) | Damped |
| Need to avoid new parallel resonance | Damped or detuned |
| Loss-sensitive | Single-tuned or C-type |
Often a combination is used: single-tuned at the 5th and 7th, damped high-pass above.
Conditions to state
- Harmonic spectrum of loads and background distortion; see capacitor overload from background harmonics.
- Network configurations including transformer outages; see harmonic amplification after one transformer is removed.
- Component tolerances and drift range.
- Resonance scans with realistic damping; see resonance scans with frequency-dependent transformer damping.
- Losses and ratings at worst case.
What this article does not cover
It does not recommend any filter as universal; performance always depends on network and spectrum.
Where this reasoning stops. Bandwidth formula is approximate for high Q; damped filters need full impedance calculation.
Practical takeaway
Use single-tuned filters for a dominant harmonic on a stable network, damped filters for broad spectra or changing networks, include resistor losses, and specify against stated spectra and network cases.
Reference framework
- IEEE 1531, Guide for the application and specification of harmonic filters.
- IEC 61642, Industrial a.c. networks affected by harmonics: application of filters and shunt capacitors.