41FR

SPEAKER ENCLOSURE CALCULATION — 41FRX8-360B
DRIVER IDENTIFICATION
  Code:              41FRX8-360B
  Name:              41FR
  Category:          Full-Range (dual-purpose: mid-woofer / full-range)
  Size:              4 inch
  Brand:             REDCATT

  NOTE: The manufacturer describes the 41FR as a "ferrite based mid-woofer, developed
  for applications where small size mid-woofer is required. This version was developed
  with extended HF response and in some cases could be used as full-range driver."
  Key features list includes "can be used without HF unit" and "Array applications,
  2-way systems." Both use cases are covered in this document.

CONSTRUCTION
  Nominal Impedance: 8 Ω (Re = 5.6 Ω DC)
  AES Power:         20 W
  Continuous Power:  40 W
  Peak Power:        80 W
  Voice Coil:        25.4 mm diameter, CCAW wire, Kapton former
  Magnet:            Ferrite
  Basket:            Steel
  Cone:              Carbon fiber reinforced paper (Paper CF), optimized-geometry profile
  Surround:          NBR rubber
  Spider:            Nomex
  Overall Dia.:      105.5 mm
  Depth:             55.9 mm
  Net Weight:        0.78 kg

THIELE-SMALL PARAMETERS (measured, broken-in)
  Fs   = 134.0 Hz         (free-air resonant frequency)
  Re   =   5.6 Ω          (DC voice coil resistance)
  Qes  =   0.81           (electrical Q)
  Qms  =  10.60           (mechanical Q — very high; very low mechanical losses)
  Qts  =   0.75           (total Q — near-Butterworth in free air; see below)
  Vas  =   1.30 L         (equivalent air volume)
  Sd   =  50.3 cm²        (effective cone area)
  Mms  =   3.8 g          (moving mass — low; CCAW voice coil advantage)
  Rms  =   0.30 kg/s      (mechanical resistance — very low, consistent with Qms = 10.6)
  Cms  =   0.37 mm/N      (compliance)
  Bl   =   4.78 T·m       (force factor)
  Le   =   0.09 mH        (voice coil inductance — very low)
  Xmax =   1.1 mm         (one-way linear excursion)
  Xmech=   6.1 mm         (one-way mechanical limit)
  Xprot=   7.0 mm         (one-way protection limit)

SENSITIVITY
  Sensitivity (2.83V/1m): 89.44 dB  (CSV Sensitivity field — self-consistent ✓)
  1W/1m reference (Lm):   87.98 dB  (CSV Lm field)
  Verification:  87.98 + 10×log10(8.009/5.6) = 87.98 + 1.55 = 89.53 dB ≈ 89.44 dB ✓

  NOTE ON Qms = 10.6:
  The exceptionally high Qms reflects very low mechanical damping in the suspension
  system. In practice this means the driver relies primarily on electrical damping
  (from the amplifier's output impedance and motor back-EMF) for resonance control.
  The combination of Qms = 10.6 and Qts = 0.75 implies Qes = 0.81 — moderate
  electrical damping provides sufficient system control. Qts = 0.75 is very close
  to the Butterworth threshold of 0.707, so the free-air frequency response is
  essentially maximally-flat in the bass region with negligible resonance overshoot.

DERIVED PARAMETERS
  Volume displacement:    Vd = Sd × Xmax = 50.3 cm² × 0.11 cm = 5.53 cm³
  Inductance rolloff:     f_Le = Re / (2π × Le) = 5.6 / (2π × 0.00009) = 9,911 Hz
  Cone radius:            r_cone = √(Sd/π) = 4.00 cm
  Cone beaming onset:     f_beam = c / (π × r_cone) = 34400 / (π × 4.00) = 2,737 Hz
  Max SPL (AES, 20W):     1W/1m + 10×log10(20) = 87.98 + 13.0 = 101.0 dB at 1 m
  Zobel network:          Rz = 5.6 Ω; Cz = Le / Re² = 2.9 μF (series, across driver)
  Column array limit:     f_array = c / (2 × OD) = 34400 / (2 × 10.55) = 1,630 Hz ≈ 1.63 kHz
FREE-AIR / OPEN-BACK ANALYSIS (Qts = 0.75 — near-Butterworth alignment)
  With Qts = 0.75 > 0.707, any sealed enclosure raises the system resonance above
  the free-air f-3dB. Free-air / open-back mounting produces the lowest achievable
  bass cutoff and is the recommended primary installation.

  Free-air resonant frequency: Fs = 134 Hz
  Free-air f-3dB calculation:
    1/Qts² = 1.778; 2 − 1.778 = 0.222
    u = (−0.222 + √(0.222² + 4)) / 2 = (−0.222 + 2.012) / 2 = 0.895
    Ω = √0.895 = 0.946
    Free-air f-3dB ≈ 0.946 × 134 = 127 Hz

  RESONANCE PEAK IN FREE AIR:
    Qts = 0.75 is only marginally above the Butterworth threshold of 0.707. The
    theoretical in-band peak is less than 0.1 dB — completely inaudible and
    unmeasurable in practice. The free-air bass response is considered maximally-flat
    for all engineering purposes. No DSP correction is required for the resonance.
    This is the best-case free-air frequency response shape of any driver in the
    free-air / open-back subset of the full-range family.

  SEALED ENCLOSURE — NOT RECOMMENDED:
    Any sealed box raises f-3dB above the free-air value of 127 Hz. For reference:
      Vb = 1.3 L (= Vas):  Qtc ≈ 1.06 → f-3dB ≈ 148 Hz (worse)
      Vb = 3.0 L:          Qtc ≈ 0.84 → f-3dB ≈ 128 Hz (no improvement)
    No sealed alignment improves on the free-air f-3dB of 127 Hz.
ENCLOSURE RECOMMENDATION SUMMARY
  PRIMARY: FREE-AIR / OPEN-BACK
    f-3dB ≈ 127 Hz  |  <0.1 dB resonance deviation (effectively flat)
    Suitable for: column speaker arrays, open-back baffle designs, 2-way systems
    with dedicated woofer below 150–200 Hz, and standalone full-range use where
    bass below 127 Hz is not required.

  AS MID-WOOFER IN A SEALED 2-WAY SYSTEM:
    When used as the bass/midrange driver in a 2-way system (crossed to a tweeter),
    a sealed enclosure may be used to achieve a defined bass rolloff point and
    controlled baffle step compensation. In this application the elevated f-3dB
    of a sealed alignment is acceptable because the bass is managed by the crossover:
      Qtc = 0.85 → Vb ≈ 0.55 L  |  fc ≈ 161 Hz  |  f-3dB ≈ 138 Hz
      Qtc = 1.00 → Vb ≈ 0.24 L  |  fc ≈ 191 Hz  |  f-3dB ≈ 150 Hz
      Qtc = 1.20 → Vb ≈ 0.10 L  |  fc ≈ 229 Hz  |  f-3dB ≈ 169 Hz
    These compact sealed volumes (0.10–0.55 L) are practical for desktop or
    column 2-way enclosures. The driver's extended HF response (f_Le = 9,911 Hz)
    allows crossover to a tweeter as high as 3,000–4,000 Hz in a 2-way design.

  High-pass filter: 90–110 Hz subsonic filter recommended in all open-back
  installations. Xmax = 1.1 mm limits sustained high-level bass content below 100 Hz.
CROSSOVER AND SYSTEM DESIGN NOTES
  INDUCTANCE ROLLOFF (f_Le = 9,911 Hz — well above the audio band):
    Le = 0.09 mH is the lowest inductance value in the full-range family. Combined
    with Re = 5.6 Ω, this gives the highest f_Le (9,911 Hz) alongside the 40NFRX16-223
    (9,785 Hz). The impedance characteristic is essentially resistive from 20 Hz through
    9 kHz, making the 41FRX8-360B highly compatible with passive crossover networks.
    No Le-related HF rolloff occurs within the audio band — a direct consequence of
    the CCAW lightweight winding minimizing coil length and hence inductance.

  CONE BEAMING (f_beam = 2,737 Hz):
    Pistonic wide-dispersion operation extends to ~2,737 Hz. In 2-way designs,
    targeting a crossover to a tweeter at 2,000–2,500 Hz ensures consistent
    horizontal and vertical off-axis response through the crossover region.
    For full-range use without a tweeter, output above 2,737 Hz becomes increasingly
    directional — this is common to all 4-inch drivers in the family.

  COLUMN ARRAY DIRECTIVITY (f_array = 1.63 kHz for 105.5 mm OD):
    The 105.5 mm OD (the largest in the full-range family) gives the lowest column
    array coherence limit at 1.63 kHz. In column array applications, a co-located
    tweeter is required for coverage above this point. As with the 40NFRX16-223
    (OD = 103.5 mm, f_array = 1.66 kHz), the 4-inch driver's bass extension advantage
    comes at the cost of reduced HF array coherence.

  FULL-RANGE USE WITHOUT TWEETER:
    The key feature description explicitly states "can be used without HF unit."
    With f_Le = 9,911 Hz and f_beam = 2,737 Hz, the driver maintains flat on-axis
    response through most of the audio band. In near-field desktop or close-proximity
    column applications, the progressive beaming above 2,737 Hz is less audible
    than in wide-listening-angle configurations. A mild HF shelving boost (2–4 dB
    above 4 kHz) via DSP may extend perceived HF "air" in standalone installations.

  ZOBEL NETWORK:
    A Zobel network (5.6 Ω + 2.9 μF in series, placed across driver terminals) is
    recommended for passive crossover designs. The very low Le (0.09 mH) means the
    Zobel capacitor is small (2.9 μF) and the impedance rise from Le is minimal —
    passive crossover designs will be largely unaffected by Le even without a Zobel.
4-INCH DRIVER COMPARISON (41FRX8-360B vs 40NFRX16-223)
  Parameter              40NFRX16-223 (Neo, 16Ω)     41FRX8-360B (Ferrite, 8Ω)
  Re                     12.3 Ω                       5.6 Ω
  AES Power              25 W                         20 W
  Voice Coil Wire        CCAW                         CCAW
  Former                 Kapton                       Kapton
  Fs                     115 Hz                       134 Hz
  Qts                    1.10                         0.75
  Vas                    1.50 L                       1.30 L
  Sd                     50.2 cm²                     50.3 cm²
  Mms                    4.4 g                        3.8 g
  Qms                    6.20                         10.60
  Bl                     5.3 T·m                      4.78 T·m
  Le                     0.20 mH                      0.09 mH
  Xmax                   0.45 mm                      1.1 mm
  Vd                     2.26 cm³                     5.53 cm³
  1W/1m (Lm)             84.39 dB                     87.98 dB
  2.83V/1m               85.52 dB*                    89.44 dB
  Max SPL (AES)          98.4 dB                      101.0 dB
  Enclosure              Free-air only                Free-air (primary)
  Free-air f-3dB         ~87 Hz (+1.8 dB peak)        ~127 Hz (<0.1 dB peak)
  Bass-response shape    Peaked (needs EQ at 88 Hz)   Near-Butterworth (flat)
  Net Weight             0.20 kg                      0.78 kg
  f_Le                   9,785 Hz                     9,911 Hz
  f_beam                 2,738 Hz                     2,737 Hz
  f_array (OD)           1.66 kHz (103.5 mm)          1.63 kHz (105.5 mm)
  * 40NFRX16-223 Sensitivity/Lm fields not self-consistent with Re=12.3Ω; see notes.

  KEY DIFFERENCES:
  • The 40NFRX16-223 (Qts=1.10, Fs=115Hz) achieves a deeper free-air bass cutoff
    (87 Hz) but requires DSP correction for its 1.8 dB resonance peak at 88 Hz.
  • The 41FRX8-360B (Qts=0.75, Fs=134Hz) provides a near-Butterworth free-air
    response (127 Hz, <0.1 dB peak) — the flattest bass alignment in the free-air
    family subset, requiring no EQ correction.
  • The 41FRX8-360B has significantly higher sensitivity (87.98 vs 84.39 dB, 1W/1m),
    larger Xmax (1.1 vs 0.45 mm), larger Vd (5.53 vs 2.26 cm³), and higher Max SPL
    (101.0 vs 98.4 dB) despite lower power rating.
  • The 41FRX8-360B's ferrite motor and 8Ω impedance are compatible with standard
    amplifier outputs; the 40NFRX16-223's 16Ω enables multi-driver parallel wiring
    and requires a higher-voltage amplifier for equivalent power delivery.
  • Choose 40NFRX16-223 where: maximum bass extension (87 Hz) with DSP management is
    required; 16Ω column array parallel wiring; ultra-lightweight construction (0.20 kg).
  • Choose 41FRX8-360B where: flat, DSP-free bass response is preferred; higher
    sensitivity and SPL are priorities; 8Ω is required; mid-woofer/full-range dual
    use without tweeter is a selection criterion.
FULL-RANGE FAMILY COMPARISON (11 drivers)
  Code              Size  Ω   W AES  Qts   Motor    Fs    Enclosure             −3dB    1W/1m  MaxSPL  OD     f_array
  20NFRX4-345A      2"    4   10     0.52  Neo      185   Free-air / open-back  272 Hz  79.6   89.6    48 mm   3.58 kHz
  21NFRX16-393D     2"    16  10     0.68  Neo      157   Free-air / open-back  164 Hz  85.8   95.8    57 mm   3.00 kHz
  22NFRX8-462A      2"    8   20     0.85  Neo      255   Free-air / open-back  219 Hz  83.5   96.5    61 mm   2.84 kHz
  25NFRX8-279       2.5"  8   20     0.71  Neo ring 123   Free-air / open-back  123 Hz  82.3   95.4    65 mm   2.65 kHz
  30FFX8-264B       3"    8   20     0.78  Ferrite  119   Free-air / open-back  109 Hz  83.6   96.6    79 mm   2.18 kHz
  31NFRX8-229       3"    8   30     0.88  Neo      115   Free-air / open-back   97 Hz  83.5   98.3    79 mm   2.18 kHz
  32NFRX8-463A      3"    4†  30     0.32  Neo ring 118   Vented (75–115 Hz)     75 Hz  89.4  104.1    83 mm   2.07 kHz
  35FRX4-155        3.5"  4   25     0.34  Ferrite   67   Vented (70–80 Hz)      70 Hz  83.1   97.1    93 mm   1.85 kHz
  35FRX8-406B       3.5"  8   20     0.63  Ferrite  128   Sealed / open-back    148 Hz  87.6  100.6    93 mm   1.85 kHz
  40NFRX16-223      4"    16  25     1.10  Neo      115   Free-air / open-back   87 Hz  84.4   98.4   104 mm   1.66 kHz
  41FRX8-360B       4"    8   20     0.75  Ferrite  134   Free-air / open-back  127 Hz  88.0  101.0   106 mm   1.63 kHz
  † Re = 5.5 Ω
  −3dB: free-air for free-air/open-back drivers; Fb range for vented; Qtc=0.85 for 35FRX8-406B.

  FAMILY NOTES:
  • 41FRX8-360B is the second 4-inch driver in the family and the 8Ω ferrite complement
    to the 40NFRX16-223 (Neo, 16Ω). It offers the flattest free-air bass response
    alignment (<0.1 dB peak) of any free-air driver in the family.
  • At 87.98 dB (1W/1m), the 41FRX8-360B has the second-highest sensitivity of any
    ferrite driver in the lineup, behind only the 32NFRX8-463A (89.37 dB, vented).
  • Le = 0.09 mH is the lowest in the entire family, contributing jointly with the
    40NFRX16-223 (Le=0.20mH, Re=12.3Ω) to the two highest f_Le values — both
    well above 9 kHz and fully within passive crossover design range.
  • With f_array = 1.63 kHz, the 41FRX8-360B has the lowest column array coherence
    limit in the family due to its 105.5 mm OD; a tweeter is mandatory in column arrays.
  • The family now spans: 2" to 4" format; 4Ω to 16Ω; 10W to 30W AES; free-air/
    open-back, sealed, and vented enclosure types; Neo, Neo ring, and Ferrite motors;
    Qts range from 0.32 to 1.10.
SUMMARY
The 41FRX8-360B is a 4-inch full-range / mid-woofer driver featuring a ferrite magnet
motor, steel basket, carbon fiber reinforced paper cone with optimized geometry profile,
NBR rubber surround, Nomex spider, and a 25.4mm CCAW voice coil wound on a Kapton former.
The CCAW winding minimizes voice coil mass (Mms = 3.8 g) and inductance (Le = 0.09 mH —
the lowest in the full-range family), contributing directly to the driver's high sensitivity
and the inductance rolloff onset of 9,911 Hz — effectively placing the impedance rolloff
above the audible range. The driver is positioned for dual use: as a small mid-woofer in
2-way systems and as a standalone full-range driver in column arrays and desktop speakers.
The manufacturer explicitly notes it can be used without a high-frequency unit. The 8Ω
nominal impedance and ferrite motor construction provide a cost-effective, standard-load
solution for column array and 2-way enclosure designs.

Fs = 134 Hz, Qes = 0.81, Qms = 10.60, Qts = 0.75 — a compliant suspension design with
very low mechanical losses (Qms = 10.6) suited to free-air and open-back installations,
where the near-Butterworth Qts produces a maximally-flat bass alignment with less than
0.1 dB in-band deviation — the flattest free-air response of any driver in the free-air
family subset. Vas = 1.30 L, Sd = 50.3 cm², Xmax = 1.1 mm (one-way), Vd = 5.53 cm³.
Sensitivity is 87.98 dB at 1W/1m (Lm) / 89.44 dB at 2.83V/1m, with a maximum SPL of
101.0 dB at 1 metre (20W AES). The voice coil inductance Le = 0.09 mH gives the
inductance rolloff onset of 9,911 Hz — the highest in the full-range family alongside
the 40NFRX16-223 — providing a flat, resistive impedance characteristic across the full
20 Hz to 9 kHz range. Cone beaming onset at 2,737 Hz defines the upper limit of wide-
dispersion operation. Zobel network: 5.6 Ω + 2.9 μF in series across driver terminals.

  Enclosure alignments:
  • Free-air / open-back (primary — full-range and column array use):
      f-3dB ≈ 127 Hz; <0.1 dB resonance deviation (no EQ correction required)
      High-pass filter at 90–110 Hz recommended in all installations
  • Sealed (secondary — mid-woofer in 2-way system, crossed to tweeter):
      0.55 L / Qtc = 0.85 / fc = 161 Hz / f-3dB = 138 Hz
      0.24 L / Qtc = 1.00  / fc = 191 Hz / f-3dB = 150 Hz
      0.10 L / Qtc = 1.20  / fc = 229 Hz / f-3dB = 169 Hz

In column array applications, the 105.5 mm driver OD limits coherent vertical directivity
to approximately 1.63 kHz — the lowest in the full-range family; a co-located tweeter is
mandatory. In standalone full-range installations without a tweeter, progressive HF
beaming above 2,737 Hz is characteristic of the 4-inch cone size; a 2–4 dB DSP HF shelf
may extend perceived HF coverage in near-field or close-proximity applications. A high-
pass filter at 90–110 Hz is recommended in all free-air installations to protect against
excursion over-excursion below the natural rolloff frequency.

The 41FRX8-360B is suited for column speaker arrays requiring a maximally-flat free-air
bass response from a 4-inch ferrite driver without DSP bass correction; 2-way desktop,
bookshelf, and column enclosures where the driver covers bass and midrange in a sealed
alignment (0.10–0.55 L) crossed to a tweeter at 2,000–3,000 Hz; standalone full-range
use in near-field and desktop applications where the extended HF response (f_Le = 9,911 Hz)
and low Le make a tweeter optional; and cost-sensitive installed sound systems where ferrite
motor construction, standard 8Ω impedance, and high sensitivity (101.0 dB max SPL) provide
a practical and affordable full-range solution.