4FR

SPEAKER ENCLOSURE CALCULATION — 4FRX4-322
DRIVER IDENTIFICATION
  Code:              4FRX4-322
  Name:              4FR
  Category:          Full-Range / Mid-Woofer (dual-use)
  Size:              4 inch
  Brand:             REDCATT

CONSTRUCTION
  Nominal Impedance: 4 Ω (Re = 3.5 Ω DC)
  AES Power:         30 W
  Continuous Power:  60 W
  Peak Power:        120 W
  Voice Coil:        25.4 mm diameter, copper wire, aluminum former
  Magnet:            Ferrite
  Basket:            Steel
  Cone:              Paper (Paper CF), optimized profile
  Surround:          NBR rubber
  Spider:            Nomex
  T-Plate:           5 mm
  Overall Dia.:      105.5 mm
  Bolt Circle Dia.:  106 mm
  Baffle Cutout:     93.6 mm
  Mounting Holes:    4
  Depth:             56 mm
  Net Weight:        0.77 kg

NOTE ON ALUMINUM FORMER AND COPPER VOICE COIL:
  The aluminum former provides a direct conduction path from the voice coil
  windings to the magnetic circuit, improving heat transfer compared to a Kapton
  former. This allows the copper winding to sustain 30W AES / 60W continuous
  power without the thermal runaway risk associated with a poorly heat-sunk coil.
  The copper winding (not CCAW) provides full cross-section conductivity, which
  at Re = 3.5 Ω delivers higher current for a given voltage, increasing acoustic
  output at low drive levels relative to the CCAW ferrite designs in the family.

THIELE-SMALL PARAMETERS (measured, broken-in)
  Fs   =  79.0 Hz          (free-air resonant frequency — lowest of 4-inch family)
  Re   =   3.5 Ω           (DC voice coil resistance)
  Qes  =   0.61            (electrical Q)
  Qms  =   3.47            (mechanical Q)
  Qts  =   0.52            (total Q — sealed enclosure preferred; see below)
  Vas  =   1.80 L          (equivalent air volume)
  Sd   =  50.3 cm²         (effective cone area)
  Mms  =   7.9 g           (moving mass)
  Rms  =   1.13 kg/s       (mechanical resistance)
  Cms  =   0.51 mm/N       (compliance)
  Bl   =   4.8 T·m         (force factor)
  Le   =   0.09 mH         (voice coil inductance)
  Xmax =   2.8 mm          (one-way linear excursion)
  Xmech=   7.8 mm          (one-way mechanical limit)
  Xprot=   6.6 mm          (one-way protection limit)

SENSITIVITY
  Datasheet Sensitivity:  84.14 dB  (2.83V/1m, per CSV Sensitivity field)
  1W/1m reference (Lm):  83.66 dB  (per CSV Lm field — used for Max SPL calculations)
  NOTE: For a 4 Ω driver, applying 2.83V delivers approximately 2.29W (8.009/3.5).
        The expected relationship is Sensitivity (2.83V) ≈ Lm + 3.6 dB, giving an
        expected Sensitivity of approximately 87.3 dB. The CSV shows 84.14 dB —
        inconsistent with this relationship by approximately 3.1 dB. This is the
        same pattern observed for the 35FRX4-155 (also 4 Ω). The Lm = 83.66 dB
        field is used as the 1W/1m reference for all Max SPL calculations, as this
        is consistent with verified 8 Ω drivers in the family.

DERIVED PARAMETERS
  Volume displacement:    Vd = Sd × Xmax = 50.3 cm² × 0.28 cm = 14.08 cm³
  Inductance rolloff:     f_Le = Re / (2π × Le) = 3.5 / (2π × 0.00009) = 6,189 Hz
  Cone radius:            r_cone = √(Sd/π) = √(50.3/π) = 4.00 cm
  Cone beaming onset:     f_beam = c / (π × r_cone) = 34400 / (π × 4.00) = 2,737 Hz
  Max SPL (AES, 30W):     1W/1m + 10×log10(30) = 83.66 + 14.77 = 98.4 dB at 1 m
  Zobel network:          Rz = 3.5 Ω; Cz = Le / Re² = 7.4 μF (series, across driver)
  Column array limit:     f_array = c / (2 × OD) = 34400 / (2 × 10.55) = 1,630 Hz ≈ 1.63 kHz

FREE-AIR ANALYSIS (Qts = 0.52 — sealed enclosure preferred, not free-air)
  Free-air calculation for reference only:
    1/Qts² = 3.698; 2 − 3.698 = −1.698
    u = (1.698 + √(1.698² + 4)) / 2 = (1.698 + √6.882) / 2 = (1.698 + 2.623) / 2 = 2.161
    Ω = √2.161 = 1.470
    Free-air f-3dB ≈ 1.470 × 79 = 116 Hz
  The free-air f-3dB of ~116 Hz (with a 0.52 Qts peak above Fs) makes standalone
  free-air operation possible but not optimal; a sealed enclosure provides flatter
  response and better power handling.
ENCLOSURE RECOMMENDATIONS
PRIMARY: SEALED
  Qts = 0.52 is in the sealed-preferred range (0.50–0.70). The sealed box provides
  the flattest frequency response and simplest construction for this driver.
  The low Fs = 79 Hz means sealed alignments extend bass to the lowest frequencies
  of any 4-inch driver in the family at equivalent Qtc values.

  --- SEALED ALIGNMENTS ---

  Qtc = 0.707 (Butterworth — flattest):  Vb = 2.12 L  |  fc = 107 Hz  |  f-3dB = 107 Hz
    Note: This is a large enclosure for a 4-inch driver; yields the lowest
    bass extension in the sealed family. Best for designs where enclosure
    volume is not constrained.

  Qtc = 0.85 (preferred balanced):       Vb = 1.08 L  |  fc = 129 Hz  |  f-3dB = 111 Hz
    Note: Recommended for most installations. Half the volume of the Butterworth
    alignment with only 4 Hz loss in bass extension.

  Qtc = 1.00 (compact):                  Vb = 0.67 L  |  fc = 152 Hz  |  f-3dB = 119 Hz

  Qtc = 1.20 (very compact):             Vb = 0.42 L  |  fc = 182 Hz  |  f-3dB = 134 Hz

SECONDARY: VENTED (PORTED)
  A vented enclosure is a viable secondary option, providing extended bass at the
  cost of greater enclosure volume and higher port velocity relative to other
  family members. Port: 30 mm diameter (Ap = 7.07 cm²).
  End corrections: flanged end 12.8 mm + unflanged end 9.2 mm = 22.0 mm total.

  --- VENTED ALIGNMENTS (30 mm port) ---

  Alignment V1: Vb = 1.5 L  |  Fb = 75 Hz
    Effective port length:  251 mm  →  Physical port length: ~229 mm
    Port air velocity:      9.4 m/s peak  (within 17 m/s hi-fi limit)

  Alignment V2: Vb = 2.0 L  |  Fb = 70 Hz
    Effective port length:  216 mm  →  Physical port length: ~194 mm
    Port air velocity:      8.8 m/s peak

  Alignment V3: Vb = 3.0 L  |  Fb = 65 Hz
    Effective port length:  167 mm  →  Physical port length: ~145 mm
    Port air velocity:      8.1 m/s peak

  Note: Port velocities for this driver are higher than the neodymium vented
  designs (32NFRX8, 41NFRX16) due to the lower Xmax (2.8 mm vs. 3.15 mm) and
  smaller port diameter (30 mm vs. 40 mm). All three alignments remain within
  the hi-fi limit; sealed is preferred where chuffing is a concern.
CROSSOVER AND SYSTEM DESIGN NOTES
  INDUCTANCE ROLLOFF (f_Le = 6,189 Hz — above primary audio band):
    Le = 0.09 mH is the same as the 41FRX8-360B (also 0.09 mH) and tied for the
    lowest in the full-range family. The rolloff onset at 6,189 Hz is well above
    the typical crossover region, meaning this driver operates without significant
    Le-related amplitude drop in its working passband. In standalone full-range
    operation, a tweeter or whizzer cone is recommended for coverage above f_beam
    (2,737 Hz), but the Le rolloff is not a limiting factor here.

  CONE BEAMING (f_beam = 2,737 Hz):
    The 4-inch cone with Sd = 50.3 cm² begins transitioning to narrowing directivity
    above 2,737 Hz — the same as the 41FRX8-360B and 40NFRX16-223 with similar Sd.
    For wide-dispersion 2-way systems, a tweeter crossover at 2,000–2,500 Hz is
    recommended. As a mid-woofer in a 2-way system, typical crossover points of
    2.5–4 kHz are practical, with the Le being no limitation.

  COLUMN ARRAY DIRECTIVITY (f_array = 1.63 kHz for 105.5 mm OD):
    Coherent vertical directivity in a column array is maintained to approximately
    1.63 kHz — identical to the 41FRX8-360B (same OD). A co-located tweeter
    with crossover at 1.5–2.0 kHz is mandatory for full-range column coverage.

  4 Ω IMPEDANCE AND WIRING:
    The 4 Ω nominal impedance (Re = 3.5 Ω) is the lowest in the 4-inch family.
    Two drivers in parallel = 2 Ω — approaching the minimum load for many
    amplifiers; parallel wiring should be used with care. Single-driver operation
    at 4 Ω is the standard configuration. In a 2-way column where the woofer and
    tweeter share an amplifier channel, 4 Ω drivers require careful crossover
    impedance design to avoid amplifier overload.

  EXCURSION AND POWER HANDLING:
    Xmax = 2.8 mm and Vd = 14.08 cm³. In a sealed enclosure below fc, cone
    excursion rises proportionally to voltage; a subsonic high-pass filter is
    recommended if the driver is used with full-range program material in a sealed
    box with fc > 100 Hz. In the vented alignments, below Fb the cone is unloaded
    and Xmax can be reached on low-frequency transients; a high-pass filter at
    Fb − 10 Hz (55–65 Hz) is recommended.

  ZOBEL NETWORK:
    A Zobel network (3.5 Ω + 7.4 μF in series, placed across driver terminals)
    is recommended for passive crossover designs. The Le is low (0.09 mH) so the
    impedance rise from inductance is modest, but the Zobel improves crossover
    network accuracy at high frequencies.
4-INCH DRIVER COMPARISON (4 variants)
  Parameter              40NFRX16-223       41FRX8-360B        41NFRX16-464A      4FRX4-322
                         (Neo, 16Ω)         (Ferrite, 8Ω)      (Neo ring, 16Ω)    (Ferrite, 4Ω)
  Re                     12.3 Ω             5.6 Ω              12.2 Ω             3.5 Ω
  AES Power              25 W               20 W               40 W               30 W
  Voice Coil Wire        CCAW               CCAW               Copper             Copper
  Former                 Kapton             Kapton             Kapton             Aluminum
  Fs                     115 Hz             134 Hz             98 Hz              79 Hz
  Qts                    1.10               0.75               0.37               0.52
  Vas                    1.50 L             1.30 L             2.10 L             1.80 L
  Sd                     50.2 cm²           50.3 cm²           56.75 cm²          50.3 cm²
  Bl                     5.3 T·m            4.78 T·m           10.0 T·m           4.8 T·m
  Le                     0.20 mH            0.09 mH            0.58 mH            0.09 mH
  Xmax                   0.45 mm            1.1 mm             3.15 mm            2.8 mm
  Vd                     2.26 cm³           5.53 cm³           17.88 cm³          14.08 cm³
  1W/1m (Lm)             84.39 dB           87.98 dB           89.12 dB           83.66 dB
  Max SPL (AES)          98.4 dB            101.0 dB           105.1 dB           98.4 dB
  Enclosure              Free-air only      Free-air (primary) Vented (required)  Sealed (primary)
  Bass −3dB              87 Hz (free-air)   127 Hz (free-air)  65–80 Hz (Fb)      107 Hz (Qtc=0.707)
  f_Le                   9,785 Hz           9,911 Hz           3,348 Hz           6,189 Hz
  f_beam                 2,738 Hz           2,737 Hz           2,577 Hz           2,737 Hz
  f_array (OD)           1.66 kHz (104 mm)  1.63 kHz (106 mm)  1.65 kHz (105 mm)  1.63 kHz (106 mm)
  Mounting               Standard           Standard           Front or rear      Standard
  SELECTION NOTES:
  • 4FRX4-322 has the lowest Fs (79 Hz) and lowest sealed bass extension (107 Hz
    at Butterworth) in the 4-inch group — suited where the deepest sealed bass
    cutoff frequency is the priority, in a cost-effective ferrite package.
  • It is the only 4 Ω variant in the 4-inch family. Its aluminum former provides
    efficient thermal dissipation for sustained power handling.
  • 4FRX4-322 and 40NFRX16-223 share the same max SPL (98.4 dB); both are the
    lower-output members of the 4-inch class.
  • Choose 4FRX4-322 where: sealed box simplicity, lowest Fs in the 4" family,
    4 Ω impedance, and cost-effectiveness are the design priorities.
  • Choose 41FRX8-360B where: free-air bass (127 Hz, no enclosure needed),
    higher sensitivity (88.0 dB), and 8 Ω wiring are preferred.
  • Choose 41NFRX16-464A where: maximum SPL (105.1 dB), largest Xmax and
    volume displacement, and high power handling (40W AES) are paramount.
  • Choose 40NFRX16-223 where: ultra-lightweight (0.20 kg), deepest free-air
    bass extension (87 Hz), and neodymium efficiency in a 16 Ω array are needed.
FULL-RANGE FAMILY COMPARISON (13 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                 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
  41NFRX16-464A     4"    16  40     0.37  Neo ring     98   Vented (65–80 Hz)       65 Hz  89.1  105.1   105 mm   1.65 kHz
  4FRX4-322         4"    4   30     0.52  Ferrite      79   Sealed (107–134 Hz)    111 Hz  83.7   98.4   106 mm   1.63 kHz
  † Re = 5.5 Ω
  −3dB: free-air for open-back drivers; Fb range for vented; Qtc=0.85 f-3dB for sealed drivers.

  FAMILY NOTES:
  • The family now covers Qts range 0.32–1.10 across four enclosure types:
    free-air / open-back (7 drivers), sealed (2 drivers — 35FRX8-406B, 4FRX4-322),
    vented required (3 drivers — 32NFRX8, 35FRX4, 41NFRX16), and free-air primary
    with sealed secondary (41FRX8-360B).
  • 4FRX4-322 is the only sealed-preferred 4-inch driver and the only 4 Ω variant
    in the 4-inch class. Its Fs = 79 Hz is the lowest in the entire family, giving
    the shallowest sealed f-3dB (107 Hz, Butterworth) of any driver in the group.
  • The two lowest-Qts drivers in the family (32NFRX8-463A at 0.32, 41NFRX16-464A
    at 0.37) both use neodymium ring motors and deliver the two highest max SPL
    values (104.1 dB and 105.1 dB respectively), confirming the direct link between
    strong motor force, low Qts, and vented enclosure performance.
  • Maximum SPL range is 89.6 dB (20NFRX4-345A) to 105.1 dB (41NFRX16-464A) —
    a 15.5 dB span across 13 drivers.
SUMMARY
The 4FRX4-322 is a 4-inch full-range driver built around a ferrite magnetic
circuit, a steel basket, a paper cone with NBR rubber surround, Nomex spider, and
a 25.4mm copper voice coil wound on an aluminum former. The aluminum former provides
a direct conduction path from the voice coil to the magnetic structure, improving
thermal dissipation relative to a Kapton former and supporting the 30W AES / 60W
continuous power rating. The copper winding at Re = 3.5 Ω delivers full conductivity
at a 4 Ω nominal impedance — the only 4 Ω option in the 4-inch family. The
manufacturer describes this as a dual-use driver suited for both full-range and
mid-woofer applications, with a cone profile optimized for piston stiffness and
reduced harmonic distortion. This is the cost-effective, ferrite-based member of
the 4-inch group, positioned where the high motor force and ultra-low inductance
of the neodymium designs are not required.

Fs = 79 Hz, Qes = 0.61, Qms = 3.47, Qts = 0.52 — the lowest Fs and the only
sealed-preferred Qts in the 4-inch driver family. Vas = 1.80 L, Sd = 50.3 cm²,
Xmax = 2.8 mm (one-way), Vd = 14.08 cm³. Sensitivity is 83.66 dB at 1W/1m (Lm);
the CSV Sensitivity field (84.14 dB, 2.83V/1m) is inconsistent with the expected
IEC relationship for a 4 Ω driver (expected ~87.3 dB), consistent with the same
pattern observed on the 35FRX4-155; Lm is used for all calculations. Maximum SPL
is 98.4 dB at 1 m (30W AES). Voice coil inductance Le = 0.09 mH gives an inductance
rolloff onset at 6,189 Hz — the same as the 41FRX8-360B and well above the driver's
useful passband. Cone beaming onset at 2,737 Hz defines the upper directivity limit.
Zobel network: 3.5 Ω + 7.4 μF in series across driver terminals.

  Enclosure alignments:
  • Sealed (primary):
      2.12 L / Qtc = 0.707 / f-3dB = 107 Hz  (Butterworth — flattest; large enclosure)
      1.08 L / Qtc = 0.85  / f-3dB = 111 Hz  (recommended — balanced size and bass)
      0.67 L / Qtc = 1.00  / f-3dB = 119 Hz  (compact)
      0.42 L / Qtc = 1.20  / f-3dB = 134 Hz  (very compact)
    The Fs = 79 Hz produces the lowest sealed bass extension of any 4-inch driver in the
    family — a 107 Hz f-3dB at the Butterworth alignment vs. 127 Hz (41FRX8, free-air)
    or 87 Hz (40NFRX16, free-air).
  • Vented (secondary) — 30 mm port:
      1.5 L / Fb = 75 Hz / ~229 mm physical port / 9.4 m/s peak port velocity
      2.0 L / Fb = 70 Hz / ~194 mm physical port / 8.8 m/s peak port velocity
      3.0 L / Fb = 65 Hz / ~145 mm physical port / 8.1 m/s peak port velocity
    All within the 17 m/s hi-fi port velocity limit; sealed preferred where chuffing
    or construction simplicity is a concern.

In column array applications, the 105.5 mm OD limits coherent vertical directivity
to approximately 1.63 kHz; a co-located tweeter is mandatory for full-range coverage.
The 4 Ω nominal impedance should not be wired in parallel with other 4 Ω loads
without verifying amplifier minimum impedance rating.

The 4FRX4-322 is suited for sealed enclosure 2-way monitor and bookshelf systems
where a cost-effective 4-inch mid-woofer with the lowest sealed bass cutoff (107 Hz
Butterworth) in the 4-inch family and a usable high-frequency range to 2,700 Hz is
required; small bookshelf and satellite enclosures where the sealed box alignment
(0.42–2.12 L) allows compact or large-format cabinet designs without port construction;
background music and commercial installed sound applications where affordability and
sealed-box simplicity are the primary design criteria; and 2-way column speaker
systems where the 4 Ω impedance, sealed driver bay configuration, and low Fs
produce usable bass extension from a compact cabinet per driver bay.