35FR

SPEAKER ENCLOSURE CALCULATION — 35FRX8-406B
DRIVER IDENTIFICATION
  Code:              35FRX8-406B
  Name:              35FR
  Category:          Full-Range
  Size:              3.5 inch
  Brand:             REDCATT

CONSTRUCTION
  Nominal Impedance: 8 Ω (Re = 6.3 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), FEM-optimized profile
  Surround:          NBR rubber, FEM-optimized geometry
  Spider:            Nomex
  Overall Dia.:      93 mm
  Depth:             49 mm
  Net Weight:        0.57 kg

NOTE ON CCAW VOICE COIL:
  CCAW (Copper Clad Aluminum Wire) uses an aluminum core with copper cladding. The
  reduced density of aluminum (vs pure copper) lowers voice coil mass, which is the
  primary contributor to the low Mms = 3.1 g in this driver. The resulting high
  sensitivity (87.55 dB, 1W/1m) and extended high-frequency response reflect the
  mass reduction. Thermal handling is slightly lower than a pure copper winding of
  the same gauge; the 20W AES rating reflects this. The Kapton former provides good
  thermal stability and mechanical rigidity at elevated temperatures.

NOTE ON BL SYMMETRY:
  The manufacturer lists BL symmetry as a key design objective, indicating that the
  magnetic circuit has been engineered (FEM-optimized) for symmetric BL(x) across
  the driver's excursion range. Symmetric BL(x) suppresses even-order harmonic
  distortion — particularly second harmonic — at moderate and high drive levels,
  producing lower THD relative to non-symmetric motor designs.

THIELE-SMALL PARAMETERS (measured, broken-in)
  Fs   = 128.0 Hz         (free-air resonant frequency)
  Re   =   6.3 Ω          (DC voice coil resistance)
  Qes  =   0.68           (electrical Q)
  Qms  =   7.76           (mechanical Q)
  Qts  =   0.63           (total Q — sealed enclosure preferred; free-air viable)
  Vas  =   1.14 L         (equivalent air volume)
  Sd   =  40.7 cm²        (effective cone area)
  Mms  =   3.1 g          (moving mass — very low; CCAW voice coil advantage)
  Rms  =   0.32 kg/s      (mechanical resistance)
  Cms  =   0.50 mm/N      (compliance)
  Bl   =   4.8 T·m        (force factor)
  Le   =   0.25 mH        (voice coil inductance)
  Xmax =   2.35 mm        (one-way linear excursion)
  Xmech=   6.35 mm        (one-way mechanical limit)
  Xprot=   8.6 mm         (one-way protection limit)

SENSITIVITY
  Sensitivity (2.83V/1m): 88.59 dB  (CSV Sensitivity field — self-consistent ✓)
  1W/1m reference (Lm):   87.55 dB  (CSV Lm field)
  Verification:  87.55 + 10×log10(8.009/6.3) = 87.55 + 1.04 = 88.59 dB ✓

DERIVED PARAMETERS
  Volume displacement:    Vd = Sd × Xmax = 40.7 cm² × 0.235 cm = 9.56 cm³
  Inductance rolloff:     f_Le = Re / (2π × Le) = 6.3 / (2π × 0.00025) = 4,011 Hz
  Cone radius:            r_cone = √(Sd/π) = 3.60 cm
  Cone beaming onset:     f_beam = c / (π × r_cone) = 34400 / (π × 3.60) = 3,042 Hz
  Max SPL (AES, 20W):     1W/1m + 10×log10(20) = 87.55 + 13.0 = 100.6 dB at 1 m
  Zobel network:          Rz = 6.3 Ω; Cz = Le / Re² = 6.3 μF (series, across driver)
  Column array limit:     f_array = c / (2 × OD) = 34400 / (2 × 9.3) = 1,849 Hz ≈ 1.85 kHz

FREE-AIR / OPEN-BACK ANALYSIS (Qts = 0.63)
  With Qts = 0.63, free-air (open-back) mounting is viable — particularly for column
  speakers or panel-mount applications where a woofer handles bass below 150–200 Hz.
  Qts < 0.707 means no resonance peak in free-air; response rolls off monotonically
  below Fs. Free-air f-3dB is below the Butterworth point, at:
    fc = Fs = 128 Hz (resonant frequency, unchanged in free air)
    1/Qts² = 2.519; 2 − 2.519 = −0.519
    u = (0.519 + √(0.519² + 4)) / 2 = (0.519 + 2.066) / 2 = 1.293
    Ω = √1.293 = 1.137
    Free-air f-3dB ≈ 1.137 × 128 = 146 Hz
  For column arrays crossed to a woofer above 200 Hz, free-air mounting provides
  adequate bass integration without requiring an enclosure behind the driver.
ENCLOSURE RECOMMENDATIONS
PRIMARY: SEALED
  Qts = 0.63 sits in the sealed-preferred range (0.50–0.70). The manufacturer
  designates this driver for sealed enclosure use in column, 2-way, and 1-way
  systems. Sealed volumes assume nominal net volume; subtract driver chassis
  displacement (~15–20 mL) from gross enclosure volume.

  --- SEALED ALIGNMENTS ---

  Qtc = 0.707 (Butterworth): Vb = 4.38 L  |  fc = 144 Hz  |  f-3dB = 144 Hz
    (Large volume — theoretical reference; practical only in floor-standing formats)

  Qtc = 0.85 (practical bass):  Vb = 1.39 L  |  fc = 173 Hz  |  f-3dB = 148 Hz
  Qtc = 1.00 (compact):         Vb = 0.75 L  |  fc = 203 Hz  |  f-3dB = 160 Hz
  Qtc = 1.20 (column / slim):   Vb = 0.43 L  |  fc = 244 Hz  |  f-3dB = 179 Hz
  Qtc = 1.50 (very compact):    Vb = 0.24 L  |  fc = 305 Hz  |  f-3dB = 213 Hz

  Recommended range: Qtc = 0.85–1.20 (Vb = 0.43–1.39 L) balances bass extension
  with practical enclosure dimensions for column and bookshelf products.
  For column speaker integration with a woofer crossing above 200–250 Hz, Qtc = 1.20
  (0.43 L, f-3dB = 179 Hz) is a compact and predictable choice.

SECONDARY: FREE-AIR / OPEN-BACK
  For multi-way column arrays or panel-mount designs where bass below 150 Hz is
  handled by a dedicated woofer, open-back mounting (free-air, Qts = 0.63) provides
  a natural f-3dB ≈ 146 Hz with no enclosure requirement. This simplifies column
  cabinet construction and avoids rear-cavity resonances. A high-pass filter at
  100–150 Hz protects against excursion below Fs.

  Passive radiator: As noted by the manufacturer, a passive radiator extending bass
  below the sealed rolloff frequency is an option in two-way standalone products.
CROSSOVER AND SYSTEM DESIGN NOTES
  INDUCTANCE ROLLOFF (f_Le = 4,011 Hz — within audio band):
    Le = 0.25 mH places the inductance rolloff onset at ~4 kHz. HF output reduction
    will be audible above this frequency. In 2-way designs, target crossover to a
    tweeter at or below 3,500–4,000 Hz. For 1-way use, DSP treble equalization above
    4 kHz is required to compensate for the rolloff. The BL-symmetric motor design
    (FEM-optimized) mitigates position-dependent inductance variation, which reduces
    the inductance-related distortion component even as the amplitude rolloff proceeds.

  CONE BEAMING (f_beam = 3,042 Hz):
    Pistonic wide-dispersion operation extends to ~3,042 Hz; designed crossover points
    should target 2,500–3,000 Hz or lower for optimal off-axis coverage. The FEM-
    optimized cone and surround geometry is intended to maintain smooth frequency
    response through the upper midrange to the beaming onset frequency.

  COLUMN ARRAY DIRECTIVITY (f_array = 1.85 kHz for 93 mm OD):
    Identical to the 35FRX4-155 (same OD). In a vertical column array, coherent
    vertical directivity is maintained to approximately 1.85 kHz. Array designs
    require a co-located tweeter for HF coverage above 1.85 kHz, or must accept
    progressive vertical beam narrowing above this frequency.

  IMPEDANCE AND WIRING:
    Nominal 8 Ω with Re = 6.3 Ω. Available in 4 Ω, 8 Ω, and 16 Ω variants (per
    manufacturer), enabling flexible column array wiring:
      — 4× 8 Ω in series = 32 Ω (not typical)
      — 2× 8 Ω in parallel = 4 Ω (standard 4 Ω amplifier channel)
      — 4× 8 Ω in series-parallel = 8 Ω (four drivers to 8 Ω channel)
      — 16 Ω version: 4× 16 Ω in parallel = 4 Ω (standard column configuration)

  HIGH-PASS FILTER:
    A high-pass filter at 80–100 Hz is recommended in all sealed configurations to
    protect against over-excursion at low frequencies. Below Fs (128 Hz), the sealed
    enclosure provides minimal acoustic loading and displacement rises steeply. With
    Xmax = 2.35 mm, the driver has meaningful excursion capability; however, cone
    excursion at high levels below 100 Hz can approach Xmech without adequate filtering.

  ZOBEL NETWORK:
    A Zobel network (6.3 Ω + 6.3 μF in series, placed across driver terminals) is
    recommended for passive crossover designs to flatten the rising impedance from Le.
35FR VARIANT COMPARISON (same form factor — 3.5 inch, 93 mm OD)
  Parameter              35FRX4-155 (4 Ω)          35FRX8-406B (8 Ω)
  Re                     3.5 Ω                      6.3 Ω
  AES Power              25 W                       20 W
  Voice Coil Wire        Copper                     CCAW (Cu-clad Al)
  Former                 Aluminum                   Kapton
  Fs                     67 Hz                      128 Hz
  Qts                    0.34                       0.63
  Vas                    1.60 L                     1.14 L
  Sd                     38.5 cm²                   40.7 cm²
  Mms                    7.5 g                      3.1 g
  Bl                     5.46 T·m                   4.8 T·m
  Xmax                   0.55 mm                    2.35 mm
  Vd                     2.12 cm³                   9.56 cm³
  Sensitivity (2.83V/1m) 83.7 dB*                   88.59 dB
  1W/1m (Lm)             83.13 dB                   87.55 dB
  Max SPL (AES)          97.1 dB                    100.6 dB
  Enclosure type         Vented (primary)            Sealed (primary)
  Best f-3dB             ~70–80 Hz (vented)          ~148 Hz (Qtc=0.85)
  Free-air f-3dB         ~175 Hz (unusable)          ~146 Hz (viable)
  Net Weight             0.85 kg                    0.57 kg
  f_Le                   3,978 Hz                   4,011 Hz
  f_beam                 3,128 Hz                   3,042 Hz
  f_array (93 mm OD)     1.85 kHz                   1.85 kHz
  * 35FRX4-155 Sensitivity field inconsistent with Re=3.5Ω per IEC formula;
    Lm = 83.13 dB is used as 1W/1m reference.

  KEY DIFFERENCES:
  • The 35FRX4-155 (4 Ω) has a high-force motor (Bl=5.46, Qts=0.34) designed
    for vented enclosures with bass extension to 70–80 Hz — analogous to a
    small pro mid-woofer in a full-range body.
  • The 35FRX8-406B (8 Ω) uses a lightweight CCAW coil (Mms=3.1g) for high
    sensitivity (87.55 dB, 1W/1m) and extended HF response in a sealed or
    open-back format — designed for column and 2-way applications.
  • The 8 Ω variant has 4.4 dB higher sensitivity (1W/1m) and 3.5 dB higher
    Max SPL despite lower AES power rating, due to the significantly lower Mms.
  • Choose 35FRX4-155 where: bass extension to 70–80 Hz is needed; higher power
    handling (25W AES) is required; vented enclosure is practical.
  • Choose 35FRX8-406B where: sealed or open-back mounting is preferred; maximum
    sensitivity and SPL from a lightweight driver are priorities; 8 Ω system
    impedance is required; BL symmetry for low distortion is valued.
FULL-RANGE FAMILY COMPARISON (9 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    146 Hz  87.6  100.6    93 mm  1.85 kHz
  † Re = 5.5 Ω
  −3dB: free-air for free-air drivers; Fb range for vented; Qtc=0.85 sealed for 35FRX8-406B.
  35FRX8-406B free-air f-3dB ≈ 146 Hz (viable for column/open-back).

  FAMILY NOTES:
  • 35FRX8-406B is the highest-sensitivity sealed/open-back full-range driver in the
    family at 87.55 dB (1W/1m) — second only to the 32NFRX8-463A (89.37 dB, vented).
  • The two 35FR variants (4Ω and 8Ω) share OD and f_array but differ significantly
    in Qts, Fs, motor design, and intended enclosure type.
  • Choose 35FRX8-406B where: high sensitivity in a sealed or open-back column format
    is required; 8Ω simplifies multi-driver wiring; BL symmetry for low distortion
    is a selection criterion; lightweight construction (0.57 kg) matters.
  • The family now covers: 2" to 3.5" format; 4Ω to 16Ω impedance; 10W to 30W AES;
    free-air/open-back, sealed, and vented enclosure types; Neo and Ferrite motors.
SUMMARY
The 35FRX8-406B is a 3.5-inch full-range driver featuring a ferrite magnet motor,
steel basket, FEM-optimized carbon fiber reinforced paper cone with NBR rubber surround,
Nomex spider, and a 25.4mm CCAW voice coil wound on a Kapton former. CCAW (copper clad
aluminum wire) reduces voice coil mass relative to a pure copper winding, yielding an
exceptionally low Mms of 3.1 g and high sensitivity at the cost of a slightly reduced
power rating (20W AES / 40W continuous). The FEM-optimized cone and surround geometry
and BL-symmetric motor circuit target low even-order harmonic distortion across the
excursion range. The driver is the 8 Ω variant of the 35FR family (available in 4, 8,
and 16 Ω versions), sharing the 93 mm overall diameter and 49 mm depth with the 4 Ω
companion 35FRX4-155 while offering a substantially different motor and suspension
characteristic suited to sealed and open-back column speaker applications.

Fs = 128 Hz, Qes = 0.68, Qms = 7.76, Qts = 0.63 — a compliant suspension design
suited to moderate-volume sealed enclosures and open-back installations, where the
driver's natural motor damping produces consistent, low-distortion midrange performance.
Vas = 1.14 L, Sd = 40.7 cm², Xmax = 2.35 mm (one-way), Vd = 9.56 cm³. Sensitivity
is 87.55 dB at 1W/1m (Lm), with a maximum SPL of 100.6 dB at 1 metre (20W AES).
In free-air (open-back), the f-3dB is approximately 146 Hz — viable for column arrays
with dedicated bass support. The voice coil inductance Le = 0.25 mH places the
inductance rolloff onset at approximately 4,011 Hz; DSP treble correction or a 2-way
crossover below 4 kHz is required for extended HF coverage. Cone beaming onset at
3,042 Hz defines the upper boundary of wide-dispersion pistonic operation. Zobel
network: 6.3 Ω + 6.3 μF in series across driver terminals.

  Enclosure alignments:
  • Sealed (primary — per manufacturer intent):
      1.39 L / Qtc = 0.85 / fc = 173 Hz / f-3dB = 148 Hz
      0.75 L / Qtc = 1.00  / fc = 203 Hz / f-3dB = 160 Hz
      0.43 L / Qtc = 1.20  / fc = 244 Hz / f-3dB = 179 Hz
      0.24 L / Qtc = 1.50  / fc = 305 Hz / f-3dB = 213 Hz
    (Butterworth at 4.38 L / Qtc = 0.707 is provided as a reference but is impractically
     large; Qtc = 0.85–1.20 is the practical column and bookshelf range)
  • Free-air / open-back (secondary — column arrays with dedicated woofer):
      f-3dB ≈ 146 Hz; no enclosure required; high-pass filter at 100–150 Hz recommended

In column array applications, the 93mm driver OD limits coherent vertical directivity
to approximately 1.85 kHz — the lowest in the full-range family (shared with the 4 Ω
35FRX4-155). Multiple 35FRX8-406B units can be wired in 2× parallel (4 Ω) or 4×
series-parallel (8 Ω) configurations for standard column array loads. The 16 Ω variant
enables 4× parallel wiring to a 4 Ω amplifier channel. A high-pass filter at 80–100 Hz
is recommended in all installations to protect against over-excursion below Fs (128 Hz).

The 35FRX8-406B is suited for high-sensitivity sealed column speaker systems requiring
87.5+ dB 1W/1m output from a compact 3.5-inch driver with 8 Ω system impedance; 2-way
bookshelf and surface-mount loudspeakers where the sealed Qtc = 0.85–1.20 range
(0.43–1.39 L) provides an efficient, compact enclosure for midrange and upper bass;
open-back column panel designs crossed above 150–200 Hz to a woofer, where free-air
mounting simplifies construction; and installed sound and PA column systems requiring
FEM-optimized low-distortion full-range coverage up to approximately 3,000–4,000 Hz
with a dedicated tweeter above that point.