Subwoofer tools.
ENCLOSURES & PORTS / THE TOOLKIT

Passive radiator.

A passive radiator can solve a port-length problem, but it has its own compliance and excursion limit. Calculate the required mass per radiator, then inspect the coupled system.

01 / THE INPUTS
Enclosure design
Hz
Radiator parameters
N s/m
Model selection
Driver parameters
Hz
Ω
Drive & radiation
V
Ω
Air & conventions
m/s
kg/m3
Frequency sweep
Hz
Hz
02 / THE RESULTS
Added mass per radiator
120.4g
Target total mass per radiator
320.4g
Weighted free-air resonance
13.36Hz
Peak radiator excursion
45.01mm
10-200 Hz
Peak driver excursion
29.49mm
10-200 Hz
Peak sampled output
114.0dB SPL

Acoustic response

LOG FREQUENCY
Acoustic response: SPL (dB) against frequency in hertz.55.8768.3680.8593.35105.84118.34102050100200SPL (dB)Frequency (Hz)

Driver excursion reaches 29.49 mm, exceeding the 12.50 mm one-way limit within this sweep. Reduce drive or evaluate protection.

Radiator excursion exceeds its 20.00 mm one-way limit within this sweep.

Read this result with its assumptions.

Sweep: 10-200 Hz, 241 logarithmic samples. Maxima describe this sampled range, not an unrestricted operating limit.

SPL is at 1 m in ideal half-space. Electrical drive is RMS; displayed excursions and air velocities are one-way peak.

Units & assumptions

Your calculations run in this browser. No account needed.

03 / UNDER THE HOOD

The math, in plain sight.

Tune the mass. Check the movement.

Find the target mass per radiator

A radiator replaces vent air mass with a diaphragm and suspension. Its own compliance must be included. N is the number of identical radiators; every reported mass is per radiator.

Cb=Vbρc2,Cpr=Spr2Cms,pr=Vas,prρc2C_b=\frac{V_b}{\rho c^2},\qquad C_{pr}=S_{pr}^2C_{ms,pr}=\frac{V_{as,pr}}{\rho c^2}
Mpr,target=Spr2(2πfb)2(1Cpr+NCb)M_{pr,\mathrm{target}}=\frac{S_{pr}^2}{(2\pi f_b)^2}\left(\frac1{C_{pr}}+\frac N{C_b}\right)
Madd=Mpr,target−Mpr,existing,fpr=12πMpr,targetCms,prM_{\mathrm{add}}=M_{pr,\mathrm{target}}-M_{pr,\mathrm{existing}},\qquad f_{pr}=\frac1{2\pi\sqrt{M_{pr,\mathrm{target}}C_{ms,pr}}}

If added mass is negative, adding weight cannot reach the requested tuning. A lighter radiator or a different design is required.

Check the coupled response

Active-driver properties are derived as in the Thiele-Small parameter calculator. Compare the radiator excursion with its own one-way rating, not the driver rating.

Zpr(s)=Rms,pr+sMpr+1/(sCms,pr)Spr2Z_{pr}(s)=\frac{R_{ms,pr}+sM_{pr}+1/(sC_{ms,pr})}{S_{pr}^2}
Yb=sCb+NZpr,Zb=1Yb,Zm=Rms+sMms+1sCms,Ze=Re+Rg+sLeY_b=sC_b+\frac N{Z_{pr}},\quad Z_b=\frac1{Y_b},\quad Z_m=R_{ms}+sM_{ms}+\frac1{sC_{ms}},\quad Z_e=R_e+R_g+sL_e
vd=BlEZe(Zm+Sd2Zb)+(Bl)2,Ud=Sdvd,pb=−UdZbv_d=\frac{BlE}{Z_e(Z_m+S_d^2Z_b)+(Bl)^2},\quad U_d=S_dv_d,\quad p_b=-U_dZ_b
Upr,1=pbZpr,Uradiated≈Ud+NUpr,1U_{pr,1}=\frac{p_b}{Z_{pr}},\qquad U_{\mathrm{radiated}}\approx U_d+NU_{pr,1}
Xd,peak=2∣vd∣ω,Xpr,peak=2∣Upr,1∣ωSprX_{d,\mathrm{peak}}=\frac{\sqrt2|v_d|}{\omega},\qquad X_{pr,\mathrm{peak}}=\frac{\sqrt2|U_{pr,1}|}{\omega S_{pr}}

Worked example and verification

One radiator in 40 L, with Vas,pr = 100 L, area 400 cm2, and target tuning 25 Hz, needs an ideal target moving mass of about 320 g. An existing 200 g radiator therefore needs about 120 g added.

The radiator free-air resonance can create a low-frequency dip. Losses and mounting-dependent air mass also change real tuning. Verify the finished cabinet by measurement.