ENCLOSURES & PORTS / THE TOOLKIT

Fourth-order bandpass.

Both chambers load the driver, while external output comes from the front port. Inspect response, excursion, impedance, and the passband relative to its peak.

01 / THE INPUTS
Driver parameters
Hz
Ω
Enclosure design
Hz
Port geometry
Drive & radiation
V
Ω
Optional acoustic losses

Leave blank for an ideal lossless port.

Leave blank for no absorption resistance.

Leave blank for an airtight chamber.

Air & conventions
m/s
kg/m3
Frequency sweep
Hz
Hz
02 / THE RESULTS
Peak sampled output
115.4dB SPL
Lower -3 dB edge
42.04Hz
Upper -3 dB edge
93.58Hz
Peak cone excursion
14.91mm
10-200 Hz

Acoustic response

LOG FREQUENCY
Acoustic response: SPL (dB) against frequency in hertz.83.0189.9696.91103.87110.82117.77102050100200SPL (dB)Frequency (Hz)

Driver excursion reaches 14.91 mm, exceeding the 12.50 mm one-way limit within this sweep. Reduce drive or evaluate protection.

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.

Passband edges enclose the largest sampled peak and use a reference 3 dB below that peak. Other lobes or a narrow peak are not a broad, flat passband.

Units & assumptions

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03 / UNDER THE HOOD

The math, in plain sight.

Two chambers. One coupled system.

Two chamber loads

The front chamber is vented and the rear chamber is sealed. Pressures act on opposite faces of the cone, so both acoustic loads must be included. External output is the front port output.

CF=VFρc2,CR=VRρc2,LpF=1(2πfbF)2CF,ZpF=RpF+sLpFC_F=\frac{V_F}{\rho c^2},\quad C_R=\frac{V_R}{\rho c^2},\quad L_{pF}=\frac1{(2\pi f_{bF})^2C_F},\quad Z_{pF}=R_{pF}+sL_{pF}
YF=sCF+1ZpF,YR=sCR,ZF=1YF,ZR=1YRY_F=sC_F+\frac1{Z_{pF}},\quad Y_R=sC_R,\quad Z_F=\frac1{Y_F},\quad Z_R=\frac1{Y_R}
YC,i=1RA,i+1/(sCi)+1RL,iY_{C,i}=\frac1{R_{A,i}+1/(sC_i)}+\frac1{R_{L,i}}

When loss factors are entered, the last expression replaces the ideal chamber compliance admittance. This calculator references both chamber loss factors to the front tuning; port resistance uses Rp = omega_b Lp / Qp.

Driver motion and radiated output

The driver properties follow the relationships published on the Thiele-Small page. Reported -3 dB edges are found numerically relative to the sampled response peak, over the stated sweep.

Zm=Rms+sMms+1sCms,Ze=Re+Rg+sLeZ_m=R_{ms}+sM_{ms}+\frac1{sC_{ms}},\quad Z_e=R_e+R_g+sL_e
pF=ZFUd,pR=−ZRUd,Ud=Sdvp_F=Z_FU_d,\qquad p_R=-Z_RU_d,\qquad U_d=S_dv
v=BlEZe[Zm+Sd2(ZF+ZR)]+Bl2,Uport=pFZpFv=\frac{BlE}{Z_e[Z_m+S_d^2(Z_F+Z_R)]+Bl^2},\qquad U_{\mathrm{port}}=\frac{p_F}{Z_{pF}}
pRMS≈∣ρsUportΩre−sr/c∣p_{\mathrm{RMS}}\approx\left|\frac{\rho sU_{\mathrm{port}}}{\Omega r}e^{-sr/c}\right|
Xd,peak=2∣v∣ω,Zdriver,in=Re+sLe+Bl2Zm+Sd2(ZF+ZR)X_{d,\mathrm{peak}}=\frac{\sqrt2|v|}{\omega},\quad Z_{\mathrm{driver,in}}=R_e+sL_e+\frac{Bl^2}{Z_m+S_d^2(Z_F+Z_R)}

A peak is not a broad passband

The lumped-port model does not predict every higher-frequency pipe or chamber mode. A bandpass box is not a replacement for appropriate electrical filtering. Narrow peaks need careful interpretation and physical verification.