4th Order Bandpass

Why Your 4th Order Bandpass is Tuned High

Modern 4th Order Bandpass Concepts

Is Your 4th Order Bandpass Tuned “Too High"?

It’s not too high — it’s intentionally tuned this way. Modern 4th order bandpass designs take advantage of your vehicle’s cabin acoustics, the sealed chamber behavior, and ported tuning to deliver maximum efficiency, output, and reliability. Here’s how it works.

Matching Fb to Fc: The Core Principle

In a well-designed 4th order bandpass, the ported tuning (Fb) is intentionally matched to the sealed chamber resonance (Fc). This creates an alignment that produces high efficiency, strong output, and controlled cone motion.

Why Matching Fb and Fc Works

  • Peak Efficiency: When Fb and Fc align, the system becomes highly efficient around that frequency.
  • Reinforced Bandwidth: Both chambers support output in the same region, widening usable bandwidth.
  • Controlled Excursion: Minimum cone motion at the shared resonance point.

The Role of the Sealed Chamber

The sealed chamber dictates how the subwoofer behaves below tuning. Modern designs intentionally use a small sealed chamber because it:

  • Raises Fc into the 40–50 Hz region
  • Increases mechanical control at low frequencies
  • Improves power handling and reliability
  • Shapes the high-pass behavior of the system

A sealed chamber around 1.5–2.0 ft³ for a 15" sub is common in modern builds, not because the woofer “needs” it — but because the system performs better as a whole.

How Cabin Gain Complements the Alignment

  • Smaller vehicles: Cabin gain begins around 40–60 Hz.
  • Larger vehicles: Cabin gain begins around 20–40 Hz.

By placing Fc and Fb in the 40–50 Hz range:

  • Vehicle gain fills in the bottom end naturally
  • Overall output increases without forcing the woofer into dangerous excursion
  • The system avoids “boomy” tuning in the 60–70 Hz range found in many old-school designs

Tuning Above Playback Frequencies: Why It’s Not a Problem

Lower Reactive Impedance

  • Below Fb, impedance drops and power increases.
  • This allows strong output even when playing 25–40 Hz content.

Controlled Cone Motion

  • The sealed chamber keeps excursion under control below tuning.
  • This prevents bottoming out and distortion during low-frequency playback.

Real-World Output

  • A 45 Hz Fb still produces huge output in the 25–55 Hz range.
  • Vehicle acoustics fill the very bottom end, while the system’s peak energy sits right where the cabin is strongest.

Example System

  • Driver: 15" Subwoofer
  • Sealed Chamber: 1.75 ft³
  • Ported Chamber Tuning (Fb): 45 Hz
  • Sealed Chamber Resonance (Fc): 45 Hz

Result:

  • Huge efficiency around 45 Hz
  • Strong bandwidth from ~28–65 Hz depending on vehicle
  • Excellent cone control in the low end

Technical Notes: Fc, Qtc, and Their Role in 4th Order Bandpasses

How to Calculate Fc (Sealed Chamber Resonance)

Once the woofer is placed in the sealed chamber, its resonance shifts upward due to the stiffness of the trapped air. The sealed-box resonant frequency Fc is calculated as: 

Fc = Fs × √( (Vas / Vb) + 1 )
  • Fs = free-air resonance
  • Vas = compliance equivalent volume
  • Vb = sealed enclosure volume (net)

Smaller sealed boxes dramatically increase Fc — which is exactly what modern 4th orders rely on.

Is Qtc Related?

Qtc = Qts × √( (Vas / Vb) + 1 )
  • Higher Qtc (0.9–1.2+): tighter cone control, higher Fc
  • Lower Qtc (0.5–0.8): flatter, looser control

In 4th orders, Qtc is not “tuned.” It is a byproduct of choosing the sealed volume required to set the correct Fc.

Bandwidth Behavior of a 4th Order Bandpass

A 4th order is two filters:

  • Sealed side = High-pass filter
  • Ported side = Low-pass filter

The distance between their cutoff frequencies determines bandwidth:

  • If Fb ≈ Fc: Wide bandwidth and high efficiency
  • If Fb < Fc: Narrow peak, poor output
  • If Fb > Fc: Weak low-end

Excursion and Impedance Behavior

The sealed and ported chambers each control cone motion differently:

  • Above Fb: Ported chamber controls excursion
  • At Fb: Minimum cone motion, maximum efficiency
  • Below Fb: Sealed chamber controls excursion

When Fc ≈ Fb, the sealed-side impedance peak and the ported-side impedance peak merge into a strong, efficient single peak — the signature of a well-designed 4th order.

Sealed-to-Ported Chamber Ratio

The ratio between sealed (Vb1) and ported (Vb2) volumes shapes both bandwidth and peak output:

  • Small sealed / large ported: High efficiency, strong peak, narrower bandwidth
  • Larger sealed / smaller ported: Flatter response, wider bandwidth, less output

Modern car-audio systems almost always use small sealed / large ported because the cabin already boosts low frequencies naturally.

The Bottom Line

Your 4th order bandpass isn’t tuned “too high.” It’s tuned correctly for modern vehicle acoustics. Matching Fb to Fc produces:

  • Peak efficiency in the 40–60 Hz region
  • Low-frequency extension from cabin gain
  • Controlled cone motion across the entire bandwidth
  • Strong, reliable output without unnecessary excursion

This is the modern strategy that maximizes performance in real-world vehicles.