擴展頻寬

PRD 擴散器設計原根擴散器

PRD 擴散器使用原根序列取代二次餘數，提供比傳統 QRD 設計更寬的有效頻寬。原根的數學特性產生出色的自相關特性，實現優越的寬頻擴散。

What is a PRD Diffuser?

Mathematical Foundation

PRD (Primitive Root Diffuser) extends the principles of QRD by using primitive root sequences instead of quadratic residues. A primitive root g of a prime number P is an integer whose powers generate all residues from 1 to P-1.

This mathematical property creates a more evenly distributed sequence of well depths, which can produce a different diffusion pattern than a QRD of comparable size. Whether that translates into a wider usable bandwidth depends on the specific geometry, depth, and well width chosen — it should not be assumed without comparing the actual designs.

How It Works

The PRD sequence is generated by raising a primitive root g to successive powers and taking the modulus with a prime number P. For example, with P=11 and g=2, the sequence becomes: 1, 2, 4, 8, 5, 10, 9, 7, 3, 6.

This sequence has different autocorrelation properties compared to quadratic residues. In principle this can reduce periodic gaps in coverage, but the practical effect depends on the built geometry and should be verified with measurement or simulation.

Acoustic Properties

PRD diffusers can offer a different scattering pattern than QRD designs, which may be useful when asymmetric or alternative lobe behavior is desired for a specific room.

Any claimed bandwidth advantage depends on the actual geometry, depth, well width, and measurement or simulation data for the specific design — not on the choice of PRD sequence alone.

使用情境

Mastering & Critical Listening Rooms. Ideal for environments requiring the most accurate acoustic response. The wider bandwidth ensures consistent diffusion across the entire frequency spectrum, critical for making precise mixing and mastering decisions.
High-End Home Theaters. Superior to QRD for home cinema applications where both music and film soundtracks demand consistent diffusion. Provides natural spaciousness without frequency-specific artifacts.
Recording Studio Live Rooms. Creates a more musical diffuse field for recording acoustic instruments. The extended bandwidth preserves the natural timbre of instruments from bass to high frequencies.
Concert Halls & Auditoria. Large-scale PRD applications provide uniform sound distribution for audiences. Particularly effective for orchestral and acoustic performances requiring natural reverberation control.
Broadcast & Dubbing Stages. Maintains speech intelligibility while controlling room acoustics. The broadband performance ensures clear dialogue recording without frequency-dependent reflections.
Upgrade from QRD. When existing QRD installations show frequency-dependent performance issues, PRD offers a direct upgrade path with improved bandwidth and more uniform diffusion characteristics.

優點

Can offer a different scattering pattern than QRD for a comparable depth (350Hz-5kHz is a typical planning range, not a guarantee)
Can produce more uniform diffusion coefficients across frequency, depending on the specific design
Different autocorrelation properties than QRD, which can reduce periodic coverage gaps in some designs
May produce a flatter, more neutral frequency response — worth verifying by measurement
Can perform differently than QRD at the same well depth; compare geometries directly rather than assuming
Grounded in published number-theory research on primitive root sequences
Used by some acousticians for critical listening environments alongside QRD
Can use the same fabrication methods as QRD

注意事項

More complex mathematical design than QRD
Requires software for sequence calculation
Slightly higher fabrication complexity due to sequence pattern
Less widely known than QRD among builders
Still limited to one-dimensional diffusion
Similar depth requirements to QRD for low frequencies
Higher cost than simple broadband absorbers
Performance benefits most noticeable in critical applications

設計參數

Prime Number (P). Common values: 11, 13, 17, 23, 29: The prime determines both the number of wells (P-1) and the bandwidth characteristics. Larger primes provide even broader coverage.
Primitive Root (g). Selection: Automatically calculated or manually chosen: Each prime has multiple primitive roots, which produce different (but mathematically valid) depth sequences. ResonAia selects a primitive root automatically; you can also choose manually.
Maximum Well Depth. Typical range: 75mm - 200mm (3" - 8"): As with QRD, depth still determines fmin using the λ/4 relationship, as a planning estimate — verify with simulation or measurement rather than comparing designs by depth alone.
Well Width. Typical range: 25mm - 75mm (1" - 3"): Well width affects the high-frequency limit, similar to QRD. Compare specific designs rather than assuming PRD tolerates wider wells at the same frequency.
Frequency Range. Planning range: Typically 350Hz - 5kHz: Frequency limits are planning estimates. The low limit is mainly constrained by maximum well depth; the high limit is mainly constrained by well width and edge detail. Whether a given PRD design outperforms a QRD design of the same depth and width should be confirmed by simulation or measurement, not assumed.
Material & Finish. Same as QRD: MDF, plywood, or hardwood: PRD uses identical fabrication methods to QRD. The mathematical differences don't affect machining complexity, only the well depth sequence.

How to Design a PRD Diffuser

Choose your goal and constraints. Decide what you want to improve (spaciousness, echo control) and note your available depth, width, and placement distance.
Select prime number P. Choose a prime number P; it affects sequence length and panel width. Ensure the resulting size fits your space.
Choose primitive root g. Pick a primitive root g of P to generate the sequence. Different valid roots can produce different patterns.
Set depth and well width. Choose maximum depth based on the lowest target frequency, then choose well widths and overall dimensions that match your build method.
Build and install. Use rigid materials, keep tolerances consistent, and install at the planned location with adequate listening distance.

擴散器設計器 · 價格

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