For those determined to try, search for the “MJK worksheets” archive on the Internet Archive or diyAudio threads – and expect to spend a weekend reading the accompanying PDFs before simulating your first line.
Martin J. King is widely recognized in the audio engineering community for his development of General Quarter Wave theory, which he translated into a series of highly influential Mathcad worksheets. These tools revolutionized how hobbyists and professional engineers design transmission line (TL) loudspeakers. The Core Purpose
Before King’s work, transmission line design was largely based on "rules of thumb" or trial and error. King applied classical acoustic theory and fluid dynamics to create a mathematical model that accurately predicts how sound waves behave inside a cabinet. His Mathcad worksheets allow users to simulate the frequency response of a speaker driver within a specific enclosure before a single piece of wood is cut. Key Features of the Worksheets
The worksheets are essentially interactive calculators that require the user to input specific data:
Thiele/Small Parameters: The physical and electrical characteristics of the speaker driver (e.g., resonant frequency, moving mass, and motor strength).
Enclosure Geometry: The length, cross-sectional area, and taper (whether the pipe gets wider or narrower) of the internal line.
Damping Material: Users can specify the density and location of "stuffing" (like polyfill or wool), which is critical for smoothing out unwanted resonances in TL designs. Why Mathcad?
King chose Mathcad because of its ability to handle complex matrix algebra and differential equations while displaying them in a readable, "whiteboard" format. This transparency allowed users to see the physics at work, rather than just interacting with a "black box" software program. The worksheets calculate the complex impedance and pressure at both the driver and the terminal (port), then sum them to show the final acoustic output. Impact on Audio Design
The "King Worksheets" democratized high-end speaker design. They proved that:
Geometry Matters: Even slight changes in the taper or the driver’s position along the line significantly impact performance.
Predictability: TL speakers, once thought "fussy" or unpredictable, could be engineered for flat, deep bass response comparable to much larger ported or sealed boxes. Modern Availability
While Martin J. King has retired and no longer updates the original Mathcad files, his models remain the "gold standard" for quarter-wave theory. Many of his equations have since been ported into modern software like Leonard Audio’s Transmission Line software or AkAbak, ensuring his contributions continue to influence speaker building today.
Martin J. King (often referred to as MJK) is a legendary figure in the DIY audio community. His Mathcad worksheets are considered the "gold standard" for modeling quarter-wave loudspeaker enclosures (Transmission Lines, TQWTs, and Horns).
However, opening his worksheets for the first time can be intimidating. They are dense, filled with proprietary scripts, and require a specific workflow.
Here is a guide to navigating and understanding Martin J. King’s Mathcad worksheets.
In a standard TL, the driver is at the closed end. King provided specific worksheets to model placing the driver 1/3 or 1/2 down the line, which helps smooth out standing wave ripples.
When you open a standard MJK worksheet (e.g., TL Open End V4), you will see a vertical stream of calculations. Do not try to read it like a book from top to bottom immediately. Look for these structural elements:
Due to the takedown, here is the ethical and functional path:
This is the holy grail. This worksheet allows you to model a straight, tapered, or expanding transmission line. Input parameters include:
Outputs: The worksheet generates SPL (Sound Pressure Level) graphs, cone excursion, impedance curve, and group delay.
To understand the value of martin j king mathcad worksheets, you must understand the tool. Mathcad (now owned by PTC) is unique because it treats the worksheet like a whiteboard. You see the equations exactly as you would write them in a textbook.
King chose Mathcad because:
This is the only part you should edit. It usually starts with the driver parameters (Fs, Qts, Vas, Sd) and the enclosure dimensions.