Bachller

hillerCrossover Design with MATLAB: Tutorial
March 24, 2007

What today is all about By now we’ve learned a bit about how speakers work and how sound waves interact; and we want to be able to design our own speaker system. So, it’s time to put our knowledge to good use. We’ll get acquainted with MATLAB - a powerful program for science and math - and use it to do the nasty computations involvedwith impedances. We can design filters that use resistors, inductors, and capacitors and use MATLAB to simulate their effects on actual speaker drivers. This way, we can experiment with lots of different drivers and filter circuits without actually having to build speakers. You’ll first learn how the system works by simu­ lating a simple 2-way speaker design, and then you’ll be able to createcrossovers to go with any combination of different woofers, midranges, and tweeters. I hope you have a good time. Using MATLAB On the MIT Server computing system at MIT, we have a program called MATLAB which can do lots of calculations very quickly, even with complex numbers (which describe, for example, both a signal amplitude and a phase shift). It also helps us make graphics to observe the results ofour simulations. We will take advantage of this to analyze the effect of crossover networks on the responses of speaker drivers. Starting MATLAB 1. Start the MATLAB program: Start -> Math/Plotting -> MATLAB 2. Load the graphical interface: type desktop and hit enter. 3. Switch the working directory: on the list of folders in the upper left, doubleclick on hsspmatlab.

I had to write the functionsto simulate crossover circuits; they’re not included in MATLAB. To use them, you will need to change the working directory (the place where MATLAB looks for data) to the folder where I put the files, like it says in step 3 above.

You’re now all set to simulate crossover circuits... let’s give it a shot. Tutorial crossover design To help you get started, here are directions for simulating anactual working speaker design. Shown below are the crossover circuit schematics and a picture of the completed product. Does the speaker look familiar?

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Crossover Design with MATLAB

Audio and Speaker-building

March 24, 2007

R: 0.5 ohm L: 1.5 mH
R1011 L1011 source D11 Dayton RS150 6" aluminum cone midwoofer PE# 295-362

C: 10 uF
C1021

Lowpass Branch

C: 10 uF
C2031 sourceL-pad R: 3 ohm Branch R2051 R: 5 ohm
R2061 D21 Dayton DC28 1-1/8" soft dome tweeter PE# 275-070 R2041 L2041

R: 0.7 ohm L: 0.4 mH Highpass Branch

Image by MIT OCW.
To simulate the response of the circuit, there are a few steps. Here are examples of the four main functions you can use. Don’t enter in these exact commands... the tutorial is a couple of paragraphs down. Example Steps forCrossover Simulation 1. Load data for each driver: woofer = load(’rs180’); 2. Create circuit branches: lowpass = branch(’RL’, [0.4 2.5], ’C’, 6.8); 3. Simulate their effect on each driver: highsection = simulate(lowpass, woofer); 4. Combine networks together to form complete speaker: result = combine(lowsection, highsection); In the MATLAB command window, there’s a prompt (>> ) where you enter in linesof code for the inter­ preter to execute. Most of the commands you’ll use for simulating crossovers involve calling a function (such as branch), passing that function some input data (the circuit components and their values: ’RL’, [0.4 2.5], ’C’, 6.8), and receiving its output (the resulting impedance and frequency response: lowpass). Sometimes the code will generate a lot of numbers, which wouldnormally go on the screen. You can enter a semicolon (;) at the end of a line to suppress this output if you want. I like to do it this way. Also, be careful to match up parentheses, square brackets, and quotes correctly... MATLAB can’t exactly figure out what you meant to type. Anyway, on to the circuit for the small 6” two-way speaker we’ve been listening to in class. This speaker uses the...