Spice Analysis Of The C-Note Speaker

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Near field studio monitors and computer gaming audio systems serve similar functions. Usually, studio monitors are slightly larger than gaming systems, but are still small enough to be desk mounted, (or immediately behind the desk, wall or stand mounted.)

A near field studio/computer audio system should be capable of producing 85 dB SPL at 1 meter, program level, and a little over 100 dB SPL peak, for compliance with EBU R68-2000, R89-1997, SMPTE RP155/RP200, THX, (except LFE,) and be OSHA 1910.95 compliant for 8 hours per day listening. The frequency response of near field studio monitors is usually about 40 Hz., low frequency F3, (maybe a little higher to about 50 Hz. on some commercial models,) to 20 kHz., -3 dB.

The C-Note speakers are a viable example at 11" H x 7.5" W x 9.5" D, with an F3 frequency of 43 Hz., (to 20 kHz., -3 dB,) and a cost of about $100 per stereo system. The C-Note speakers are billed as a bookshelf speakers, and were chosen as an evaluation example.

Inexpensive amplifiers, (LM3886, TPA3116/8, TDA7492, PAM8610, TDA2020/4, TDA7492 based units,) are available from the Internet stores for $10 to $30, (stereo,) and are quite adequate for the specifications. The LM3886 based amplifiers require a bipolar power supply, and a Lepai LP-2020TI based on the TPA3118 chip was chosen for its low distortion characteristics, and adequate output power on a single 12 V power supply, (which has the additional advantage of being both automotive and solar power compatible.)

12 V and 15 V at greater than 5 A LED string power supplies are available at the internet stores for $8 to $16, depending on reliability specification, and are quite adequate for the power output specification. An S-60-12 12 V, 5 A, (from an unknown manufacturer,) power supply was chosen.

The C-Note enclosures were assembled, as per the directions, in about two days, and tested with the amplifier and power supply, Using the Panasonic WM61A as a Measurement Microphone. Besides meeting the frequency response and sound intensity specification at 1 meter, the distortion characteristics were impressive-at 100 dB SPL at 1 meter the distortion, (THD,) measured -55 dB, (total loopback: using a Linux PC as a signal source; through the amplifier; through the speakers; through the microphone; through a mixer/bridge; and back to the PC for FFT distortion analysis.) The test results were beyond the capability of the test setup, (particularly the non-linearites of the WM61A electret microphone at these levels,) and indicate that the C-Note speaker, at 100 dB SPL @ 1 meter was capable of producing a THD somewhat around/below -60 dB = 0.1%. The magnitude of the harmonics of an EBU R68-2000 0 dBFS, 997 Hz. alignment signal which fall in the most sensitive frequency range of human hearing of the Fletcher-Munson curves, (about 2 kHz. to 5 kHz.,) were:

  • Fundamental, -13 dB
  • 2nd, -74 dB
  • 3rd, -67 dB
  • 4th, -90 dB
  • 5th, -105 dB

actual test data, 15' X 16' non-acoustically treated room, as measured in the test setup with the Baudline Fast Fourier Transform program, (level ~ 0 dBFS ~ 100 dB SPL @ 1 meter.)

Spice Analysis of the C-Note Speaker:

The optimal maximally-flat enclosure volume for the DSA135-8 5" woofer is about 6.6 liters, with an enclosure resonant frequency, Fb, of 55 Hz., (and an F3 of 56 Hz.) Referring to the manufacturer's data, the C-Note speaker has an impedance minima of about 40 Hz., (meaning Fb ~ 40 Hz.,) and a physical enclosure volume of about 9 liters, (about 8.5 to 8.75 liters acoustical volume,) extending the F3 of the C-Note speaker to 43 Hz.

Using these parameters, the complete C-Note speaker system, (including crossovers,) were simulated using gEDA and ngspice as a design environment. The design database is available as a tape archive, c-note.tar.gz, to facilitate replication of the design.


Figure I. Schematic of the C-Note Speaker Simulation

Figure 1, ((1600X1200),) is the schematic of the C-Note speaker used in the simulation. Note that the mid-range woofer, tweeter, crossover, and baffle step are simulated. Both of the speaker drivers are simulated using slightly modified Thiele/Small parameters. The parameters were modified for better agreement at high frequencies with the individual driver's FRZ data.


Figure II. Simulated Frequency Response of the C-Note Speaker

Figure 2 is the simulated frequency response of the C-Note speaker. By comparison, see: C-Note Crossover Schematic with Frequency Response. Also, for comparison, the low frequency response data for independently measured popular commercial studio monitors was collected from around the Internet, including the Altec-Lansing VS2421 specification, which is a popular computer gaming audio system.


Figure III. Simulated Maximum SPL Response of the C-Note Speaker

Figure 3 is the simulated maximum SPL response of the C-Note speaker. The speaker is a ported design, and very low frequency de-coupling of the woofer driver cone limits the maximum SPL of the speaker. The speaker is capable of producing full power, 100 dB SPL @ 1 meter, down to its low frequency cut off-the low frequency full power bandwidth, (FPBW,) is about 43 Hz., and subsonic filters would probably not be required, except in very critical applications. (The C-Note speaker is capable of producing white noise signals at levels of 83 dB SPL @ 1 meter without subsonic filters.)


Figure IV. Simulated Phase Response of the C-Note Speaker

Figure 4 is the simulated phase response of the C-Note speaker.

Figure V. Simulated Group Delay of the C-Note Speaker

Figure 5 is the simulated group delay of the C-Note speaker. The graph has two data points, one rather theoretical, one empirical, (which are in reasonable agreement,) showing the limits of audibility of group delay in speaker systems. The C-Note speaker group delay would be audible only under extremely controlled conditions, (i.e., an acoustically treated room.)


Figure VI. Simulated 5 Hz. Transient Response of the C-Note Speaker

Figure 6 is the simulated 5 Hz. transient response of the C-Note speaker. This would sound like 5 Hz. "clicks" due to the high pass characteristics of speakers, (any speakers will sound like this, unless the room is very small, and completely sealed-i.e., adiabatic compression.)


Figure VII. Simulated 1 kHz. Response of the C-Note Speaker

Figure 7 is the simulated 1 kHz. response of the C-Note speaker. Note the time alignment between the tweeter transient and leading edge of the woofer transient. This may, or may not, exist-the acoustic centers of the two drivers are not known, (but if they were, they could be modeled as a spice time delay.) But, if they do exist, the transient fundamental is about 21 uS, (24 kHz.,) probably beyond human audibility.


Figure VIII. Measured Frequency Response of the C-Note Speaker

Figure 8 is the measured frequency response of the C-Note speaker. There are two plots: 100 dB SPL @ 1 meter, 40 to 20 kHz. frequency sweep; and, 85 dB SPL @ 1 meter, 0 to 20 kHz. white noise. Frequency is logarithm scale.

The room environment where the measurement was made is far from optimal, and is typical of a SOHO office or computer work/gaming station scenario. The room has no acoustical treatment of any kind, (i.e., has a large glass window, large white board, uncovered wood floors, two solid wood closet doors, uncovered wood door, large wood desk, computer stand, printer stand, etc.,) and is about 19' X 11' X 8' physical dimensions, all orthogonal; the area of all walls/ceiling/floor is about 83.5 square meters.


Figure VIX. Measured Low Frequency Response of the C-Note Speaker

Figure 9 is the measured low frequency response of the C-Note speaker, (same data as Figure 8.) The frequency is linear scale. In addition, the heuristic Room Acoustics is plotted, including the Eigen values at the center of the room, (the antinodes are the bottom "dots," minimum pressure, oblique mode; the top "dots," axial mode, the middle "dots," tangential mode.) The Schroeder cutoff frequency is about 83 Hz., above which, the accuracy deteriorates rapidly. The listener's position, (microphone placement,) was offset from the center of the room, (the values in the 'O' parameters.)

Replicating the Analysis of the C-Note Speaker

To replicate the analysis in its entirety, Debian Linux, versions 7, 8, or, 9, will be required with Ngspice, the Baudline FFT time-frequency browser, Gnuplot, GNU Emacs, GNU RCS, gEDA and, Calc programs, all of which are available from one's favorite Linux repository. (Other programs required are the "standard" Unix/Linux utilities, installed with one's choice of Linux distributions.)

Quick Start:

  1. tar xvfz c-note.tar.gz
  2. cd c-note/ported/
  3. make co
  4. make
  5. makeit
  6. emacs
  7. make realclean

Which should generate all files portrayed above, leaving a clean directory.

Additional actions in the c-note/ported/ directory:

  • cp schematic-lm833.sch schematic.sch

    will change the top level schematic to use electronic/active crossovers, instead of the standard passive LC crossovers distributed with the C-Note speakers.

  • standard.values

    will change the theoretical/calculated values in the *.inc files, (ngspice include statements read these files in the various schematics of the electronic/active crossovers,) produced by the *.calc files to industry standard values.

  • standard.components-lm833

    will change the electronic crossover schematics to use LM833 dual audio operational amplifier ngspice models. (Likewise, for the file standard.components-ne5534 to install NE5534 low noise operational amplifier ngspice models.)

  • make lm833

    will make the artwork for commercially produced PCBs of the electronic/active crossovers. There are many versions available in the RCS/ directory as tape archives, (i.e., tar.gz files,) for example, the RCS/single-layer.tar.gz file (i.e. co single-layer.tar.gz; tar xvfz single-layer.tar.gz,) will install the autorouted PCBs for the electronic crossovers, (all 6 of them, 2.75" X 2.75", each,) and can be prototyped with the DIY PCB system.

For further information, see c-note/ported/Makefile.

File Structure of the c-note/ directory:

  • c-note/RCS

    contains the master revision control files for the entire analysis. Other RCS directories will link, (ln -s,) common files to the files in this directory-like a master library function.

  • c-note/ported

    contains the master design.

  • c-note/ported/PA

    contains the analysis of power amplifier loading by the C-Note speaker. It's function is for stability analysis, (the installed device is an LM3886, and includes the Texas Instruments/National spice model-see instructions in the lm3886a.sch file for installation.) The file constructionals are the same as above.

  • c-note/ported/butterworth/

    is an analysis of different speaker configurations, (butterworth, acoustic-suspension, bessel, critically damped, and, the DSA135 optimal enclosure size. The file constructionals are the same as above for each directory, including the c-note/ported/butterworth directory. The presentation compares the simulation, portrayed above, with the different configurations, all with a low frequency cutoff of about 40 Hz.

  • c-note/ported/models/dsa135-8/ and c-note/ported/models/nd25fw-4 directories are an analysis of the modifications made to the Thiele/Small parameters for increased high frequency accuracy, in comparison to the individual driver's FRZ data. The "standard" T/S models can be used by changing the include file(s) in ported.sch and tweeter.sch in the top level schematic.


A license is hereby granted to reproduce this design for personal, non-commercial use.


So there.

Copyright © 1992-2018, John Conover, All Rights Reserved.

Comments and/or problem reports should be addressed to:

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