Archive for August 14, 2013

Electric Equivalent Model of Loudspeakers スピーカーの電気モデル

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Hello again,

In this article i will present a way to model the impedance of a speaker driver and how to use that in crossover design. Most crossover calculators on the internet assume a linear fixed impedance as the load of the filter but as you will see this is not the case. For this purpose I created a spreadsheet that will calculate the parameters for you.

The spreadsheet uses Electrical and Mechanical parameters of the loudspeaker driver and calculates the equivalent electrical component value to be used with any circuit simulation software (e.q. SPICE).

Re and Le are electrical components and describe the voice coil properties. Lces, Cmes and Res are mechanical components that are shifted via the BL coupling factor to the electrical side of the impedance model.

It is important to take this fact into consideration because more often than not the mechanical part of the impedance has an influence on the way the filter will respond.

In the below example you can see a standard L-R lowpass filter with a corner frequency of 1kHz. You can see the filter applied to a 8 ohm resistor in the way the most online calculators are being used and you can also see the filter applied to a complex load which represents the electrical model of the loudspeaker (without a box).

2nd order LR 1khz LPFNow lets look at the filters response ( dashed line represent the 8 ohm resistor load and the solid line represents the advanced electrical model load )

Compare Response of load on low pass filter

As you can see the differences cannot be negligible. Below you can find the attached spreadsheet that you can use to build the model. Also it can calculate the box influence for a closed box or bass reflex. The tree elements are connected in series and form  a branch that is connected in parallel to the mechanical equivalent components.

Electric Model of Loudspeakers



Project Harbinger: High Efficiency Loudspeaker System 高効率スピーカーシステム Part 1

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Hello, こんにちは





For me, to reach a live like sound it means i need great dynamics, high sensitivity and big radiation area. Many of my projects start with these aspects in mind and it is clear now that all these are related to efficiency.

Efficiency is a power ratio and in acoustics it is acoustic power delivered vs electric power consumed. There is some debate on how important this parameter is (many manufacturers don’t even publish it), because most audio amplifiers are designed as voltage sources and not power sources. Since impedance of a loudspeaker varies with frequency we can say that the power drawn from the amplifier will vary with frequency.

In the below simulation you can see this variation.

Impedance curve of woofer model

Modeled impedance curve of high efficiency woofer


Calculated input power with constant voltage source having the above impedance as load

Calculated input power with constant voltage source having the above impedance as load


You can easily see how power drawn in the low frequencies drops pretty much this causes sensitivity to drop but not because of low efficiency in the low register but because of how amplifiers are made.

A very important aspect i found to be true is to use high power amplifiers with high efficiency loudspeakers. These amplifiers will most likely have their output stages powered by high voltage and this allows for high voltage swings necessary when driving the high impedance at high levels.

Horns are by far the most efficient sound reproduction systems but since they are passive components they get very large at low frequencies. Because of size and complexity a large number of systems were designed using a direct radiator for low frequencies and horn loading for medium and high frequencies. But can a direct radiator reach a good enough efficiency?

It really depends on its components. For high efficiency you will need a big motor (strong magnetic flux), you will need a light moving assembly (light cones and voice coil) and you will need a big radiating area (large cone diameter).

It is my belief that for good bass from direct radiators one needs at least a 12 inch cone. For domestic use i like the 15 inch cone and there are many great drivers at this diameter that have proven their worth over the years.

At these diameters most drivers one can find come from the professional audio sector. There are many very good designs on the market, it can be hard to find something that can totally please me but given the fact that i like to modify the drivers a new project begun.

First thoughts were to make a standard 2 way system using the 500Hz sectoral horns i had in stock. For this purpose i build a couple of test boxes but first i will introduce the drivers.

First 15 incher was 6523C having a 3 inch voice coil and while the motor provided a good flux density in the gap, the thickness of the top plate was about 10mm. Not the thinnest but the greatest either. The structure is very simple with straight poles and no faraday rings. On the mechanical side again it revealed this was not a woofer for this project for the filter needed alot of optimization to make it work good with a xover point around 1kHz.

Here is the impedance model for this woofer:

Impedance model for 15 inch woofer

High efficiency 2 way horn loudspeakerHigh efficiency 2 way horn loudspeaker

The second 15 incher is based on the 8512F which i modified in various ways. Originally this woofer is designed compact bandpass pro applications, the suspension system is pretty stiff and it needs alot of power to get it moving. So first i changed its spider and outer suspension.

15 incher high efficiency woofer

15 incher high efficiency woofer


15 incher high efficiency woofer


The unit has a tremendous motor designed to match JBL 2226H with a 220mm ceramic magnet ring and 12mm thick top plate. A 4 inch voice coil, a T shaped pole piece makes this 15 incher a real beast.

High efficiency 15 inch woofer

The first compression driver tested was a 1″ exit with Ti diaphragm and Ti suspension. I later replaced the suspension with mylar one. I had a sheet of mylar and cut out a ring to form the suspension. This improved on the transition region between the woofer and the CD as i will later show.

compression driver diaphragm

Compression driver mylar suspension

15 incher and enclosure model

Phase plug is after the old Tannoy Monitor Gold and should provide a better low frequency response.

Below you can see the model for the 15 incher and the bass reflex box. The box is tuned lower as the xover will bring the second peak down a bit.


simulated impedance

Here are some of the first ideas for the enclosure:

2 way horn high efficiency loudspeaker

2 way horn high efficiency loudspeaker

I will end here the first article and will continue soon.

Thank you for visiting,