J. Audio Eng. Soc., Vol 39, No. 7/8, 1991 July August
Page 557
Engineering Reports - "Electroacoustic design with Spice" - By W. M. Leach, Jr.
It contains a very interesting Spice simulation.
This is probably the mother of all bass-reflex speaker design softwares.
Worth reading it !
Here is a link : http://users.ece.gatech.edu/mleach/papers/spice_electro.pdf
More here : Dr. Leach's Refereed Papers.
I tried to transfer this onto LTspiceIV.
Without second-order effects.
Here are some suggestions.
It seems to work.
I wanted to make this simulation compatible with the closed box case.
Therefore, I have kept Cab (the box compliance) inside the loudspeaker coil loop, instead of moving Cab into the vent inductance loop like W. M. Leach, Jr. did.
I wanted to have all LTspiceIV circuit elements having their values equal to their physical values without any scale factor.
The box compliance value on the LTspiceIV schematic is the box compliance seen by the woofer. This compliance comes in series with the driver suspension compliance.
The suspension compliance equals 214µm/N.
The box compliance seen by the woofer equals 170µm/N.
As a consequence if you close the vent, and if you try moving the woofer membrane by 1 millimeter, you will need to apply a force equal to :
0.001 Newton divided by the suspension compliance (= 4.67 Newton)
plus
0.001 Newton divided by the equivalent box compliance (= 5.88 Newton)
total
10.55 Newton
The vent mass value on the LTspiceIV schematic is the actual air mass contained into the vent volume. Physically, this air mass resonates with the box volume according to the Helmholtz law. The Helmholtz law can be described as a spring-mass system with almost no damping. The spring effect comes from the box volume, hence compliance SEEN BY THE VENT CROSS-SECTION AREA. The mass effect comes from the air mass contained into the vent volume.
Most of the time, the vent cross-surface area is much smaller than the driver membrane surface. The box compliance perceived by the vent cross-surface area will therefore be much higher (= easier to move) than the box compliance perceived by the driver membrane. The compliance amplification factor perceived by the vent equals the ratio of the two surfaces : driver membrane surface / vent cross-section area.
Thus, and this is the vicious trick, on the LTspiceIV schematic, we need to represent the fact that the box compliance gets perceived by the vent cross-section (and mass) as an amplified compliance.
Consider now a box compliance equal to zero. This means that the driver gets connected to the vent, without any intermediate box. You then realize that the same amplification will shows regarding the speed. If you press the woofer 1 millimeter, the air in the vent will move 1 millimeter times the amplification factor defined by the ratio of the two surfaces.
Looking to the LTspiceIV schematic, we realize that any current stolen by the inductance representing the vent, is the air speed into the vent.
Therefore if there is 1 milliamp stolen from the Compl_Box capacitor, physically, there must be 1 milliamp times the amplification factor inside the inductance representing the vent.
Now we understand the why and how of the chain made of V1, H1 and G1. This chain replaces a current multiplier. There is no current multiplier (current controlled current source) in LTspiceIV. I needed to build one using an ammeter (V1) followed by a voltage-controlled voltage source (VCVS) followed by a voltage-controlled current source (VCCS). With an amplification factor equal to the ratio of the surfaces.
At this stage we may feel happy, having implemented the vent air speed gain caused by the surface ratio. We now need to respect energy considerations. Having articifially boosted the current in the vent inductance by a certain factor, we need to artificially reduce the stimulation voltage accordingly. This is done by multiplying the voltage developping on the coil, by the same factor, then transferring this multiplied voltage back to the cause. This is the role of E1, a voltage-controlled voltage source. This way, the energy gets balanced. Yes, indeed there is a current amplification in the process, but the back-EMF generated by the inductance gets multiplied by the same facor, and this provokes a negative feedback the way the circuit is laid out. I have no better explaination.
We have not dealt yet with the initial idea of the vent seeing an amplified compliance. Is our circuit producing this feature now ? The meaning of an "amplified compliance" is that if the vent cross-section area develops a force (like an inertia force), the whole vent cross-section will move more easy than the driver membrane because the vent cross-section area is much smaller than the driver membrane surface.
A mechanical force on the vent cross-section translates into a voltage appearing at the input of E1. This voltage is multiplied by E1 and transferred across the capacitor representing the box compliance. The V1 voltage source being equal to zero by definition, this amplified voltage will equal the voltage present on the capacitor representing the box compliance. This equilibrium condition will be reached thanks to additional current starting to flow in the system, with G1 providing the current amplification hence speed amplification hence ease of move. I have no better explaination.
I would like to know if this modelization is viable.
Of course, neglecting the second-orders effects.
Steph
Page 557
Engineering Reports - "Electroacoustic design with Spice" - By W. M. Leach, Jr.
It contains a very interesting Spice simulation.
This is probably the mother of all bass-reflex speaker design softwares.
Worth reading it !
Here is a link : http://users.ece.gatech.edu/mleach/papers/spice_electro.pdf
More here : Dr. Leach's Refereed Papers.
I tried to transfer this onto LTspiceIV.
Without second-order effects.
Here are some suggestions.
It seems to work.
I wanted to make this simulation compatible with the closed box case.
Therefore, I have kept Cab (the box compliance) inside the loudspeaker coil loop, instead of moving Cab into the vent inductance loop like W. M. Leach, Jr. did.
I wanted to have all LTspiceIV circuit elements having their values equal to their physical values without any scale factor.
The box compliance value on the LTspiceIV schematic is the box compliance seen by the woofer. This compliance comes in series with the driver suspension compliance.
The suspension compliance equals 214µm/N.
The box compliance seen by the woofer equals 170µm/N.
As a consequence if you close the vent, and if you try moving the woofer membrane by 1 millimeter, you will need to apply a force equal to :
0.001 Newton divided by the suspension compliance (= 4.67 Newton)
plus
0.001 Newton divided by the equivalent box compliance (= 5.88 Newton)
total
10.55 Newton
The vent mass value on the LTspiceIV schematic is the actual air mass contained into the vent volume. Physically, this air mass resonates with the box volume according to the Helmholtz law. The Helmholtz law can be described as a spring-mass system with almost no damping. The spring effect comes from the box volume, hence compliance SEEN BY THE VENT CROSS-SECTION AREA. The mass effect comes from the air mass contained into the vent volume.
Most of the time, the vent cross-surface area is much smaller than the driver membrane surface. The box compliance perceived by the vent cross-surface area will therefore be much higher (= easier to move) than the box compliance perceived by the driver membrane. The compliance amplification factor perceived by the vent equals the ratio of the two surfaces : driver membrane surface / vent cross-section area.
Thus, and this is the vicious trick, on the LTspiceIV schematic, we need to represent the fact that the box compliance gets perceived by the vent cross-section (and mass) as an amplified compliance.
Consider now a box compliance equal to zero. This means that the driver gets connected to the vent, without any intermediate box. You then realize that the same amplification will shows regarding the speed. If you press the woofer 1 millimeter, the air in the vent will move 1 millimeter times the amplification factor defined by the ratio of the two surfaces.
Looking to the LTspiceIV schematic, we realize that any current stolen by the inductance representing the vent, is the air speed into the vent.
Therefore if there is 1 milliamp stolen from the Compl_Box capacitor, physically, there must be 1 milliamp times the amplification factor inside the inductance representing the vent.
Now we understand the why and how of the chain made of V1, H1 and G1. This chain replaces a current multiplier. There is no current multiplier (current controlled current source) in LTspiceIV. I needed to build one using an ammeter (V1) followed by a voltage-controlled voltage source (VCVS) followed by a voltage-controlled current source (VCCS). With an amplification factor equal to the ratio of the surfaces.
At this stage we may feel happy, having implemented the vent air speed gain caused by the surface ratio. We now need to respect energy considerations. Having articifially boosted the current in the vent inductance by a certain factor, we need to artificially reduce the stimulation voltage accordingly. This is done by multiplying the voltage developping on the coil, by the same factor, then transferring this multiplied voltage back to the cause. This is the role of E1, a voltage-controlled voltage source. This way, the energy gets balanced. Yes, indeed there is a current amplification in the process, but the back-EMF generated by the inductance gets multiplied by the same facor, and this provokes a negative feedback the way the circuit is laid out. I have no better explaination.
We have not dealt yet with the initial idea of the vent seeing an amplified compliance. Is our circuit producing this feature now ? The meaning of an "amplified compliance" is that if the vent cross-section area develops a force (like an inertia force), the whole vent cross-section will move more easy than the driver membrane because the vent cross-section area is much smaller than the driver membrane surface.
A mechanical force on the vent cross-section translates into a voltage appearing at the input of E1. This voltage is multiplied by E1 and transferred across the capacitor representing the box compliance. The V1 voltage source being equal to zero by definition, this amplified voltage will equal the voltage present on the capacitor representing the box compliance. This equilibrium condition will be reached thanks to additional current starting to flow in the system, with G1 providing the current amplification hence speed amplification hence ease of move. I have no better explaination.
I would like to know if this modelization is viable.
Of course, neglecting the second-orders effects.
Steph
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