Calculate the Thiele-Small Parameters of a Loudspeaker

Calculate the Thiele-Small parameters of a Loudspeaker

Aim of the Experiment To Find the Fundamental small signal mechanical parameters

We need to find the values of RE , LE , Cms , Mms , Rms and Bl • Mms - Mass of the diaphragm/coil, including acoustic load, in kilograms. Mass of the diaphragm/coil alone is known as Mmd • Cms - Compliance of the driver's suspension, in metres per newton (the reciprocal of its 'stiffness').

• Rms - The mechanical resistance of a driver's suspension (ie, 'lossiness') in N·s/m • Le - Voice coil inductance measured in millihenries (mH) (Frequency dependent, usually measured at 1 kHz).

• Re - DC resistance of the voice coil, measured in ohms.

• Bl - The product of magnet field strength in the voice coil gap and the length of wire in the magnetic field, in tesla-metres (T·m).

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Equipment Required • • • • •

PC A Data Acquisition System (DAQ) Multimeter Power Amplifier Transducer

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Experimental Setup(If monitoring ports present on amplifier) • The sound output of the PC is connected to the input of the Power Amplifier.

• The output of the power amplifier is connected to the Transducer.

• The DAQ input is connected to the Voltage & Current monitoring ports of the power amplifier.

• The DAQ is connected to the PC through an USB cable ACOUSTIC LAB | IIT KANPUR

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Setup

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Experimental Setup(If monitoring ports not present on amplifier) • The sound output of the PC is connected to the input of the Power Amplifier.

• The output of the power amplifier is connected to the Transducer through a known precise shunt resistance.

• The DAQ input is connected to the Voltage output across the driver and also to the Voltage output across the shunt resistance.

• The DAQ is connected to the PC through an USB cable • Current can be found by dividing the Voltage across shunt by the resistance value using Vshunt=I*Rshunt ACOUSTIC LAB | IIT KANPUR

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Setup

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Loudspeaker Circuit Mobility Analogy:

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Loudspeaker Circuit Mobility Analogy:

Equivalent Electrical Circuit:

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To find RE For DC current, equivalent circuit would be:

• Measure the resistance directly with a multimeter.

• It will give the value of RE ACOUSTIC LAB | IIT KANPUR

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To Find LE At high frequency, the equivalent electrical circuit would be:

• Z= RE + jωLE + (Bl)2/(jωMm) • For high frequencies Z ≈ RE + jωLE │Z│ = *RE2 + (jωLE)2]1/2 • RE is known, So, by measuring impedance at high frequencies, LE can be calculated ACOUSTIC LAB | IIT KANPUR

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Example Data • At Vrms=.2V

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To Find Rms Equivalent electrical circuit at resonance frequency:

At resonant frequency, │Z│=│Z│max • • •

Z= RE + jωLE + Rms(Bl)2 │Z│=* (RE + Rms(Bl)2)2 + (ωLE)2 ]1/2 Rms(Bl)2 = * │Z│2max - (ωLE)2 ]1/2 - RE

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To Find Mms and Cms •

At resonance frequency:

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From equivalent electrical circuit, resonance occurs at maximum impedance

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Play the white noise sound file present on the PC

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White noise signal is amplified by the power amplifier and then sent to the speakers

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Voltage and Current flowing in the transducer can be recorded in LabView through the DAQ(Data Acquisition System)

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If monitoring ports are not available in the amplifier divide the voltage across the shunt by the shunt value to get the current.

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Perform FFT(Fast Fourier Transform) on the data stored and then calculate Z=(V/I) for different frequencies.

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To Find Mms and Cms • Plot Z vs Frequency •

Frequency corresponding to maximum impedance(Z) is the resonance frequency(ω).

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Repeat the same experiment by adding known extra mass (m)

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So, (1) (2) Using (1) and (2) , the values of Mms and Cms can be calculated ACOUSTIC LAB | IIT KANPUR

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Example Data Impedance(Z) vs Frequency(logf) At Vrms=.2V

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Example Data Impedance(Z) vs Frequency(logf) At Vrms=.2V with added mass(m)=10.004 gm

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