Investigating Electromagnetic and Acoustic Properties of Loudspeakers Using Phase

Sensitive Equipment

Katie ButlerDePaul University

Advisor: Steve Errede

Why investigate loudspeakers?

•Most important link in the audio chain•Last piece of equipment audio signal passes through•Many variables in loudspeakers; permanent magnet, size and weight, material of cone, size and type of enclosure, etc.

TheToneChamber.com

How speakers work• Voice coil (electromagnet) is positioned in constant

magnetic field from permanent magnet• Current across voice coil constantly changes, changing

the magnetic field polarity and strength causing the voice coil and diaphragm to move

Cross-section of typical loudspeaker

Loudspeaker analogous circuit

Using electrical components to model the mechanical components of the loudspeaker, further work must be done to accurately calculate these using data collected

Low distortion power amplifier

• No audio amplifiers readily available in lab

• Need to amplify signal from function generator to power loudspeaker

• Building amp using widely available LM3875 chip amp

• Constant voltage source, typical for powering speakers Component going into amplifier

Amplifier pictures

Data acquisition technique for measuring electromagnetic properties of loudspeaker

Based on UIUC Physics 498POM PC-Based Pickup Impedance Measuring System

Complex pressure p and particle velocity u measurements

Acoustic measurements will be taken at the same time as electromagnetic measurements

Impedance and Power

Electrical Impedance(Ohms, e)

Electrical Power (W)

Radiation Impedance(Pa-s/m ac)

Acoustic Intensity (W/m2)

( )( )

( )em

V fZ f

I f

( , )

( , )( , )ac

p r fZ r f

u r f

*( ) ( ) ( )emP f V f I f *( , ) ( , ) ( , )acI r f p r f u r f

Phase sensitive equipment• SR830 Dual-Channel DSP lock-in amplifiers

The Speaker

• Italian Jensen C12N• Ceramic magnet• 12”, 8• 50 watt rated power• Designed to emulate

American made Jensens from the 1960s

Apparatus

• Took measurements 3 ways: in free air, on baffle board, in speaker cabinet

• Microphones are on movable arms controlled by computer program

• Current and voltage cables attached underneath

• Foam sound absorbers used under speaker to prevent reflections

Setup with speaker on baffle board

Speaker Cabinet •Designed and built by Steve Errede, based on Marshall 1965B 410 straight speaker cabinet

•Sound absorptive material placed in cabinet behind speaker

Frequency Sweep Data

Complex acoustic impedance; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data

Complex sound intensity; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data

Complex electrical impedance; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data

Complex electrical power; speaker in free air (blue), on baffle board (green), in cabinet (red)

Voltage versus particle velocity

Magnitude of voltage (left) and magnitude of particle velocity (right), the electromagnetic resonance (120.5 Hz)

appears as a resonance in particle velocity at 0.40 centimeters above the speaker

Acoustic pressure of speaker in free air versus mounted on baffle board

Acoustic pressure across surface at 0.40 centimeters above speaker in free air (left) and speaker mounted on 24” square baffle

board (right), driven at 120 Hz

Particle velocity of speaker in free air versus mounted on baffle board

Particle velocity across surface at 0.40 centimeters above speaker in free air (left) and speaker mounted on 24”

square baffle board (right), driven at 120 Hz

Sound intensity across surface of speaker driven at various frequencies

Magnitude of sound intensity

across surface of speaker in enclosure

Driven at 130.5 Hz (left), 3485.0 Hz

(center), and 10,000 Hz (right)

30 Hz – 20,000 Hz

Acoustic intensity (top) and EM power (bottom) versus frequency for speaker in enclosure at a height of 0.40 centimeters.

Sound Intensity Level(s)

RHS plot: Sound Intensity Level SIL= 10log10(I/Io) (blue), Sound Pressure Level SPL=20log10(p/po) (green), Sound Particle

Velocity Level SUL = 20log10(u/uo) (red) versus frequency for speaker in enclosure at a height of 0.40 centimeters.

LHS plot: The differences dSLip = SPL-SIL (blue), dSLiu = SIL-SIU (green) and dSLpu = SPL-SUL (red) versus frequency for speaker in

enclosure at a height of 0.40 centimeters.

Acknowledgments

Special thanks to Professor Steve Errede for his commitment to our projects. Also thank you to Gregoire Tronel for sharing the lab space and

equipment.

Thank you to the REU program for this research opportunity, which is supported by the National

Science Foundation Grant PHY-0647885.