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| university:courses:alm1k:circuits1:alm-cir-11 [06 Oct 2018 16:26] – [Activity 11: Measuring a Loudspeaker Impedance Profile] Doug Mercer | university:courses:alm1k:circuits1:alm-cir-11 [05 Apr 2023 18:44] (current) – [Procedure to use the ALICE Impedance Analyzer to measure speaker impedance:] Doug Mercer |
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| ======Activity: Measuring a Loudspeaker Impedance Profile====== | ======Activity: Measuring a Loudspeaker Impedance Profile, - ADALM1000====== |
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| =====Objective:===== | =====Objective:===== |
| =====Notes:===== | =====Notes:===== |
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| As in all the ALM labs we use the following terminology when referring to the connections to the M1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the M1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage / measure current -V is added as in CA-V or when configured to force current / measure voltage -I is added as in CA-I. When a channel is configured in the high impedance mode to only measure voltage -H is added as CA-H. | As in all the ALM labs we use the following terminology when referring to the connections to the M1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the M1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage / measure current –V is added as in CA-V or when configured to force current /measure voltage –I is added as in CA-I. When a channel is configured in the high impedance mode to only measure voltage –H is added as CA-H. |
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| Scope traces are similarly referred to by channel and voltage / current. Such as CA-V , CB-V for the voltage waveforms and CA-I , CB-I for the current waveforms. | Scope traces are similarly referred to by channel and voltage / current. Such as CA-V, CB-V for the voltage waveforms and CA-I , CB-I for the current waveforms. |
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| =====Background:===== | =====Background:===== |
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| Knowing the resonate frequency and the minimum and maximum impedances are important when designing cross over filter networks for multiple driver speakers and the physical enclosure the speakers are mounted in. | Knowing the resonate frequency and the minimum and maximum impedances are important when designing cross over filter networks for multiple driver speakers and the physical enclosure the speakers are mounted in. |
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| | Dynamic loudspeakers are abysmally inefficient electro-mechanical conversion devices, as [[wp>Loudspeaker|Wikipedia]] substantiates: “Loudspeaker efficiency is defined as the sound power output divided by the electrical power input. Most loudspeakers are inefficient transducers; only about 1% of the electrical energy sent by an amplifier to a typical home loudspeaker is converted to acoustic energy.” Yes, 1% is an abysmal efficiency as we try to “be more green”, but so far it is the best we have that sounds good (and each dynamic transducer only sounds good over a limited frequency range). |
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| ====Loudspeaker Impedance Model==== | ====Loudspeaker Impedance Model==== |
| • F<sub>S</sub> is the resonant frequency of a loudspeaker. The impedance of a loudspeaker is a maximum at F<sub>S</sub>. The resonant frequency is the point at which the total mass of the moving parts of the loudspeaker become balanced with the force of the speaker suspension when in motion. The resonant frequency information is important to prevent an enclosure from ringing. In general, the mass of the moving parts and the stiffness of the speaker suspension are the key elements that affect the resonant frequency. A vented enclosure (bass reflex) is tuned to F<sub>S</sub> so that the two work in unison. As a rule, a speaker with a lower F<sub>S</sub> is better for low-frequency reproduction than a speaker with a higher F<sub>S</sub>. | • F<sub>S</sub> is the resonant frequency of a loudspeaker. The impedance of a loudspeaker is a maximum at F<sub>S</sub>. The resonant frequency is the point at which the total mass of the moving parts of the loudspeaker become balanced with the force of the speaker suspension when in motion. The resonant frequency information is important to prevent an enclosure from ringing. In general, the mass of the moving parts and the stiffness of the speaker suspension are the key elements that affect the resonant frequency. A vented enclosure (bass reflex) is tuned to F<sub>S</sub> so that the two work in unison. As a rule, a speaker with a lower F<sub>S</sub> is better for low-frequency reproduction than a speaker with a higher F<sub>S</sub>. |
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| • R represents the mechanical resistance of a driver's suspension losses. | • R represents the mechanical resistance of a driver's suspension losses. Part of the “mechanical resistance” in the system is the resistance of the cone to moving through the air, which happens to be the mechanical process that produces the pressure variations that we perceive as ‘sound’. |
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| ====Materials:==== | ====Materials:==== |
| ADALM1000 hardware module\\ | ADALM1000 hardware module\\ |
| Solder-less Breadboard\\ | Solder-less Breadboard\\ |
| 1 - 100 Ω Resistor (or any similar value)\\ | 2 – 100 Ω Resistors (or any similar value)\\ |
| 1 - Loudspeaker, it is best if the speaker is one with a cone diameter larger than 4 inches such that is has a relatively low resonant frequency. | 1 – Loudspeaker from ADALP2000 Kit (it is even better if the speaker is one with a cone diameter larger than 4 inches such that is has a relatively low resonant frequency) |
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| | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-fig2.png?300 |}} |
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| | <WRAP centeralign>Figure 2, Small Loudspeaker from ADALP2000 Parts Kit</WRAP> |
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| ====Directions:==== | ====Directions:==== |
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| First build the circuit shown in the top half of figure 2, preferably using your solder-less breadboard. The loudspeaker can be in an enclosure or not. This configuration allows us to measure the voltage across the speaker V<sub>L</sub> using channel B. | First build the circuit shown in the figure 3, preferably using your solder-less breadboard. The loudspeaker can be in an enclosure or not. This configuration allows us to measure the voltage across the speaker V<sub>L</sub> using channel B voltage trace and the load current I<sub>L</sub> as the channel A current trace. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-fig2.png?500 |}} | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-fig3.png?500 |}} |
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| <WRAP centeralign>Figure 2 Speaker measurement setups for both V<sub>L</sub> and I<sub>L</sub></WRAP> | <WRAP centeralign>Figure 3, Speaker measurement setup for V<sub>L</sub> and I<sub>L</sub></WRAP> |
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| ====Procedure to use ALICE-SA spectrum analyzer:==== | Start the ALICE Desktop software. |
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| Start the ALICE-SA spectrum analyzer software. | In the main Scope screen, the ALICE software calculates and can display the RMS values of the voltage and current waveform traces. Under the CA Meas drop down menu, in the voltage section select RMS, and in the current section select RMS. Under the CB Meas drop down menu, in the voltage section select RMS. |
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| Under the Mode drop down menu select Peak hold mode. Under the FFT window menu select Flat top window. Click the +Samples button until 16384 samples is selected. Under the Curves menu select CA-dBV, CB-dBV and Phase B-A. | |
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| Under the Options drop down menu click on Cut-DC to select it. | We can calculate the speaker impedance Z at a single frequency by dividing the RMS voltage across the speaker (channel B RMS voltage) by the RMS current through the speaker, (channel A RMS current). To display this calculation, we can use the channel B User measurement display. The two variables used are SV2 for the channel B RMS Voltage and SI1 for the channel A RMS current. Click on User under the CB Meas drop down menu. Enter Z for the label. Enter (SV2/SI1)*1000 as the formula. We need to multiply by 1000 to get ohms because the current is in mA. |
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| Set Channel A Min value to 1.0 Volts and the Max to 4.0 V. Set AWG A Mode to SVMI and Shape to Sine. Set AWG channel B Mode to Hi-Z. Be sure the Sync AWG check box is selected. | Try setting channel A to a few different frequencies and see how the voltage across the speaker and the calculated Z changes. |
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| Use the Start Frequency button to set the frequency sweep to start at 10 Hz and use the Stop Frequency button to set the sweep to stop at 500 Hz. Under the Sweep Gen drop down menu select CHA as the channel to sweep. Also use the Sweep Steps button to enter the number of frequency steps, use 300 as the number. | {{ :university:courses:alm1k:circuits1:loudspeaker_imp_bb.png?300 |}} |
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| Hit the green Run button. After the sweep stops under the Options menu press the Store trace button to save the current screen traces. Under the Curves menu select RA-dBV, RB-dBV and RPhase B-A to display the stored traces. | <WRAP centeralign>Figure 4, Breadboard Connections</WRAP> |
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| Now Export the data, as magnitude not in dB to make the math easier, to a comma separated values file ( File menu - Save Data ) and load it into a spreadsheet program such as Excel. All the frequency data from 0 to 50 KHz is saved to the file so you will want to remove ( delete ) all the data above 500 Hz before making any calculations. You will use the 10 Hz to 500 Hz Channel B data from this file as the V<sub>L</sub> values. | ====Procedure to use the ALICE Bode Plotter:==== |
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| Now change the connections on your breadboard to look like the configuration in the bottom half of figure 2. This configuration now allows us to measure the voltage across the 100 Ω resistor with channel B. You will use these measurements to calculate I<sub>L</sub>. | Select the Bode Plotting tool. Under the Curves menu select CA-dBV, CB-dBV and Phase B-A. |
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| After double checking your changes, hit the green Run button again. After the sweep stops you should see the frequency response plot that looks something like figure 3. The source voltage ( a flat line ) will be the light and dark green lines which should be right on top of each other. Voltage across the speaker ( dark orange ) and the current through the speaker represented as the voltage across the 100 Ω resistor ( light orange ). The Phase plots show the relative phase of the voltage and current to the source voltage. Note the points where the phase is zero. The data on the screen is plotted in dB so the vertical scale is not in volts. Your speaker will probably look much different than this example. | Under the Options drop down menu click on Cut-DC to select it if it not already. Change the FFT Zero stuffing factor to 3. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-screen1.png?650 |}} | Set Channel A Min value to 1.0 Volts and the Max to 4.0 V. Set AWG A Mode to SVMI and Shape to Sine. Set AWG channel B Mode to Hi-Z. Be sure the Sync AWG check box is selected. |
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| <WRAP centeralign>Figure 3 Example sweep for both configurations</WRAP> | Use the Start Frequency entry to set the frequency sweep to start at 50 Hz and use the Stop Frequency entry to set the sweep to stop at 1000 Hz. Select CHA as the source channel to sweep. Also use the Sweep Steps entry to enter the number of frequency steps, use 150 as the number. Select single sweep. |
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| Again Export the data, as magnitude to a comma separated values file ( File menu - Save Data ). Load this new 10 Hz to 500 Hz data to the same spreadsheet that contains the 10 Hz to 500 Hz data from the first sweep. | Now Export the data, as magnitude not in dB to make the math easier, to a comma separated values file ( File menu – Save Data ) and load it into a spreadsheet program such as Excel. You will use the 50 Hz to 1000 Hz Channel B data from this file as the V<sub>L</sub> values. |
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| | Note the frequency points where the phase is at its positive maximum, zero and negative minimum. The data on the screen is plotted in dB so the vertical scale is not in volts. Your speaker will probably look different than this example. |
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| | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-screen1.png?600 |}} |
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| | <WRAP centeralign>Figure 5 Example frequency sweep</WRAP> |
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| By saving the data as magnitude the signal generator amplitude (in volts rms) is saved to the file. You can calculate the magnitude of the speaker impedance Z is by dividing the voltage across the speaker V<sub>L</sub> by the current I<sub>L</sub>. I<sub>L</sub> is of course the voltage across the resistor divided by the resistance. | By saving the data as magnitude the signal generator amplitude (in volts rms) is saved to the file. You can calculate the magnitude of the speaker impedance Z is by dividing the voltage across the speaker V<sub>L</sub> by the current I<sub>L</sub>. I<sub>L</sub> is of course the voltage across the resistor divided by the resistance. |
| <m>Z = V_L/I_L</m> | <m>Z = V_L/I_L</m> |
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| <m>V_L = CB_mag</m> from sweep 1 | <m>V_L = CBmag</m> |
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| <m>I_L = CB_mag /100</m> from sweep 2 | <m>I_L = (CAmag - CBmag)/50</m> |
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| You can now plot the calculated impedance Z vs Frequency. An example plot is shown in figure 4. Your speaker will probably look much different than this. | Subtracting the channel B voltage magnitude values from the channel A voltage magnitude values and dividing by the 50 Ω resistor allows you to calculate the current magnitude I<sub>L</sub>. The impedance Z will be the channel B voltage magnitude divided by the current magnitude I<sub>L.</sub> |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-fig4.png?600 |}} | You can now plot the calculated impedance Z vs Frequency. An example plot is shown in figure 6. Your speaker will probably look different than this. |
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| <WRAP centeralign>Figure 4 Calculated example impedance plot</WRAP> | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-fig5.png?600 |}} |
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| The speaker impedance is very small in the linear region but is much higher at the resonance frequency F<sub>S</sub>. | <WRAP centeralign>Figure 6, Example Plot of Calculated Impedance</WRAP> |
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| | The speaker impedance is small, approximately equal to the DC resistance in the linear region but is much higher at the resonance frequency F<sub>S</sub>. |
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| ====Questions:==== | ====Questions:==== |
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| Based on your measured data extract the L C and R for the speaker electrical model shown in figure 1 for the speaker you used. You can measure Rdc with a DC ohmmeter if you have one available. Ignore L<sub>INPUT</sub> as it will be small compared to L. Enter these values into a circuit simulation schematic of the model and generate a frequency response sweep from 10 Hz to 500 Hz and compare your model to the data you measured in the lab. | Based on your measured data extract the L C and R for the speaker electrical model shown in figure 1 for the speaker you used. You can measure Rdc with the DC ohmmeter tool. Ignore L<sub>INPUT</sub> as it will be small compared to L. Enter these values into a circuit simulation schematic of the model and generate a frequency response sweep from 50 Hz to 1000 Hz and compare your model to the data you measured in the lab. |
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| ====Procedure to use the ALICE Impedance Analyzer to measure speaker impedance:==== | ====Procedure to use the ALICE Impedance Analyzer to measure speaker impedance:==== |
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| Change the connections to the speaker back as shown in figure 5. Channel B again measures V<sub>L</sub> the voltage across the speaker. The impedance analyzer software uses the difference between the channel A voltage and channel B voltage as well as the relative phase between the channels to calculate the impedance based the value of R<sub>1</sub>. | As shown in figure 7, Channel B again measures V<sub>L</sub> the voltage across the speaker. The impedance analyzer software uses the difference between the channel A voltage and channel B voltage as well as the relative phase between the channels to calculate the impedance based the value of the combined R<sub>1</sub>, R<sub>2</sub>. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-fig5.png?650 |}} | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-fig6.png?500 |}} |
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| <WRAP centeralign>Figure 5, Speaker impedance measurement setup</WRAP> | <WRAP centeralign>Figure 7, Speaker impedance measurement setup</WRAP> |
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| Run the ALICE-VVM software tool. | Open the ALICE Impedance Analyzer software tool. |
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| Set Ext Res = 100, set Freq to a value well below the resonate frequency of your speaker. In this first example measurement 43 Hz was used. Set the Ohms/div to 10. As can be seen from the data the series resistance of the speaker is around 11 Ω and the reactance is inductive. | Set Ext Res = 50, set the channel A Freq to a value well below the resonate frequency of your speaker. In this first example measurement 100 Hz was used. Set the Ohms/div to 10. As can be seen from the data, the phase angle should be positive. The series resistance of the speaker is around 7 Ω and the reactance is inductive. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-screen2.png?650 |}} | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-screen2.png?600 |}} |
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| <WRAP centeralign>Figure 6, Measurement at frequency below resonance</WRAP> | <WRAP centeralign>Figure 8, Impedance Measurement at frequency below resonance</WRAP> |
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| Now set the frequency to the resonate value from the frequency sweeps. You may want to fine adjust the value to find the exact point where the reactance is zero as shown in figure 7. | Now set the frequency to the resonate value you obtained from the frequency sweep. You may want to fine adjust the value to find the exact point where the reactance is zero as shown in figure 9. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-screen3.png?650 |}} | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-screen3.png?600 |}} |
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| <WRAP centeralign>Figure 7. Measurement at resonate frequency</WRAP> | <WRAP centeralign>Figure 9. Impedance Measurement at resonate frequency</WRAP> |
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| This result should agree with the results from the frequency sweeps. Now set the frequency to a point above the resonate frequency where the phase is near its negative peak as shown in figure 8. | This result should agree with the results from the frequency sweeps. The phase angle should be small and the series resistance is now larger at about 15 Ω. |
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| {{ :university:courses:alm1k:circuits1:alm-cir-lab11-screen4.png?650 |}} | Now set the frequency to a point above the resonate frequency where the phase is near its negative peak as shown in figure 10, 500 Hz was used here. |
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| <WRAP centeralign>Figure 8, Measurement at frequency above resonance</WRAP> | {{ :university:courses:alm1k:circuits1:alm-cir-laba11-screen4.png?600 |}} |
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| As can be now seen from the data the series resistance of the speaker is around 16 Ω and the reactance is capacitive. | <WRAP centeralign>Figure 10, Impedance Measurement at frequency above resonance</WRAP> |
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| | As can be now seen from the data, the phase angle should be negative. The series resistance of the speaker is still around 7 Ω but the reactance is capacitive. |
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| Explain your results based on the parallel LC loudspeaker impedance model in figure 1. | Explain your results based on the parallel LC loudspeaker impedance model in figure 1. |
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| **For Further Reading:** | **Resources:** |
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| [[http://www.analog.com/static/imported-files/application_notes/236037846AN_843.pdf|Measuring a Loudspeaker Impedance Profile Using the AD5933]]\\ | * Fritzing files: [[downgit>education_tools/tree/master/m1k/fritzing/loudspeaker_imp_bb |loudspeaker_imp_bb]] |
| http://en.wikipedia.org/wiki/Electrical_characteristics_of_dynamic_loudspeakers | * LTSpice files: [[downgit>education_tools/tree/master/m1k/ltspice/loudspeaker_imp_ltspice | loudspeaker_imp_ltspice]] |
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| [[university:tools:m1k:alice:desk-top-users-guide|ALICE Desk-top User's Guide]] | **For Further Reading:** |
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| **Return to ALM Lab Activity [[university:courses:alm1k:alm_circuits_lab_outline|Table of Contents]]** | [[adi>static/imported-files/application_notes/236037846AN_843.pdf|Measuring a Loudspeaker Impedance Profile Using the AD5933]]\\ |
| | [[wp>Electrical_characteristics_of_dynamic_loudspeakers|Electrical characteristics of dynamic loudspeakers]]\\ |
| | [[university:tools:m1k:alice:desk-top-users-guide|ALICE 1.3 DeskTop Software]] |
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| | **Return to ALM Lab Activity [[university:courses:alm1k:alm_circuits_lab_outline|Table of Contents]]** |
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