release reactive energy, a frequency is incremented for 1/24 octave (or 1/48 octave) and the process is being repeated form step 1) until the predefined stop frequency is reached. In FFT mode, a simple measurement procedure is as follows:
1. The LIMP generates the Pink PN as a discrete periodic sequence with a period equal to N. We
assume that this sequence drives the generator shown in Fig. 2.1.
2. After one preaveraging cycle, which is necessary to reach the steady state, voltages at both end of
3. The DFT is applied to time series u1 and u2 to get spectral components U1 (f) and U2(f). They are
used in the equation (1) to calculate the impedance Z(f).
Important note: The signal generation in the stepped sine mode gives sinusoidal components with at least 30dB higher level than it is possible in FFT mode. That is why, in FFT mode the measurement results can be greatly affected by the noise that can be generated by the measured loudspeaker.
2.4 Measurement in a noisy environment
The main source of the measurement noise is a loudspeaker that acts as a microphone for the environmental noise and vibrations. Fig. 2.2 shows modified circuit for the loudspeaker impedance measurement, with included the noise generator En.
Figure 2.2 A circuit for the loudspeaker impedance measurement, with the noise generator En If we apply equations for impedance measurement (1) to this circuit, we get the estimated impedance value:

Z estimated R

R Z Rg U2 Z U1 U E g / En
What this equation shows is that estimated impedance differs from the true impedance Z by the term that is dependant on the S/N ratio (Eg/En) and values of resistors R, Rg and the impedance Z. We can conclude:
1. The signal generator must supply a high voltage, to assure high S/N. In practice, we need a
generator with at least 1V of a peak output voltage. This can easily be achieved with stepped sine excitation. 2. When we use FFT method the measurement results are highly affected with noise. The loudspeaker act as a microphone with a highest sensitivity in the region of the membrane resonance. It means the highest level of the noise at low frequencies, so we must generate the signal with highest level at low frequencies, i.e. the pink noise. 3. Values of resistors R and Rg must be small, an optimum being a value close to the magnitude of the measured impedance. Practically, we can use R = 10-27 ohm to get a very good impedance estimation, but then we need a power amplifier to supply large current. If we use the soundcard phone output as a signal generator, then we can use R = 47-100 ohms. If we use the soundcard line output as a signal generator, due to the limited current capability, we must use R>600 ohms. In that case we can't get a good estimation with FFT method, but still we can use stepped sine method.

2.4.1 Lowering measurement noise in stepped sine mode
In stepped sine mode LIMP uses "heterodyned" principle to filter all spectral components that are out of the passband which is centered at the measured frequency. The bandwidth of the filter is equal to 1/T where T is integration time of the Fourier integral. For example, if we use integration time 200ms, then the width of the passband of the "heterodyne" filter is 5Hz.
2.4.2 Lowering measurement noise in FFT mode with periodic noise excitation
The noise can be partly lowered by using the averaging technique in the estimation of U1 and U2. The LIMP averages the auto-spectrum of U1 and the cross-spectrum of U1 and U2, giving the following estimated impedance:

Z esitimated

R U1U1* U 2U1*
Note: brackets <> denotes averaged values and star denotes the conjugate complex value. Two type of the averaging can be applied in the LIMP. In a "time domain synchronous averaging" the LIMP generates multiple periods of one noise sequence (Fig. 2.3). In a "frequency domain asynchronous averaging" the LIMP generates a different noise sequence for every acquired FFT block (Fig. 2.4). The Frequency Domain Asynchronous Averaging can give slightly better results than the synchronous averaging in systems with nonlinear distortion, but it needs longer time for measurements.
Figure 2.3 Signal generation and acquisition during the synchronous time domain averaging process
Figure 2.4 Signal generation and acquisition during the asynchronous frequency domain averaging

3. Hardware Setup

The simplest measurement configuration is shown in Fig. 3.1. The soundcard phone-out (or loudspeaker out) is used as a signal generator output. The soundcard left line-input is used for recording the voltage U and the soundcard right line-input is used for recording the voltage U.
Note: If the soundcard has no phone-out or loudspeaker-out, then we have to use the line-out and a external power amplifier, as shown in Fig. 3.2.

Figure 3.1 Measurement setup for loudspeaker impedance measurements, using the phone output
Figure 3.2 General measurement setup for loudspeaker impedance measurements
To protect the soundcard input form large voltage that is generated at a power amplifier output, it is recommended to use the voltage probe circuit with Zener diodes, as shown on Fig. 1.3. Values of resistors R1 and R2 have to be chosen for arbitrary attenuation (i.e. R1=8200 and R2=910 ohms gives probe with -20.7dB (0.0923) attenuation if the soundcard has usual input impedance - 10k). In a single channel mode this probe is not connected.
Figure 3.3 Voltage probe with the soundcard input channel overload protection

4 Working with LIMP

When you start the LIMP you get the program window shown in Fig. 4.1. There are: menu bar, toolbar and a dialog bar at a top of the window and a status bar on the bottom of the window. The central part of the window will show the magnitude and the phase plot.
Figure 4.1 Main program window

Figure 4.2 Toolbar icons

Figure 4.3 Status bar shows the peak level (ref. full scale) of left and right line inputs

Generator type

Sampling Frequency (Hz)

Size of FFT block

Averaging type

Reset averaging

Figure 4.4 Top and right dialog bars
Normally, we work with graph windows and dialog boxes. We also need to get the copy of the graph or the graph window picture. Copying of the full window picture is simple. User needs to simultaneously press keys Ctrl+P. After that command the window picture will be saved in the System Clipboard, from were the user can paste it in other opened Windows applications (MS Word, MS Paint and Adobe Paint Shop). To obtain the copy of the graph picture, that is shown inside the window, user needs to simultaneously press keys Ctrl+C or activate the menu command 'Edit->Copy', or press appropriate 'Copy' button. In main window toolbar, the 'Copy' button is shown as toolbar icon. This command opens the dialog box 'Copy to Clipboard with Extended Information', shown in Figure 1.16. Here user has to set three copying options:
LIMP User Manual 1) In the Edit box user optionally enters the text that will be appended at the bottom of the graph. 2) Check box 'Add filename and date' enables adding text to the graph that shows file name, date and time. 3) Check box ' Save text' enables saving entered text for the next copy operation. 4) Bitmap size is chosen by selecting one of following combo box items: Current screen size - variable width and height option Smallest (400 pts) - fixed graph width 400 points Small (512 pts) - fixed graph width 512 points Medium (600 pts) - fixed graph width 600 points Large (800 pts) - fixed graph width 800 points Largest (1024 pts) - fixed graph width 1024 points The options with fixed width gives graph copy with the aspect ratio 3:2. Pressing the button 'OK' copies the graph to the system clipboard. Pressing the button 'Cancel' cancels the copy operation.

4.2 Soundcard Setup

Activate the menu Setup->AudioDevices. You will get the 'Soundcard Setup' dialog box shown in Fig. 4.6. In this dialog box you choose which soundcard will be used as an input or output device. Generally, choose the same card as an input and output device.
Figure 4.6 Soundcard setup The 'Audio Device Setup' dialog box has following controls:
Soundcard driver - chooses the type of soundcard driver (WDM windows multimedia driver or one of installed ASIO drivers). Input channels - chooses the soundcard input stereo channels. ASIO driver can have large number of channels. Output Device - chooses the soundcard output stereo channels. Generally, user chooses input and output channels of the same soundcard (mandatory in ASIO driver mode). Control panel button if WDM driver is chosen, it opens sound mixer on Windows 2000/XP or Sound control panel in Vista/Win7. If ASIO driver is chosen, it opens ASIO control panel. Wave format on Windows 2000/XP chooses Windows wave format: 16 bit, 24 bit, 32 bit or Float. Float means IEEE floating point single precision 32-bit format. It is recommended to use 24-bit or 32-bit modes when using a high quality soundcard (many soundcards are declared as 24-bit, but their real bit-resolution is less than 16-bits). For Windows Vista / Windows 7 it is recommended to choose resolution type Float. This control has no effect in the ASIO mode, where a bit resolution has to be setup in the ASIO control panel.
Important notice: Please mute the line and microphone channels at the output mixer of the soundcard; otherwise you might have a positive feedback during measurements. If you use a professional audio soundcard, switch off the direct or zero-latency monitoring of the line inputs.
4.2.1 Windows 2000 / XP WDM driver setup
After selection of the soundcard user has to disable (mute) line-in and microphone inputs in output mixer. Also user has to select which input will be used for recording: Line In or Microphone (Mic). For a standard PC soundcards the procedure is as follows:

5) In Audio device setup dialog click the button Control panel to open the Windows Master Volume dialog box, which is shown on Fig. 4.8. 6) Click on menu Options->Property and select soundcard channel that will be used for output (playback), as shown in Fig. 4.7. 7) Mute Line In and Mic channels in dialog Master Volume (Fig. 4.8) 8) Set Master Volume and Wave Out volume to maximum. 9) Click on menu Option->Property and select soundcard channel that will be used for input and enable Line In and Mic channels in recording mixer. 10) Choose Line In or Mic Input. Normally, Limp uses Line In input on which external microphone amplifier should be connected. 11) Set volume control of Line In to some lower position. Later it will be set more precisely.
Figure 4.7 Dialog for choosing soundcard and input/output channels
Figure 4.8 Typical setup of a soundcard output mixer in Windows XP
Note: Most professional audio soundcards have their own program for adjustment of input and output channel, or have hardware control of input monitoring, and input and output volume controls.
4.2.2 Vista / Windows 7 WDM driver setup
Microsoft has changed their approach in control of sound devices in Vista / Win7. Now operating system (also, sometimes in conjunction with control programs of professional soundcards) is responsible for setting soundcard native sampling rate and bit resolution. Operating system changes native resolution to floating point format for high quality mixing and eventually for the sample rate conversion. For LIMP, this means that it is strongly recommended to use Float resolution and sets the sampling rate to the native format. Access to these values is in Windows sound control panel, which user gets by clicking on the button Control Panel in Audio Device Setup dialog. Fig. 4.9 shows Vista/7 control panel, that has four property pages. As first step, user has to adjust 'Playback page' and later repeat the same procedure for 'Recording page'. Adjustment steps are: 1) Click on channel info to choose a playback channel. It is not recommended to use the measurement channel as a default audio channel. 2) Click on button Properties to opens channel Sound properties dialog. 3) Click on the tab Levels to open the output mixer (as in Fig. 4.10). Then mute Line In and Mic channels, if exist. 4) Click on the tab Advanced' to set the channel resolution and a sample rate (as in Fig. 4.11) 5) Repeat previous procedure 1) to 4) for recoding channel, and choose the same sampling rate as in the playback channel.

Figure 4.9 Vista Sound Control panel
Figure 4.10 Playback channel properties Output levels
Figure 4.11 Setting the native bit resolution and sampling rate in Vista Note: There are a lot of drivers that do not work stable under Windows 7. In that case please use ASIO driver if it is available for your soundcard.

4.2.3 ASIO driver setup

ASIO drivers are decoupled from the operating system control. They have their own control panel to adjust native resolution and memory buffer size. The buffer is used for the transfer sampled data from the driver to the user program. User opens the ASIO control panel by clicking button Control Panel in the Audio Device Setup dialog. Fig. 4.12 shows an example of ASIO control panel.
Figure 4.12 E-MU Tracker Pre ASIO Control panel for setting bit-resolution and buffer size In music applications user usually sets buffer size as small as it is possible for the stable work. That gives the lowest input/output latency (system introduced delay).
LIMP User Manual In Limp, the latency is not problem, as it is encountered in software, but it is not recommended to use buffer with size larger than 2048 samples, or smaller than 256 samples. Some ASIO control panels express the buffer size in samples, while other express the buffer size in time [ms]. In that case we can calculate the size in samples using following expression: buffer_size [samples] = buffer_size[ms] *samplerate[kHz] / number_of_channels. Some ASIO drivers allow setup of buffer size (in samples) that is a power of number 2 (256, 512, 1024, ). In that case Limp adjusts buffer size automatically. Limp always work with two input channels, and two output channels, treating them as a stereo left and right channels. As ASIO support multichannel devices, user has to choose in a dialog box Audio Device Setup which pair of channels will be used (1/2, 3/4, ).

4.3 Generator Setup

Two types of excitation signals are possible in the LIMP:
Sine Pink periodic noise (Pink PN).
Choose the signal type in the top dialog bar or in the 'Generator Setup' dialog box shown in Fig. 4.13. You get it by clicking the menu Setup -> Generator or by clicking the toolbar icon.
Figure 4.13 Signal generator setup
The dialog Generator Setup has following controls: Type - chooses the excitation signal: Sine or Pink PN. Sine freq. (Hz) - enter test frequency of the sine generator. Pink cut-off (Hz) - enters the low-frequency cut-off of the pink noise generator. Output level (dB) - chooses the output level (0-15dB). Test - starts/stops generator with current settings. Input level monitor - the input volume peak meter. Meter bars are shown in following colors: green (for levels bellow -3dB), yellow (for levels between -3dB and 0dB) and red (for input overloaded).

Recommendation:

For most reliable results use sine generator, but don't push loudspeaker into large displacement (the largest displacement is at frequencies below the loudspeaker resonance frequency). For measurements of bass or mid-bass loudspeakers set the Pink cut-off frequency close to the loudspeaker resonance frequency (20-100 Hz). Press the button Test to monitor input/output levels. If peak meter bars are in red color input channels are overloaded, then lower the output volume until bars go to yellow or green color.

4.4 Measurement Setup

For setup of measurement parameters use the 'Measurement setup' dialog box, shown in Fig. 4.14. You get it by clicking the menu Setup->Measurement or by clicking the toolbar icon.
Figure 4.14 Measurement setup
The dialog ' Measurement setup ' has following controls: In section Measurement config: Reference channel - sets the reference channel (U1) to: Left or Right. Reference resistor - enters the value for the referential resistor. In section Frequency range: High cut-off - enters measurement upper frequency margin. Low cut-off - enters measurement lower frequency margin. Sampling rate (Hz) - chooses the sampling rate (from 8000 to 96000Hz). In section Stepped sine mode: Frequency increment - sets to 1/24 or 1/48 octave Min. integration time (ms) - enters minimal integration time (the higher value gives higher noise reduction).
Transient time (ms) - enters transient time to allow the system to get to the steady state (before starting the integration). Intra burst pause (ms) - enters time needed for system to release the energy from reactive components. In section FFT mode (pink noise excitation): FFT size - chooses the length of the FFT block ( 32768 or 65536). Type - chooses: None, Linear or Exponential averaging. Max. Averages - enters the maximum number of averaging for the 'Linear' mode. Asynchronous averaging - check box to use the asynchronous averaging.
4.5 Measurement Procedures
After you have done the audio device setup, the generator setup and the measurement setup you are ready for measurements. a) Procedure in FFT mode Connect loudspeaker in test fixture (Fig. 3.1 or 3.2) and click the menu Record->Start or click the toolbar icon. Measurements will be periodically repeated and results shown as an impedance plot. You will get the graph like one shown in Fig. 4.15. You can stop the measurements by clicking the menu Record->Stop or by clicking the toolbar icon.
You can copy the graph bitmap by clicking the menu Edit->Copy or by clicking the toolbar icon
Figure 4.15 Impedance measurement without averaging a noisy measurement If you set averaging to Linear, measurements will be repeated and averaged until the number of averaging reach the predefined value for Max averages in the 'Measurement setup' dialog box. You can stop the averaging at any time by clicking the menu Record->Stop or by clicking the toolbar icon. You will get the graph like one shown in Fig. 4.16. You can also choose the exponential averaging. It differs from linear averaging in a way that it gives more weight to results from last five measurements.

Figure 4.16 Impedance measurements with averaging
a) Procedure in Stepped sine mode Measurement procedures for stepped sine mode are almost the same as in FFT mode. The only difference is that in FFT mode user will see the impedance plot for full measured frequency range almost instantly, while in stepped sine mode procedure will be repeated for many frequencies. Cursor will show current progress in measurements, and that process will be very slow.
4.6 Graph Setup and Browsing
The menu command Setup->Graph Setup (or by right-clicking mouse in the plot area), opens the 'Graph Setup' dialog box, shown in Fig. 4.17. Use this dialog box to adjust the impedance magnitude range shown and the frequency range shown.
Figure 4.17 Graph setup The 'Graph Setup' dialog box has following controls:
Impedance range (ohm) section: Graph range enters the impedance magnitude range. Graph bottom enters the impedance magnitude for graph bottom margin. Freq. range (Hz) section: High enters the highest frequency shown (in Hz). Low enters the lowest frequency shown (in Hz).
View All enables the view of all DFTspectrum components that are used in impedance estimation. View Phase enables a phase plot. Update updates the graph with a new setup.
Figure 4.18 Dialog boxes for a graph colors setup
Figure 4.19 Standard Windows dialog for color setup Graph colors can be changed in two ways. The first one is to change the background color from "Black" to "White" by clicking the menu command View->B/W color or by clicking the toolbar icon. 23
LIMP User Manual The second way to change graph colors is a "user mode". User sets an arbitrary color for every graph element using the 'Color Setup' dialog box, shown in Fig. 4.18. This dialog can be activated by clicking the menu Edit->Colors. Clicking the left mouse button on colored rectangle opens the standard Windows dialog box 'Color' (Fig. 4.19). Button 'Default' restores default colors. A check box 'Use dotted graph grid' enables drawing of grid with dotted line style. We can browse the graph by moving the cursor. At the bottom of the graph the label 'Cursor:' denotes values of the magnitude and the phase, at the cursor position.

.LIM binary file format is as follows:
char id[4]; unsigned version; unsigned reserved; int numdata; int cursorpos; int fftlen; float fs; float data[3*numdata] int infolength; char string[infolength]; // // // // // // // // // // four characters id {'L', 'I', 'M', '\0' }; version number - started from 0xnumber of data points last position of cursor length of FFT in FFT mode sampling frequency contains frequency, magnitude and phase info string length info string data

5 Loudspeaker parameters

This chapter gives some definitions and measurement procedures for the estimation of loudspeaker parameters.
5.1 Definition of physical and dynamical loudspeaker parameters
An electrodynamic loudspeaker that is mounted in the infinite baffle is usually ([10], [11]) characterized by the following physical parameters: Electromagnetic parameters: RE - voice coil DC resistance () LE - voice coil self-inductance (H) L2 - inductance due to inductive coupling of eddy currents (H) R2 - resistance due to eddy currents () Bl - force factor (Tm) Mechanical parameters: S - effective area of membrane (m2) CMS - membrane mechanical compliance (m/N) MMS - mechanical mass of membrane plus mass of air load on membrane (kg) RMS - mechanical resistance plus membrane radiation resistance (kg/s) (Note: The piston area S is normally obtained from a cone diameter measurement that includes the 1/3 of the surround.) Fig. 5.1 shows wideband and low-frequency equivalent circuits of an electrodynamic loudspeaker that is mounted in a infinite baffle. The circuit for definition of low-frequency input impedance uses following elements:
LCES Bl CMS , RES Bl / RMS , CMES M MS / Bl
Figure 5.1 a) Wideband analogous electrical circuit of an electrodynamic loudspeaker that is mounted in the infinite baffle, and b) circuit for the estimation of the low- frequency input impedance
Using these analogous circuit elements, Thiele and Small [6, 7] introduced dynamical loudspeaker parameters. They are defined in the Table 5.1.
Resonant frequency in free air (Hz)

1 , 2 M MS CMS

S M MS

1 M MS CMS

Mechanical Q-factor

QMS QES

S CMS RMS

Electrical Q-factor

S M MS RE

Total Q-factor

QTS S CMES
RE RES Q Q MS ES RE RES QMS QES
Power available efficiency (%)

0 S 2 Bl c RE M MS 2

Sensitivity (1W/1m) in dB
c L p 1W / 1m 10log 20log pref 112,1 10log0 2
Equivalent acoustical volume (m3)

VAS 0 c 2 S 2CMS

Table 5.1 Thiele-Small dynamical loudspeaker parameters ( 0 = 1.18kg/m3, c = 345m/s, pref = 20Pa) Thiele and Small have shown that by using these parameters it is easy to express the response of closed box as 2nd order high-pass filter and response of bas-reflex box as 4th order high-pass filter. Today, almost every loudspeaker manufacturer gives physical and Thiele-Small parameters in their loudspeaker data sheets. Note on electrical inductance: An industry standard is to measure voice coil inductance at 1 kHz. In the LIMP, an inductive impedance component (as well capacitive one) can be measured at any frequency, as shown in chapter 4.6. The truth is that we cannot specify the exact value of the voice coil inductance LE, because it is a circuit element that depends on frequency. The voice coil inductance can be better described as a primary coil of the "transformer" whose secondary winding is the pole piece. Eddy currents in the pole piece give rise to primary circuit resistance. The simplest model [8] for a primary input impedance is K + jK, where K is some constant. The impedance increases with rather than. This model is not practical as engineers in many numerical simulations use some form of an analogous electrical circuit that closely matches measurement data. The most commonly used circuit for the electrical voice coil impedance is serial connection of resistor RE, inductor LE and parallel connection of resistor R2 and inductor L2, as shown in Fig. 5.1. It has been proven as useful model in many simulations. LIMP estimate value of LE, R2 and L2 as values that give the least sum of squared differences of the model impedance and a measured impedance over all frequencies. The voice coil resistance RE should be measured with a DC ohmmeter.

5.2 Estimation of Thiele-Small parameters
It is easy to estimate Thiele-Small parameters if we have measured data for the loudspeaker impedance. At low frequencies the influence of a voice coil inductance and eddy currents is small and an expression for the loudspeaker input impedance has the following form:

where s = j, Ts = 1/s.

sS 2 QMS 1 sTS / QT s 2Ts RE 2 s sTS / QMS s 2Ts S S s 2 QMS
The impedance has maximum value at the resonance frequency:
Z max Z S RE QES / QT RE RES

because QES>QT.

Figure 5.2 Typical impedance curve of a loudspeaker that is mounted in a free air
At frequencies f1 and f2, (where f1<fS<f2,
f1 f2 = fS2) impedance values are of equal magnitude;

Z j1 Z j2 r1RE , if

12 S 2
If we substitute this expression in the impedance equation, we get

Z j1, 2 r1 RE RE

r0 QMS / S . QMS / S
From this equation we get the mechanical Q-factor:

fs f 2 f1

r0 rr1 1
Now we can define a step-by-step procedure for the measurement of Q factors: 1. Measure a voice coil resistance RE with a dc ohm-meter 2. From impedance curve find fS and Zmax. Define ro=Zmax/RE. 3. Choose some impedance magnitude RE<|Z1|<Zmax and find both frequencies (f1 and f2) where Z = Z1. Define r1=Z1/RE. 4. Calculate QMS (from the above equation), 5. Calculate QES using the equation QES=QMS / (ro-1). 6. Calculate QT using the equation QT=QESQMS / (QES+QMS).
5.3 Estimation of physical loudspeaker parameters
Two methods are used [7] for the estimation of physical loudspeaker parameters (MMS, CMS and RMS); 1. Added mass method, 2. Closed box method. Both methods are implemented in the LIMP.

5.3.1 Added Mass Method

In this method, we first measure the impedance curve and estimate Thiele-Small parameters fS, QMS and QES, for the loudspeaker mounted in a free air. Then we put an additional mass (Madded) on the membrane, measure impedance curve and estimate the shifted resonance frequency fM and electrical Q-factor QEM. From equations for QEM and QES we get:
M added f S QEM 1 f M QES
When we know MMS and fS, it is easy to get the mechanical compliance CMS, resistance RMS and force factor Bl. By using equations that are defined in Table 5.1 we get

1 M MSS

VAS 0 c 2 S 2CMS ,

S M MS RE

S M MS

5.3.2 Closed Box Method

In this method we first measure the impedance curve and estimate Thiele-Small parameters fS, QMS and QES, for the loudspeaker mounted in a free air. Then we mount the loudspeaker in a closed box, of known volume VB, measure impedance curve and estimate Thiele-Small parameters fC, QMC, QEC. From these we find

VAS VB (

f C QEC 1) f S QES
Then, by using equations that are defined in Table 5.1, we get
S M MS RE 1 VAS M , M MS , Bl , RMS S MS 2 QES QMS 0c S CMSS
5.4 Automatic estimation of physical and dynamical loudspeaker parameters
LIMP procedures for the estimation of loudspeaker parameters are as follows. To estimate Q-factors of a loudspeaker we need: 1. measured impedance data, 2. measured voice coil dc resistance (in ohms), 3. estimated membrane diameter in cm (cone diameter measurement that includes 1/3 of the surround). By clicking the menu Analyze->Loudspeaker parameters Added mass method, we get the 'Loudspeaker Parameters - Added Mass Method ' dialog box, shown in Fig. 5.2. In this dialog box, we enter values for Voice coil resistance and Membrane diameter. Press on button Calculate gets the report shown in the left edit box. This report can be pasted to the clipboard by pressing the button Copy.
Figure 5.2 Dialog box for the estimation of loudspeaker Q-factors

5.4.1 Added Mass Method

To estimate all physical and dynamical loudspeaker parameters we must make two impedance measurements of the loudspeaker in a free air. In one of the two measurements, the membrane must be loaded with an additional mass. That is what we need:

1. 2. 3. 4. 5. 6.

measured impedance data, impedance data measured with an additional mass on the membrane (as in Fig. 5.3), one of curves (1 or 2) must be set as an overlay graph, measured additional mass - in grams, measured the voice coil dc resistance - in ohms, diameter of the membrane - in cm (cone diameter that includes 1/3 of the surround),
Figure 5.3 Impedance curves (the one with lower resonance frequency is obtained by adding mass to the membrane)
Then we activate the menu Analyze->Loudspeaker parameters Added mass method to get the 'Loudspeaker Parameters' dialog box, shown in Fig. 5.4.
Figure 5.4 Dialog box for the estimation of loudspeaker parameters
Finally, we enter values for Voice coil resistance, Membrane diameter and Added mass. Press on the button 'Calculate' gets the report shown in the left edit box. This report can be pasted to the clipboard by pressing the button 'Copy'.

5.4.2 Closed Box Method

To estimate all loudspeaker parameters we must have two impedance measurements. In one of measurements the loudspeaker must be mounted in a closed box of known volume. That is what we need: 1. 2. 3. 4. 5. 6. measured impedance data, impedance data measured with loudspeaker mounted in a closed box, one of curves (1 or 2) must be set as an overlay graph (as in Fig. 5.5), estimated value of box volume - in liters, measured the voice coil dc resistance - in ohms, diameter of the membrane - in cm (cone diameter that includes 1/3 of the surround),

Figure 5.5 Impedance curve (the one with higher resonance frequency is obtained by mounting the loudspeaker in a closed box) Then we activate the menu Analyze->Loudspeaker parameters Closed box method to get the 'Loudspeaker parameters Closed Box Method' dialog box, shown in Fig. 5.6.
Figure 5.6 Dialog for the estimation of loudspeaker parameters using Closed Box Method
Finally, we enter values for Voice coil resistance, Membrane diameter and Closed box volume. Press on the button 'Calculate' gets the report shown in the left edit box. This report can be pasted to the clipboard by pressing the button 'Copy'.

6 RLC measurement

The LIMP can be used to measure value of resistors, capacitors and inductors, simply by calculating resistive, inductive or capacitive parts of the measured impedance. For example, Fig. 6.1 shows impedance curves of an inductor with nominal value of 1.5mH.
Figure 6.1 The impedance graph of a 1.5mH inductor
By clicking menu command Analysis->RLC Impedance value at cursor position we get the dialog box with report as shown on Figure 6.2. LIMP reports that measured impedance has resistive part of 0.776 ohms and imaginary part is inductive with value of 1.589mH.
Figure 6.2 Impedance of an air core inductor
The same way LIMP measures the capacitance.
6.1 Importance of calibration
When measuring impedance and capacitance it is very important to calibrate the system before the measurement, and it is best to make the calibration with the impedance connected (DUT). Why?
Even if there is a very small difference between channel sensitivities (i.e. 0.1dB) the LIMP can give very erroneous result, because inductor impedance has phase close to 90 degree, and capacitor impedance has phase close to minus 90 degree. In that case if there is a difference in sensitivity of measured generator voltage V1 and impedance voltage V2 (if sensitivity of probe V2 is larger than sensitivity of probe V1) estimated impedance gives phase values that are larger than 90 degree and graph shows warped jump in the phase for 180 degree. Figure 6.3 shows the case of measuring capacitor without the calibration. In half the range the phase is close to 90 degree. It is very erroneous results as it suggest that we deal with an inductance. Figure 6.4 shows capacitor impedance after the calibration. We see correct values for phase in the whole frequency range.
Figure 6.3 Wrongly estimated impedance of plastic capacitor 4.7uF/250V (measured without the calibration)