# 17.5: Procedure

1. Figure 17.4.1 shows a typical model of a dynamic moving voice coil loudspeaker mounted on an infinite baffle1. Rvc and Lvc represent the resistance and inductance of the of the voice coil. Lces represents the driver compliance (i.e., springiness of suspension and air), Cmes represents the driver’s mass, and Res represents the frictional losses of the suspension. At DC, the impedance will equal Rvc. At high frequencies Lvc will dominate the response. The parallel resonant portion will create an impedance peak in the bass. This is normally referred to as the free air resonance of the driver, or $$f_s$$.

2. Using the woofer, measure the DC resistance using the DMM and record the value in Table 17.6.1.

3. In order to measure both the magnitude and phase of the impedance across frequency, it is desirable to drive the loudspeaker with a fixed current source. By measuring the voltage across the loudspeaker with an oscilloscope, both amplitude and time delay can be measured, and thus both magnitude and phase of impedance can be calculated. A current source may be approximated by placing a large resistor in series with the function generator. If the resistance value is many times greater than the loudspeaker impedance, the loudspeaker may be ignored to a first approximation. Therefore, virtually all of the generator voltage drops across the series resistor. For this exercise, a 1 k$$\Omega$$ value will suffice. For all measurements, simply place a 1 k$$\Omega$$ resistor in series with the generator and the loudspeaker under test. Place oscilloscope probes at both ends of the resistor (i.e., input signal and loudspeaker signal). Make sure that the Bandwidth Limit of the oscilloscope is engaged for both channels. This will reduce the signal noise and make for more accurate readings.

4. Hook up the woofer between the resistor and ground. Make sure that the woofer is magnet-side down, with the cone facing up, and unobstructed.

5. First, find the resonant frequency. To do this, set the output of the generator to approximately 100 Hz, sine wave, and 10 volts peak. Adjust the frequency in small amounts, up and down, until the maximum voltage is found. This is the experimental free air resonant frequency. Record it in Table 17.6.1. Note the amplitude. Sweep the frequency above and below the resonant frequency until the experimental $$f_1$$ and $$f_2$$ are found. These will occur at a voltage amplitude of approximately 0.707 times the resonant voltage (i.e., the half-power points). Record these frequencies in Table 17.6.2. Copy the three frequencies to the first three entries of Table 17.6.3.

6. For the frequencies in Table 17.6.3 determine the amplitude and time delay at the loudspeaker and compute the phase shift. Be sure to include whether the loudspeaker signal is leading (+) or lagging (-) the source.

7. Swap the woofer with the general purpose loudspeaker and repeat steps 2 through 6 using Tables 17.6.4 through 17.6.6. Plot the magnitude and phase of each device on semi-log paper. Also, try to estimate values for the schematic model of Figure 17.4.1.

## References

1Adapted from R.H.Small, Direct-Radiator Loudspeaker System Analysis, Journal of the Audio Engineering Society, June 1972