Acoustics

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6.8. Electrical input impedance

If we ignore the radiation resistance, which is a negligibly small part of the input impedance, and add the radiation mass to the mechanical mass so that M _MS = M _MD + 2M _M1, we can write the electrical input impedance Z _E from inspection of Fig. 6.2:

\begin{matrix} Z_{E} = Z_{E S} + Z_{E M} = R_{E} + j ω L_{E} + {(j ω \frac{M_{M S}}{B^{2} l^{2}} + \frac{1}{B^{2} l^{2} G_{M S}} + \frac{1}{j ω B^{2} l^{2} C_{M S}})}^{- 1} \\ = R_{E} + j ω L_{E} + \frac{B^{2} l^{2}}{R_{M S}} (\frac{\frac{j}{Q_{M S}} \cdot \frac{f}{f_{S}}}{1 - \frac{f^{2}}{f_{S}^{2}} + \frac{j}{Q_{M S}} \cdot \frac{f}{f_{S}}}) \end{matrix}

$\begin{matrix} Z_{E} = Z_{E S} + Z_{E M} = R_{E} + j ω L_{E} + {(j ω \frac{M_{M S}}{B^{2} l^{2}} + \frac{1}{B^{2} l^{2} G_{M S}} + \frac{1}{j ω B^{2} l^{2} C_{M S}})}^{- 1} \\ = R_{E} + j ω L_{E} + \frac{B^{2} l^{2}}{R_{M S}} (\frac{\frac{j}{Q_{M S}} \cdot \frac{f}{f_{S}}}{1 - \frac{f^{2}}{f_{S}^{2}} + \frac{j}{Q_{M S}} \cdot \frac{f}{f_{S}}}) \end{matrix}$

(6.45)

The electrical impedance curve of a typical 100 mm loudspeaker in an infinite baffle is plotted in Fig. 6.8. The peak at 125 Hz coincides with the suspension resonance frequency f _S. If we ignore the effect of the coil inductance L _E, the input impedance at f _S is approximately Z _E = R _E + R _ES, where R _ES = B ² l ²/R _MS (=R _E Q _MS/Q _ES). Therefore, a high peak indicates a large Bl factor or small mechanical damping resistance or both. At high frequencies, the impedance rises due to the increasing contribution of the coil inductance L _E. At very low frequencies, the impedance approaches the DC resistance R _E asymptotically, which in this case is 7 Ω.

Figure 6.8 Electrical impedance Z _E of an electrodynamic loudspeaker in an infinite baffle with the same parameters as those in Fig. 6.7.

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6.8. Electrical input impedance

Table of Contents for
Acoustics