Secrets Q & A

A New Way to Plot Speaker Impedance: the Smith Chart

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An Example: Impedance of Gallo Reference 3.1s Speakers

Here, I show the impedance results measured with a Smith and Larson Audio Woofer Tester 2 impedance analyzer of my Gallo Reference 3.1 speakers. First, I'll show the results plotted in the normal way, with one plot showing the magnitude of the impedance as a function of frequency, and another plot showing the phase angle as a function of frequency.

Gallo reference

We see that the phase deviates in the capacitive direction quite a lot at high frequencies, and that the real part of the impedance gets very high at about 5 kHz. From rules of thumb, you can say that this speaker should be not too difficult to drive, but things get a little funky towards the high end. Since tweeters consume very little power, this shouldn't be too big of a deal in terms of taxing the amplifier. Still, this plot is a little difficult to interpret at one glance. The actual load in terms of resistance and reactance is a combination of both plots at the same time. A high or low resistance magnitude is OK as long as it does not also come with a high phase angle. A high phase angle means more resistance or capacitance if the magnitude of the impedance is high at the same time.

What if we plot the same data on the Smith chart? Now we see both the real and imaginary part at the same time. The plot is set to have 8 ohms in the center. A perfect 8 ohm resistive load would be a speck at the center of the plot. Deviation from a perfect 8 ohm load moves the line away from the center of the plot. This plot is relatively easy to interpret. The closer the squiggly line is to the center of the plot, the easier the speaker is to drive. Failing that, it's better to move along the center-line than deviate a lot above or below.

Smith chart

To get back some of the frequency information I've put a green marker (+) on the plot, with a frequency of 10.2 kHz corresponding to the marker (10,200 Hz). We can see here that the speaker does well throughout most of its range, but becomes more difficult to drive at one frequency extreme. To tell what frequency extreme requires either the other plotting method, or using a marker as shown. This plot has an adjustable "reference impedance." Here Z0, the reference impedance, is set to 8 ohms. The center-line of the plot shows the real part of the impedance in fractions of Z0. The center is 1 times Z0, or 8 ohms. 0.5 to the left is 0.5 times Z0, or 4 ohms, 2.0 to the right is 2.0 times Z0 or 16 ohms. For simplicity, I have left off the units for the capacitance and inductance.

Really, the units are not important for using this plot to quickly analyze a speaker load. The main thing is how close to the center of the plot the line is. I would call an "easy load" any impedance that remains inside the green circle on the plot (within a factor of two of 8 ohms). The Gallos do well for most of the range, but the tweeter rapidly runs away in impedance.  This wacky tweeter impedance could be a problem for some electronics, and is probably a result of the "crossoverless" design of the Gallos.

Luckily, a tweeter that presents a difficult load is not that big of a deal. If this same impedance issue were present at the other frequency extreme (low frequencies), there would be a big problem. Engineering an amp capable of driving a woofer with an impedance that crazy would be quite a feat.

Conclusions

While the Smith chart certainly is not the typical way to plot speaker impedance in audio engineering, I believe it does have a place. It makes speaker impedance far easier to interpret at a glance than the normal method using two separate plots, without having to be a speaker guru.