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Revision History
03 September 2009 Original


Introduction and Loudspeaker Model

After recently acquiring an HP 4192A LF impedance meter, I thought it would be interesting to see how the impedance of typical loudspeakers used with amateur radio equipment vary with frequency.

Loudspeakers have an interesting mix of electrical and mechanical parameters, as reflected in the simple model below.

In the inexpensive loudspeakers commonly used with communications receivers, are constructed with a solenoid shape voice coil attached to a paper cone diaphragm. The voice coil is suspended in a magnetic field from a permanent magnet and the magnetic field produced by the voice coil due to input signal current causes the diaphragm to move corresponding, thus producing sound.

The wire used to wind the voice coil has resistance and the voice coil solenoid has inductance. These parameters are shown in the model below as Rvc and Lvc. Neither Rvc nor Lvc are necessarily constant with frequency, as skin effect will cause Rvc to change and proximity effect will cause Lvc to change with frequency.

The three motional parameters are more complex.

First, let's return to the voice coil parameters Rvc and Lvc. When the voice coil moves within the magnetic field, there is, by Faraday's and Lenz's laws, a counter-electromotive force or voltage opposite to the applied voltage. This counterpoising EMF alters the measured electrical parameters of the voice coil.

If the voice coil were clamped in place, unmovable, then Rvc and Lvc would have stable values at any given frequency. In the real world, however, the voice coil moves with applied signal and the degree to which the voice coil moves depends upon the mechanical construction of the loudspeaker and, to some degree, the enclosure in which the loudspeaker is installed.

These mechanical parameters are due to the compliance of the suspension—its "springiness" and the cone mass. In addition, there are always losses, due to motional friction in cone material and suspension and, to some degree, acoustical radiation of the sound energy.

These mechanical effects are modeled by Rloss (mechanical losses), Csc (compliance) and Lm (cone mass) in the circuit.

The electrical equivalent circuit should show a generally rising impedance with increasing frequency due to the increasing impedance of Lvc. In addition, the motional parameters will resonate at some frequency,  thereby causing an impedance peak.

Further, the motional parameters may exhibit harmonic or overtone resonance, where, for example, part of the speaker suspension resonates in a quarter wave mode and then at a three-quarter wave mode, etc.


Elecraft K2 Low Power Lid and Loudspeaker

Let's look at the loudspeaker Elecraft provides with its K2 transceiver. In this case, the QRP or low power version. My K2 has the optional 100 watt amplifier in the lid, so I have the leftover QRP lid and speaker for experimentation.

Elecraft  K2 lid with speaker. This is from the QRP (low power) version of the K2.
Business side of the K2 lid.

The figure below shows the input impedance if the loudspeaker installed on the lid, but not on the radio. I set the lid on my test bench, pointing upwards. This arrangement provides open space on three of the four sides and therefore may not model the speaker's behavior when installed in a K2.

The plot below shows the input impedance over the range 100 Hz - 10 KHz. There's a clear parallel resonance due to the speaker's motional parameters at approximately 400 Hz. There's also an area of ripple between 2 and 5 KHz which may be due to higher order mechanical resonances.

Another way of looking at impedance data is a Nyquist plot. The horizontal axis is resistance and the vertical axis is reactance. Positive reactance is inductive, negative is capacitive and zero crossings are points of resonance. Numbers on the plot identify the frequency. You can view a larger version of the plot by clicking here or on the small image.
Nyquist plot of K2 speaker in lid. Click on the image for a larger version.
To see the degree to which mounting the speaker on the lid influences the impedance, I removed the speaker and suspended it in air with a short length of string. The plot below shows the in-lid and suspected variation. Click here or on the small image for a larger version.
K2 speaker suspended in air and installed on lid. Click on the image for a larger version.
The Nyquist plot shows a small shift in resonance frequency, but a large shift in resistance at resonance. Since the motional parameters models loss as parallel resistance, the higher resistance at resonance when suspended indicates less loss. This may be a combination of less radiated audio energy and less mechanical loss due to removal of coupling to the aluminum lid. Click here or on the image for a larger version of the plot.
Nyquist plot of K2 speaker installed in lid and in free space. Click on the image for a larger view.
NEC Speaker

I acquired a pair of small NEC loudspeakers at a hamfest a few years ago. These are small (the scale is 6 inches long) but have a good communications sound. At this size, there isn't much low frequency response, but that's generally not useful in listening to a communications receiver. The enclosure is not open at the rear.


NEC small loudspeaker

The Nyquist plot shows the NEC to have a smoother response with fewer wiggles and small loops compared with the K2 speaker.  For a larger version, click here or on the small image.
Nyquist plot of NEC speaker. Click on the small image for a larger version.
Drake MS7 Speaker

I also looked at my old Drake MS7 loudspeaker. (MS stands for "matching speaker" I believe, and MS7 is the matching speaker for Drake's "7" line.). It's a 4 ohm speaker in an open back enclosure.

Drake MS7 loudspeaker. Drake used paint for some 7-line runs that changed from textured black to a soft, tacky dingy gray over time. Unfortunately, my MS7 and R7 receiver suffer from this paint problem.

The MS7 has a rather different appearance from either of the two measured speakers. The higher frequency line (from 2 KHz to 10 KHz) is well outside the low frequency plot  A secondary resonance point at 500 Hz or so (about twice the fundamental resonance frequency of approximately 250 Hz) can also be seen.

For a larger version of the Nyquist plot click here.

Drake MS7 Nyquist plot. Click on the image for a larger version.