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Comments on the Elecraft reflector suggest that headphones present a variable impedance over the normal amateur radio operating range of say, 300 to 3000 Hz.

I've measured several headphones and a couple of communications loudspeakers as well. The data demonstrates little impedance variation for common headphones I tested. My limited loudspeaker data shows much greater resonance effects.

Table of Contents
Test_Setup
Headphones_and_Speakers_Tested_
Western_Electric_U1
Four_Modern_Headphones_
On-Head_/_Off-Head_
Telex_Pro_Comm_460_Headphones
Loudspeakers

Written 04 September 20008
Revised 05 Sept 2008 to add on head / off head impedance plots

I originally hoped I could use my HP87510A vector network analyzer to measure headphone impedance. Although the 87510A has a minimum guaranteed frequency of 100 KHz, it can be used with quite reasonable accuracy down to 3 KHz, with some care. However, research shows that the dominant variation in headphone impedance is from diaphragm resonance occurring in the range around 1 KHz and below.

The advantage of using a VNA is that the real and imaginary component of impedance can be measured. After looking at data over the range 3 - 20 KHz, however, it turned out that the headphones I measured were close to purely resistive over this frequency range. Measuring the headphone inductance at 100 Hz and 1 KHz also showed rather low values.

Accordingly, I decided to use a measurement method that determines the magnitude, but not the phase angle, of the headphone impedance. The test setup, illustrated below, is essentially an AC ohmmeter, with a computer controlled frequency source. The computer program sets the test frequency, reads the current through the headphones under test and the voltage across the headphones. This process is repeated across the target frequency range.

|Z| = |V|/|I|, where the | | symbol indicates magnitude.

The data is taken over a frequency range of 20 - 6000 Hz, in 25 Hz steps. 6 KHz as an upper frequency range is well over  the typical 3 or 3.5 KHz maximum communications response. As a check on the accuracy of the setup, I also ran a sweep on a 750 ohm 1% resistor over the same frequency range. The computed resistance was within ±0.1% of the DC value of the resistor, as determined with the HP34410A digital multimeter in 4-wire ohms mode.
 

I took impedance data for the following headphones:

• Heil Pro Set (older model, no phasing switch)
• Heil ?? Similar to the Pro Set but with smaller ear cups resting on your ears, not surrouding your ears like the Pro Set. I've owned both Heil headsets for 10 or 12 years or more and can't locate the model numbers at the moment.
• Sony MDR-V600 "hi-fi" headphones with large earcups.
• Sony MDR-62, "hi-fi" headphones with small ear pads that rest on top of your ears.
• Telex Pro Comm 460, 600 ohm mono headphones that are 25 years old or so.

As a comparison headphone point:

• Western Electric U1 handset receiver from a 500 series desk telephone, date of manufacture 4-9-63,

The loudspeakers are:

• Unknown manufacturer 2.75 inch diameter loudspeaker without enclosure, operated facing upward resting on the test bench.
• General Electric MASTR PRO two-way radio loudspeaker in the MASTR PRO cast metal enclosure. The enclosure has louvers on the rear panel.
• Drake MS7 speaker in enclosure—the matching speaker for Drake's 7-line (TR-7/R7). The speaker enclosure has an open back.

All headphones except the Telex Pro Comm unit are stereo. My tests operate the left and right reproducers in parallel. Hence, the impedance data should be multiplied by two if individual  reproducer results are required.

I removed the U1 from the 500 series telephone instrument but placed the plastic cap over  the U1 reproducer as a partial attempt to duplicate its normal environment. The  telephone network is intentionally restricted to 300 - 3000 Hz, and over this range,  the U1's impedance varies from 60 ohms to 230 ohms. Impedance peaks are quite pronounced around 1500 Hz and 3500 Hz.

The four "modern" headphones I looked at show very little impedance change with frequency. (My definition of "modern" may differ from yours; the last headphones I purchased are at least 10 or 12 years old now.)

Two headphones show a modest impedance peak around 150 Hz, which is below the normal amateur radio frequency range. As I understand it, this peak is likely due to diaphragm resonance.

Over the frequency range 300 Hz - 3000 Hz, all four of these headphones can be considered for all practical purposes as resistive loads of the value indicated on the plot.

Why don't we see more variation, such as the Western Electric U1 displays? The answer is that the headphone designers have done their best to provide constant impedance over a wide frequency range. This  requires a combination of low inductance coils in the reproducer and, to intentionally  reduce the electrical Q, high series resistance, compared with the inductive reactance of the reproducer coil. (Why do designers want flat impedance? When fed from a voltage source, as is normally the case, the audio power delivered to the headphones is inversely proportional to the impedance. To maintain constant audio power to the headphones, therefore, requires constant impedance. The Western Electric engineers had a different goal—to shape the U1's sound reproduction to match human hearing peaks and reduce network bandwidth. Hence, the U1's design for non-constant impedance. There's another point, of course; to transform the electrical audio signal into sound pressure in a way that does not substantially vary with frequency. That's well beyond our purpose, however, so I'll leave that discussion for another day.)

Geoff, GM4ESD, asked whether headphones demonstrate impedance shifts when measured in open air versus the normal on-head position.

To assess the difference, I measured my Sony MDR-V600 and Heil Pro Set headphones under two conditions; open air with the cups facing outward and in the normal mode, clamped on an "artificial head." I don't have a real artificial head and I didn't care to sit with for a series of measurements with the 'phones clamped on my head, so I used two thick catalogs (one from Mouser and one from DigiKey) and adjusted the headphones so the ear muffs made good contact with the catalogs. I don't know if this represents a  good or bad model of a human head.

The two plots below show rather modest changes in impedance between open air and my "simulated head," on the order of 1% or less.

The plots below appear to show greater change with frequency than the consolidated plot above. This is a consequence of the vertical scale used in the plots. The total change with frequency is around 10% from minimum impedance to maximum impedance for the Sony MDR-V600 and around 15% for the Heil Pro Set. The expanded and offset vertical axis in the two plots below emphasize this rather small variation.

If, by the way, you are interested in how data should be visually presented, I'm aware of no better books than the ones by Edward Tufte, http://www.edwardtufte.com/tufte/. I own three of his books and each is a gem, worth reading and re-reading every couple of years.

The MDR-V600 headphones show a main resonance around 200 Hz, and significant secondary resonances around 1500,  3500 and 5000 Hz. These could well represent multiple drivers within the headphones or different dimensional resonances of the headphones. The speed of sound in dry air is 1129 feet/sec. The three secondary resonance peaks, therefore, correspond to wavelengths of 9.0, 3.9 and 2.7 inches. If we look for a half-wave resonance mode, i.e., reflection from a fixed point 0.25 wavelengths distant, the relevant distances are 2.25, 1.0 and 0.63 inches. These dimensions are quite similar to the headphones' height, width and thickness. Whether this is a coincidence or related to the impedance peaks, I don't know, but it is curious.

Also remember that the two plots below are for a single transducer, i.e., stereo mode, one channel. The multiple headphone plot above parallels the left and right channels to better model how these headphones are used with most communications receivers. Elecraft's K3, however, has separate left and right amplifiers, so the single transducer impedance is more directly useful. That is, if you wish to simulate a Heil Pro Set when looking at the K3's audio output, a 220 ohm resistor from tip to sleeve and a second 220 ohm resistor from  ring to sleeve would be appropriate. At no frequency over the range 20 - 6000 Hz will the resistor depart from the measured headphone impedance by as much as 10% and for almost the entire frequency range it will be within 5%.

Although the peak looks quite pronounced in this plot due to the Y-axis offset, in fact, the peak represents only about a 30% increase in impedance.

Because the Telex Pro Comm 460, 600 ohm headphones have such a different impedance, I'll use a separate plot for it. I also looked at these headphones up to 12 KHz and the upward slope seen above 1 KHz is not due to resonance but seems to be related to the transducer's inductance as it continues in a similar fashion up to the highest data point I collected at 12 KHz. I don't have an explanation for the kinks and inflection points, as these occur well above the frequency of normal mechanical resonance. It may be related to electrical resonance of the transducer inductance.

Unlike the headphones, all three loudspeakers exhibit pronounced mechanical resonance impedance peaks. The open air and MASTR PRO speakers show smaller impedance peaks at harmonics of the main mechanical resonance. (All  three speaker seem to be 3.2 ohm nominal devices.) The resonant frequency and Q, as I understand it, depends upon both the speaker construction and enclosure.

Loudspeakers of the type studied are designed to convert electrical energy to sound pressure with high efficiency. Headphone designers are much less concerned with efficiency, and can therefore trade efficiency against flat impedance response.

The MASTR PRO speaker has some unusual characteristics. First, note that the resonance peak is the smallest of the three speakers studied. More interesting, however, is the drop in impedance with increasing frequency. This is indeed odd, as the normal characteristic is for the impedance to slightly dip after resonance and then increase with increasing frequency, due to the voice coil's inductance. Some speaker designs employ special construction techniques to flatten  the high frequency rise in impedance, but the MASTR PRO speaker drops down to 1.5 ohms or so by 6 KHz. I first thought the MASTR PRO data was contaminated, so I ran it a second time and found the second data points laid exactly on top of the original data set, so the impedance drop with increasing frequency is real.