Planar magnetic DC resistance vs. impedance?

[Few]

Does anyone have a ballpark sense, or perhaps the pertinent formula, for predicting how different the operating impedance of a planar magnetic driver will be from the DC resistance of the driver? I assume it will depend on the acoustic impedance seen by the diaphragm but I'm hoping someone can provide either

1. A formula that applies to rectangular diaphragms, or
2. Some empirical data I can use to get started. For example, what are the DC resistance and midband impedance of the midrange section of a Magneplanar, or something similar?

Thanks.
Few

 

[Davey]

If you make the assumption that DC resistance is equal to impedance you'll be correct.

The drivers in Magnepan's measure as almost purely resistive loads throughout the audio band. The woofers start to turn inductive, but only at fairly high frequencies.

Dave.

 

[Few]

Thanks Dave. I know drivers like those in Magneplanars tend to be nearly purely resistive, but is the impedance at say 500 Hz or 1000 Hz the same as the DC resistance? I would think that the energy radiated as sound would have to be reflected in an impedance measurement.
Few

 

[Davey]

It's pretty flat throughout the band.

Just for info, here's an impedance plot (attached) of the woofer transducers from my MMG's. (Note the scale on the left.)
Notice that the driver starts to become inductive above approximately 3khz. (The impedance becomes fairly high at higher-than-audio frequencies.) A simple Zobel of about 2uF/5.0 ohms will effectively level this impedance to very high frequencies.

Also, for the sharp-eyed, you can see the effects of the L/R tuning dot arrangement. Notice the yellow trace has four peaks created by the three dots on one panel, and the green trace has two peaks created by one dot on the other panel. You can see that, as designed, none of the peaks line up with each other.

The tweeter (not shown) is basically ruler flat at 3.6 ohms across the whole audio range.

Cheers,

Dave.

 

[gootee]

Does anyone have a ballpark sense, or perhaps the pertinent formula, for predicting how different the operating impedance of a planar magnetic driver will be from the DC resistance of the driver? I assume it will depend on the acoustic impedance seen by the diaphragm but I'm hoping someone can provide either

1. A formula that applies to rectangular diaphragms, or
2. Some empirical data I can use to get started. For example, what are the DC resistance and midband impedance of the midrange section of a Magneplanar, or something similar?

Thanks.
Few

I gave you the link to the resistance formula in your other thread, at:

http://www.diyaudio.com/forums/plan...nar-magnetic-central-tweeter.html#post2851562

Quoting from the link (from there) to my calculations:

--------------------------

Resistance of an aluminum conductor is

R = pL/A,

where R is in Ohms, p is 2.6 x 10^(-8), i.e. .000000026 Ohm-meters, L is length in meters, and A is cross-sectional area in square meters. From that, the Ohms per meter would be .026 / (area in sq mm).

So, with aluminum foil length in meters but foil thickness and width both in mm:

(1) width = (.026 x length) / (Ohms x thickness)

and

(2) thickness = (.026 x length) / (Ohms x width)

So, with those equations, we could calculate the needed width or thickness of the foil, if we specified the thickness or width and knew the length and resistance that we were replacing. (Also, remember that the length is in meters but the thickness and width are both in mm.)

Also:

(3) Ohms = (.026 x length) / (thickness x width)

(4) length = Ohms x (thickness x width) / .026


--------------------------

I measured my Magnepan MG-12/QR mid/bass panel's resistance with an LCR meter and it was 3.9 Ohms, at 100 Hz, 1000 Hz, and 10 kHz (my meter's limit). They are made with about 38 meters of 23 AWG aluminum wire, which has a cross-sectional area of about 0.2588 square mm.

(Note, also, that to replace the MG-12's mid/bass wires with foil, which was what was being discussed at that link, one solution that used relatively narrow foil would require dividing the panel into two separate runs of foil of 8 Ohms each which would then be connected in parallel to get back to the original 4 Ohms. That would have made the total mass of the foil less than 20% of the mass of the original wires, in the case that was discussed.)

 

[Few]

Thanks all. Gootee, can you tell me whether the DC resistance of the panel you measured is 3.9 ohm--the same value you measured at audio frequencies? That's what I'm trying to get at.

I have no problem calculating the DC resistance of a conductor but I want to know whether that's the load the amplifier will see when driving the speaker at audio frequencies. The resonance hump in the impedance plot of a conventional woofer in a sealed box demonstrates that the mechanical and acoustical loads experienced by the voicecoil are reflected in the measured impedance. I'm trying to determine whether there is any broadband shift in the impedance of a planar magnetic driver relative to the DC resistance that is calculated or measured. Davey's plot shows the effect of the resonances. I'm trying to find out if there's any effect away from the resonances (such as the DC resistance being 3 ohms while the impedance between 200 Hz and 2 kHz is 4 ohms).

 

[Davey]

Few,

The impedance seen at low frequencies continues down to DC. Even though my impedance plot only goes down to 20Hz, it's still a straight line at 4.8 ohms all the way to DC.

Maybe you could outline why this is of interest for you. What's your ultimate question?

Cheers,

Dave.

 

[Few]

Thanks Dave. The reason I'm asking the question is that I'm designing the conductor pattern for a planar magnetic driver. I want the load the amplifier sees to be low enough to make good use of the amp's current capability but not so low that the amp gets unhappy--let's say 4 ohms, for example.

It occurred to me that the DC resistance I calculate based on the resistivity of aluminum and the conductor dimensions might not be the impedance the amp sees. The woofer example I gave in a previous post was intended to point out that more goes into a speaker's impedance than DC resistance and inductance. The radiation impedance the cone experiences plays a roll also.

For a planar magnetic driver it seems (based on evidence such as you provided) that knowing the DC resistance really is enough to predict the load the amplifier sees. Armed with that knowledge I can choose an appropriate conductor resistance target. I can design for a DC resistance of 4 ohms rather than aiming for 3 ohms to end up at 4 ohms.

I get the feeling this question is not making sense to anyone so perhaps that indicates it's just not a smart question.

 

[gootee]

It's a very good question. But the answer, as you are correctly deducing, is to shoot for the DC resistance to be what you want your amplifier to see. Planar magnetic speakers are almost a purely-resistive load, at audio frequencies. And the resistance is the same at DC.