Re: Ribbon Microphones

Chris Hornbeck wrote:
On Mon, 28 Aug 2006 14:58:41 -0700, Bob Cain
<arcane@xxxxxxxxxxxxxxxxx> wrote:

<mostly snipped, 'cause ya already read and saved it>

Beautiful; thanks as always.

<blush>

I do have two (closely related) unresolved issues though. The first is
that this ideal model is based on a diaphragm that appears massless
forever. It assumes that the diaphragm can always respond to the
instantaneous pressure differential across itself.

Not massless at all. It just acts as a multiplier in the relationship

v ~= F/f.

More specifically

v = F/(M*f).

for the velocity of the ribbon in response to the force on it. BTW,
these symbols for force, velocity, pressure, etc. all represent the
amplitudes of sinusoidal signals.

So mass just scales the velocity response to the force on the ribbon
by a constant which is why it only affects the sensitivity. I should
have been more explicit about why this is so in my other post.

The assumption is good for most of its passband, but not forever.

It's good so long as it's the mass that is primarily controlling the
response of the ribbon. As you move toward forever, the v just gets
smaller and smaller in proportion to the reciprocal of the frequency.

Where this fails is when the pressure difference between front and
back begins failing as a measure of the pressure gradient at the
ribbon due to phase shift interference. Unfortunately this occurs in
the upper audio band because of the size of the objects used to
measure that front-back approximation to the gradient. This isn't
about the mass though.

As you go down toward never, the compliance of the ribbon becomes
significant and eventually dominates the mass so that these simple
relationships again fail to be good approximations.


Just as we would like for a flat frequency response to pressure. Thus
the ribbon response to pressure is inherently flat over the band in
which it is mass controlled and that certainly includes the higher
frequencies. The effect of higher ribbon mass is just to reduce the
sensitivity of the mic.

The second is the possibility of misunderstanding from the use
of the words "mass controlled". Its plainest meaning is that
we're operating above fundamental resonance, but many other
meanings are often implied.

I just mean that in the approximate equivalent circuit there is only a
mass involved in calculating velocity/pressure relationships and, yes,
that would be well above the resonance caused by the mass and
compliance of the ribbon.

When this came up last summer, some posters had conflated the
term to mean that the diaphragm somehow "lagged behind" instantaneous
pressure differential in the passband.

It does, just as the (sinusoidal) velocity response of a mass lags the
stimulating force. It affects the phase relationship between them in
the same way that the current in an inductor lags the voltage across it.

It occurs to me that the amplitude compensating frequency dependance
of the pressure gradient does not have a lead that compensates the
mass lag. That would make the overall system an allpass with constant
amplitude and frequency dependent lagging phase shift. Don't hold me
to this, however, it's just off the top of my head.

Anywho, a freely suspended diaphragm in moving air has its own
upper limit of response to differential pressure because of its
mass.

There is no knee if that is what you mean. The velocity response to a
constant amplitude force/pressure just keeps getting smaller and
smaller as you go up in frequency as per the above equation.

Otherwise, the models predict some ringing around the
geometrical region, then response (plus 6dB) forever.

Sorry, I don't follow you here.


Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein
.

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