Amplifier Output Impedance (Damping Factor) and Speakers

[xnor]

I don't understand the issue. Aren't aiding/opposing voltage sources electronics 101 stuff? Opposing if the two voltage sources in series have both their positive terminals connected to each other. Aiding if the terminals are connected positive to negative... like stacking a bunch of AA batteries.

So if you measure a positive voltage across the amp terminals you should also measure a (smaller) positive voltage across the speaker terminals - that's the counter EMF.

 

[Suffolkhifinut]

Please conduct this test yourself and speak later. I'm not sure why it is so hard to understand that braking current has to flow in opposite direction to current causing motion (that's what Lenz says). In order for this to happen voltage generated by the membrane motion has to be the same as voltage applied that causes motion in the same direction. You have to think, instead of quoting laws that you clearly don't understand. I had big hopes, that experiment might finally convince you, but I see it is hopeless. I'm out.

Think I did say the induced EMF (-e) is opposite in direction to the applied EMF. Your assertion that the induced EMF has the same value as the applied voltage is wrong -e = L(di/dt). The Induced EMF increases with load inductance and how fast the current tries to decrease, not the same as the applied EMF. Some home experiment isn’t really valid and how did you come to your conclusion?

 

[Suffolkhifinut]

I don't understand the issue. Aren't aiding/opposing voltage sources electronics 101 stuff? Opposing if the two voltage sources in series have both their positive terminals connected to each other. Aiding if the terminals are connected positive to negative... like stacking a bunch of AA batteries.

So if you measure a positive voltage across the amp terminals you should also measure a (smaller) positive voltage across the speaker terminals - that's the counter EMF.

No what you measure across the speaker terminals:
Speaker terminal voltage = Amp terminal voltage - speaker cable voltage drop.

 

[xnor]

Of course, with the speakers connected in normal operation.
What I meant is that if you looked only at the inductance, the part that produces the counter EMF.

If the amp switched from 0V to +1V instantaneously then you would measure a negative voltage spike in series or a positive voltage spike if you had terminals for the inductance just like the speaker terminals. Is that where the confusion comes from or did I just add to the confusion?

 

[Kijanki]

Think I did say the induced EMF (-e) is opposite in direction to the applied EMF. Your assertion that the induced EMF has the same value as the applied voltage is wrong -e = L(di/dt). The Induced EMF increases with load inductance and how fast the current tries to decrease, not the same as the applied EMF. Some home experiment isn’t really valid and how did you come to your conclusion?

In order to produce membrane's braking force induced current has to flow in the opposite direction to the amps current that causes membrane motion in the same direction. Agree?
Now, in order for this to happen polarity of voltage induced on the speaker has to be the same as polarity of voltage applied to speaker that causes same motion. It is because when polarity from the amp is positive (positive voltage to + terminal) current flows from + of the amp to + of the speaker, then thru the speaker to - terminal and back to - of the Amp.
When membrane moves on its own in the same direction voltage that appears on the speaker terminal is positive. Current flows from + of the speaker thru the amp and back to negative terminal. Direction of this current is opposite to previous direction, causing motion of the membrane in the opposite direction, thus braking motion of the membrane.

 

[Ingenieur]

I don't understand the issue. Aren't aiding/opposing voltage sources electronics 101 stuff? Opposing if the two voltage sources in series have both their positive terminals connected to each other. Aiding if the terminals are connected positive to negative... like stacking a bunch of AA batteries.

So if you measure a positive voltage across the amp terminals you should also measure a (smaller) positive voltage across the speaker terminals - that's the

Of course, with the speakers connected in normal operation.
What I meant is that if you looked only at the inductance, the part that produces the counter EMF.

If the amp switched from 0V to +1V instantaneously then you would measure a negative voltage spike in series or a positive voltage spike if you had terminals for the inductance just like the speaker terminals. Is that where the confusion comes from or did I just add to the confusion?

They must be equal in magnitude and opposite in phase.
The loop must sum to 0.

The speaker is absorbing and releasing reactive power, mostly L, or at least what is not offset by the crossover C.
You want the amp to absorb this.
Not oscillate in the wire and distort the signal you want to control the speaker.

An analogy for why a woofer Z increases beyond it's rated homicide value.

A motor when starting has low Z, no load,
A 480/3 50 Amp motor will draw 400 A when starting, Z = 480/400 ~ 1.2 Ohm, only the Rbof the winding. Once running 480/50 ~ 9.6 Ohm. The windings did not change, A back EMF is resisting the motion.


A speaker is a linear motor.
No load ~ speaker in free space.
Put a woofer in an enclosure, now it is pumping air, doing work. Apparent Z increases.

 

[KSTR]

I've found it always useful to look at a behavioral physical model of speaker rather than at its direct electrical network equivalent.

The Force -- Velocity Speaker model:

• The speaker driver's motion is steered (but not controlled) by the force the voice coils exerts on the cone, and the force is proportional to electrical current. This is the actuator. There are other forces at work, too (spring force).
• The drivers voice coil always produces an (open load) voltage proportional to cone velocity, no matter what caused the movement. Some call this Back-EMF, I prefer to call it microphonic velocity voltage as the more general and physical term. This is the sensor.

The Voice Coil, as seen from the driver terminals, is the interface for this "black box". Let's see what happens when we short the terminals (which is what our ideal amp does, apply a voltage -- including zero -- with zero output impedance).

Consider the voice coil as a sensor produces +1V of velocity voltage at the moment. This voltage is applied across the transfer impedance of the driver, Re+Le and forces a current to flow in Re and Le and the same current (though negative) must flow through the VC as a motor, -0.25A in this case.

The applied force opposes the velocity, reducing it. The relationship of velocity signal vs force injection is complex (introducing phase angles vs frequency etc) but for the given purpose we may neglect this here and use it as a black box which we know at least is passive/dissipative.

By this, as long as any movement is present the short produces a corrective signal to reduce the movement. The better the short, the better driver opposes its own "parasitic" movement (degenerative local feedback). But we cannot get any better than Re (and Le to some part) allows, unless we start trickery with negative amplifier output resistance and such...

That's all what this Damping and Back-EMF stuff is about, in the end.

 

[Suffolkhifinut]

Of course, with the speakers connected in normal operation.
What I meant is that if you looked only at the inductance, the part that produces the counter EMF.

If the amp switched from 0V to +1V instantaneously then you would measure a negative voltage spike in series or a positive voltage spike if you had terminals for the inductance just like the speaker terminals. Is that where the confusion comes from or did I just add to the confusion?

The problem arises when an inductive circuit current is reduced. When current is increasing the induced EMF will oppose the rise, under normal circuit operating conditions this isn’t a problem. Trying to feed an induced EMF back into an electrical supply is when the problems start.
In electrical supply systems great efforts have to be made to minimise the damage it can cause. Circuit breakers using ‘air blast‘ to lengthen and therefore weaken the ‘Arc’, ‘SF6 and vacuum‘ systems being used to prevent arcing. Not to mention the effect inductive loads have on Power Factor ergo power measured in Volt/Ampere vs Watts.

 

[Suffolkhifinut]

I've found it always useful to look at a behavioral physical model of speaker rather than at its direct electrical network equivalent.

The Force -- Velocity Speaker model:

• The speaker driver's motion is steered (but not controlled) by the force the voice coils exerts on the cone, and the force is proportional to electrical current. This is the actuator. There are other forces at work, too (spring force).
• The drivers voice coil always produces an (open load) voltage proportional to cone velocity, no matter what caused the movement. Some call this Back-EMF, I prefer to call it microphonic velocity voltage as the more general and physical term. This is the sensor.

The Voice Coil, as seen from the driver terminals, is the interface for this "black box". Let's see what happens when we short the terminals (which is what our ideal amp does, apply a voltage -- including zero -- with zero output impedance).
View attachment 179920
Consider the voice coil as a sensor produces +1V of velocity voltage at the moment. This voltage is applied across the transfer impedance of the driver, Re+Le and forces a current to flow in Re and Le and the same current (though negative) must flow through the VC as a motor, -0.25A in this case.

The applied force opposes the velocity, reducing it. The relationship of velocity signal vs force injection is complex (introducing phase angles vs frequency etc) but for the given purpose we may neglect this here and use it as a black box which we know at least is passive/dissipative.

By this, as long as any movement is present the short produces a corrective signal to reduce the movement. The better the short, the better driver opposes its own "parasitic" movement (degenerative local feedback). But we cannot get any better than Re (and Le to some part) allows, unless we start trickery with negative amplifier output resistance and such...

That's all what this Damping and Back-EMF stuff is about, in the end.

While the idea has some merit the equation Re + Le is incorrect. Re is resisting the flow of current and instead of L it should be inductive reactance Xl and the formula isn‘t Re + Xle.
Z (impedance) = (R x R) + (Xl x Xl).
Sorry for the lack of scientific functions on my iPad.

 

[Suffolkhifinut]

In order to produce membrane's braking force induced current has to flow in the opposite direction to the amps current that causes membrane motion in the same direction. Agree?
Now, in order for this to happen polarity of voltage induced on the speaker has to be the same as polarity of voltage applied to speaker that causes same motion. It is because when polarity from the amp is positive (positive voltage to + terminal) current flows from + of the amp to + of the speaker, then thru the speaker to - terminal and back to - of the Amp.
When membrane moves on its own in the same direction voltage that appears on the speaker terminal is positive. Current flows from + of the speaker thru the amp and back to negative terminal. Direction of this current is opposite to previous direction, causing motion of the membrane in the opposite direction, thus braking motion of the membrane.

No just the opposite! The voltage induced it the speaker must always oppose the applied voltage. Otherwise you would get out electrically more than you put in and in any machine, even a speaker efficiency can never reach 100% never mind exceed it.

 

[pogo]

But we cannot get any better than Re

But according to Ben Duncan, Re is not constant!
Each turn of the voice coil couples individually and proportionately, so the resistance is distributed.

 

[KSTR]

While the idea has some merit the equation Re + Le is incorrect.

Agreed. I was trying to keep notation and math simple, sorry.
For sinusoids, yes, complex-valued Z(f) = Re + j*2*pi*f*Le.
In reality, we don't have a true inductance here, its partly shorted (by eddy currents), it is position- and current-dependant, etc. And even Re is temperature-dependant, so much for that.
Le is just meant as composite container for the reactive parts of the impedance which doesn't have much influence at the low frequencies we're looking at, wrt damping.

 

[KSTR]

But according to Ben Duncan, Re is not constant!
Each turn of the voice coil couples individually and proportionately, so the resistance is distributed.

Re is the ohmic part. But yes, it is distributed and it is not truly constant as the used metals (copper, aluminum) have a temperature-dependant resistance.

 

[Suffolkhifinut]

But according to Ben Duncan, Re is not constant!
Each turn of the voice coil couples individually and proportionately, so the resistance is distributed.

Resistance is always constant. Inductive reactance increases with frequency and cannot exist in a steady current DC state as
f = 0 Hz. Capacitive reactance falls as frequency rises, it’s the reason satellite signals are picked up using an LNB or as they are called in the US a Low Noise Down Convertor.
If you look at widely used K band satellite signals they transmit at around 10 to 12 GHz. The coaxial cable connected to your satellite receiver would virtually short circuit the signal as the cable’s Capacitive Reactance would be extremely low.

 

[Suffolkhifinut]

Re is the ohmic part. But yes, it is distributed and it is not truly constant as the used metals (copper, aluminum) have a temperature-dependant resistance.

That’s not really relevant to what we’re discussing. If my memory is correct and it’s been a long time, think the stated resistivity of a conductor is given at a temperature of 20*C. Just like Mass is constant and weight isn’t.
if you’re referring to the circuit diagram in a post by KSTR, it isn’t suggesting the resistance and inductance of a coil are separate.

 

[pogo]

Resistance is always constant.

But not when the speaker is in motion.
In the voice coil structure, the Re is also dependent on frequency, time, level and temperature.

 

[KSTR]

if you’re referring to the circuit diagram in a post by KSTR, it isn’t suggesting the resistance and inductance of a coil are separate.

Physically, the voice coil assembly is, well, the voice coil assembly.
Its electrical representation the elements can be seperated and we have the DC resistance and the Inductance forming the static transfer impedance on the left side and the actuator and sensor mechanisms on th right. The current translates into force and the velocity translates back into a voltage.

 

[Ingenieur]

For the system under discussion R can be considered constant.

Just so we all are on the same page:
Xl = 2 Pi f j L = j (|Xl)
Xc = 1/(2 Pi f C j) = -j (|Xc|)
Z = R + j(Xl - Xc) = R + Xj
|Z| = (R^2 + X^2)
phase = arctan(X/R) in deg
Z = |Z| / phase as a phasor
j = 90 deg phase shift = i = sqrt(-1)

For example, V amp out = 100/0
If load Z = 10/30
i = V/Z = 100/0 / 10/30 = 10/-30
i lags V, inductive

This is complex since frequency varies but can be plotted.
Most speaker Z plots show |Z| and phase

Like in a generator if the load becomes too low relative to the gen output Z an oscillation occurs.
By convention the gen supplies reactive power (capacitive)
Rotor angle in a gen, caps in the amp
The load absorbs and returns
Motor coils
Inductive

S = P + jQ
S = total power VA
P = active or 'real' power W
Q = reactive or 'imaginary' power VAr

From above
S = 100/0 x 10/-30 = 1000/30 VA
P = 1000 cos 30 = 866 W
Q = 1000 sin 30 = 500 VAr
The lagging L load is being supplied reactive power

 

[KSTR]

But not when the speaker is in motion.
In the voice coil structure, the Re is also dependent on frequency, time, level and temperature.

Just that it's not Re (the DC resistance) but the total Impedance Ze (including the reactive element) that you are talking about when it comes to frequency dependance. Other than for temperature Re strictly remains constant.

 

[Suffolkhifinut]

But not when the speaker is in motion.
In the voice coil structure, the Re is also dependent on frequency, time, level and temperature.

Resistance is not frequency dependant or on time or level, it will change with temperature. The temperature in a coil of wire will not be constant, the outside layers will be cooler. When fitting thermistors to windings we had to be sure they were embedded deeply into the windings. If they were lying near the surface we couldn’t monitor relevant temperature rise. In the voice coil of a speaker will the resistance rise sufficiently to make a difference? if it does the rise in resistance will reduce the circuit current and coil temperature will fall. The heat produced in an electrical circuit is given by the formula:

P = I x I x R Watts