Radical Tweeter Capacitor...
This thread was split off from here: The "Elsinore Project" Thread - Page 46 - diyAudio
LET'S GET RADICAL - THE RADICAL TWEETER CAPACITOR
This is the beauty of DIY, please read the following as it is an optional add-on to the Elsinore design.
I have stated previously that I reckon the series capacitor to the Tweeter, the so-called High-Pass filter capacitor, is the single most critical crossover component (not that the others remain unimportant). There are some fairly unknown (generally speaking) reasons behind this and here is the first time I have actually stated more precisely the reasons for it.
Research has shown that THIS capacitor is prone to nonlinear distortions and particularly of the IMD (intermodulation distortion) kind. When capacitors directly in the signal path sees an AC signal that traverses zero Volt DC - and that is really what AC does - the distortion is primarily odd order (bad kind), but if the same capacitor is biased DC wise, then it becomes more even order (sweet kind). We know that if we have to choose between those we'd take the latter any day.
What this means is that capacitors directly in the signal path will sound better in most amplifer circuits where it is used to block DC, such as in tube amplifiers, BUT... when it comes to speakers, there is no DC and hence in speakers the very same capacitor will potentially sound worse.
Since we don't want DC in our speakers, we really are stuck with a bad situation.
Or are we?
Take a look at this:
BEFORE: Shows the current crossover.
AFTER: Shows the same crossover in-so-far that the series capacitor has the same 4.7uF value when the series-parallel configuration is taken into account. Then the crossover function is exactly as before.
So what is going on here. Simply the 9V battery (should be new alkaline and about 9.5V) available at just about any corner shop, biases the coupling from the centre outwards. Without any signal to the Tweeter, both sets of caps see the same 9.5V across it. This is because it is 0 Volt DC on the other side of both caps.
When an actual AC signal (music) comes along, when positive, the voltage will swing upwards above the 9.5V and there will be no celing and when it goes negative, it will eat into the 9.5V of the battery. So the available voltage swing where DC remains across both side (caps) is +infinite/-9.5V - or put is another way, it is able to swing 6.7V RMS before the bias (not the signal) clips on the negative side.
Now can you guys understand why I like and recommend external crossovers (easier access)?
PARTS: You will need to quadruple the number of your 4.7uF caps, although you could also use 10uF - but the result will be 5uF instead of 4.7uF, so you might perceive a little more energy in the presence region. The 100K resistor should be a good quality 1 Watt type. The battery should be a long life alkaline type. The resistor limits current to 100uA pretty much all the type. A couple of battery snaps/wires that clips onto the batttery.
BTW, you could double up on the battery and get an effective 19V DC Bias. Whether that would be audible probably depends how loud you like music? Haven't tried, only 9.5V.
How long will the battery last? Almost certainly for years and close to its shelf life. Just check its voltage from time to time.
I am not going to tell you in advance about any sonic gains. I don't want to telegraph your reactions and I want them to be fresh and in your own words.
SO WHO WILL BE THE FIRST CAB OFF THE RANK?
Joe R.
This thread was split off from here: The "Elsinore Project" Thread - Page 46 - diyAudio
LET'S GET RADICAL - THE RADICAL TWEETER CAPACITOR
This is the beauty of DIY, please read the following as it is an optional add-on to the Elsinore design.
I have stated previously that I reckon the series capacitor to the Tweeter, the so-called High-Pass filter capacitor, is the single most critical crossover component (not that the others remain unimportant). There are some fairly unknown (generally speaking) reasons behind this and here is the first time I have actually stated more precisely the reasons for it.
Research has shown that THIS capacitor is prone to nonlinear distortions and particularly of the IMD (intermodulation distortion) kind. When capacitors directly in the signal path sees an AC signal that traverses zero Volt DC - and that is really what AC does - the distortion is primarily odd order (bad kind), but if the same capacitor is biased DC wise, then it becomes more even order (sweet kind). We know that if we have to choose between those we'd take the latter any day.
What this means is that capacitors directly in the signal path will sound better in most amplifer circuits where it is used to block DC, such as in tube amplifiers, BUT... when it comes to speakers, there is no DC and hence in speakers the very same capacitor will potentially sound worse.
Since we don't want DC in our speakers, we really are stuck with a bad situation.
Or are we?
Take a look at this:
An externally hosted image should be here but it was not working when we last tested it.
BEFORE: Shows the current crossover.
AFTER: Shows the same crossover in-so-far that the series capacitor has the same 4.7uF value when the series-parallel configuration is taken into account. Then the crossover function is exactly as before.
So what is going on here. Simply the 9V battery (should be new alkaline and about 9.5V) available at just about any corner shop, biases the coupling from the centre outwards. Without any signal to the Tweeter, both sets of caps see the same 9.5V across it. This is because it is 0 Volt DC on the other side of both caps.
When an actual AC signal (music) comes along, when positive, the voltage will swing upwards above the 9.5V and there will be no celing and when it goes negative, it will eat into the 9.5V of the battery. So the available voltage swing where DC remains across both side (caps) is +infinite/-9.5V - or put is another way, it is able to swing 6.7V RMS before the bias (not the signal) clips on the negative side.
Now can you guys understand why I like and recommend external crossovers (easier access)?
PARTS: You will need to quadruple the number of your 4.7uF caps, although you could also use 10uF - but the result will be 5uF instead of 4.7uF, so you might perceive a little more energy in the presence region. The 100K resistor should be a good quality 1 Watt type. The battery should be a long life alkaline type. The resistor limits current to 100uA pretty much all the type. A couple of battery snaps/wires that clips onto the batttery.
BTW, you could double up on the battery and get an effective 19V DC Bias. Whether that would be audible probably depends how loud you like music? Haven't tried, only 9.5V.
How long will the battery last? Almost certainly for years and close to its shelf life. Just check its voltage from time to time.
I am not going to tell you in advance about any sonic gains. I don't want to telegraph your reactions and I want them to be fresh and in your own words.
SO WHO WILL BE THE FIRST CAB OFF THE RANK?
Joe R.
Maybe a bit more explanantion is in order:
Yes, biasing caps is not new. In fact happens in almost every tube amp made (although Lynn Olson's tube power amp eschews coupling caps). But the idea that this is some kind of 'crossover distortion' is way of the mark. That kinda sounds nice as a theory, but doesn't really explain anything.
Let us make two rules about any signal capacitor, whether film or non-polar:
1. Capacitors are two plates, there should always be potential across these two plates for optimum operation. It doesn't matter what the quality (or the price) of the cap.
2. This 'Bias' voltage must never reverse polarity, not while music is playing.
It has nothing to do with crossover distortion, but it has to do with the electrodes (plates) loosing tension and that they move with relation to each other. Their proper relationship via the dialectric gets disturbed. Keep it under some tension and you are in a better situation, reverse the voltage and the cap now has to resettle all over again.
BTW, this is actually covered in an AES 2008 paper and if I may quote part of it:
"... capacitance is not a constant, it depends on the charge on the capacitor. Charging the capacitor will result in an attractive force [tension] acting on the conducting plates. As no material is infinitely stiff, this force will reduce the thickness of the dielectricum and thus increase the capacitance. The force is always attractive, reversing the polarity will result in the same attractive force [now in the opposite direction]. This phenomenon will therefore lead to non-linear distortion; with an AC signal, odd harmonics are created and [when] the AC signal is superimposed on a DC voltage, it will mostly be even harmonics. It will be obvious that the more flexible the insulating layer is, the larger the distortion will be."
Please note brackets were added by me. Superimposing is what happens in tube amps, and the amplitude, voltage swings, never exceeds the Bias voltage across the cap. This is what is lacking in crossovers and the same cap will sound better when used as a tube power amp coupling cap and potentially the same cap in a speaker crossover will be significantly compromised performance wise.
The AES paper actually demonstrates how the distortion can be measured, so we are talking objective here, not just subjective. Menno vd Veen, who wrote the paper, also shows the Diff EQ maths (I don't claim to be up on this level of maths). But I like Menno because he is a really down to earth guy and quite interesting to disguss things on the concept level with him. So his paper is partly dry but also able to illuminate in a less dry way.
Now there is no mention of biasing crossover capacitors, but due to high-current requirements in speakers he says the following:
"The non-linear properties as outlined above become apparent in crossover filters where mostly large AC signals are applied in combination with large capacitors (both in capacitance and size) because of the large currents ...not really surprising that crossover filters are often mentioned when audible properties of capacitors are discussed."
If we can keep tension or attractive force one way only, we will predominantly have even order distortions, whereas if the reversing of this mechanism at a rate commensurate with the changes in a musical signal becomes odd-order nonlinear distortion. It does not take high-level maths to comprehend the logic behind that.
Menno does not mention DC biasing of crossover caps and he does not specifically mention the series Tweeter cap, he doesn't have to, but it is obvious that is where our focus should be first. Also, and I have said so on numerous occasions, in crossovers it is the High-Pass function that is the source of major problems in a way that Low-Pass is not to the same degree. Gradually we are getting more evidence of those facts.
I have not yet mentioned this to Menno yet (besides there are other issues I need to discuss with him) and looking forward to his response. I think it will be quite positive. He will also be interested in any responses posted here.
Now the question:
What is the optimum Bias?
It depends on the amplifier and its power rating. If a 100 Watt amp, it needs to supply 28.3V RMS into 8 Ohm - the maths says that the amp need to swing 80 Volt peak-to-peak. The optimum Bias would be half that, that is 40 Volt.
But in reality, even as low as 9.5V will keep the problem away most of the time. In high power situations, simply use TWO batteries to give 19V Bias, and I think that would do nicely. But when we get this high there will now be some level of stored energy in the cap and this could lead to 'clicks' when connecting leads etc.
Joe R.
Yes, biasing caps is not new. In fact happens in almost every tube amp made (although Lynn Olson's tube power amp eschews coupling caps). But the idea that this is some kind of 'crossover distortion' is way of the mark. That kinda sounds nice as a theory, but doesn't really explain anything.
Let us make two rules about any signal capacitor, whether film or non-polar:
1. Capacitors are two plates, there should always be potential across these two plates for optimum operation. It doesn't matter what the quality (or the price) of the cap.
2. This 'Bias' voltage must never reverse polarity, not while music is playing.
It has nothing to do with crossover distortion, but it has to do with the electrodes (plates) loosing tension and that they move with relation to each other. Their proper relationship via the dialectric gets disturbed. Keep it under some tension and you are in a better situation, reverse the voltage and the cap now has to resettle all over again.
BTW, this is actually covered in an AES 2008 paper and if I may quote part of it:
"... capacitance is not a constant, it depends on the charge on the capacitor. Charging the capacitor will result in an attractive force [tension] acting on the conducting plates. As no material is infinitely stiff, this force will reduce the thickness of the dielectricum and thus increase the capacitance. The force is always attractive, reversing the polarity will result in the same attractive force [now in the opposite direction]. This phenomenon will therefore lead to non-linear distortion; with an AC signal, odd harmonics are created and [when] the AC signal is superimposed on a DC voltage, it will mostly be even harmonics. It will be obvious that the more flexible the insulating layer is, the larger the distortion will be."
Please note brackets were added by me. Superimposing is what happens in tube amps, and the amplitude, voltage swings, never exceeds the Bias voltage across the cap. This is what is lacking in crossovers and the same cap will sound better when used as a tube power amp coupling cap and potentially the same cap in a speaker crossover will be significantly compromised performance wise.
The AES paper actually demonstrates how the distortion can be measured, so we are talking objective here, not just subjective. Menno vd Veen, who wrote the paper, also shows the Diff EQ maths (I don't claim to be up on this level of maths). But I like Menno because he is a really down to earth guy and quite interesting to disguss things on the concept level with him. So his paper is partly dry but also able to illuminate in a less dry way.
Now there is no mention of biasing crossover capacitors, but due to high-current requirements in speakers he says the following:
"The non-linear properties as outlined above become apparent in crossover filters where mostly large AC signals are applied in combination with large capacitors (both in capacitance and size) because of the large currents ...not really surprising that crossover filters are often mentioned when audible properties of capacitors are discussed."
If we can keep tension or attractive force one way only, we will predominantly have even order distortions, whereas if the reversing of this mechanism at a rate commensurate with the changes in a musical signal becomes odd-order nonlinear distortion. It does not take high-level maths to comprehend the logic behind that.
Menno does not mention DC biasing of crossover caps and he does not specifically mention the series Tweeter cap, he doesn't have to, but it is obvious that is where our focus should be first. Also, and I have said so on numerous occasions, in crossovers it is the High-Pass function that is the source of major problems in a way that Low-Pass is not to the same degree. Gradually we are getting more evidence of those facts.
I have not yet mentioned this to Menno yet (besides there are other issues I need to discuss with him) and looking forward to his response. I think it will be quite positive. He will also be interested in any responses posted here.
Now the question:
What is the optimum Bias?
It depends on the amplifier and its power rating. If a 100 Watt amp, it needs to supply 28.3V RMS into 8 Ohm - the maths says that the amp need to swing 80 Volt peak-to-peak. The optimum Bias would be half that, that is 40 Volt.
But in reality, even as low as 9.5V will keep the problem away most of the time. In high power situations, simply use TWO batteries to give 19V Bias, and I think that would do nicely. But when we get this high there will now be some level of stored energy in the cap and this could lead to 'clicks' when connecting leads etc.
Joe R.
Calling our erstwhile moderator.
Hi Dave,
It occurs me that this topic should be a thread on its own as most DIY'ers can try this and it can be applied to all order High Pass crossovers, both to Tweeters and also Midranges in 3-Way systems (see below). What do you reckon? This is not just an Elsinore tweak.
Sorry Dave, but full-range guys miss out, but maybe they have had an advantage all along. Talk about the last laugh, maybe they had the last laugh first.
Maybe the topic should read "DC Bias in Crossovers (mostly Tweeters)."
Joe R.
Hi Dave,
It occurs me that this topic should be a thread on its own as most DIY'ers can try this and it can be applied to all order High Pass crossovers, both to Tweeters and also Midranges in 3-Way systems (see below). What do you reckon? This is not just an Elsinore tweak.
Sorry Dave, but full-range guys miss out, but maybe they have had an advantage all along. Talk about the last laugh, maybe they had the last laugh first.
Maybe the topic should read "DC Bias in Crossovers (mostly Tweeters)."
An externally hosted image should be here but it was not working when we last tested it.
Joe R.
Thanks Dave (planet10)for setting this new thread up.
Some additional notes:
For those interested in Menno's AES paper:
www.mennovanderveen.nl/nl/download/download_4.pdf
The first example above was the first applied to Elsinore crossover, so ignore the L, R and C components. Analyse your own crossover and what parts are required. The change in capacitors should not change the AC filter function of the crossover, so the combined value including the additional caps stay the same. Other components also stay the same.
Also, an explanation for the added 1K resistor showed in later examples; without it grounding the input, the potential charging of the first cap when amp is turned On, some amps, especially SS might not like it. Should keep things safe under all circumstances and not harmful to any amp.
Using 9V or 18V? With small SE amps like 300B, then there should not be any advantage going above 9V, but in most cases 18V is recommended. In real high power situs, use 3 x 9V - I doubt if more than that would be required.
Please note, the DC does not appear to the 'outside' world. Under those higher voltages I would make sure the caps are rated at least 100V.
How effective DC Bias will be may well depend on what caps you are using now. If they are perfect, the DC Bias should not show any improvement, but since they are not perfect... it will be interesting in getting feedback and see/hear the results.
Joe R.
Some additional notes:
For those interested in Menno's AES paper:
www.mennovanderveen.nl/nl/download/download_4.pdf
The first example above was the first applied to Elsinore crossover, so ignore the L, R and C components. Analyse your own crossover and what parts are required. The change in capacitors should not change the AC filter function of the crossover, so the combined value including the additional caps stay the same. Other components also stay the same.
Also, an explanation for the added 1K resistor showed in later examples; without it grounding the input, the potential charging of the first cap when amp is turned On, some amps, especially SS might not like it. Should keep things safe under all circumstances and not harmful to any amp.
Using 9V or 18V? With small SE amps like 300B, then there should not be any advantage going above 9V, but in most cases 18V is recommended. In real high power situs, use 3 x 9V - I doubt if more than that would be required.
Please note, the DC does not appear to the 'outside' world. Under those higher voltages I would make sure the caps are rated at least 100V.
How effective DC Bias will be may well depend on what caps you are using now. If they are perfect, the DC Bias should not show any improvement, but since they are not perfect... it will be interesting in getting feedback and see/hear the results.
Joe R.
It does indeed depend on the cap and a perfect cap in theory should not need it. But the 'attractive force' and reversal should impact to some extent even on the best.
Have you also watched the video linked on Post #3 - with Paul Dodds. It's clear that the imperfections in crossover caps may well be engineered in to suit a certain taste. Note especially comments on the physical evidence towards the end of the video, that "passive" capacitors are reactive devices, just like drivers are, even if not deliberately. When capacitors can "sing" like transducers, it is clear that this is not minor stuff [re-statement from the Elsinore thread].
Joe R.
Have you also watched the video linked on Post #3 - with Paul Dodds. It's clear that the imperfections in crossover caps may well be engineered in to suit a certain taste. Note especially comments on the physical evidence towards the end of the video, that "passive" capacitors are reactive devices, just like drivers are, even if not deliberately. When capacitors can "sing" like transducers, it is clear that this is not minor stuff [re-statement from the Elsinore thread].
Joe R.
danieljw said:hopefully get to it on the weekend. so busy at the moment !
is there anty thing to watch out for with tweeter and amp safety
i dont particulary want to damage my hiraga amp
-dan
Should be quite safe. Don't forget the 1K resistor. Make sure of your wiring and check with a DC meter, should read zero across the Tweeter and zero on the input to the crossover that interfaces with the amp.
Today connected my Elsinores up to a gainclone amp (SS) and no drama at all. Didn't expect any.
Joe R.
No electrolits benifit the most by being battery biased. If you look at the old article Picking Audio Capacitors by Walter Jung he has some test using biased elecrolits. I replaced the large cap in a solitstate amp the one that helps null the dc offset with a pair of battery biased caps and was rewarded with a LOT more clarity. I used a 500k resistor and a 9v battery.
Hello Joe
Do you realize JBL has been doing this for years on their SOTA designs?? All my DIY networks are Charge Coupled only difference is they use a 2-3meg as the resistor value.
http://www.audioheritage.org/vbulletin/showthread.php?t=3555
Rob
Do you realize JBL has been doing this for years on their SOTA designs?? All my DIY networks are Charge Coupled only difference is they use a 2-3meg as the resistor value.
http://www.audioheritage.org/vbulletin/showthread.php?t=3555
Rob
woody said:
Sound like a good application to me. I think, and I am repeating myself, that the idea is to keep the 'attractive force' - phrase used by both Menno and also Paul Doods IMSMR - from reversing polarity. The moment the cap has to do that, the force is interrupted and has to reset again. The force remains the same even if the polarity has changed, but what happens at the moment it does reverse? The resetting of the plates and dialectric tension as well as potentially setting off mechanical resonances etc. So we should hear an improvement and, as you say and it's one of my favourite words, more clarity.
Robh3606 said:Hello Joe
Do you realize JBL has been doing this for years on their SOTA designs?? All my DIY networks are Charge Coupled only difference is they use a 2-3meg as the resistor value.
http://www.audioheritage.org/vbulletin/showthread.php?t=3555
Rob
Hi Rob
Very well spotted. The R value just needs to be high and MOhm would do it too. Isn't it interesting they came up with a phrase that's saleable - "Charge-Coupled" - but any tech would call it just plain DC bias. No need to invent new when the old is still OK.
But is it 'crossover' distortion a la Class A vs Class B as they say? I suppose we could end up with a semantic discussion about that, but again it's just clever/good ad-speak. But I think we now have better ways of explaining what's going on - but they managed to get it right in execution, so that recognition is deserved. But Menno has now tackled the maths on this. I simply read hi paper and it occurred to me right there and then that this was the obvious thing to do. Others have to, but coming from a different point.
But why is it not more common? Maybe we can help it become so as this is the sort of edge and challenge DIY'ers love.
Joe R.
It is kind of simple idea
a capacitor is a bucket with water splashing back and forth and losing charge with each splash so just making sure that it is full when it has to splash in the forward direction, I am surprised some one has come up with using metal hydride and using redirected energy into a charging system in the network
a capacitor is a bucket with water splashing back and forth and losing charge with each splash so just making sure that it is full when it has to splash in the forward direction, I am surprised some one has come up with using metal hydride and using redirected energy into a charging system in the network
"... capacitance is not a constant, it depends on the charge on the capacitor. Charging the capacitor will result in an attractive force [tension] acting on the conducting plates. As no material is infinitely stiff, this force will reduce the thickness of the dielectricum and thus increase the capacitance. The force is always attractive, reversing the polarity will result in the same attractive force [now in the opposite direction]. "
Joe,
I don't disagree with the statement as form the paper, but your edit is incorrect. The force does not change direction. That's not a big deal but let's look at the effects of bias. The force between two plates of a cap is proportional to q^2, the charge of the cap squared. If the cap is ideal except for the compression of the dielectric then when the a positive voltage, +V is applied the cap will have a charge of +q. When the voltage is -V, the charge will be -q. In both cases the force is of the same magnitude and direction such that it pulls the plates together. Since q = proportional to V, for V = sin(wt) then q^2 (thus F) goes like (sin(wt))^2 = (1 - cos(2wt))/2. Thus the force varies between 0 and 1 but varies at twice the frequency. This results in a perfectly symmetric system where the change in C is the same for a + or - swing in voltage about 0 volts. This symmetric system will have only odd order distortion. Now, if we apply a DC bias the voltage across the cap is V = sin(wt) + DC and since q^2 goes like V^2, and V^2 = (sin(wt))^2 + DC^2 + 2 DC sin(wt) = (1 - cos(2wT))/2 + DC^2 + 2DC sin(wt). This is a highly non-symmetric system and while I can see that it will introduce even order distortion I can not see how it would reduce odd order distortion, at least not by the argument that the capacitance changes due to the force pulling the plates together. The figure below shows the variation of the force between the plates of a parallel plate cap over one cycle, with and w/o bias. This does not include the effect of a resulting change in C, however, including it would only make the force more asymmetrical since if the capacitance increased as the force increased the charger would increase for a given voltage across the cap further increases the force. I know the application of a DC bias is used in this way, but I can't see a positive effect arising from the force argument.
Do you have the full reference to the AES paper? I'd like to take a look.
The arguments I have heard for biasing cap has centered on dielectric absorption, i.e the JBL argument, well part of it.
As an after though, if the DC bias were much, much greater than the AC signal magnitude, then the AC variation could be viewed as a small perturbation and in such a case greater linearity could be achieved. But we aren't talking abut high bias levels. But it would still depend on the elastic nature of the dielectric.
Joe,
I don't disagree with the statement as form the paper, but your edit is incorrect. The force does not change direction. That's not a big deal but let's look at the effects of bias. The force between two plates of a cap is proportional to q^2, the charge of the cap squared. If the cap is ideal except for the compression of the dielectric then when the a positive voltage, +V is applied the cap will have a charge of +q. When the voltage is -V, the charge will be -q. In both cases the force is of the same magnitude and direction such that it pulls the plates together. Since q = proportional to V, for V = sin(wt) then q^2 (thus F) goes like (sin(wt))^2 = (1 - cos(2wt))/2. Thus the force varies between 0 and 1 but varies at twice the frequency. This results in a perfectly symmetric system where the change in C is the same for a + or - swing in voltage about 0 volts. This symmetric system will have only odd order distortion. Now, if we apply a DC bias the voltage across the cap is V = sin(wt) + DC and since q^2 goes like V^2, and V^2 = (sin(wt))^2 + DC^2 + 2 DC sin(wt) = (1 - cos(2wT))/2 + DC^2 + 2DC sin(wt). This is a highly non-symmetric system and while I can see that it will introduce even order distortion I can not see how it would reduce odd order distortion, at least not by the argument that the capacitance changes due to the force pulling the plates together. The figure below shows the variation of the force between the plates of a parallel plate cap over one cycle, with and w/o bias. This does not include the effect of a resulting change in C, however, including it would only make the force more asymmetrical since if the capacitance increased as the force increased the charger would increase for a given voltage across the cap further increases the force. I know the application of a DC bias is used in this way, but I can't see a positive effect arising from the force argument.
Do you have the full reference to the AES paper? I'd like to take a look.
The arguments I have heard for biasing cap has centered on dielectric absorption, i.e the JBL argument, well part of it.
As an after though, if the DC bias were much, much greater than the AC signal magnitude, then the AC variation could be viewed as a small perturbation and in such a case greater linearity could be achieved. But we aren't talking abut high bias levels. But it would still depend on the elastic nature of the dielectric.
An externally hosted image should be here but it was not working when we last tested it.
Thinking about this a little more, I failed to consider the properties of the gap between the plates. If the dielectric is elastic as a linear spring, then my previous post makes sense. However, if the gap can not be considered as a linear spring, but rather as a car suspension with bump stops, then an applied bias of sufficient magnitude can compress the plates against the bump stops and hole it there. But in this case the DC bias must be high enough so as to maintain the required minimum voltage across the cap so that the plates are against the bump stops. This means the bias must be sufficiently greater than the peak to peak voltage swing of the applied signal.
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