Except that the "given" here is a driver that is essentially in free air. Nothing more than an 18 inch wide by 48 inch tall baffle board to support the test driver.
Since there is no air load due to the absence of an enclosure, the driver's native characteristics pretty much stay in place. This includes the huge impedance rise at free air resonance. To further compound the complexities, we wish this driver to exhibit something closer to the flat response it would have, had it been mounted in a conventional box, but hey, we don't need no stinkin box--- we will just use equalization. Whether passive, or active, it does not matter for discussion sake here. Let's just say we need 12 db more. Now, we are asking said power amplifier to deliver even more power than it was already limited to- due to the impedance rise.
A current source amp to the rescue, perhaps ?
Since there is no air load due to the absence of an enclosure, the driver's native characteristics pretty much stay in place. This includes the huge impedance rise at free air resonance. To further compound the complexities, we wish this driver to exhibit something closer to the flat response it would have, had it been mounted in a conventional box, but hey, we don't need no stinkin box--- we will just use equalization. Whether passive, or active, it does not matter for discussion sake here. Let's just say we need 12 db more. Now, we are asking said power amplifier to deliver even more power than it was already limited to- due to the impedance rise.
A current source amp to the rescue, perhaps ?
But you do NOT need 12 dB more, that´s the whole point.
You will keep running in circles until you understand that.
To say exactly the same in other words:
1) when your speaker is at resonance, it will have 75 ohm impedance.
2) it will take 12dB less power from a regular (constant voltage) amplifier.
3) it will NOT have a 12 dB dip in frequency response or SPL , so you do NOT need 12 dB boost to keep frequency response or SPL flat.
4) do not trust me or all others saying the same just based on pure faith, look at speaker frequency response curves yourself, they will NOT show a 12dB dip at resonance; in fact a few might show a small bump.
I usually don't write much here, but now I feel like stepping in, because I do not consider the original question extremely dumb nor fully answered. More precisely, it has been answered, but obviously not in a way that made it clear. So I'll try and put it in my own words:
1. We are just talking voltage amplifiers here, which aim to be an "ideal voltage source". We can safely assume that this is appropriate, as a) these are the only commercially available designs for some decades now and b) @Scott L did not indicate at any point in time, that he's talking about a somehow "unusual" amplifier. An ideal voltage source has zero output resistance.
2. For sake of this discussion there are three important restrictions on real world amplifiers that keep them from actually being an ideal voltage source: a) They have a max. voltage limit. b) They have a max. current limit. c) They have a non-zero output resistance. As has been said, the maximum voltage swing is limited by the amp's supply rail voltage. The maximum current an amplifier can supply over a defined period of time is limited by several factors from transformer to output transistors. The reasons for the non-zero output resistance are closely related.
3. Max. power output of an amplifier has little practical but a lot of marketing meaning. Try not to think in terms of power, but of voltage and current. Any two values of voltage, current and impedance can be used to calculate the third and power.
4. Real world loudspeakers do not present a resisitive load, in particular close to the drivers resonant frequency. This is why I picked the term "impedance" over "resistance" in point 3. Ohm's law still applies, if you are using complex numbers for calculation. A complex load is only partly resistive, the other part is either capacitive or inductive.
5. Very good solid state amplifiers can provide a fairly constant voltage (within their max. output limit) into different complex loads. But usually max. voltage and max. current drop when the resistance is low and/or the capacitance or inductance is high. To keep things simple, I will not go into complex loads in more depths, because the point can be made without it. Just keep in mind that complex loads make everything worse, potentially.
6. All technical data of drivers are published driven from a voltage amplifier. If the SPL diagram is smooth and on target (so no active correction is needed) and none of the amplifier's limits is hit, this is what you get. It doesn't matter if the actual power output is higher or lower at any given frequency. The impedance peak right at your drivers resonant frequency is just a result of this resonance. Resonance really means, that very little power is needed to have the system oscillate at that frequency. Voltage remains the same, current goes down, no problem whatsoever.
7. There still is the need to boost the SPL, depending on the application of the driver. When used in an open baffle (I don't comment on no-baffle applications, not a sensible concept for dynamic drivers), you need to make up for the SPL roll off at low frequencies. In fact, this is exactly the scenario mentioned by @Scott L.
8. Depending on how much boost you need (depending on target sensitivity and target max. SPL of the entire system and baffle size), the voltage limit could well kick in.
Now on to a made up but more or less realistic example.
As mentioned by @rayma, your 100 W into 8 ohms amplifiers actually has a voltage limit of roughly 28,3 V. Let's assume a driver sensitivity of 96 db at 2,83 V (= 1 W for a nominal 8 ohm driver) above the open baffle roll off frequency, a 90 db target sensitivity at 2,83 V and a baffle size that requires a 12 db boost at the woofers resonant frequency. Since the woofer's sensitivity is 6 dB above target the amplifier just needs to provide a 6 dB boost. To equalize SPL to 90 dB at fs the amplifiers needs to put out sqrt(6) * 2,83 V, which is about 7 V. Your max. voltage is around 4 times this much, so max. power will be 16 times this much, so max. SPL will be 16 dB more: 106 dB.
If your target SPL (determined by the MF and HF drivers of fullrange driver) was higher, the amp would need to provide more of a boost of course.
Where in this example did we use the speaker's impedance? We didn't, because it really doesn't matter, because the amp is a voltage source. In this case it is just the amplifiers maximum voltage output that must be obeyed. The fact that the output power at the resonant frequency is lower than e.g. in the midrange band does not matter. This has been said before, but I hope this made it a little more clear.
PS: Depending on the woofer's actual impedance curve, the setup could still be limited by the amp's max. current, the woofers mechanical excursion limit, your neighbors or whatever.
1. We are just talking voltage amplifiers here, which aim to be an "ideal voltage source". We can safely assume that this is appropriate, as a) these are the only commercially available designs for some decades now and b) @Scott L did not indicate at any point in time, that he's talking about a somehow "unusual" amplifier. An ideal voltage source has zero output resistance.
2. For sake of this discussion there are three important restrictions on real world amplifiers that keep them from actually being an ideal voltage source: a) They have a max. voltage limit. b) They have a max. current limit. c) They have a non-zero output resistance. As has been said, the maximum voltage swing is limited by the amp's supply rail voltage. The maximum current an amplifier can supply over a defined period of time is limited by several factors from transformer to output transistors. The reasons for the non-zero output resistance are closely related.
3. Max. power output of an amplifier has little practical but a lot of marketing meaning. Try not to think in terms of power, but of voltage and current. Any two values of voltage, current and impedance can be used to calculate the third and power.
4. Real world loudspeakers do not present a resisitive load, in particular close to the drivers resonant frequency. This is why I picked the term "impedance" over "resistance" in point 3. Ohm's law still applies, if you are using complex numbers for calculation. A complex load is only partly resistive, the other part is either capacitive or inductive.
5. Very good solid state amplifiers can provide a fairly constant voltage (within their max. output limit) into different complex loads. But usually max. voltage and max. current drop when the resistance is low and/or the capacitance or inductance is high. To keep things simple, I will not go into complex loads in more depths, because the point can be made without it. Just keep in mind that complex loads make everything worse, potentially.
6. All technical data of drivers are published driven from a voltage amplifier. If the SPL diagram is smooth and on target (so no active correction is needed) and none of the amplifier's limits is hit, this is what you get. It doesn't matter if the actual power output is higher or lower at any given frequency. The impedance peak right at your drivers resonant frequency is just a result of this resonance. Resonance really means, that very little power is needed to have the system oscillate at that frequency. Voltage remains the same, current goes down, no problem whatsoever.
7. There still is the need to boost the SPL, depending on the application of the driver. When used in an open baffle (I don't comment on no-baffle applications, not a sensible concept for dynamic drivers), you need to make up for the SPL roll off at low frequencies. In fact, this is exactly the scenario mentioned by @Scott L.
8. Depending on how much boost you need (depending on target sensitivity and target max. SPL of the entire system and baffle size), the voltage limit could well kick in.
Now on to a made up but more or less realistic example.
As mentioned by @rayma, your 100 W into 8 ohms amplifiers actually has a voltage limit of roughly 28,3 V. Let's assume a driver sensitivity of 96 db at 2,83 V (= 1 W for a nominal 8 ohm driver) above the open baffle roll off frequency, a 90 db target sensitivity at 2,83 V and a baffle size that requires a 12 db boost at the woofers resonant frequency. Since the woofer's sensitivity is 6 dB above target the amplifier just needs to provide a 6 dB boost. To equalize SPL to 90 dB at fs the amplifiers needs to put out sqrt(6) * 2,83 V, which is about 7 V. Your max. voltage is around 4 times this much, so max. power will be 16 times this much, so max. SPL will be 16 dB more: 106 dB.
If your target SPL (determined by the MF and HF drivers of fullrange driver) was higher, the amp would need to provide more of a boost of course.
Where in this example did we use the speaker's impedance? We didn't, because it really doesn't matter, because the amp is a voltage source. In this case it is just the amplifiers maximum voltage output that must be obeyed. The fact that the output power at the resonant frequency is lower than e.g. in the midrange band does not matter. This has been said before, but I hope this made it a little more clear.
PS: Depending on the woofer's actual impedance curve, the setup could still be limited by the amp's max. current, the woofers mechanical excursion limit, your neighbors or whatever.
Sir: Your reading and comprehension skills are above superb. Your explanation is excellent. I already suspected this would be the exact case, but I wished to hear it from an amplifier expert. Thank you kindly for contributing to this discussion. Even more impressive is that your sign on Moniker is that of the German Flag, yet your English is precise.
Thanks for pointing this out. Looks like I was too busy to make my example look "realistic", so I started off wrong. To put it very clear, the max. SPL at fs is determined by the driver, its enclosure and possibly the amp (when ignoring the room's influence). It doesn't matter if we need to match another driver's sensitivity (defining a "target sensitivity") or not.
What is left from my above example? I still assume an 8 ohm woofer with 96 dB SPL at 2.83V. It is mounted in an open baffle. Baffle size and driver Q are such that we need a 12 dB SPL boost at fs to achieve a flat response, so the actual SPL at fs without equalization is 84 dB at 2.83 V. Of course, we don't just need at 12 dB peak at the resonant frequency, but we have to compensate for the open baffle roll off slope between fs (specific to the driver) and the roll off frequency (specific for the baffle size, baffle shape and speaker position on the baffle).
A 3 dB SPL boost needs twice the power. On a logarithmic scale this is 10 * log(2) = + 3 dB power. Power is voltage^2/impedance, so 2 times the power requires sqrt(2) times the voltage. On a logarithmic scale this is 20 * log(sqrt(2)) = + 3 dB voltage. So, the voltage required for 87 dB SPL at fs would be about 1.414 * 2.83 V = 4.0 V.
Accordingly, a 12 dB SPL boost requires + 12 dB power, equaling +12 dB voltage increase, which is roughly 3.98 * 2.83 V = 11.27 V.
The max. voltage of 28.3 V is + 8 dB higher than that (20 * log(28.3/11.27)), resulting in 8 dB higher SPL (104 dB). Of course, we could have simply calculated this in just one step: If we get 84 dB SPL at 2.83 V, ten times the voltage (+ 20 dB) will result in a 20 dB higher SPL.
Now back to the scenario where we would match this woofer with another lower sensitivity driver, e.g. a fullrange driver with 90 dB SPL at 2.83 V. In an active setup with separate power amplifiers we would reduce the input of the woofer amp so that it puts out -6 dB voltage compared to the fullrange amp (1.4 V vs. 2.8 V, 0.25 W vs. 1 W).
This makes it a little less likely, that the woofer amp's voltage limit is what is limiting how loud the whole speaker can play, but it does not change the max. SPL. And still the impedance rise at the woofer's resonant frequency does not call for a beefier amp.
Is this better?
What is left from my above example? I still assume an 8 ohm woofer with 96 dB SPL at 2.83V. It is mounted in an open baffle. Baffle size and driver Q are such that we need a 12 dB SPL boost at fs to achieve a flat response, so the actual SPL at fs without equalization is 84 dB at 2.83 V. Of course, we don't just need at 12 dB peak at the resonant frequency, but we have to compensate for the open baffle roll off slope between fs (specific to the driver) and the roll off frequency (specific for the baffle size, baffle shape and speaker position on the baffle).
A 3 dB SPL boost needs twice the power. On a logarithmic scale this is 10 * log(2) = + 3 dB power. Power is voltage^2/impedance, so 2 times the power requires sqrt(2) times the voltage. On a logarithmic scale this is 20 * log(sqrt(2)) = + 3 dB voltage. So, the voltage required for 87 dB SPL at fs would be about 1.414 * 2.83 V = 4.0 V.
Accordingly, a 12 dB SPL boost requires + 12 dB power, equaling +12 dB voltage increase, which is roughly 3.98 * 2.83 V = 11.27 V.
The max. voltage of 28.3 V is + 8 dB higher than that (20 * log(28.3/11.27)), resulting in 8 dB higher SPL (104 dB). Of course, we could have simply calculated this in just one step: If we get 84 dB SPL at 2.83 V, ten times the voltage (+ 20 dB) will result in a 20 dB higher SPL.
Now back to the scenario where we would match this woofer with another lower sensitivity driver, e.g. a fullrange driver with 90 dB SPL at 2.83 V. In an active setup with separate power amplifiers we would reduce the input of the woofer amp so that it puts out -6 dB voltage compared to the fullrange amp (1.4 V vs. 2.8 V, 0.25 W vs. 1 W).
This makes it a little less likely, that the woofer amp's voltage limit is what is limiting how loud the whole speaker can play, but it does not change the max. SPL. And still the impedance rise at the woofer's resonant frequency does not call for a beefier amp.
Is this better?
Last edited:
3.98 in terms of voltage
15.80 in terms of power
This tells me that you would need 15.8 times as much power to compensate for the baffle rolloff, than would otherwise be necessary. If 20 watts makes a conventional equivalent speaker system sing along just fine, then we would need to increase this to 316 watts. I know I said, "we". I have a mouse in my shirt's top pocket. So now I am being told that 316 watts into 75 ohms is possible and to never mind the impedance. Okay, I am going home now.
Well, not quite. I told you to never mind power, not impedance. 
Actual power output to achieve the + 12 dB boost in SPL into 75 ohms at fs is still just 11.27 V^2/75 ohms = 1.7 Watts. The important thing to note is that your amplifier will be able to deliver the same voltage into any load, be it 8 ohm or 75. And this is all that your woofer needs.
Some argue that movement of the voice coil of a dynamic speaker is caused by current through the coil in a magnetic field, not by voltage. That's correct. But due to the very nature of resonance, very little current (and power) is required to move it at frequencies close to the resonant frequency.
In practical terms many amplifiers are limited rather by the amount of current they can supply when talking about open baffle equalization. Looks like I also failed to make my point: When dealing with open baffle equalization, you never have to worry about impedance peaks. You might have to worry about the speaker's minimum impedance.
I run my own open baffles (2 x Eminence Alpha 15 per channel in parallel up to around 230 Hz, 1 Mark Audio Alpair 12p per channel from this up) off two Quad 306 power amplifiers. Max power output into 5.5 ohm is 100 W, but that doesn't say much. Due to the voltage limit, max. power is down to 70 W into 8 ohm and 40 W into 14.5 ohm. This is not a problem at all, it's not constant power that is needed. Potential problems stem from the fact, that max. power is down to 55 W into 3 ohm for up to 5 seconds and down to 20 W into 3 ohm for continuous operation. The setup still works very good.
.
Actual power output to achieve the + 12 dB boost in SPL into 75 ohms at fs is still just 11.27 V^2/75 ohms = 1.7 Watts. The important thing to note is that your amplifier will be able to deliver the same voltage into any load, be it 8 ohm or 75. And this is all that your woofer needs.
Some argue that movement of the voice coil of a dynamic speaker is caused by current through the coil in a magnetic field, not by voltage. That's correct. But due to the very nature of resonance, very little current (and power) is required to move it at frequencies close to the resonant frequency.
In practical terms many amplifiers are limited rather by the amount of current they can supply when talking about open baffle equalization. Looks like I also failed to make my point: When dealing with open baffle equalization, you never have to worry about impedance peaks. You might have to worry about the speaker's minimum impedance.
I run my own open baffles (2 x Eminence Alpha 15 per channel in parallel up to around 230 Hz, 1 Mark Audio Alpair 12p per channel from this up) off two Quad 306 power amplifiers. Max power output into 5.5 ohm is 100 W, but that doesn't say much. Due to the voltage limit, max. power is down to 70 W into 8 ohm and 40 W into 14.5 ohm. This is not a problem at all, it's not constant power that is needed. Potential problems stem from the fact, that max. power is down to 55 W into 3 ohm for up to 5 seconds and down to 20 W into 3 ohm for continuous operation. The setup still works very good.
.
Could it be that my comprehension skills let me down and you're questioning the open baffle concept in general or the power requirement I came up with?
Open baffle equalization down to low frequencies at high volume does require a powerful amp. Much more powerful that required for feeding monopol speakers. Period. I took the 12 dB boost you had already mentioned for granted. Increasing the baffle size is the only way around it, as it lowers the role off frequency. Placing the speaker on the floor of an actual living room can usually be seen as a virtual baffle increase. The floor can be considered reflective for low frequencies, acting as a "shadow source".
Just talked to the cat on my shoulder and she agrees with what I wrote.
Open baffle equalization down to low frequencies at high volume does require a powerful amp. Much more powerful that required for feeding monopol speakers. Period. I took the 12 dB boost you had already mentioned for granted. Increasing the baffle size is the only way around it, as it lowers the role off frequency. Placing the speaker on the floor of an actual living room can usually be seen as a virtual baffle increase. The floor can be considered reflective for low frequencies, acting as a "shadow source".
316 watts into 75 ohms is possible, but not with a 100 W into 8 ohms amplifier. Nor is it needed.
Just talked to the cat on my shoulder and she agrees with what I wrote.
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.