Investing amplifier gain frequency response in speakers
High frequency Response of CE Amplifier. ➢ At high The Miller effect occurs only in inverting amplifiers –it is the inverting gain that. Inverting Amplifier is a normal OP-Amp in which the output is given as feedback to the inverted terminal of input by means of a feedback resistor. Problem with. Only a small fraction of the available power would be developed in the speaker. We can show this by calculating the ratio of power dissipated in the speaker to. NBA BETTING ODDS TOMORROW
He asked if I could design a small loudspeaker that must deliver deep, powerful bass and yield super high efficiency, so that small tube-based amplifiers could be used. My answer was, "No. In fact, no one can, as such a loudspeaker is theoretically impossible with conventional loudspeaker drivers. Why should he, as so many other audio gurus told him it was possible?
Yet, no small speaker delivering deep, powerful bass along with super high efficiency has appeared in his product lineup—or in any other company's product line. Small speaker enclosures with deep, powerful bass are certainly possible, but they won't be efficient. See post Since we cannot expect a flea-power amplifier to deliver the required amount of power into a small loudspeaker enough to produce loud and deep bass, we must make up the difference in wattage with an internal, integral solid-state power amplifier.
The assumption here is that the midrange and tweeter offer sufficient efficiency for the flea-power amplifier to drive them entirely; in other words, it is only the woofer that will need boosting. Adding power amplifiers allows us to magnify the flea-power amplifier's output, while still presenting an 8-ohm load to the flea-power amplifier. The first integral power amplifier functions as an impedance-multiplying circuit IMC , which doubles the woofer's impedance. This is important, as an 8-ohm load effectively appears as a 4-ohm load in this quasi-bridge-amplifier configuration.
With the IMC in place, the 4-ohm apparent load impedance doubles to 8-ohms, making the flea-power amplifier happy. Note that the inverting amplifier does not see full-bandwidth input signal, only the frequencies below the crossover frequency.
If we look at the circuit with current-referenced glasses on, we see that the flea-power amplifier and IMC deliver each one half of the current flow, while the bottom inverting amplifier must deliver all of the require current flow. In other words, the inverting amplifier will do twice the work and get twice as hot as the IMC's power amplifier. We can arrange the IMC and the inverting amplifier as a balanced-output amplifier, which requires a two-resistor voltage divider to function as an attenuator of the flea-power amplifier's output voltage swings.
This arrangement works far better with most solid-state power amplifiers, as it limits the input signal voltage swings to the IMC's input. Too large an input voltage will crash the input stage due to cascoded differential amplifiers and constant-current sources and current mirrors employed in the input stage.
In addition, most chip amplifier are nowhere near unity-gain stable, most require a gain of at least ten to prove stable. This arrangement allows us to attenuate the flea-power amplifier's output voltage by ten or much more and then set the balanced amplifier gain to ten or much more , resulting in unity-gain. In the example shown above, the attenuation is 0. The following schematic shows the AC voltage relationships. The flea-power amplifier delivers—at its maximum—4W, 8Vpk and 1Apk into 8 ohms.
Physics was never cheated, as we had to pay for the increase in effective SPL by providing the needed power augmentation with the integral power amplifiers. As far as the eye can see, it sees a tiny flea-power amplifier and tiny loudspeaker enclosures delivering far deeper and louder bass than would seem possible with a wee amplifier. Since the inverting amplifier must deliver twice the current that the IMC's amplifier, we can double up on the inverting amplifiers.
This time, the flea-power amplifier is a burly brute that delivers 16W, 16Vpk, and 2Apk into 8 ohms. It might appear confusing at first, but the arrangement is simple enough. The two inverting power amplifiers work in parallel, receiving the same input signal from the IMC's negative feedback loop.
The two 2k resistors are effectively in parallel, as the inverting amplifier inputs are effectively a faux ground connection; thus, they represent a 1k resistance to the IMC's negative feedback loop, making the IMC's gain equal to two. At the same time, the 2k resistor and 4k feedback resistor define a gain of The best power supply arrangement would be an internal bipolar power supply, as the asymmetrical current draw on the power supply precludes our using a two-resistor voltage divider to create a faux ground.
Speaking of current draw, here is the current relationships. It all makes sense, right? I hope so, as here is an example with greater attenuation and gain. As all three internal power amplifiers dissipate the same amount of heat, each should get the same amount of heatsink area. Missing from all the schematics is the woofer's passive crossover and its Zobel network. As far as the flea-power amplifier is concerned, it is just attached to an 8-ohm woofer, so we can place an inductor in series with the flea-power amplifier's output and the woofer and its supporting circuitry.
The passive crossover is an asymmetrical type, with the tweeter getting a 3rd-order high-pass filter, while the woofer sees only a 1st-order low-pass filter, with the assumption that the woofer's own natural high-frequency rolloff completes the 3rd-order low-pass filtering. Even if we can pull this off, which won't be easy, the woofer still has an inductor in series with it.
Ideally, we would prefer not to have any inductors in series with any loudspeaker driver. We eliminate the inductor by imposing a 1st-order low-pass filter on the integral inverting amplifier's output. The way this works is that at high-frequencies, the inverting amplifier ceases to be an inverting amplifier, becoming instead a unity-gain non-inverting amplifier. At low frequencies, in contrast, it inverts the flea-power amplifier's output signal.
Since a loudspeaker driver is an intrinsically differential device, the woofer only responds to low frequencies, as that is when it sees as a differential signal across its terminals. At high-frequencies, the woofer sees the exact same signal, both in amplitude and in phase. No difference, no sound. The big problem is hitting the target frequency, where the woofer's natural rolloff occurs.
What makes it difficult is that few woofers roll-off smoothly. In addition, as the frequency rises, the woofer tends to beam more strongly, almost as if the cone were a horn of sorts, which to a certain extent it is, as the woofer's cone often effectively decouples from the voicecoil at high-frequencies. One workaround that I had some success with is to adhere to the inside of the speaker grill cloth, just in front of the woofer, a round patch of quarter-inch thick felt, slightly smaller than the cone diameter.
At low frequencies, the felt is transparent, but it shades higher frequencies, thereby imposing a gentle low-pass filter. High-Frequency Phase-Shifting Filter In the previous example, we saw how we could replace the woofer's series inductor with a phase-shifting circuit that creates a low-pass filter function. Well, we can do the same to create a 1st-order high-pass filter.
This time we want DC and low frequencies to pass in phase from the inverting integral power amplifier's output, but high frequencies to leave inverted. All we have to do is to flip the resistor and capacitor placements. Resistor R and capacitor C set the crossover frequency based on the following simple formula. At the left, we see the AC signal source. The two voltage meters allow us to track both the amplifier's output and that output relative to the input.
The 4. The transition frequency is 1kHz. Although it is hard to see, the output is down 3dB at 1kHz. Note that the amplifier's output undergoes a complete phase reversal at about kHz and no phase shift at 10Hz. It is the phase shift that creates the high-pass filter. Let's say the flea-power amplifier put out a huge DC offset voltage of 8Vdc. Since the bottom, inverting amplifier no longer inverts, it puts out 8Vdc at its output and the delicate tweeter see zero net differential voltage, so it is safe.
Okay, now that we have seen both a low-pass filter and high-pass filter action, let's look at the combining of both. Two inverting power amplifiers are needed, each getting its own phase-shifting circuit. The result is a 1st-order two-way active crossover. As far as the flea-power amplifier is concerned, it is running fullrange into an 8-ohm load. As far as the inverting amplifiers are concerned, they are working into 4-ohm loads. Not only do we get rid of the passive crossover's inductor and large-valued capacitor, we have quadrupled the flea-power amplifier's output power.
Here is the wrinkle: it's never a good idea not the place a capacitor in series with a tweeter. Hum and buzz and DC offsets can kill the tweeter. For example, imagine you knock loose the external power supply plug and the connection is lost and the tweeter's inverting amplifier goes wonky; nothing will protect the tweeter.
On the other hand, if we place a safety capacitor in series with the tweeter, the tweeter is likely to survive screw-ups. We might as well put the extra capacitor to some use. The added capacitor and inductor have created a 2nd-order Linkwitz-Riley crossover. Note the reversal of the tweeter's terminals. Now, both drivers are down -6dB at the crossover frequency and they sum to a flat frequency response, but not a flat phase response, sadly. Still, the steeper crossover slopes better protect the tweeter and prevent the woofer from muddying up the upper midrange.
Just like a conventional passive Linkwitz-Riley crossover, the resulting impedance plot is not flat, but peaks at the crossover frequency. My workaround is to place an impedance-flattening network in parallel with the drivers. The added network results in a flat 8-ohm load for the flea-power amplifier. Some might argue that since we have gone so far down this path, we might as well go all the way to the end, where the flea-power amplifier is not needed, as we would have a fully self-powered loudspeaker.
I believe this is the future, as class-D amplifiers have become cheaper and smaller than high-quality crossover parts. Do not forget that the flea-power amplifier is actually doing one fourth of the work in this arrangement but its sonic signature will be mimicked by all the integral power amplifiers, as their signal source is the flea-power amplifier's output. For example, a strong 2nd harmonic will remain strong. Passive-Active 3rd-Order Crossovers Let's return to the example of the high-frequency driver getting a passive 3rd-order filter, while the woofer sees an active 1st-order low-pass filter, working on the assumption that the woofer's own natural high-frequency rolloff will complete a 3rd-order filter.
On the other hand, if we choose a much lower crossover frequency, say 1kHz, we can just give the woofer its own 3rd-order low-pass filter. The crossover alignment is a 3rd-order Butterworth, with both a flat summed frequency response and impedance plot. Note that, in this arrangement, both the IMC and the inverting amplifier see the full bandwidth delivered by the external flea-powered amplifier.
Alas, the phase is not flat. We must give up a flat phase response in order to gain a lower crossover frequency and still protect the tweeter. This arrangement has delivered four times the power into woofer—which is welcome—but we still have a lot of huge capacitors and inductors in the signal path.
It's a shame to have all this active solid-state circuitry and not also get an active crossover. Well, this situation irked me, but no solution seemed possible. Of course, we could just treat the flea-power amplifier as a robust line-stage amplifier, using its output voltage as the signal to drive an active crossover, but not deliver any power into the loudspeaker drivers, as that task would be entirely taken up by the integral power amplifier, which would function as unity-gain power buffers.
Before turning off the light and falling asleep, it hit me. IT being the solution, a dang clever solution, the sort that makes me happy for days. Let's start with no impedance-multiplier circuit IMC. We assume a woofer and high-frequency driver with equal SPL per watt at one meter.
Next, we realize that we cannot place any component in series with the flea-power amplifier's output. So how do we impose an active crossover? We place the circuitry in driver's return path to ground. The fundamental resonance of the system is determined by the physical parameters of the driver and the box and usually will be found somewhere between 60 and Hz. Below fundamental resonance the output of the loudspeaker will fall at the rate of 12 dB per octave for a closed box and 18 dB per octave for a ported or drone cone arrangement.
The design approach to solve both the high and low frequency problems associated with the single full range driver system is to add additional drivers, smaller drivers for the high frequencies and larger drivers for the low frequencies. Cross-over circuits are employed to restrict the driver signals to frequencies within the operating range of the drivers.
Conventional practice usually leads to a boxed to inch driver for the low frequencies with a combination of the driver and box exhibiting a fundamental resonance somewhere between 30 and 60 Hz. During the past decade, considerable attention has been given to improving the low frequency response of speakers with a view towards extending the response below that which can be obtained with the common unequalized voltage driven closed box.
Serious techniques used, however, extend the bass response about 1 octave, at the most, below which the response falls off at a rate of 24 to 30 decibels per octave with accordingly large phase shifts. It is now well recognized that these phase shifts are as detrimental to accurate sound reproduction as are frequency response anomalies.
Another approach to enhanced low frequency performance uses sub-woofer units which cross-over below Hz. These sub-woofer units are very high priced. They are physically large boxes enclosing high-mass drivers, a combination of which is used to move the fundamental resonance as low as possible. The sub-woofer itself employs no unusual techniques, but rather embodies a very direct approach to extending low frequency response by lowering fundamental resonance.
The previously described prior art speaker systems operate primarily above fundamental resonance. Attempts have been made to extend response well below resonance by the use of a closed loop feedback scheme. Commercial embodiments of this scheme use an accelerometer mounted on the speaker cone. The output from the accelerometer is processed to produce a displacement scaled signal which is then compared to the speaker input signal.
The resulting error signal is used as negative feedback to the power amplifier for reducing distortion. There are a number of inherent difficulties associated with this scheme since distortion will produce ambiguities and confusion in the drive displacement signal. It is imperative that a feedback scheme use a directly scaled displacement transducer. A still further approach found in the prior art is the use of a special amplifier employing techniques associated with the use of negative output resistance.
In the simple case, negative output resistance can be used to cancel the effects of finite voice coil resistance. In the more complex case, the imposition of a suite of conjugate impedances can be used to nullify the deleterious affects of mechanical and acoustic compedances of the system.
While this technique is perhaps the most complete available, it is by necessity very expensive and difficult to implement. With the exception of the aforementioned accelerometer scheme, none of the prior art devices extend the low frequency response of loudspeaker systems more than an insignificant amount below fundamental resonance.
The range below fundamental resonance can be viewed, in some respects, as an uncharted region into which successful audio forays are rarely made without sophisticated and expensive equipment. In the past, the fundamental resonant frequency Fr has been viewed as the lower limit below which accurate sound reproduction was difficult or economically impossible to obtain. Fr is determined by the combination of speaker driver parameters and the internal volume of the box which encloses the driver.
Fc is the normal high frequency cut-off point of a loudspeaker system, the point at which the response falls to 3 dB. Above Fc the response falls off rapidly. Fc is determined normally by the parameters of the loudspeaker driver only and is not dependent on box parameters. The response in the range above Fr is mass controlled and in the range below Fr is stiffness controlled. The rate of roll off in the stiffness controlled range below Fr is mainly determined by the type of baffle.
For a closed box system, the rate of decrease in output below Fr is 12 dB per octave, and the usable speaker output range is generally thought of as the range above Fr and below Fc. The conventional method of compensating for the decrease in acoustical output below Fr is extending the uniform output to some frequency below Fr by increasing the electrical input to the system by means of a bass boost equalizer ahead of the amplifier which drives the system.
A separate roll-off filter is used to cause a decrease in acoustical output with increasing frequency, usually at some point well below Fc but above Fr in order to effect a smooth transition between the bass system and the upper range system with which it is to be used. In our invention, the loudspeaker system resonance Fr determines the upper frequency cutoff point, above which the final acoustical output of the speaker will be decreasing with increasing frequency.
In the instant invention, the audio signal is processed to provide reciprocal compensation for the decrease in acoustical output below Fr so that the resultant speaker output is uniform with frequency below Fr. The rate of decrease in acoustical output for decreasing frequency is 12 dB per octave for a closed box loudspeaker system.
The instant invention processes the audio signal to provide an increase of 12 dB per octave with decreasing frequency so as to provide exact compensation and cause a uniform acoustical output below Fr. A double integrating circuit provides exactly the right amount of compensation to obtain a uniform acoustical output below Fr and also provides some inherent benefits in the region above Fr. In the region above Fr, where the acoustical output of the conventional loudspeaker system is uniform with frequency, our double integrator will provide a decrease in output with increasing frequency of 12 dB per octave.
Above Fc, where the acoustical output of the conventional system decreases naturally, our double integrator will cause an even greater rate of decrease. The instant invention provides, therefore, a very simple means for obtaining uniform speaker output below fundamental resonance. The highest frequency for which uniform output can be obtained with the apparatus of this invention is determined by the loudspeaker driver and box parameters.
While a double integrator provides the right composition for a closed box system, the characteristics of a vented box system call for the use of a triple integrator to provide uniform acoustic output below Fr. Similarly, an unenclosed system will require the use of a quadruple integrator to produce the same results.
The present invention can be easily implemented through the use of inexpensive operational amplifiers installed ahead of a power amplifier. Alternatively, power amplifiers can be designed with the appropriate circuitry of this invention as an integral part. Various means for accomplishing the electrical equivalent of integration, such as differentiating a signal and subtracting the differential from the signal itself to provide the equivalent of one step of integration may be employed as well as piece-wise approximation techniques which employ a multiplicity of RC networks.
These and other means of accomplishing the equivalent of integration are well known in the art and can be used to practice a method and apparatus of this invention. The invention possesses other objects and features of advantage, some of which of the foregoing will be set forth in the following description of the preferred form of the invention which is illustrated in the drawings accompanying and forming part of this specification.
It is to be understood, however, that variations in the showing made by the said drawings and description may be adopted within the scope of the invention as set forth in the claims. Fr is the system resonance frequency which is determined by the combination of loudspeaker driver and box parameters.
Fc is the high frequency cut-off determined by the loudspeaker driver parameters only. The rate of increase in output versus decreasing frequency is 12 dB per octave. The difference between curves A, B, and C are due to gain differences only. These gain versus frequency curves are characteristic of a double integrating amplifier set at three different gain levels to produce the three illustrated curves.
Adjustable gain allows the user to match the acoustical output of bass frequencies to match the acoustical output of other loudspeakers which will be used to reproduce the upper frequency ranges. The method of the instant invention calls for changing the strength of an audio signal at a constant rate in inverse proportion to the audio signal frequencies.
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