COMPENSATION OF RISING FREQUENCY RESPONSE
IN PASSIVE CURRENT-DRIVEN LOUDSPEAKERS
The invention relates to electro-dynamic moving-coil loudspeakers which are designed to be used with current-output amplifiers. It discloses a means for correcting the rising free-field frequency response, that is characteristic to cone type speakers under current-drive because the filtering action of voice coil inductance is not present. The response correction is achieved in a fashion that preserves the speaker driver unit essentially in the current-drive mode. The passivity of loudspeaker means here that the loudspeaker does not contain amplifier functions.
Background: the Qualitative Superiority of Current-Drive
Today all commercially available audio amplifier and loudspeaker equipment works on voltage drive principle without significant exceptions. This means that the amplifier acts as a voltage source and therefore has small output impedance. However, both technical aspects and listening experiences indicate plainly that voltage drive is the wrong choice if sound quality is considered important. The reason is that the electromotive forces (EMF) generated by the speaker driver disturb the voltage-to-current conversion that in the voltage drive principle is left as the job of the loudspeaker.
The driving force (F), that sets the diaphragm in motion, is proportional to the current (i) flowing through the voice coil according to the formula F = Bli, where the product Bl is called force factor (B = magnetic flux density; l = wire length in the magnetic field). In a voltage-controlled driver, however, this current becomes corrupted in a plurality of ways.
The electrical equivalent circuit of a moving-coil driver unit can be presented as in Figure 1. Rc represents voice coil resistance, voltage source em represents the back-EMF (motional EMF) of the driver and is calculated by em = Blv (v = voice coil velocity), and voltage source ei represents the inductance EMF, that is generated by the lossy inductance of the voice coil.
When looking at the impedance curve of a typical driver, it is easy to think that em is significant only near the fundamental resonant frequency, or that ei is significant only at the highest operating frequencies. Instead, in a typical cone or dome driver, the sum of the magnitudes of em and ei is in fact at least of the same order than the voltage drop in Rc throughout the whole operation frequency range.
Both em and ei are subject to several disturbance factors, for which reason these voltages do not follow the applied signal linearly but include very manifold distortion components. When feeding the equivalent circuit of Fig. 1 by a conventional low-output-impedance amplifier, that functionally corresponds to a voltage source, sources em and ei and all the indefinite distortion components contained by these modulate the voltage that is left across resistance Rc and hence the current flowing in the circuit, with consequences that are very detrimental to sound quality all over the world.
Instead, by feeding the equivalent circuit of Fig. 1 by a high-output-impedance amplifier, that functionally corresponds to a current source, sources em and ei and the indefinite distortion components contained by these are not able to modulate the current flowing in the circuit, which current is now determined directly by the feeding current source, that follows the applied signal without interference.
The following interference factors muddle voice coil current under voltage drive but naturally not under current-drive:
1) Voice coil acting as a microphone for sound waves reflecting from inside the cabinet and passing through the diaphragm
2) Voice coil acting as a microphone for sound waves from adjacent drivers
3) Mechanical and pneumatic non-idealities of the moving parts causing uncontrollable EMF effects
4) Bl-variation causing fluctuation in impedance's angle and hence phase modulation of current at middle frequencies
5) Position-dependent inductance of voice coil causing both amplitude and phase modulation in current
6) Voice coil inductance depends strongly on signal level causing nonharmonic distortion
7) Resistance changes due to temperature variations and manufacturing tolerances
8) Program-signal-dependent contact resistance variations in connectors and switches
Detailed information about these serious interference mechanisms and current-drive in general is found in the book: Esa Meriläinen: Current-Driving of Loudspeakers, CreateSpace 2010, USA (ISBN: 1450544002).
How Current-Drive Is Established
A completely ideal current-drive, as well as a completely ideal voltage drive, cannot be realized, so, in practice, one always has to settle for a compromise that lies somewhere between these two extremes. In which mode the driver eventually operates, is determined by the ratio of the impedances of the feeding source and the driver.
In Fig. 2a, a driver is fed from a voltage source (E) through a series impedance (Z). If Z is very small with respect to the load impedance ZL, the load current IL is determined almost solely by ZL, and the load voltage UL essentially follows the feeding source E; so the driver operates, in this case, under voltage drive. (When comparing impedances, the absolute value, i.e. the length of the vector, is considered.)
In turn, if Z is very high with respect to ZL, ZL forms only a very small part of the circuit's total impedance. The load current IL is then almost independent of ZL and its variations, so the driver operates under current-drive. A high series impedance also requires a high source voltage if the current is to be kept sufficient; so, in practice, it is not economical to implement current-drive on the principle of Fig. 2a.
If Z is of the same order than ZL, it can be said that the current is determined in half by both impedances, and the variations of ZL are reflected to the current with a half strength, compared with the case where Z = 0. The operation mode may then be regarded as a half way between voltage- and current-drive.
In Fig. 2b, the voltage source has been replaced by a current source and the series impedance by a parallel one. Looking from the load, the circuits of Figures 2a and 2b operate totally identically if I = E/Z. Thus, either of the two models may be used, depending on the need, when analyzing the operation mode of the driver.
If Z in Fig. 2b is very low compared to the load impedance ZL, voltage UL is determined almost solely by Z since the load current is then very low. The operation of the driver is thus essentially voltage-driven. In turn, if Z is very high compared to ZL, the significance of Z is left diminutive, and the driver operates essentially under current-drive.
Therefore, in both models, a high value of Z denotes current-drive and a low value, respectively, voltage drive. Instead, the magnitude of the sources is irrelevant to the driving mode, so they can even be considered to be zeroes. A zero-valued voltage source corresponds to a short-circuit and a zero-valued current source, in turn, a break; so, irrespective of which model is used, the impedance seen by the driver, that is, the impedance that determines the driving mode, is always Z (Fig. 2c).
The models of Fig. 2 can be used to represent a network made up of linear elements also generally, not only in the case of a single source and a single source impedance. Any network, consisting of resistances, capacitances, inductances, and voltage and current sources, can namely always be substituted, between any two nodes, by a series connection of one voltage source and one impedance, referred to as the Thévenin equivalent of the network. In the substitution, one may also as well use the parallel connection of a current source and impedance (or admittance), referred to as the Norton equivalent.
In order to keep Z high, besides the amplifier also the possible crossover filter has to be designed for high impedance, whereupon it is mostly 1st-order filters that are suitable. (It must be recognized that totally corresponding restrictions would also apply to conventional voltage drive systems if in them one would correspondingly hold on to the requirement of low impedance seen by the driver. In practice however, this matter is just not cared about; and so the actual operation mode of the drivers is often found in some middle ground between voltage- and current-drive, generally, however, closer to voltage drive.)
From the standpoint of sound quality, the most essential factor is how great are the current components generated in the voice coil by the interference-containing electromotive forces em and ei, compared to the signal current flowing in the voice coil without these forces. In practice, the magnitude of the motional EMF, em, cannot be decreased without decreasing the driver's sensitivity. The inductance EMF can be reduced to some extent by design of the magnetic circuit and by shorting rings but not conclusively. Therefore, the only working means to eliminate or minimize the flowing of these detrimental current components is that the electrical impedance seen by the driver unit, indicated by Z in Fig. 2c, is made as high as possible.
To investigate the matter, one can imagine as though an extraneous voltage source appearing in series with the driver unit, in the manner of Fig. 1, and then study how great relative current this source introduces in the voice coil of the driver in question and in the voice coils of possible other drivers operating in the same circuit.
The introduction of current-drive has perhaps been hampered by a prejudice according to which the fundamental resonance of the bass driver could not easily be damped, as so-called electrical damping, that pertains to voltage drive, is absent. However, the needed resonance damping is established by using a driver of low mechanical Q value, by filling the enclosure with effective damping material, and by using an appropriate active or passive attenuation network, by which the bass response can be fine-tuned in place.
According to a widely spread but ill-justified notion, the amplifier's output impedance should be as low as possible in order to "control" cone movement and to somehow suppress the EMF:s generated by the driver. The physical fact is that cone movement (more precisely the acceleration) can be governed only by current, and the EMF:s themselves can never be suppressed without suppressing the whole speaker; simply because the law em = Blv can never cease to hold, no matter what impedances or circuits are used. Instead, it is the harmful EMF-derived currents that can and must be suppressed, and this is only done by careful current-drive design.
Description of the Problem
Current-drive requires thus that the output impedance of the amplifier must be high compared to the impedance of the driver unit. However, the rest of the circuitry, including crossover network, must not violate the current-drive principle by lowering the total (Thévenin) impedance seen by the driver. Therefore, simple parallel connected RC-networks cannot be used for response correction, because doing so shifts the operation mode into some middle ground between voltage- and current-drive.
On the other hand, a typical cone type speaker under current-drive needs attenuation at high frequencies because at short wavelengths the cone acts as a horn for vibrations emanating from the center and voice coil inductance doesn't cause low-pass filtering as happens in conventional use. Another reason that causes rising frequency response is the directivity of the cabinet's front panel ("baffle step"). At short wavelengths radiation namely occurs into half space and is therefore more efficient than at long wavelengths, where sound emanates from the speaker into all directions.
General Scheme of the Invention
The present invention describes a means to correct the rising frequency response of a current-driven loudspeaker by the scheme shown in Fig. 3. A dual voice coil speaker driver 2 is connected to a current-divider network 3, that allows both voice coils (4a, 4b) to operate normally at low frequencies but disables one of the coils totally or partially at high frequencies, where the other coil is still fully or partially operative.
By "low frequencies" is meant frequencies low enough (typically below 100 Hz) that the need for attenuation due to above-described reasons in driver 2 is yet essentially negligible. By "high frequencies" is meant frequencies high enough (typically a few kilohertzes) that full attenuation need has essentially been reached.
Detailed Description of the Invention
Figure 3 depicts a general outline of the invention
Figure 4 shows a simple embodiment of the invention capable of 6 dB attenuation.
Figure 5 shows an embodiment of the invention for more than 6 dB attenuation
Figure 6 shows for comparison an alternative but less ideal method for attenuating high frequencies using and ordinary driver.
Figures 7 and 8 show performance characteristics obtained by the circuits in Figures 4 and 5.
Fig. 4 shows a simple embodiment of the invention. The voice coils 4a and 4b are connected in series, and inductor 5, capacitor 6, and resistor 7 together make up the current-divider network. At low frequencies, essentially all current that is fed through points 8 and 9 flows through inductor 5 and voice coils 4a and 4b. Current through capacitor 6 is then negligible, and the speaker operates in full drive. At high frequencies, essentially all current flows through capacitor 6, resistor 7, and voice coil 4b, bypassing voice coil 4a. Assuming the voice coils are identical, the sound level becomes therefore attenuated by 6 dB. At intermediate frequencies (in the transition region), current through voice coil 4a decreases gradually with increasing frequency, and the desired compensation characteristics can be achieved by optimizing inductance 5 and capacitance 6. If the desired attenuation is less than 6 dB, a resistor can be added in parallel with inductor 5.
Resistor 7 increases the impedance seen by voice coil 4a at the frequency where inductance 5 and capacitance 6 cancel each other and therefore helps to keep voice coil 4a in the current-drive mode. Increasing resistance 7 also increases the total impedance between points 8 and 9 at high frequencies, so resistance 7 should be chosen so that maximum allowable total impedance is not exceeded.
In Fig. 4, the impedance seen by voice coil 4b is infinite, so this coil operates on current-drive without compromises at all frequencies. The impedance seen by voice coil 4a is the impedance of the series connection of inductance 5, capacitance 6, and resistance 7 and can be made quite high at both low and high frequencies. If resistance 7 is e.g. three times the nominal impedance of voice coil 4a, the impedance of said series connection remains reasonably high also at those frequencies where the impedances of inductor 5 and capacitor 6 are relatively low.
It is important that the impedance seen by voice coil 4a is high also at high frequencies despite the fact that the coil does not pass signal current in that region. This is because the electromotive forces resulting from mutual inductance and coil movement are still present and must not be allowed to produce unwanted currents in the loop containing voice coil 4a.
The 6 dB attenuation achieved with the circuit of Fig. 4 is often sufficient for small-sized cone drivers. In larger loudspeakers, however, the on-axis sensitivity tends to rise with frequency more steeply, and hence more compensation may be needed. The solution is shown in Fig. 5. Resistor 10 and capacitor 11 form a new current path, along which a portion of the signal current bypasses at high frequencies voice coil 4b also, thus establishing the required extra attenuation. With the resistance values shown in Fig. 5, the total attenuation at high frequencies will be 10 dB (ignoring inductance of voice coil 4b). The desired total compensation characteristics can be realized by optimizing resistance 10 and capacitance 11 together with inductance 5 and capacitance 6 e.g. with a circuit simulation program.
The inclusion of resistor 10 and capacitor 11 affects the impedance seen by voice coil 4a only little, and the impedance seen by voice coil 4b remains quite high even at high frequencies because the sum of resistances 7 and 10 is in practice many times greater than the nominal impedance of voice coil 4b.
If any tweeter is not used in the system, it may be necessary to expand bandwidth by decreasing the attenuation at the most high frequencies. This can be done favorably e.g. by inserting a parallel resonance network, made up of an inductor and a capacitor, in series with resistor 10 and by setting the impedance peak of said resonance network to the highest frequencies to be reproduced. At the same time, capacitance 11 can be decreased substantially. One remarkable benefit of current-drive is also that, as the attenuation introduced by voice coil inductance is absent, it becomes possible to employ a one-way system in many such applications where usually would be needed the aid of a tweeter.
Figures 4 and 5 show in parentheses example values for the circuit components assuming 4 Ω voice coils. Figure 7 shows the attenuation characteristics (vector sum of voice coil currents) obtained using these values; the solid line representing the Fig. 4 circuit and the dashed line, respectively, the Fig. 5 circuit. Figure 8 shows, respectively, the total impedance developed between points 8 and 9.
Capacitors should be preferably of plastic dielectric, but bipolar electrolytics may be used where only cost is important. Inductor 5 is not yet too large to be air-cored. In final design, the lossy self-inductance of each voice coil and the mutual inductance between them have to be taken into account and modelled with appropriate equivalent circuits.
Fig. 6 shows an alternative but less ideal method to attenuate high frequencies in current-driven loudspeakers. Here, an ordinary single-voice-coil driver is fed using an RCL-circuit, that can be tuned to realize almost similar filtering function than the circuits in Figures 4 and 5 provide.
For comparison, we assume that the same driver unit is used in Figures 4 and 6 (voice coils in series). Then, for a given sound level the electromotive forces induced in voice coil 4a in Fig. 4 are half of that induced in the driver in Fig. 6. Further, the force factor of coil 4a is half of the force factor in Fig. 6. Therefore, for a given level of EMF-derived sound effects, the EMF-generated currents passing through coil 4a in Fig. 4 must be 2-fold compared with the EMF-currents passing through the driver in Fig. 6. Thus, the impedance seen by voice coil 4a in Fig. 4 can be allowed to be less than 1/4 of that seen by the driver in Fig. 6 to maintain same sound quality. This advantage is enough in practice to make the dual coil method more ideal in performance compared with the single coil alternative.
The superiority of the dual coil method is especially clear at high frequencies. With the example values given, the impedance seen by voice coil 4a increases almost directly proportional to frequency already from about 1 kHz, whereas in Fig. 6 the impedance seen by the driver levels off at high frequencies to the sum of resistances R1 and R2 .
Supplements and Clarifications
The voice coils 4a and 4b don't need to be identical. By making the number of turns of the coils different, one can establish different attenuation factors. However, this is not necessarily very practical. The voice coils can also be connected in series already in the inner structure of the driver, thus saving one outcoming wire. Several dual voice coil drivers may also be used instead of one. Voice coil 4a can be a series or parallel combination of the first coils from several dual voice coil drivers, and voice coil 4b can be a combination of the second coils of the same drivers.
Parallel connection of voice coils can also be used on current-drive provided that the drivers are similar. When a disturbing EMF appears in one of the parallel-connected coils, the disturbance current generated by the EMF flows in opposite direction in the other voice coil, and therefore audible EMF-generated effects are largely canceled out, even though the true impedance seen by each voice coil is left relatively low.
The current-divider network 3 may also include drivers for other frequency bands and crossover filter circuits, to make up a multiway system. The principle of high source impedance, however, limits the preferred crossover designs to mostly 1st-order filters. (Corresponding limitation would also apply to voltage-driven systems, if one wanted to minimize the source impedance.) The response of driver 2 may also need correction to damp the fundamental resonance, by which reason the impedance seen by voice coils 4a and 4b may stay relatively low at bass frequencies.
It is also possible to realize the same compensation by using two single-coil driver units instead of one dual-coil unit. In certain conditions, this can yield even better EMF current suppression. However, using single-coil drivers in this manner is more expensive and space consuming and is not covered by the present invention.
When talking about dual voice coil drivers, it is meant that the coils are on the same coil former or actuate the same vibrating diaphragm. Hence, for instance, the bass and treble units of so-called coaxial drivers are in this regard different drivers.