This invention relates generally to a loudspeaker system, and more particularly to a loudspeaker system having an amplifier, post-amplifier passive filters, and multiple speaker drivers.
It may be difficult to produce a speaker driver that accurately reproduces the 20 Hz to 20 kHz frequency range (audible spectrum) of sound generally associated with human hearing. Therefore, speaker drivers have been produced that accurately reproduce a more limited range. These limited-range speaker drivers may be used in conjunction with one another to more accurately reproduce the full range of sound. For example, a full range loudspeaker system may include a low frequency speaker driver, a midrange frequency speaker driver, and a high frequency speaker driver.
Loudspeaker systems having two or more limited-range speaker drivers are known as “multi-way” loudspeaker systems. For example, a loudspeaker system having a low-frequency speaker driver and a high-frequency speaker driver is known as a “two-way” loudspeaker system. A loudspeaker system additionally having a mid-frequency speaker driver is known as a “three-way” loudspeaker system, and so on.
Because a limited-range speaker driver is designed to handle a particular range of frequencies, it may be desirable to filter frequencies outside of this particular range from the electrical signal driving the limited-range speaker driver. For example, a two-way loudspeaker system may include a low-pass filter and a high-pass filter. A three-way loudspeaker system may include a low-pass filter, a band-pass filter, and a high-pass filter. Multi-way loudspeaker systems having more than four different limited-range speaker drivers (four-way, five-way, etc.) may include multiple band-pass filters in addition to a low-pass filter and a high-pass filter.
Frequencies that are dividing points in a frequency range are known as crossover frequencies. For example, a two-way system may have one crossover frequency, so that frequencies above the crossover frequency are reproduced by a high-frequency speaker driver and frequencies below the crossover frequency are reproduced by a low-frequency speaker driver. Likewise, in a three-way loudspeaker system, it may be desirable to select two crossover frequencies, so that signals below the first crossover frequency drive the low-range speaker driver, signals above the first crossover frequency but below the second crossover frequency are sent to the mid-range speaker driver, and signals above the second crossover frequency drive the high-range speaker driver. Low-pass, band-pass, and high-pass filters used to filter signals for a multi-way loudspeaker system in this manner are known as crossover filters.
Crossover filters can be placed in a signal path between a signal source, such as a microphone, tape deck, compact disc player, or the like, and power amplifiers that provide power to a multi-way loudspeaker system. In such an arrangement, each power amplifier receives signals in a certain frequency range, and drives limited-range speaker drivers that operate in that frequency range. Alternatively, crossover filters can be placed in a signal path between a power amplifier and limited-range speaker drivers of a multi-way loudspeaker system. In the latter case, the crossover filters may be passive inductor-capacitor (LC) networks. The advantage of a post-amplifier crossover arrangement may be a reduced number of amplifiers in the sound system.
In a multi-way loudspeaker system using a post-amplifier crossover arrangement, it may be desirable to design crossover filters that achieve a flat response throughout a frequency range. To achieve a flat frequency response in a post-amplifier crossover arrangement, a crossover filter may be designed based on an impedance of a limited-range speaker driver that will operate with the crossover filter. For example a passive LC second order low-pass filter has all of its inductor (L) and capacitor (C) values chosen based upon the driver's impedance, say 4 Ohms. If the driver's impedance were to double and the crossover were to remain correctly tuned, the inductors would need to double in value and the capacitors would need to halve in value.
When a multi-way loudspeaker system using a post-amplifier passive crossover arrangement is operated at high levels for a period of time, the tonal quality of the loudspeaker system may become altered. It has been discovered that this alteration in response is due to changes in the impedances of speaker drivers in a multi-way loudspeaker system as the coils in the speaker drivers become hot. These changes in impedances may cause “bumps” in the frequency response of the multi-way loudspeaker systems, because the crossover filters are usually designed to operate with the “cold” impedances of the speaker drivers and may not be able to adjust inductance (L) and capacitance (C) values to compensate for the higher driver impedances. It would be desirable to provide a sound system that compensates for changes in speaker drivers' impedances in a multi-way loudspeaker system using a post-amplifier crossover arrangement.
A loudspeaker is provided for receiving an incoming electrical signal and transmitting an acoustical signal. The loudspeaker may include a power amplifier that receives the incoming electrical signal and provides a power signal to two or more passive filters, such as low-pass, band-pass, or high-pass filters, which are coupled to the output of the power amplifier. The passive filters may be coupled to one or more speaker drivers so that the arrangement of passive filters and speaker drivers has a single input with a single combined input impedance. The amplifier may have an output impedance between about 25% and about 400% of the combined input impedance of the arrangement of passive filters and speaker drivers. The power amplifier may include a current-feedback amplifier that is configured to maintain the desired impedance at the output.
Alternatively, the power amplifier may include a voltage-source amplifier and a “ballast” resistor in series with the output of the voltage-source amplifier. In this arrangement, the resistance of the ballast resistor may be between about 25% and about 400% of the combined input impedance of the arrangement of passive filters and speaker drivers.
When the power amplifier has an output impedance that is between a quarter and four times the impedance of the combined input impedance of the arrangement of passive filters and speaker drivers, impedance changes in the one or more speaker drivers may not affect the loudspeaker's frequency response as significantly as when the power amplifier has either an output impedance near zero (voltage source) or near infinity (current source).
Other systems, methods, features and advantages of the invention will be, or will become, apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the following claims.
The invention can be better understood with reference to the following figures. The components in the figures are not necessarily to scale; emphasis is instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views.
The speaker drivers 106 and 110 may each be either a wide-range speaker driver or a limited-range speaker driver, and may cover complimentary parts of the audible spectrum. The speaker drivers 106 and 110 may have coils (not shown) with respective impedances of ZA and ZB that may vary with, for example, coil frequency or temperature. The filters 104 and 108 may each be a high-pass, band-pass, or low-pass filter, and may be passive inductor-capacitor filters.
For example, the first filter 104 may include a fourth-order Butterworth low-pass filter, as shown in
As shown in
The first filter 104 may include an input 202 and an output 204. The input 202 may have an input impedance (as seen from the power amplifier 102 (
ωc=2*π*fc (1)
The inductor 206 may have an inductance of L1, the second inductor 208 may have an inductance of L2, the first capacitor 210 may have a capacitance of C1, and the second capacitor 212 may have a capacitance of C2. Where the first filter 104 is designed to have a zero Ohm input characteristic termination impedance at input 202, and an output characteristic termination impedance of RF1 at output 204, values for L1, L2, C1 and C2 may be determined as follows:
L1=(1.531*RF1)/ωc (2)
C1=1.577/(RF1*ωc) (3)
L2=(1.082*RF1)/ωc (4)
C2=0.383/(RF1*ωc) (5)
The equations (2)-(5) are equations for calculating component values for a fourth-order Butterworth filter. In other example filters, the components and equations for calculating the component values may be different. The first filter 104 may provide a filtered output signal to the speaker driver 106. The speaker driver 106 may have a “cold” impedance ZA of RF1, so that in this example the impedance of the first filter 104 is chosen to match the cold impedance of the first speaker driver 106.
Turning to
Where the second filter 108 is designed to have a zero Ohm input characteristic termination impedance at input 302, and an output characteristic termination impedance of RF2 at output 304, values for C1, C2, L1 and L2 may be determined as follows:
C1=0.653/(RF2*ωc) (6)
L1=0.634*RF2/ωc (7)
C2=0.924/(RF2*ωc) (8)
L2=2.613*RF2/ωc (9)
The equations (6)-(9) are equations for calculating component values for a fourth-order high-pass Butterworth filter. The second filter 108 may provide a filtered output signal to the second speaker driver 110. The second speaker driver 110 may have a cold impedance ZB of RF2, so that in this example the impedance of the second filter 108 is chosen to match the cold impedance of the second speaker driver 110.
As mentioned above, the loudspeaker system 100 may exhibit a degradation in tonal quality if the coils of the speaker drivers 106 and 110 become hot, and the impedances of the coils change. In laboratory experiments, impedances of speaker drivers were observed to increase by as much as 100%. For example, a speaker driver having a cold impedance of 4 Ohms may have an impedance of 8 Ohms when the coil is hot. Such heating may occur, for example, in professional sound reinforcement applications, where power amplifiers frequently produce more than a kilowatt of continuous power. The effect of speaker driver impedance changes on frequency response is described in detail below.
In this example, the cold and hot impedances of each speaker driver 106 and 110 are 4 Ohms and 8 Ohms, respectively. For cases where the speaker drivers 106 and 110 are heated to a lesser degree, the impedance increase may be less. The solutions disclosed for correcting tonal quality problems caused by impedance increases work equally well over a wide range of impedance increases, and the use of a 4 Ohm increase in this example should not be considered a limitation. As can be seen in
Many commercially available power amplifiers are “voltage source” amplifiers that have an output impedance that is near zero Ohms. A voltage source power amplifier 102 may have an output impedance of, for example, 5 milli-Ohms.
Plot lines 602 and 604 show the magnitudes of currents that flow through the first speaker driver 106 and plot lines 606 and 608 show the magnitudes of currents that flow through the second speaker driver 110. The intrinsic forcing function of a speaker driver is directly related to currents (Lorentz force) flowing through the speaker driver's coil, not voltages across the coil. For example, when the coil's impedance increases, but voltage driving the coil does not, there will be an attendant gain compression as a consequence of a reduction in the voice coil's current. Therefore, the gains of interest for determining how the loudspeaker system 100 “sounds” are current gains for the coils of the speaker drivers 106 and 110.
As can be seen in
The loudspeaker system 100 lessens frequency response variations, such as those shown in
The frequency response variations shown in
Alternatively, the frequency response variations may be lessened by using a voltage-source amplifier and a “ballast” resistor having an impedance about equal to the input impedance of the driver circuit 114, where the ballast resistor is coupled in series with the output of the voltage-source amplifier. Such a ballast resistor, however, may dissipate approximately half of the output power of the amplifier. The current-feedback power amplifier 102, on the other hand, may provide the desired output impedance with almost no power loss.
As shown in
V1(s)=Io(s)*Rs*KA (10)
The power amplifier 102 may also include a summer 416 and a feedback circuit 414. The feedback circuit 414 may have a transfer ratio of ZF(s) and generate a feedback signal V2(s). Therefore, the transfer ratio of ZF(s) of the feedback circuit 414 may be:
ZF(s)=V2(s)/V1(s) (11)
The summer 416 may receive the input signal Vi(s) and sum it with the feedback signal V2(s) from the feedback circuit 414. Therefore, the output signal Vo(s) may be represented as:
Vo(s)=[G*Vi(s)]+[G*Io(s)*Rs*KA*ZF(s)] (12)
Because impedance is equal to voltage divided by current, the output 404 may have an output impedance of Zo(s) that can be expressed as:
Zo(s)=Vo(s)/Io(s) (13)
Solving equations (10) through (13) for Vi(s)=0, Zo(s) may be also be expressed as:
Zo(s)=G*Rs*KA*ZF(s) (14)
As shown by equation (14), the power amplifier 102 may be designed to have a desired output impedance Zo(s) by choosing a feedback circuit 414 having a transfer ratio of like form. The product G*Rs*KA may be approximately unity, in which case the output impedance Zo(s) is equal to the transfer ratio ZF(s).
The relative flatness between the hot frequency response plots 904 and 908 and the cold frequency response plots 902 and 906 is more clearly shown in
As mentioned above, the output impedance Zo(s) of the power amplifier 102 may be designed to be more or less than the cold input impedance of the driver circuit 114. Other values for the output impedances Zo(s), such as 2 Ohms and 8 Ohms, also provide flatter relative frequency responses than a voltage-source amplifier provides. Where 2 Ohms is used for the output impedance Zo(s) of the power amplifier 102, however, the relative frequency response may be under compensated, resulting in a “valley” at the cutoff frequency with two adjacent “bumps” that are about 2 dB above the valley. This result, while not ideal, may still be significantly better than the relative frequency response shown in
Where 8 Ohms is used for the output impedance Zo(s) of the power amplifier 102, the relative frequency response may be over compensated, resulting in a “bump” at the cutoff frequency with two adjacent “valleys” that are about 2 dB below the bump. Again, this result may not be ideal, but may still be significantly better than the relative frequency response shown in
In conclusion, matching an output impedance of an amplifier to a cold input impedance of an arrangement of filters and speaker drivers that is coupled to the output of the amplifier compensates for frequency response changes that may result when the voice coils of the speaker drivers become heated. The loudspeaker system 100 is one such matched configuration that includes a current-feedback amplifier, two speaker drivers, and two fourth-order Butterworth filters. The loudspeaker system 100, however, could also comprise other types of filters, and/or more filters and speaker drivers.
For example, when using odd order filters, it may not be possible to obtain a completely flat relative frequency response by impedance matching alone. In such cases, it may be desirable to match the output impedance for the amplifier 102 to a “nominal working” input impedance of the driver circuit 114, which is somewhere between a hot and a cold input impedance, so that the hot and cold frequency responses are above and below the nominal frequency response.
While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible that are within the scope of this invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.
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