FIELD OF DISCLOSURE 
     This disclosure relates to audio amplifiers, and in particular, to power supplies for such amplifiers. 
     BACKGROUND 
     Known audio amplifiers include those in which amplifying units can be configured by a user to drive speakers. Since it is not known in advance how the user will ultimately connect the amplifying units, it can be difficult to know in advance how much current the power supply should be capable of handling. 
     It is possible to simply provide the power supply with components that can handle even the most taxing configurations. But such configurations are rarely encountered in practice. Therefore, it is economically wasteful to adopt such a solution. 
     SUMMARY 
     The invention is based in part on the recognition that there exists a need to protect a power supply against excessive current draw, but without having to over-engineer the amplifier. 
     In one aspect, the invention features an apparatus for driving speakers. Such an apparatus includes amplifier cells, each of being connected between first and second power rails. The amplifier cells are user-configurable for driving selected speakers. The apparatus also includes a synchronous rectifier circuit for providing current on the power rails for consumption by all the amplifier cells. This current depends on a user-defined configuration of the amplifier cells relative to the speakers. The apparatus further includes a control system for implementing a model of the synchronous rectifier circuit and the amplifier cells. This control system is configured to control an audio input signal in response to information concerning electrical outputs of the amplifier cells, thereby limiting current drawn from the synchronous rectifier circuit. 
     In some embodiments, the control system includes a feedback control system having two feedback loops. A first feedback loop is associated with electrical power processed by the synchronous rectifier circuit, and a second feedback loop is associated with controlling a temperature of the synchronous rectifier circuit. 
     In some embodiments, the model includes a thermal model for estimating a temperature based on an estimate of dissipated by the rectifier circuit. Among these embodiments are those in which the model further includes a temperature controller for receiving a difference between the estimated temperature provided by the thermal model and a maximum permissible temperature, and estimating, therefrom, a maximum power dissipation. 
     Additional embodiments are those in which the model includes a rectifier power dissipation model that provides an estimate of total power dissipated by the rectifier circuit as a function of the electrical outputs of the amplifier cells. Among these embodiments is a first set of embodiments which includes those embodiments in which the power dissipation model is configured to generate a first current by filtering the sum of the powers dissipated by each amplifier cell by a first time constant and to generate a second current by filtering the sum of the currents output from each amplifier cell by a second time constant that is shorter than the first time constant. Within this first set of embodiments is a second set of embodiments in which the power dissipation model is also configured to determine a first rail current by summing the first and second currents and to determine a second rail current by calculating a difference between the first and second current. Within this second set of embodiments is a third set of embodiments in which the power dissipation model is further configured to determine switching losses and conductive losses associated with the first rail current, and also to determine switching losses and conductive losses associated with the second rail current. Within this third set of embodiments is a fourth set of embodiments in which the power dissipation model is configured to output the larger of the sum of switching losses and conductive losses associated with the first rail current and the sum of the switching losses and conductive losses associated with the second rail current. 
     In another aspect, the invention features an apparatus for driving speakers. Such an apparatus includes amplifier cells, each of which is connected between a positive rail and a negative rail. The amplifier cells are user-configurable for driving selected speakers. The apparatus also includes a synchronous rectifier circuit for providing current on the positive rail and on the negative rail for consumption by the amplifier cells. This current depends on a user-defined configuration of the amplifier cells relative to the speakers. The apparatus also includes a rectifier power dissipation model that provides an estimate of total power dissipated by the rectifier circuit as a function of electrical outputs of the amplifier cells; a thermal model for estimating a temperature based on the estimate provided by the rectifier circuit; a temperature controller for receiving a difference between the estimated temperature provided by the thermal model and a maximum permissible temperature, and estimating, therefrom, a maximum permissible power dissipation; a power dissipation controller for receiving a difference between the maximum permissible power dissipation and the estimate of total power dissipated by the rectifier circuit; and a limiter for receiving a gain control signal from the power dissipation controller and applying the gain control to an audio signal to limit power dissipation by the synchronous rectifier circuit. 
     In some embodiments, the rectifier power dissipation model is configured to generate a slow current by filtering a sum of powers dissipated by each amplifier cell by a slow time constant and to generate a fast current by filtering a sum of currents output from each amplifier cell by a fast time constant. Among these embodiments are a first set of embodiments in which the power dissipation model is further configured to determine a positive-rail current by summing the slow current and the fast current, and to determine a negative-rail current by calculating a difference between the slow current and the fast current. Among the embodiments in this first set are those in a second set of embodiments, in which the power dissipation model is further configured to determine switching losses and conductive losses associated with the positive-rail current, and determine switching losses and conductive losses. Within this second set of embodiments is a third set of embodiments, which includes those embodiments in which the power dissipation model is configured to output the larger of a sum of the switching losses and conductive losses associated with the first rail current, and a sum of the switching losses and conductive losses associated with the second rail current. 
     In another aspect, the invention features an apparatus for driving speakers. Such an apparatus includes a plurality of amplifier cells, each of which is connected between a first power rail and a second rail. These amplifier cells are user-configurable for driving selected speakers. The apparatus further includes means for providing current for consumption by all the amplifier cells. This current depends on a user-defined configuration of the amplifier cells relative to the speakers. Also included in the apparatus is a means for controlling the means for providing current to limit current provided by the means for providing current in response to information concerning electrical outputs of the amplifier cells. 
     Among the embodiments of the apparatus are those in which the means for controlling includes means for controlling an input audio signal in response to the information concerning the electrical output. 
     These and other features of the invention will be apparent from the following detailed description, and the accompanying figures, in which: 
    
    
     
       DESCRIPTION OF THE FIGURES 
         FIG. 1  shows an amplifier configured to drive a set of speakers; 
         FIG. 2  shows a power supply for the amplifier of  FIG. 1 ; 
         FIG. 3  shows a four-quadrant isolation converter used in the power supply of  FIG. 2 ; 
         FIG. 4  shows current on positive and negative rails drawn by the amplifier cells of  FIG. 1 ; 
         FIG. 5  shows steps in determining whether to limit the output of the rectifier shown in  FIG. 3 ; 
         FIG. 6  is a block diagram of a feedback control system for controlling the output of the rectifier shown in  FIG. 3 ; 
         FIG. 7  is a diagram of a rectifier power dissipation model suitable for incorporation into the feedback control system of  FIG. 6 ; 
         FIG. 8  shows an amplifier cell from  FIG. 1  driving a speaker; 
         FIG. 9  is a dynamic model of the power supply shown in  FIG. 2 ; and 
         FIG. 10  is a thermal model used in the control system used in  FIG. 6 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows an amplifier  10  having multiple half bridge unit amplifier cells  12  that can be configured by a user to drive multiple speakers  14  in various configurations. The particular example shows eight amplifier cells  12  each of which drives a corresponding speaker  14  in a half-bridge configuration. Such an amplifier  10  is described in more detail in U.S. application Ser. No. 12/717,198, filed on Mar. 4, 2010 and entitled “Versatile Audio Power Amplifier,” the contents of which are herein incorporated by reference. 
     The amplifier cells  12  are controlled by a control system  16  that either converts analog input into a digital input using an A/D converter  18 , or receives a digital input directly. In either case, a digital audio input  19  is ultimately provided to a digital signal processor (DSP)  20  controlled by a microcontroller  22 . The DSP  20  provides time-division multiplexing (“TDM”) commands to the amplifier cells  12  and also receives, from each amplifier cell  12 , information about the electrical output (i.e. voltage and current) of that cell  12 . The amplifier cells  12  receive power via a shared positive rail  24  and a shared negative rail  26 . 
     Referring to  FIG. 2 , a power supply  28  maintains each of these rails  24 ,  26  at an operating voltage. In the embodiment shown, the operating voltages are +80 volts and −80 volts. In particular, first and third rectifier transistors  44 A,  44 C process power on the positive rail  24 , while second and fourth rectifier transistors  44 B,  44 D process power on the negative rail  26 . 
     The power supply  28  features a power factor correction block  30  that eliminates non-sinusoidal components from an AC input and outputs a boosted DC voltage across a capacitor  32 . This DC voltage becomes the input to a four quadrant isolation converter  34 , the details of which are shown in more detail in  FIG. 3 . The isolation converter  34  maintains a voltage across the positive and negative rails  24 ,  26 , shown in  FIG. 3  with their respective intrinsic capacitances,  25 ,  27 . 
     A controller  36  controls operation of the power factor correction block  30  based on monitored values of its input and output. In the typical embodiment shown, the power factor correction block  30  accepts an AC input between 90 and 264 VAC and provides a 400 V DC signal across the capacitor  32 . 
     Referring next to  FIG. 3 , the isolation converter  34  features an input inverter  38  having four inverter field-effect transistors (FETs)  40 A-D that switch on and off in a coordinated way to convert the DC voltage provided by the power factor correction block  30  into an AC voltage. This AC voltage couples to an output rectifier  42  having four rectifier transistors  44 A-D across a transformer  46  having a primary winding  47  and two secondary windings  49 A-B. The four rectifier transistors  44 A-D likewise switch on and off in a coordinated manner to place an output DC voltage across the positive and negative rails  24 ,  26 . In particular, first and third rectifier transistors  44 A,  44 C process power on the positive rail  24  and second and fourth rectifier transistors  44 B,  44 D process power on the negative rail  26 . 
     A difficulty that arises in certain configurations of the amplifier cells  12  impose considerable thermal stress on the four rectifier transistors  44 A-D. For example, in a sensible configuration, low frequency sources would be driven across a pair of amplifier cells  12  connected as a bridge-tied load (“BTL”) pair. However, because the amplifier  10  is freely configurable by a user, nothing in principle would prevent the user from configuring the amplifier cells  12  as shown in  FIG. 1  and applying a bass-rich signal long enough to overheat the output rectifier  42 . 
       FIG. 4  illustrates the difficulty that can arise in one example. The vertical axis of  FIG. 4  represents the sum of all currents drawn by the amplifier  10  as a function of output amplifier voltage. when driving a worst-case load (about 2.7 ohms). With the output amplifier voltage at approximately 50 volts, an 80 volt positive rail  24  would source approximately 125 amps, while at the same time, approximately an additional 25 amps is sunk on the negative rail  26 . Thus, the output rectifier  42  would process approximately 12 kilowatts of power. If high frequencies dominate the spectrum of the audio signal, much of the current would be sourced by bus capacitances downstream from the output rectifier  42 . However, as discussed below in connection with  FIG. 9 , in the event that low frequencies dominate the spectrum, much of this current would pass through the rectifier transistors  44 A-D. This current can overheat, and possibly damage, the rectifier transistors  44 A-D. 
     One approach to overcoming this difficulty would be to simply design the rectifier  42  to handle larger currents with ease. This can be done by using rectifier transistors  44 A-D with higher current ratings, larger heat sinks, fans, and even liquid cooling systems. 
     On the other hand, the configuration shown in  FIG. 1  would not be regarded as good practice to begin with. Under these circumstances, it would seem wasteful to accommodate this and other unusual configurations using expensive and bulky components. 
     Another approach to overcoming the foregoing difficulty would be to measure the rectifier current and to provide some mechanism for limiting dangerously high values of that current. However, rectifier currents can be quite large, on the order of hundreds of amperes. Current sensors for measuring such currents would be large and expensive. 
     Yet another approach to overcoming the above difficulty is to exploit the information already being provided to the control system  16  concerning the electrical output at each of the amplifier cells  12 , as shown in  FIG. 1 . Given an appropriate model, this information can be used to obtain a real time estimate of current supplied by the rectifier  42 . 
     As shown in  FIG. 5 , the individual output voltage and current measurements  48  provided to the control system  16  are used to calculate the current drawn from the output rectifier  42  (step  50 ). Based on this estimate, a prediction is made (step  52 ) concerning the power dissipated by the output rectifier  42 . This prediction is then used, in conjunction with a model of the rectifier&#39;s properties and those of its associated power dissipation system, to predict the rectifier&#39;s operating temperature (step  54 ). Using both the prediction of the rectifier&#39;s power dissipation and that of its operating temperature, a decision is made (step  56 ) concerning whether or not to control or limit the audio input signal  19  to limit current drawn from the output rectifier  42 . This decision is then provided to a limiter  58  as needed. 
       FIG. 6  shows a nested feedback loop implemented by the control system  16  to regulate the temperature of the output rectifier  42 . The feedback loop outputs an audio gain reduction factor  60  to be applied to all amplifier cells  12  simultaneously. This audio gain reduction factor  60  is calculated based on both the power dissipated  62  by the output rectifier  42  and on a predicted die temperature  64  of the rectifier transistors  44 A-D. 
     In the illustrated feedback loop, measurements  48  of voltage and current from each amplifier cell  12  are provided to a rectifier power dissipation model  66 . Based on these measurements, the rectifier power dissipation model  66  determines the total electrical power being processed by the rectifier transistors  44 A- 44 D and estimates the thermal power, Pd, being dissipated by the rectifier transistors  44 A- 44 D during the course of processing that electrical power. This estimate is provided to a thermal model  68  that estimates the junction temperatures at each of the rectifier transistors  44 A-D. The highest of these temperatures, T j , is the output of the thermal model  68 . This output is provided to a first summing node  69  that compares it with a maximum temperature, T max . The difference between the two, T e , is provided to a temperature controller  70 , which calculates based on that difference the maximum power, P max , that should be dissipated by the rectifier  42 . 
     The thermal model  68 , the first summing node  69 , and the temperature controller  70  thus form the outer loop. This outer loop ensures that an estimate of the highest junction temperature, T j , within a rectifier transistor  44 A-D never exceeds a specified upper limit, T max . 
     The estimate  62  of power dissipated from the rectifier power dissipation model  66  is also provided to a second summing node  72 , where it is compared with the maximum permissible power dissipation, as calculated by the outer loop. The difference between the two provides a basis for a power dissipation controller  74  to choose a gain reduction factor  60  to apply to all amplifier cells  12 . This gain reduction factor  60  ranges from zero to one. It takes on the value of unity when the power being dissipated is less than the maximum permitted power dissipation. 
     The second summing node  72  and the power dissipation controller  74  thus define an inner loop. This inner loop does not directly control temperature. It simply ensures that the rectifier  42  always dissipates an amount of power that is less than an allowable maximum value. This maximum value, meanwhile, comes from the outer loop. 
     A variety of ways can be used to implement the rectifier power dissipation model  66  shown in  FIG. 6 . However, in at least one embodiment, shown in  FIG. 7 , the individual voltage and current measurements  48  are combined to generate a “slow” current and a “fast” current. The sum of the slow and fast currents is the total current provided by the rectifier  42  on the positive rail  24 ; the difference between the slow and fast components is the total current provided by the rectifier  42  on the negative rail  26 . 
     The terms “slow” and “fast” arise from the dynamics of energy transfer within the four quadrant isolation converter  34 , shown in  FIG. 3 . In particular, the fast time constant arises from energy transferred between the positive and negative rails  24 ,  26 , whereas the slow time constant arises from energy transferred across the transformer  46  from the primary winding  47  to the secondary windings  49 A,  49 B. As discussed below and shown in  FIG. 7 , the slow time constant is used to derive the slow current and the fast time constant is used to derive the fast current. 
     The slow current is proportional to the amplifier&#39;s total power output. This slow current causes real power to be drawn from the rectifier  42 . The fast current corresponds to the total current output of all amplifier cells  12 . This fast current circulates through the rectifier  42  and causes heating of the rectifier transistors  44 A-D and the transformer  46 , but not of the power supply  28  as a whole. It is this current that is reduced when a speaker  14  is driven in a full bridge configuration rather than a half bridge configuration, and it is primarily for this reason that rectifier heating tends to be lower when a speaker  14  is driven by a fully bridged amplifier. 
     Referring now to  FIG. 7 , the rectifier power dissipation model  66  includes multipliers  76 , one for each amplifier cell  12 , for multiplying voltage and current from each amplifier cell  12  to obtain that cell&#39;s power output. The resulting individual powers from each amplifier cell  12  are summed together at a first summer  78  to generate a total power. Meanwhile, the individual currents at each amplifier cell  12  are summed together at a second summer  80  to generate a total current. 
     The total power and total current are each weighted by different time constants. In particular, the total power is weighted by the slow time constant  82  whereas the total current is weighted by the fast time constant  84 . In a typical embodiment, the slow time constant is approximately 5.8 ms and the fast time constant is approximately 0.8 ms. Details concerning where these time constants originate are provided below. 
     First and second scaling modules  86 ,  88  then scale the weighted total power and current to yield the slow and fast currents respectively. The first scaling module  86  scales its input by the inverse of the voltage difference between the negative and positive rail, 2B, to convert power back into current. 
     A first summer  90  then combines the slow and fast currents to determine the current, I pos , on the positive rail  24 . Meanwhile, a second summer  92  evaluates a difference between the slow and fast currents to determine the current, I NEG , on the negative rail  26 . 
     The first and second time constants can be derived from consideration of  FIG. 9 , which models the dynamics of the four-quadrant isolation converter  34  shown in  FIG. 3 . In  FIG. 9 , the current IB 1  represents the sum of the currents drawn from the positive rail  24  by all of the amplifier cells  12 , and the current IB 2  represents the sum of the currents drawn from the negative rail  26  by all of the amplifier cells  12 . Capacitances C 1  and C 2  represent the total bus filter capacitance on the rails  24 ,  26 . The resistances R 1 , R 2  and R 3  represent the effective coupling impedance imposed by the resistance and leakage inductance of the transformer  46  and the resistance of the transistors in the isolation converter  34 . The real resistances combine with the leakage inductances of the transformer which, at the typical operating frequency of 350 kHz, look like lossless resistors (i.e., a component in which voltage is proportional to current, but no power is dissipated). These impedances and capacitances act together to produce a system with a slow and a fast time constant. 
     Because of large bypass capacitors C 1  and C 2  between the rails  24 ,  26  and ground, and because of the effective coupling impedances R 1 , R 2  and R 3 , associated with the transformer  46 , the rail currents supplied by the rectifier transistors  44 A-D, Ipos and Ineg are filtered versions of the currents actually on the rails  24 ,  26 , namely IB 1  and IB 2 . At low frequencies, Ipos and Ineg are almost the same as IB 1  and IB 2 . This means that most of the current will be supplied from the rectifier transistors  44 A-D. At high frequencies, most of the current will be supplied from the intrinsic rail capacitances C 1  and C 2 . It is in part for this reason that sustained low frequency audio signals pose difficulty for the rectifier transistors  44 A-D. 
     The fast time constant comes from the loop in  FIG. 9  that includes the rail capacitances C 1  and C 2 , and the impedances coupling the two rails, R 1  and R 2 . Assuming a total resistance of 0.05 ohms and a capacitance of 0.0167 farads, the time constant is (R 1 +R 2 )*(C 1 *C 2 /(C 1 +C 2 )), or 0.8 ms. The slow time constant comes from a loop in  FIG. 9  that also includes R 3 , the impedance coupling the secondary windings  49 A,  49 B to the primary winding  47 . This time constant is (R 1 *R 21 (R 1 +R 2 )+R 3 )*(C 1 +C 2 ), which, for R 3 =0.075 ohms, yields a time constant of 5.8 ms. These time constants are long enough so that frequency components above about 1 kHz contribute very little to the peak currents, thus reducing the rate at which computations need to be performed. 
     Referring again to  FIG. 7 , two power loss models  94 ,  96  model the power dissipated in the rectifier transistors  44 A-D as a sum of conduction losses and switching losses. The conduction loss is modeled as the product of the square of the current magnitude and a first constant, C 1 . The switching loss is modeled as the product of a second constant, C 2 , and the magnitude of the current. The first constant depends on the drain-source resistance Rds(on) of the rectifier transistors  44 A,  44 B,  44 C,  44 D and is corrected for duty cycle, which is usually about 40% on and 60% off. The second constant depends on switching frequency, rail voltage, and switching time, with switching time usually being obtained from measurements. The conduction loss and switching loss for the first and third rectifier transistors  44 A,  44 C, which are associated with the positive rail  24 , and similar losses for the second and fourth rectifier transistors  44 B,  44 D associated with the negative rail  26 , are combined at corresponding third and fourth summers  98 ,  100 . The power dissipated by the transistors on the positive rail  24  and the power dissipated by the transistors on the negative rail  26  are then compared at a comparator  102 . The larger of the two becomes the output of the rectifier dissipation model  66  shown in  FIG. 6 . 
     The overall transfer function of the rectifier power dissipation mode  66  is a decidedly nonlinear one. The nonlinearity has a multiplicative component that affects the amplitude of the signal and an absolute component that shifts frequency up by a factor of two or higher. The first component can be dealt with by small signal modeling at different operating points, but the second component cannot. 
     One approach to determining the overall transfer function is to assume that the frequency nonlinearity amounts to only a doubling of frequency, and to continue to use small signal models for different operating points subject to that assumption. This would provide a corresponding transfer function at each operating point. If the dynamic response does not change significantly within a 6-12 dB frequency range, such a model can then be used as a reasonable starting point for conservative controller design, which can then be further tuned in simulations with a full nonlinear model. 
     Referring back to  FIG. 6 , the power dissipation controller  74  that ultimately relies on the output of the power dissipation model  66  is typically a proportional-integral controller. To ensures that it also works for the lower operating points, the power dissipation controller  74  is designed for the highest of the foregoing operating points. The power dissipation controller rectifier  74  can then be further tuned in full scale nonlinear simulations for optimal performance (i.e. a higher bandwidth and higher open loop gain at low frequencies). The resulting controller  74  can be expected to achieve over 100 Hz of 3 dB bandwidth. 
     The thermal model  68  can be modeled as an equivalent electric circuit, as shown in  FIG. 10 . In the thermal model  68  shown in  FIG. 10 , power corresponds to current and voltage corresponds to temperature. The capacitance C FET  and inductance THETA FET-Hs  are first order approximations of the thermal impedance between the junction in a rectifier transistor  44 A-D and its corresponding heat sink. This thermal impedance is obtained from the transistor&#39;s device data sheet. 
     Referring back to  FIG. 6 , for simplicity, the temperature controller  70  can be a proportional controller since the maximum temperature T max  is fixed, and can be set to account for DC error arising from limited low frequency gain. The temperature controller  70  can thus be tuned for a narrow bandwidth of 2-3 Hz.
An apparatus for driving speakers includes user-configurable amplifier cells for driving selected speakers, a synchronous rectifier circuit, and a control system. Each cell connects between power rails. The rectifier circuit provides current on the rails for consumption by the cells. The current depends on the configuration. The control system implements a model of the rectifier circuit and cells and uses it to control an audio input signal in response to information concerning electrical outputs of the amplifier cells. This indirectly limits current drawn from the synchronous rectifier circuit.