Patent Publication Number: US-2022240358-A1

Title: Current-splitter circuit for led lighting systems

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Application No. 63/140,772, filed Jan. 22, 2021, the contents of which are incorporated herein. 
    
    
     TECHNICAL FIELD 
     The invention relates to electric circuits, specifically switching circuits and methods for splitting current at high frequencies, including cascoded transistor arrangements. 
     BACKGROUND OF THE INVENTION 
     In electronics, transistors are circuit elements which use an electric field to control a flow of current. They include bipolar junction transistors (BJTs) and field-effect transistors (FETs) which are unipolar. A common type of FET used is the metal-oxide-semiconductor field-effect transistor (MOSFET). In typical operation a BJT allows a small amount of current applied at its base lead to control a much larger flow of current between its emitter and collector leads. Similarly, a FET allows a voltage applied to its gate terminal to control current flow between its source and drain terminals. These characteristics of transistors are useful in building amplifying or switching circuits. BJTs being bipolar, both electrons and electron holes are used as charge carriers. An abundance of either carrier can be created in a semiconductor, leading to p-type having electron holes and n-type having mobile electrons. BJTs can be arranged in PNP or NPN configurations. 
     One drawback of some single-stage amplifiers is that they are subject to the Miller effect, which is the increased effective capacitance seen by inverting amplifiers such as common-emitter or common-source amplifiers, built with BJTs or FETs, respectively. The Miller effect reduces the bandwidth of such amplifiers by degrading performance at high frequencies. One arrangement used to mitigate the Miller effect is a two-stage amplifier called a cascode, which consists of a common-emitter stage feeding into a common-base stage if built with BJTs or a common-source stage feeding into a common-gate stage if built with FETs. The purpose of the cascode is to improve input-output isolation, reducing feedback and improving stability and bandwidth. 
     A circuit for splitting high-voltage currents with a wide bandwidth is disclosed in U.S. Pat. No. 10,615,132, issued to the current inventor, but would consume too much power for the application at hand and must be substantially modified. Referring to  FIG. 1 , the approach used in U.S. Pat. No. 10,615,132 is branches of cascoded elements, such as the cascode linking elements X 14  and M 4 , to ensure high-voltage capability and current accuracy. Elements M 1 , M 2 , M 3  and M 4  of  FIG. 1  are MOSFET transistors in common gate configurations with a primary leg to perform current mirroring. Diodes  106 A- 106 D are biased such that the lowest drain potential will determine the gate voltage. 
     What is desired is a low-cost circuit and method to split currents of about 100 mA-5 A into a plurality of branches with low power consumption and sufficient bandwidth to accommodate a pulse-width modulated (PWM) signal with a base frequency in the kHz. The invention provides such a solution. 
     SUMMARY OF THE INVENTION 
     The invention is a low-cost, low-power circuit and method of splitting a primary current into multiple branches, nominally four, such that the current in each branch does not exceed a given maximum value and having good performance given a relatively high-frequency PWM input signal, for use in a high-efficiency LED lighting system. The circuit and method improve on the circuit and method disclosed in U.S. Pat. No. 10,615,132 by the present inventor. Specifically, the invention comprises a plurality of branches, each further comprising a plurality of LED elements, coupled to each other in a current-mirroring arrangement. Multiple implementations of the concept are presented as different embodiments of the invention and variations on the same. 
     The invention minimizes power loss by ensuring saturation of one of the bipolar transistors acting as self-biased current mirrors. The invention demonstrates power loss on the order of 100-200 mW per branch when said branch is subjected to current of ˜500-1000 mA. The invention can be scaled up or down to perform similar tasks at smaller or higher currents. Other applications than LED string lighting systems are equally possible. The invention allows for efficiencies greater than 99% in systems where stringed LED voltages are ˜40V. 
     To those skilled in the art to which this invention relates, many changes in construction and widely differing embodiments and applications of the invention will suggest themselves without departing from the scope of the invention as defined herein. The disclosures and the descriptions herein are purely illustrative and are not intended to be in any sense limiting. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the invention including the features, advantages and specific embodiments, reference is made to the following detailed description along with accompanying Figures, in which: 
         FIG. 1  illustrates a high-voltage current splitter (prior art); 
         FIG. 2  is a low-power current-matching circuit using bipolar transistors and Schottky diodes, in a first embodiment of the invention; 
         FIG. 3  is a low-power current-matching circuit using cascoded BFI&#39;s, in a third embodiment of the invention; 
         FIG. 4  is an expanded view of a circuit similar to that of  FIG. 2  showing the full branches, LED elements, and an additional stage, in a first embodiment of the invention; 
         FIG. 5  isolates one branch of the circuit of  FIGS. 2 and 4 , in a first embodiment of the invention; 
         FIG. 6  provides a schematic of a pair of current splitters in the first embodiment of the invention; 
         FIG. 7  provides a schematic of a pair of current splitters in the second embodiment of the invention; 
         FIG. 8  provides a schematic of a pair of current splitters in the third embodiment of the invention; 
         FIG. 9  provides a schematic of one branch of an error-detecting current splitter in a fourth embodiment of the invention; 
         FIG. 10  is a graph of showing collector currents versus collector voltage at identically stepped base-currents for two (2) NPN transistors of different layout styles using BiCMOS technology 
         FIG. 11  is a variation of the first embodiment of  FIG. 2  in which the Schottky diode is replaced by a PMOS transistor; 
         FIG. 12  is a variation of the first embodiment of  FIG. 2  in which the Schottky diode is replaced by a PNP BJT; 
         FIG. 13  is a circuit diagram illustrating a low-power current-matching circuit using a Darlington configuration; 
         FIGS. 14A-14D  are a set of graphs showing the voltage and current performance of a single branch of the circuit of  FIG. 13 ; 
         FIG. 15  is a circuit diagram illustrating a low-power current-matching circuit using a Darlington configuration with an additional cascode transistor; 
         FIG. 16  is a circuit diagram illustrating a low-power current-matching circuit using a Darlington configuration using an NMOS transistor; and 
         FIG. 17  is circuit diagram of a current dividing circuit diagram formed in an integrated circuit with external resistors. 
     
    
    
     DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
     While the making and using of the disclosed embodiments of the invention is discussed in detail below, it should be appreciated that the invention provides many applicable inventive concepts which can be embodied in a wide variety of specific contexts. Some features of the preferred embodiments shown and discussed may be simplified or exaggerated for illustrating the principles of the invention. 
     The invention is a circuit and method to split a primary current of 2400 milliamps (mA) into 4 branches of 600 mA each such that no branch current ever exceeds 700 mA. The circuit and method can be extended to primary currents between 100 mA to 5 Amperes (A). The immediate application of said circuit is to power a plurality of light emitting diodes (LED) on each branch. Said circuit and method must be capable of handling pulse-width modulated (PWM) signals with frequencies in the kHz range and pulse width in the uSec range. 
     In the invention, currents are on the order of 1 A so the circuit disclosed in  FIG. 1  can be improved by using BJTs to perform the primary current mirroring function. Bipolar transistors have properties which are conducive to the goal of a low-power current splitter, namely: their ability to conduct large currents at low collector voltages, intrinsically good matching and tighter base-to-emitter voltage (V be ) distributions compared to MOSFETs&#39; gate-to-source voltage (V gs ) distributions. 
       FIG. 2  shows a low-power current splitter stage consisting of two current splitters built using BJTs and Schottky diodes as a first embodiment of the invention. Referring to  FIG. 2 , additional identical stages would be connected at  200 ;  201   a  and  201   b  lead to branch A and branch B, respectively, each branch comprising an electrical load consisting of a plurality of LEDs connected in series as seen in  FIG. 4 ;  202  leads to V ss , the source voltage or ground. In the circuit shown in  FIG. 2 , a bias current from  207   a ,  207   b  passed through the bias resistor  203   a ,  203   b , biases the base-emitter junctions of NPN-type BJT  204   a ,  204   b , respectively. If this bias current at a given BJT is larger than its collector current divided by its current gain β, i.e. if I bias, A &gt;I collector, A /β A  or if I bias, B &gt;I collector, B /β B  and the two loads are not exactly the same, one of the two BJTs will be saturated, forward biasing either diode  205   a  or  205   b . This diode current will reduce the net transistor base current until it reaches the base current required for the non-saturated BJT to drive its load at the minimum possible voltage. Nominally the emitter resistors  206   a  and  206   b  are sized so that about 100-150 mV potential drop is present across each. In the case that the two loads are identical, both diodes  205   a  and  205   b  will conduct forward current and both BJTs  204   a  and  204   b  will be operating in saturation mode, leading again to minimum power consumption. 
     To best match currents at branch connections  201   a  and  201   b  with the method of  FIG. 2 , the transistors should have large current gain factors and low saturation voltage, and the diodes should have low forward voltage thresholds V f . Schottky diodes work well for this purpose. Additionally a large Early voltage is required of the chosen BJT such that the collector currents remain closely matched in the event their potentials are several volts apart. A large current gain factor ensures that changes in the bias current do not substantially affect the branch current. The low saturation and low diode forward voltage work together to keep collector current from saturating even when current flows forward in one of the diodes, such that the sum of saturation voltage and forward voltage is less than the base-to-emitter voltage at currents in the range of interest of the invention. Either or both diodes  205   a ,  205   b  can also be replaced by a transistor configured as a diode, accomplished by shorting the base lead to the collector lead if using a BJT or the gate terminal to the drain terminal if using a MOSFET. 
     In a second embodiment of the invention, the diodes  205   a ,  205   b  can be omitted entirely, in which case one base-collector junction will act as the forward diode and place the transistor with the lowest collector voltage in saturation. This would not be possible using MOSFETs as the gate current is effectively zero. The disadvantage to this configuration is that the collector current in the branch with the saturated transistor will be reduced, resulting in degraded current matching performance. In addition, the saturated transistor will lead to lower collector voltage and reduced power at all transistors. In cases where matching requirements are not strict and omitting components is desirable due to cost or space considerations this may be acceptable. 
     In a third embodiment of the invention, if better current matching performance is required, a cascoded circuit may be used in a manner similar to that of  FIG. 1 , but substituting BJTs for MOSFETs. Referring to  FIG. 3 , only one diode  305   a  or  305   b  is used to separate the cascoded transistors  304   a  and  308   a  or  304   b  and  308   b , respectively. The base-collector diode  205   a ,  205   b  is omitted as the cascoded transistor base-emitter junction  310   a ,  310   b  serves the same function. The resistors  303   a ,  303   b  can be omitted from the method of  FIG. 3  provided resistors  309   a ,  309   b  are sized to supply an appropriate base current to both cascoded transistors. Bias current enters from  311   a ,  311   b . Diodes  305   a ,  305   b  can be selected to ensure very low collector voltage for both BJTs  304   a ,  304   b , such that said BJTs are operating near saturation when loads are balanced at the current of interest. A diode  305   a ,  305   b  forward voltage equal to or slightly greater than the saturation voltage of its associated BJT  304   a  or  304   b  will result in good performance and relatively low power consumption. 
       FIG. 4  shows the expanded inputs and outputs to the current splitter configuration of  FIG. 2 or 3 , including the full branches  400   a ,  400   b ,  400   c ,  400   d , each having a load comprising a plurality of LED elements  401 , and an additional stage  402  corresponding to branches  400   e ,  400   d . The block  403  represents a circuit comprising two current splitters in a first, second, or third embodiment of the invention. Accordingly, letting  403  represent the pair of current splitters in the first embodiment of the invention as shown in  FIG. 2, 404   a  continues into  201   a ,  405   a  continues into  203   a ,  404   b  continues into  201   b ,  405   b  continues into  203   b ,  406  continues into  200 , and  407  continues from  202 . Output  408  corresponds to an optional error-catching signal output  608  which is shown in  FIG. 6 , and expanded upon in  FIG. 9 . These elements are mirrored in the added stage  402 . Primary current is delivered to the parallel branches  400   a - d  by  409 . It can be seen that branch  400   a  splits at junction  411 , with one leg continuing to input  405   a  and bias resistor  203   a , and the other leg continuing through two further LED elements  410  to input  404   a  and to the collector lead of BJT  204   a . This configuration ensures a voltage of at two times the forward voltage of an LED is present across each said bias resistor  203   a ; in practice this is approximately 3-6V depending on LED Vf. The design may benefit from a different number of forward biased LEDs based on voltage and current requirements or limitations. In the case where BJT collector voltage needs to increase due to a load voltage imbalance, voltage across the associated bias resistor will increase by the same amount, increasing BJT base current and effectively limiting further BJT collector voltage increases. This negative feedback property of the circuit improves performance at high frequencies by limiting transients and overshoot. 
       FIG. 5  isolates a single branch of the first embodiment of the invention, said first embodiment being an extendable current splitter built with a BJT and a Schottky diode between the gate and collector leads as shown in  FIGS. 2 and 4 . Component values of elements of  FIG. 5  are as follows: each of the LEDs  501  is of type DS186; bias resistor  502  is of size 3 kΩ; diode  503  is of type RB501VM-40; BJT  504  is of type EXT1053AK; emitter resistor  505  is of size 220 mΩ. Branch A continues from  506 , additional stages are added at  507 , and  508  is the source voltage or ground. This current splitter is optimized for 600 mA maximum and requires only four components per leg. 
     In some instances, the Schottky diode of the first embodiment of the invention can be replaced by a transistor. Referring to  FIG. 11 , the Schottky diode is replaced by a PMOS transistor (a p-channel MOSFET)  1100 . Also present in  FIG. 11  are the LED line  1101  connecting to a load comprising a plurality of LED elements, BJT  1102 , and emitter resistor  1103 . Referring to  FIG. 12 , the Schottky diode of the first embodiment is replaced by a PNP BJT  1200 . Also present in  FIG. 12  are the LED line  1201  connecting to a load comprising a plurality of LED elements, BJT  1202 , and emitter resistor  1203 . 
     These two variations are possible provided the selected replacement components (PNP or PMOS) provide a substantial base to ground current at a base to collector voltage comparable to that of a Schottky (˜+0.2 to +0.4V). In the case of the PNP this requires a large transistor and also implies that the maximum collector voltage will likely be limited by the PNP base-emitter voltage. For the PMOS this alternative requires a very low threshold voltage somewhat lower than the Schottky voltage. Integrated implementation of the invention may best benefit from these alternative if Schottky diodes are not available. Note that both PMOS and PNP variations seem to degrade the transient characteristics of the system compared to the Schottky, as both present short voltage transient spikes on the collector during turn-on, whereas the Schottky does not. 
     Criteria for Component Selection 
     In choosing a transistor, current gain h FE  should be greater than 100; the Early voltage V Early  should be as large as possible, unless low power consumption is prioritized over matching performance, in which case a low Early voltage is desirable (a lower Early voltage reduces power consumption by reducing the voltage excursion on unsaturated circuit legs, although matching performance is degraded); the saturation voltage target is V sat =˜0.3V @ I Rbias ; the desired power dissipation should be greater than the maximum current through an LED multiplied by the maximum voltage at the transistor collector lead, i.e. P D &gt;I LED, max *V collector, max ; and the maximum current should be greater than the maximum current through an LED, I max &gt;I LED,max . 
     In choosing a diode, the desired forward voltage V f  is given by V f &lt;0.7V−V sat  at the maximum current through an LED and at maximum leg-voltage difference, V sat  being the transistor criterium given by the formula above. 
     The bias resistor should be sized according to the formula: R bias =2*the LED forward voltage divided by the quantity maximum LED current times BJT current gain factor at the minimum operating temperature, i.e. R bias =2*V f, LED /(I LED, max *h FE min ). Where 2 here is the number of forward biased LEDs selected for the design bias resistor. 
     The emitter resistor should be sized as approximately 125 mV divided by the maximum LED current. 
     Below are some components which meet reasonable performance requirements for a maximum branch current of about 600 mA. Of the transistors, ZXT1053AK is preferred. h FE  is given for a collector current of about 600 mA. ZXTN25100DG has a higher h FE  at lower currents. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
             
            
               
                 Transistor 
                 P D   
                 h FE, min   
                 V sat   
                 V Early   
                 I max   
                 Package 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 ZXTN25100DG 
                 3 
                 W 
                 40-120 
                 0.10 
                 117 
                 3 A 
                 SOT223 
               
               
                 FZT855 
                 3 
                 W 
                 100 
                 0.30 
                 350 
                 5 A 
                 SOT223 
               
               
                 NSS1C301ET4G 
                 12 
                 W 
                 120 
                 0.09 
                 6.3 
                 3 A 
                 TO252 
               
               
                 ZXTN619MA 
                 1.5 
                 W 
                 84 
                 0.20 
                 84 
                 4 A 
                 DFN2mm 
               
               
                 ZXTN620MA 
                 1.5 
                 W 
                 84 
                 0.19 
                 110 
                 5 A 
                 DFN2mm 
               
               
                 ZXT1053AK 
                 4 
                 W 
                 300 
                 0.16 
                 150 
                 5 A 
                 TO252 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Diode 
                 Vf(10 mA) 
                 Bv 
               
               
                   
                   
               
               
                   
                 RB501VM 
                 0.25 
                 40 
               
               
                   
                   
               
            
           
         
       
     
     What follows is a comparison of SPICE-simulated performance characteristics of the invention in three configurations and using four different transistor models. The three configurations are the first, second, and third embodiments of the invention which accomplish current splitting using singular bipolar transistors and Schottky diodes, singular bipolar transistors without Schottky diodes, and cascoded bipolar transistors, respectively. 
       FIG. 6  provides a schematic of a stage comprising a pair of current splitters in the first embodiment of the invention, each current splitter comprising a singular bipolar junction transistor  604   a ,  604   b  and a Schottky diode  605   a ,  605   b  between the gate and collector leads of said transistor.  601   a ,  601   b  lead from branches A and B respectively, each branch comprising a load consisting of a plurality of LED elements. The first embodiment further comprises in each current splitter a bias resistor  603   a ,  6036 , and emitter resistor  606   a ,  606   b . Additional stages are added at  600  and source voltage or ground is given by  602 . See  FIG. 9  and error-catching discussion below.  609   a ,  609   b  carry bias current corresponding to  405   a ,  405   b  of  FIG. 4 . 
       FIG. 7  and the second embodiment of the invention are similar in ail respects to  FIG. 6  and the first embodiment except that the Schottky diodes  605   a ,  605   b  are omitted.  FIG. 7  provides a schematic of a stage comprising a pair of current splitters in the second embodiment of the invention, each current splitter comprising a singular bipolar junction transistor  704   a ,  704   b .  701   a ,  701   b  lead from branches A and B respectively, each branch comprising a load consisting of a plurality of LED elements. The second embodiment further comprises in each current splitter a bias resistor  703   a ,  703   b , and emitter resistor  706   a ,  706   b . Additional stages are added at  700  and source voltage or ground is given by  702 . See  FIG. 9  and error-catching discussion below.  709   a ,  709   b  carry bias current corresponding to  405   a ,  405   b  of  FIG. 4 . 
       FIG. 8  provides a schematic of a stage comprising a pair of current splitters in the third embodiment of the invention, each current splitter comprising two bipolar junction transistors in a cascoded configuration  804   a  with  811   a , and  804   b  with  811   b .  801   a ,  801   b  lead from branches A and B respectively, each branch comprising a load consisting of a plurality of LED elements. The third embodiment further comprises in each current splitter a bias resistor  803   a ,  803   b  connected to the gate leads of BJTs  811   a ,  811   b  and then through a diode  805   a ,  805   b  to the gate leads of BJTs  804   a ,  804   b . Each current splitter additionally comprises a second bias resistor  812   a ,  812   b  and emitter resistor  806   a ,  806   b . Additional stages are added at  800  and source voltage or ground is given by  802 . See  FIG. 9  and error-catching discussion below.  809   a ,  809   b  carry bias current corresponding to  405   a ,  405   b  of  FIG. 4 . 
     The following performance comparison simulation results assume a system of four branches or strings, each branch comprising a plurality of LED elements and a current splitter as presented in  FIG. 4 . In each simulation, one branch, I 1 , sees a voltage offset. With some exceptions, data are separated by BJT component model, each component model being simulated in three configurations corresponding to the three embodiments of the invention: the first embodiment being labeled “Schottky”, the second being labeled “No Schottky”, and the third being labeled “Cascade”; each component/configuration combination simulation being run at seven I 1  voltage offsets ranging from −3.2V to +3.2V, each offset being simulated at two temperatures and two current gain values. Quantities measured during simulation and compiled below are power, lumen, I 1 , I 2,3,4 , and power loss, wherein, as seen in  FIGS. 2 and 4 : 
     I 1 , is defined above; 
     I 2,3,4 , is the current in other branches (they are all equal); 
     Lumen is the light output; 
     P in  and P max  are power loss when V offset  is swept from −3.2V to +3.2V; 
     I min  is the minimum current of I 1  and I 234 ; 
     I max  is the maximum current of I 1  and I 234 ; 
     Spread is I max −I min ; and 
     Hfe is the simulated transistor gain at either minimum gain (Low) of maximum gain (high). For each component model, a summary of results is presented followed by more detailed simulation data. Data compiled in each summary consists of configuration; temperature; current gain; I min , the minimum single branch current obtained at the given configuration, temperature, and current gain; I max , the maximum single branch current obtained at the given configuration, temperature, and current gain; Spread, the difference between I max  and I min ; P min , the power when all charges are balanced (V offset =0.0V) wherein V offset  is as seen in  FIG. 4 ; P max , the power when offset voltage is +3.2V resulting in three branches having ˜V sat +3.2V on the collector. 
     It should be noted that bench testing has found that higher current transistors perform better in a discrete implementation of the invention despite simulation results suggesting that medium current transistors are satisfactory. This is a result of the simulation models used, SPICE (Simulation Program with Integrated Circuit Emphasis), having often reduced transistor modeling accuracy in the operating range of interest to the invention, namely the region between linear and saturation modes. Real-world bench measurement data suggests matching currents of 1%/V is achievable with the invention wherein %/V is the percentage of mismatch in the branch currents when one branch is X Volts above/below the other branches. An ideal current splitter would have 0%/V, or perfect current mirroring at any voltage. Additionally, with a discrete implementation it was found that a temperature difference between NPN transistors was the main source of inaccuracies in results when compared to simulations. When care is taken to thermally match transistors the expected accuracy of about 1%/V/pair is achievable. This is illustrated by using the circuit disclosed in  FIG. 15  and the corresponding performance seen in  FIG. 16 . [Insert Comeau discussion to come]. 
     Summary of Transistor NSS1C301ET4G Results 
       
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Temp 
                   
                 I min   
                 I max   
                 Spread 
                 P min   
                 P max   
               
               
                   
                 [C.] 
                 h FE   
                 [A] 
                 [A] 
                 [A] 
                 [W] 
                 [W] 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Schottky 
                 0 
                 Low 
                 0.566 
                 0.626 
                 0.060 
                 1.709 
                 6.942 
               
               
                   
                 0 
                 high 
                 0.560 
                 0.627 
                 0.067 
                 1.544 
                 6.813 
               
               
                   
                 85 
                 Low 
                 0.563 
                 0.630 
                 0.067 
                 1.567 
                 6.715 
               
               
                   
                 85 
                 high 
                 0.558 
                 0.630 
                 0.073 
                 1.460 
                 6.597 
               
               
                 No 
                 0 
                 Low 
                 0.529 
                 0.631 
                 0.102 
                 1.147 
                 5.618 
               
               
                 Schottky 
                 0 
                 high 
                 0.479 
                 0.652 
                 0.173 
                 0.547 
                 5.076 
               
               
                   
                 85 
                 Low 
                 0.514 
                 0.640 
                 0.125 
                 0.758 
                 5.352 
               
               
                   
                 85 
                 high 
                 0.475 
                 0.657 
                 0.182 
                 0.624 
                 4.817 
               
               
                 Cascode 
                 0 
                 Low 
                 0.577 
                 0.608 
                 0.031 
                 1.537 
                 6.278 
               
               
                   
                 0 
                 high 
                 0.546 
                 0.618 
                 0.072 
                 0.774 
                 5.892 
               
               
                   
                 85 
                 Low 
                 0.572 
                 0.611 
                 0.039 
                 1.176 
                 6.270 
               
               
                   
                 85 
                 high 
                 0.548 
                 0.619 
                 0.071 
                 0.927 
                 5.919 
               
               
                   
               
            
           
         
       
     
     Detailed Transistor NSS1C301ET4G Results 
       
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 V Offset   
                 Power 
                   
                 Lum/ 
                 I 2, 3, 4   
                 I 1   
                 PowerLoss 
               
               
                 [V] 
                 [W] 
                 Lumen 
                 Watt 
                 [A] 
                 [A] 
                 [W] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 112.2 
                 10252 
                 91.4 
                 0.591 
                 0.626 
                 3.51 
               
               
                 −1.6 
                 112.2 
                 10254 
                 91.4 
                 0.595 
                 0.614 
                 2.57 
               
               
                 −0.8 
                 112.3 
                 10254 
                 91.3 
                 0.598 
                 0.607 
                 2.12 
               
               
                 0 
                 112.4 
                 10255 
                 91.3 
                 0.600 
                 0.600 
                 1.71 
               
               
                 0.8 
                 114.0 
                 10254 
                 89.9 
                 0.603 
                 0.590 
                 2.89 
               
               
                 1.6 
                 115.8 
                 10252 
                 88.5 
                 0.606 
                 0.582 
                 4.21 
               
               
                 3.2 
                 119.4 
                 10249 
                 85.8 
                 0.611 
                 0.566 
                 6.94 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 112.1 
                 10252 
                 91.5 
                 0.591 
                 0.627 
                 3.41 
               
               
                 −1.6 
                 112.1 
                 10254 
                 91.5 
                 0.595 
                 0.616 
                 2.44 
               
               
                 −0.8 
                 112.1 
                 10254 
                 91.5 
                 0.597 
                 0.610 
                 1.97 
               
               
                 0 
                 112.2 
                 10255 
                 91.4 
                 0.600 
                 0.600 
                 1.54 
               
               
                 0.8 
                 113.8 
                 10253 
                 90.1 
                 0.606 
                 0.582 
                 2.67 
               
               
                 1.6 
                 115.6 
                 10252 
                 88.7 
                 0.609 
                 0.574 
                 4.04 
               
               
                 3.2 
                 119.2 
                 10248 
                 85.9 
                 0.613 
                 0.560 
                 6.81 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.5 
                 10262 
                 97.2 
                 0.591 
                 0.630 
                 3.38 
               
               
                 −1.6 
                 105.6 
                 10264 
                 97.2 
                 0.595 
                 0.616 
                 2.43 
               
               
                 −0.8 
                 105.7 
                 10265 
                 97.2 
                 0.598 
                 0.609 
                 1.98 
               
               
                 0 
                 105.7 
                 10265 
                 97.1 
                 0.601 
                 0.601 
                 1.57 
               
               
                 0.8 
                 107.3 
                 10264 
                 95.6 
                 0.605 
                 0.588 
                 2.70 
               
               
                 1.6 
                 109.1 
                 10263 
                 94.1 
                 0.608 
                 0.579 
                 4.02 
               
               
                 3.2 
                 112.7 
                 10259 
                 91.1 
                 0.613 
                 0.563 
                 6.71 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.4 
                 10262 
                 97.3 
                 0.591 
                 0.630 
                 3.30 
               
               
                 −1.6 
                 105.5 
                 10264 
                 97.3 
                 0.595 
                 0.618 
                 2.34 
               
               
                 −0.8 
                 105.5 
                 10265 
                 97.3 
                 0.597 
                 0.611 
                 1.87 
               
               
                 0 
                 105.6 
                 10265 
                 97.2 
                 0.601 
                 0.601 
                 1.46 
               
               
                 0.8 
                 107.1 
                 10264 
                 95.8 
                 0.607 
                 0.581 
                 2.51 
               
               
                 1.6 
                 108.9 
                 10262 
                 94.2 
                 0.610 
                 0.573 
                 3.86 
               
               
                 3.2 
                 112.5 
                 10258 
                 91.2 
                 0.615 
                 0.558 
                 6.60 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.2 
                 10253 
                 92.2 
                 0.590 
                 0.631 
                 2.53 
               
               
                 −1.6 
                 111.3 
                 10254 
                 92.1 
                 0.595 
                 0.615 
                 1.62 
               
               
                 −0.8 
                 111.4 
                 10255 
                 92.0 
                 0.598 
                 0.607 
                 1.25 
               
               
                 0 
                 111.8 
                 10255 
                 91.7 
                 0.600 
                 0.600 
                 1.15 
               
               
                 0.8 
                 113.0 
                 10254 
                 90.8 
                 0.605 
                 0.585 
                 1.87 
               
               
                 1.6 
                 114.6 
                 10252 
                 89.4 
                 0.612 
                 0.565 
                 3.06 
               
               
                 3.2 
                 118.0 
                 10243 
                 86.0 
                 0.624 
                 0.529 
                 5.62 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.0 
                 10250 
                 92.4 
                 0.583 
                 0.652 
                 2.39 
               
               
                 −1.6 
                 111.0 
                 10253 
                 92.3 
                 0.587 
                 0.638 
                 1.39 
               
               
                 −0.8 
                 111.1 
                 10254 
                 92.3 
                 0.590 
                 0.630 
                 0.91 
               
               
                 0 
                 111.2 
                 10256 
                 92.2 
                 0.600 
                 0.600 
                 0.55 
               
               
                 0.8 
                 112.2 
                 10246 
                 91.3 
                 0.625 
                 0.526 
                 1.08 
               
               
                 1.6 
                 113.9 
                 10240 
                 89.9 
                 0.630 
                 0.510 
                 2.38 
               
               
                 3.2 
                 117.3 
                 10227 
                 87.2 
                 0.540 
                 0.479 
                 5.08 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.7 
                 10262 
                 98.1 
                 0.588 
                 0.640 
                 2.54 
               
               
                 −1.6 
                 104.8 
                 10264 
                 98.0 
                 0.593 
                 0.623 
                 1.59 
               
               
                 −0.8 
                 104.8 
                 10265 
                 97.9 
                 0.596 
                 0.615 
                 1.14 
               
               
                 0 
                 104.9 
                 10266 
                 97.8 
                 0.601 
                 0.601 
                 0.76 
               
               
                 0.8 
                 106.3 
                 10263 
                 96.6 
                 0.611 
                 0.569 
                 1.64 
               
               
                 1.6 
                 107.9 
                 10260 
                 95.1 
                 0.618 
                 0.550 
                 2.84 
               
               
                 3.2 
                 111.2 
                 10250 
                 92.2 
                 0.630 
                 0.514 
                 5.35 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.5 
                 10259 
                 98.2 
                 0.582 
                 0.657 
                 2.43 
               
               
                 −1.6 
                 104.6 
                 10262 
                 98.1 
                 0.587 
                 0.642 
                 1.43 
               
               
                 −0.8 
                 104.6 
                 10264 
                 98.1 
                 0.590 
                 0.633 
                 0.96 
               
               
                 0 
                 104.8 
                 10266 
                 98.0 
                 0.601 
                 0.601 
                 0.62 
               
               
                 0.8 
                 105.5 
                 10255 
                 97.2 
                 0.626 
                 0.524 
                 0.94 
               
               
                 1.6 
                 107.2 
                 10250 
                 95.6 
                 0.632 
                 0.506 
                 2.20 
               
               
                 3.2 
                 110.6 
                 10236 
                 92.6 
                 0.643 
                 0.475 
                 4.82 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.6 
                 10243 
                 91.8 
                 0.597 
                 0.608 
                 2.88 
               
               
                 −1.6 
                 111.7 
                 10245 
                 91.7 
                 0.599 
                 0.604 
                 2.03 
               
               
                 −0.8 
                 111.8 
                 10245 
                 91.6 
                 0.599 
                 0.602 
                 1.68 
               
               
                 0 
                 112.2 
                 10245 
                 91.3 
                 0.600 
                 0.600 
                 1.54 
               
               
                 0.8 
                 113.4 
                 10244 
                 90.3 
                 0.601 
                 0.596 
                 2.34 
               
               
                 1.6 
                 115.2 
                 10242 
                 88.9 
                 0.603 
                 0.591 
                 3.61 
               
               
                 3.2 
                 118.8 
                 10238 
                 86.2 
                 0.608 
                 0.577 
                 6.28 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 0 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.3 
                 10243 
                 92.0 
                 0.594 
                 0.618 
                 2.63 
               
               
                 −1.6 
                 111.3 
                 10245 
                 92.0 
                 0.596 
                 0.613 
                 1.67 
               
               
                 −0.8 
                 111.3 
                 10246 
                 92.0 
                 0.597 
                 0.610 
                 1.20 
               
               
                 0 
                 111.4 
                 10246 
                 92.0 
                 0.600 
                 0.600 
                 0.77 
               
               
                 0.8 
                 112.9 
                 10244 
                 90.7 
                 0.609 
                 0.572 
                 1.79 
               
               
                 1.6 
                 114.7 
                 10241 
                 89.3 
                 0.612 
                 0.564 
                 3.14 
               
               
                 3.2 
                 118.3 
                 10234 
                 86.5 
                 0.618 
                 0.546 
                 5.89 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.1 
                 10254 
                 97.5 
                 0.597 
                 0.611 
                 2.94 
               
               
                 −1.6 
                 105.2 
                 10255 
                 97.5 
                 0.599 
                 0.606 
                 2.03 
               
               
                 −0.8 
                 105.3 
                 10256 
                 97.4 
                 0.600 
                 0.604 
                 1.58 
               
               
                 0 
                 105.3 
                 10257 
                 97.4 
                 0.601 
                 0.601 
                 1.18 
               
               
                 0.8 
                 106.9 
                 10255 
                 95.9 
                 0.603 
                 0.592 
                 2.29 
               
               
                 1.6 
                 108.7 
                 10253 
                 94.3 
                 0.606 
                 0.586 
                 3.60 
               
               
                 3.2 
                 112.2 
                 10248 
                 91.3 
                 0.610 
                 0.572 
                 6.27 
               
            
           
           
               
            
               
                 NSS1C301ET4G; Temp = 85 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.9 
                 10254 
                 97.7 
                 0.595 
                 0.619 
                 2.76 
               
               
                 −1.6 
                 105.0 
                 10255 
                 97.7 
                 0.596 
                 0.613 
                 1.81 
               
               
                 −0.8 
                 105.0 
                 10256 
                 97.7 
                 0.597 
                 0.611 
                 1.33 
               
               
                 0 
                 105.1 
                 10257 
                 97.6 
                 0.601 
                 0.601 
                 0.93 
               
               
                 0.8 
                 106.5 
                 10254 
                 96.3 
                 0.610 
                 0.573 
                 1.86 
               
               
                 1.6 
                 108.3 
                 10252 
                 94.7 
                 0.613 
                 0.565 
                 3.20 
               
               
                 3.2 
                 111.8 
                 10245 
                 91.6 
                 0.618 
                 0.548 
                 5.92 
               
               
                   
               
            
           
         
       
     
     Summary of Transistor ZXTN619MA Results 
       
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Temp 
                   
                 I min   
                 I max   
                 Spread 
                 P min   
                 P max   
               
               
                   
                 [C.] 
                 h FE   
                 [A] 
                 [A] 
                 [A] 
                 [W] 
                 [W] 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Schottky 
                 0 
                 Low 
                 0.594 
                 0.603 
                 0.010 
                 1.842 
                 7.279 
               
               
                   
                 0 
                 high 
                 0.589 
                 0.605 
                 0.015 
                 1.649 
                 7.186 
               
               
                   
                 85 
                 Low 
                 0.563 
                 0.630 
                 0.067 
                 1.567 
                 6.715 
               
               
                   
                 85 
                 high 
                 0.558 
                 0.630 
                 0.073 
                 1.460 
                 6.597 
               
               
                 No 
                 0 
                 Low 
                 0.529 
                 0.631 
                 0.102 
                 1.147 
                 5.618 
               
               
                 Schottky 
                 0 
                 high 
                 0.479 
                 0.652 
                 0.173 
                 0.547 
                 5.076 
               
               
                   
                 85 
                 Low 
                 0.514 
                 0.640 
                 0.125 
                 0.758 
                 5.352 
               
               
                   
                 85 
                 high 
                 0.475 
                 0.657 
                 0.182 
                 0.624 
                 4.817 
               
               
                 Cascode 
                 0 
                 Low 
                 0.577 
                 0.608 
                 0.031 
                 1.537 
                 6.278 
               
               
                   
                 0 
                 high 
                 0.546 
                 0.618 
                 0.072 
                 0.774 
                 5.892 
               
               
                   
                 85 
                 Low 
                 0.572 
                 0.611 
                 0.039 
                 1.176 
                 6.270 
               
               
                   
                 85 
                 high 
                 0.548 
                 0.619 
                 0.071 
                 0.927 
                 5.919 
               
               
                   
               
            
           
         
       
     
     Detailed Transistor ZXTN619MA Results 
       
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 V Offset   
                 Power 
                   
                 Lum/ 
                 I 2, 3, 4   
                 I 1   
                 PowerLoss 
               
               
                 [V] 
                 [W] 
                 Lumen 
                 Watt 
                 [A] 
                 [A] 
                 [W] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 112.3 
                 10259 
                 91.3 
                 0.599 
                 0.603 
                 3.63 
               
               
                 −1.6 
                 112.4 
                 10259 
                 91.3 
                 0.599 
                 0.602 
                 2.70 
               
               
                 −0.8 
                 112.4 
                 10259 
                 91.3 
                 0.600 
                 0.601 
                 2.25 
               
               
                 0 
                 112.5 
                 10260 
                 91.2 
                 0.600 
                 0.600 
                 1.84 
               
               
                 0.8 
                 114.2 
                 10259 
                 89.8 
                 0.601 
                 0.598 
                 3.08 
               
               
                 1.6 
                 116.1 
                 10259 
                 88.4 
                 0.601 
                 0.597 
                 4.47 
               
               
                 3.2 
                 119.8 
                 10257 
                 85.6 
                 0.602 
                 0.594 
                 7.28 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 112.2 
                 10259 
                 91.4 
                 0.598 
                 0.605 
                 3.53 
               
               
                 −1.6 
                 112.3 
                 10259 
                 91.4 
                 0.599 
                 0.603 
                 2.58 
               
               
                 −0.8 
                 112.3 
                 10259 
                 91.4 
                 0.599 
                 0.602 
                 2.10 
               
               
                 0 
                 112.3 
                 10260 
                 91.4 
                 0.600 
                 0.600 
                 1.65 
               
               
                 0.8 
                 114.0 
                 10259 
                 90.0 
                 0.602 
                 0.594 
                 2.92 
               
               
                 1.6 
                 115.9 
                 10259 
                 88.5 
                 0.603 
                 0.592 
                 4.34 
               
               
                 3.2 
                 119.7 
                 10257 
                 85.7 
                 0.604 
                 0.589 
                 7.19 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.5 
                 10262 
                 97.2 
                 0.591 
                 0.630 
                 3.38 
               
               
                 −1.6 
                 105.6 
                 10264 
                 97.2 
                 0.595 
                 0.616 
                 2.43 
               
               
                 −0.8 
                 105.7 
                 10265 
                 97.2 
                 0.598 
                 0.609 
                 1.98 
               
               
                 0 
                 105.7 
                 10265 
                 97.1 
                 0.601 
                 0.601 
                 1.57 
               
               
                 0.8 
                 107.3 
                 10264 
                 95.6 
                 0.605 
                 0.588 
                 2.70 
               
               
                 1.6 
                 109.1 
                 10263 
                 94.1 
                 0.608 
                 0.579 
                 4.02 
               
               
                 3.2 
                 112.7 
                 10259 
                 91.1 
                 0.613 
                 0.563 
                 6.71 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.4 
                 10262 
                 97.3 
                 0.591 
                 0.630 
                 3.30 
               
               
                 −1.6 
                 105.5 
                 10264 
                 97.3 
                 0.595 
                 0.618 
                 2.34 
               
               
                 −0.8 
                 105.5 
                 10265 
                 97.3 
                 0.597 
                 0.611 
                 1.87 
               
               
                 0 
                 105.6 
                 10265 
                 97.2 
                 0.601 
                 0.601 
                 1.46 
               
               
                 0.8 
                 107.1 
                 10264 
                 95.8 
                 0.607 
                 0.581 
                 2.51 
               
               
                 1.6 
                 108.9 
                 10262 
                 94.2 
                 0.610 
                 0.573 
                 3.86 
               
               
                 3.2 
                 112.5 
                 10258 
                 91.2 
                 0.615 
                 0.558 
                 6.60 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.2 
                 10253 
                 92.2 
                 0.590 
                 0.631 
                 2.53 
               
               
                 −1.6 
                 111.3 
                 10254 
                 92.1 
                 0.595 
                 0.615 
                 1.62 
               
               
                 −0.8 
                 111.4 
                 10255 
                 92.0 
                 0.598 
                 0.607 
                 1.25 
               
               
                 0 
                 111.8 
                 10255 
                 91.7 
                 0.600 
                 0.600 
                 1.15 
               
               
                 0.8 
                 113.0 
                 10254 
                 90.8 
                 0.605 
                 0.585 
                 1.87 
               
               
                 1.6 
                 114.6 
                 10252 
                 89.4 
                 0.612 
                 0.565 
                 3.06 
               
               
                 3.2 
                 118.0 
                 10243 
                 86.8 
                 0.624 
                 0.529 
                 5.62 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.0 
                 10250 
                 92.4 
                 0.583 
                 0.652 
                 2.39 
               
               
                 −1.6 
                 111.0 
                 10253 
                 92.3 
                 0.587 
                 0.638 
                 1.39 
               
               
                 −0.8 
                 111.1 
                 10254 
                 92.3 
                 0.590 
                 0.630 
                 0.91 
               
               
                 0 
                 111.2 
                 10256 
                 92.2 
                 0.600 
                 0.600 
                 0.55 
               
               
                 0.8 
                 112.2 
                 10246 
                 91.3 
                 0.625 
                 0.526 
                 1.08 
               
               
                 1.6 
                 113.9 
                 10240 
                 89.9 
                 0.630 
                 0.510 
                 2.38 
               
               
                 3.2 
                 117.3 
                 10227 
                 87.2 
                 0.640 
                 0.479 
                 5.08 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.7 
                 10262 
                 98.1 
                 0.588 
                 0.640 
                 2.54 
               
               
                 −1.6 
                 104.8 
                 10264 
                 98.0 
                 0.593 
                 0.623 
                 1.59 
               
               
                 −0.8 
                 104.8 
                 10265 
                 97.9 
                 0.596 
                 0.615 
                 1.14 
               
               
                 0 
                 104.9 
                 10266 
                 97.8 
                 0.601 
                 0.601 
                 0.76 
               
               
                 0.8 
                 106.3 
                 10263 
                 96.6 
                 0.611 
                 0.569 
                 1.64 
               
               
                 1.6 
                 107.9 
                 10260 
                 95.1 
                 0.618 
                 0.550 
                 2.84 
               
               
                 3.2 
                 111.2 
                 10250 
                 92.2 
                 0.630 
                 0.514 
                 5.35 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.5 
                 10259 
                 98.2 
                 0.582 
                 0.657 
                 2.43 
               
               
                 −1.6 
                 104.6 
                 10262 
                 98.1 
                 0.587 
                 0.642 
                 1.43 
               
               
                 −0.8 
                 104.6 
                 10264 
                 98.1 
                 0.590 
                 0.633 
                 0.96 
               
               
                 0 
                 104.8 
                 10266 
                 98.0 
                 0.601 
                 0.601 
                 0.62 
               
               
                 0.8 
                 105.5 
                 10255 
                 97.2 
                 0.626 
                 0.524 
                 0.94 
               
               
                 1.6 
                 107.2 
                 10250 
                 95.6 
                 0.632 
                 0.506 
                 2.20 
               
               
                 3.2 
                 110.6 
                 10236 
                 92.6 
                 0.643 
                 0.475 
                 4.82 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.6 
                 10243 
                 91.8 
                 0.597 
                 0.608 
                 2.88 
               
               
                 −1.6 
                 111.7 
                 10245 
                 91.7 
                 0.599 
                 0.604 
                 2.03 
               
               
                 −0.8 
                 111.8 
                 10245 
                 91.6 
                 0.599 
                 0.602 
                 1.68 
               
               
                 0 
                 112.2 
                 10245 
                 91.3 
                 0.600 
                 0.600 
                 1.54 
               
               
                 0.8 
                 113.4 
                 10244 
                 90.3 
                 0.601 
                 0.596 
                 2.34 
               
               
                 1.6 
                 115.2 
                 10242 
                 88.9 
                 0.603 
                 0.591 
                 3.61 
               
               
                 3.2 
                 118.8 
                 10238 
                 86.2 
                 0.608 
                 0.577 
                 6.28 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 0 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.3 
                 10243 
                 92.0 
                 0.594 
                 0.618 
                 2.63 
               
               
                 −1.6 
                 111.3 
                 10245 
                 92.0 
                 0.596 
                 0.613 
                 1.67 
               
               
                 −0.8 
                 111.3 
                 10246 
                 92.0 
                 0.597 
                 0.610 
                 1.20 
               
               
                 0 
                 111.4 
                 10246 
                 92.0 
                 0.600 
                 0.600 
                 0.77 
               
               
                 0.8 
                 112.9 
                 10244 
                 90.7 
                 0.609 
                 0.572 
                 1.79 
               
               
                 1.6 
                 114.7 
                 10241 
                 89.3 
                 0.612 
                 0.564 
                 3.14 
               
               
                 3.2 
                 118.3 
                 10234 
                 86.5 
                 0.618 
                 0.546 
                 5.89 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.1 
                 10254 
                 97.5 
                 0.597 
                 0.611 
                 2.94 
               
               
                 −1.6 
                 105.2 
                 10255 
                 97.5 
                 0.599 
                 0.606 
                 2.03 
               
               
                 −0.8 
                 105.3 
                 10256 
                 97.4 
                 0.600 
                 0.604 
                 1.58 
               
               
                 0 
                 105.3 
                 10257 
                 97.4 
                 0.601 
                 0.601 
                 1.18 
               
               
                 0.8 
                 106.9 
                 10255 
                 95.9 
                 0.603 
                 0.592 
                 2.29 
               
               
                 1.6 
                 108.7 
                 10253 
                 94.3 
                 0.606 
                 0.586 
                 3.60 
               
               
                 3.2 
                 112.2 
                 10248 
                 91.3 
                 0.610 
                 0.572 
                 6.27 
               
            
           
           
               
            
               
                 ZXTN619MA; Temp = 85 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.9 
                 10254 
                 97.7 
                 0.595 
                 0.619 
                 2.76 
               
               
                 −1.6 
                 105.0 
                 10255 
                 97.7 
                 0.596 
                 0.613 
                 1.81 
               
               
                 −0.8 
                 105.0 
                 10256 
                 97.7 
                 0.597 
                 0.611 
                 1.33 
               
               
                 0 
                 105.1 
                 10257 
                 97.6 
                 0.601 
                 0.601 
                 0.93 
               
               
                 0.8 
                 106.5 
                 10254 
                 96.3 
                 0.610 
                 0.573 
                 1.86 
               
               
                 1.6 
                 108.3 
                 10252 
                 94.7 
                 0.613 
                 0.565 
                 3.20 
               
               
                 3.2 
                 111.8 
                 10245 
                 91.6 
                 0.618 
                 0.548 
                 5.92 
               
               
                   
               
            
           
         
       
     
     Summary of Transistor ZXT1053AK Results 
       
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Temp 
                   
                 I min   
                 I max   
                 Spread 
                 P min   
                 P max   
               
               
                   
                 [C.] 
                 h FE   
                 [A] 
                 [A] 
                 [A] 
                 [W] 
                 [W] 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Schottky 
                 0 
                 Low 
                 0.596 
                 0.603 
                 0.007 
                 5.156 
                 7.306 
               
               
                   
                 0 
                 high 
                 0.590 
                 0.605 
                 0.015 
                 1.551 
                 7.108 
               
               
                   
                 50 
                 nominal 
                 0.592 
                 0.604 
                 0.012 
                 1.577 
                 7.097 
               
               
                   
                 85 
                 Low 
                 0.594 
                 0.605 
                 0.011 
                 1.729 
                 7.116 
               
               
                   
                 85 
                 high 
                 0.591 
                 0.606 
                 0.015 
                 1.490 
                 6.996 
               
               
                 No 
                 0 
                 Low 
                 0.575 
                 0.605 
                 0.030 
                 1.209 
                 6.047 
               
               
                 Schottky 
                 0 
                 high 
                 0.535 
                 0.621 
                 0.086 
                 0.524 
                 5.652 
               
               
                   
                 50 
                 nominal 
                 0.555 
                 0.612 
                 0.057 
                 0.631 
                 5.804 
               
               
                   
                 85 
                 Low 
                 0.573 
                 0.606 
                 0.033 
                 1.501 
                 6.005 
               
               
                   
                 85 
                 high 
                 0.525 
                 0.625 
                 0.100 
                 0.566 
                 5.418 
               
               
                   
               
            
           
         
       
     
     For transistor ZXT1053AK, simulations were run for the first and second embodiment configurations only and include an additional data point at an intermediate temperature of 50 C and an intermediate nominal h FE . The ZXT1053AK was not simulated in a cascoded configuration because it is a large TO252 package which presents physical implementation challenges. The outlier result P min  of 5.156 W was due to a slightly high R bias  value simulated in the worst-case performance conditions of 0 C and minimum h FE  leading to insufficient current gain to ensure saturation of one transistor. This can be resolved by reducing the R bias  used from the simulation value of 3 kΩ. Calculations suggest a more optimal R bias  value of 2.8 kΩ. 
     Detailed Transistor ZXT1053AK Results 
       
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 V Offset   
                 Power 
                   
                 Lum/ 
                 I 2, 3, 4   
                 I 1   
                 PowerLoss 
               
               
                 [V] 
                 [W] 
                 Lumen 
                 Watt 
                 [A] 
                 [A] 
                 [W] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 0 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 113.9 
                 10261 
                 90.1 
                 0.599 
                 0.603 
                 5.17 
               
               
                 −1.6 
                 114.8 
                 10261 
                 89.4 
                 0.599 
                 0.602 
                 5.16 
               
               
                 −0.8 
                 115.3 
                 10261 
                 89.0 
                 0.600 
                 0.601 
                 5.16 
               
               
                 0 
                 115.8 
                 10261 
                 88.6 
                 0.600 
                 0.600 
                 5.16 
               
               
                 0.8 
                 116.3 
                 10261 
                 88.2 
                 0.600 
                 0.599 
                 5.16 
               
               
                 1.6 
                 116.8 
                 10261 
                 87.9 
                 0.601 
                 0.598 
                 5.16 
               
               
                 3.2 
                 119.9 
                 10261 
                 85.6 
                 0.601 
                 0.596 
                 7.31 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 0 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 112.1 
                 10261 
                 91.5 
                 0.598 
                 0.605 
                 3.44 
               
               
                 −1.6 
                 112.2 
                 10261 
                 91.5 
                 0.599 
                 0.603 
                 2.48 
               
               
                 −0.8 
                 112.2 
                 10261 
                 91.5 
                 0.599 
                 0.602 
                 2.00 
               
               
                 0 
                 112.2 
                 10261 
                 91.5 
                 0.600 
                 0.600 
                 1.55 
               
               
                 0.8 
                 114.0 
                 10261 
                 90.0 
                 0.602 
                 0.595 
                 2.83 
               
               
                 1.6 
                 115.8 
                 10260 
                 88.6 
                 0.602 
                 0.593 
                 4.25 
               
               
                 3.2 
                 119.6 
                 10260 
                 85.8 
                 0.603 
                 0.590 
                 7.11 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 85 C.; Min h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.7 
                 10271 
                 97.1 
                 0.599 
                 0.605 
                 3.50 
               
               
                 −1.6 
                 105.8 
                 10271 
                 97.1 
                 0.600 
                 0.603 
                 2.58 
               
               
                 −0.8 
                 105.8 
                 10271 
                 97.1 
                 0.600 
                 0.602 
                 2.13 
               
               
                 0 
                 105.9 
                 10271 
                 97.0 
                 0.601 
                 0.601 
                 1.73 
               
               
                 0.8 
                 107.6 
                 10271 
                 95.5 
                 0.601 
                 0.599 
                 2.94 
               
               
                 1.6 
                 109.4 
                 10271 
                 93.9 
                 0.602 
                 0.597 
                 4.31 
               
               
                 3.2 
                 113.2 
                 10270 
                 90.7 
                 0.603 
                 0.594 
                 7.12 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 85 C.; Max h FE ; Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.6 
                 10271 
                 97.3 
                 0.599 
                 0.606 
                 3.37 
               
               
                 −1.6 
                 105.6 
                 10271 
                 97.3 
                 0.600 
                 0.604 
                 2.41 
               
               
                 −0.8 
                 105.6 
                 10271 
                 97.2 
                 0.600 
                 0.603 
                 1.93 
               
               
                 0 
                 105.7 
                 10271 
                 97.2 
                 0.601 
                 0.601 
                 1.49 
               
               
                 0.8 
                 107.4 
                 10271 
                 95.7 
                 0.603 
                 0.595 
                 2.73 
               
               
                 1.6 
                 109.3 
                 10271 
                 94.0 
                 0.603 
                 0.594 
                 4.15 
               
               
                 3.2 
                 113.0 
                 10270 
                 90.9 
                 0.604 
                 0.591 
                 7.00 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 0 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.3 
                 10261 
                 92.2 
                 0.598 
                 0.605 
                 2.55 
               
               
                 −1.6 
                 111.4 
                 10261 
                 92.1 
                 0.599 
                 0.602 
                 1.67 
               
               
                 −0.8 
                 111.5 
                 10261 
                 92.0 
                 0.600 
                 0.601 
                 1.32 
               
               
                 0 
                 111.9 
                 10261 
                 91.7 
                 0.600 
                 0.600 
                 1.21 
               
               
                 0.8 
                 113.1 
                 10261 
                 90.7 
                 0.601 
                 0.596 
                 2.00 
               
               
                 1.6 
                 114.9 
                 10261 
                 89.3 
                 0.604 
                 0.589 
                 3.31 
               
               
                 3.2 
                 118.5 
                 10259 
                 86.5 
                 0.608 
                 0.575 
                 6.05 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 0 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.1 
                 10260 
                 92.4 
                 0.593 
                 0.621 
                 2.41 
               
               
                 −1.6 
                 111.1 
                 10261 
                 92.4 
                 0.594 
                 0.618 
                 1.42 
               
               
                 −0.8 
                 111.1 
                 10261 
                 92.4 
                 0.595 
                 0.616 
                 0.94 
               
               
                 0 
                 111.2 
                 10261 
                 92.3 
                 0.600 
                 0.600 
                 0.52 
               
               
                 0.8 
                 112.5 
                 10258 
                 91.2 
                 0.616 
                 0.553 
                 1.39 
               
               
                 1.6 
                 114.3 
                 10256 
                 89.7 
                 0.618 
                 0.547 
                 2.80 
               
               
                 3.2 
                 118.0 
                 10253 
                 86.9 
                 0.622 
                 0.535 
                 5.65 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 85 C.; Min h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.9 
                 10271 
                 97.9 
                 0.599 
                 0.606 
                 2.64 
               
               
                 −1.6 
                 105.0 
                 10271 
                 97.8 
                 0.600 
                 0.603 
                 1.82 
               
               
                 −0.8 
                 105.2 
                 10271 
                 97.6 
                 0.600 
                 0.602 
                 1.55 
               
               
                 0 
                 105.7 
                 10271 
                 97.2 
                 0.601 
                 0.601 
                 1.50 
               
               
                 0.8 
                 106.7 
                 10271 
                 96.2 
                 0.602 
                 0.597 
                 2.09 
               
               
                 1.6 
                 108.4 
                 10271 
                 94.7 
                 0.604 
                 0.589 
                 3.34 
               
               
                 3.2 
                 112.0 
                 10269 
                 91.7 
                 0.610 
                 0.573 
                 6.01 
               
            
           
           
               
            
               
                 ZXT1053AK; Temp = 85 C.; Max h FE ; No Schottky 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 104.6 
                 10270 
                 98.2 
                 0.593 
                 0.625 
                 2.42 
               
               
                 −1.6 
                 104.6 
                 10271 
                 98.2 
                 0.594 
                 0.621 
                 1.44 
               
               
                 −0.8 
                 104.6 
                 10271 
                 98.2 
                 0.595 
                 0.619 
                 0.95 
               
               
                 0 
                 104.7 
                 10272 
                 98.1 
                 0.601 
                 0.601 
                 0.57 
               
               
                 0.8 
                 105.8 
                 10266 
                 97.0 
                 0.619 
                 0.547 
                 1.22 
               
               
                 1.6 
                 107.7 
                 10265 
                 95.4 
                 0.621 
                 0.539 
                 2.61 
               
               
                 3.2 
                 111.3 
                 10261 
                 92.2 
                 0.626 
                 0.525 
                 5.42 
               
               
                   
               
            
           
         
       
     
     Summary of Transistor ZXTN620MA Results 
       
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                   
               
               
                   
                 Temp 
                   
                 I min   
                 I max   
                 Spread 
                 P min   
                 P max   
               
               
                   
                 [C.] 
                 h FE   
                 [A] 
                 [A] 
                 [A] 
                 [W] 
                 [W] 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Cascode 
                 0 
                 Low 
                 0.593 
                 0.603 
                 0.010 
                 1.987 
                 6.642 
               
               
                   
                 0 
                 high 
                 0.583 
                 0.605 
                 0.023 
                 0.983 
                 6.447 
               
               
                   
                 85 
                 Low 
                 0.594 
                 0.603 
                 0.009 
                 2.565 
                 6.741 
               
               
                   
                 85 
                 high 
                 0.583 
                 0.606 
                 0.023 
                 1.093 
                 6.474 
               
               
                   
               
            
           
         
       
     
     For transistor ZXTN620MA, simulations were run for the third embodiment configuration only, as it is a small DFN2 mm package with similar performance to the ZXT1053AK. 
     Detailed Transistor ZXTN620MA Results 
       
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 V Offset   
                 Power 
                   
                 Lum/ 
                 I 2, 3, 4   
                 I 1   
                 PowerLoss 
               
               
                 [V] 
                 [W] 
                 Lumen 
                 Watt 
                 [A] 
                 [A] 
                 [W] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 ZXTN620MA; Temp = 0 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.8 
                 10254 
                 91.7 
                 0.599 
                 0.603 
                 3.09 
               
               
                 −1.6 
                 112.0 
                 10254 
                 91.6 
                 0.600 
                 0.601 
                 2.27 
               
               
                 −0.8 
                 112.2 
                 10255 
                 91.4 
                 0.600 
                 0.601 
                 2.01 
               
               
                 0 
                 112.6 
                 10255 
                 91.0 
                 0.600 
                 0.600 
                 1.99 
               
               
                 0.8 
                 113.7 
                 10254 
                 90.2 
                 0.600 
                 0.599 
                 2.60 
               
               
                 1.6 
                 115.5 
                 10253 
                 88.8 
                 0.601 
                 0.597 
                 3.89 
               
               
                 3.2 
                 119.2 
                 10251 
                 86.0 
                 0.602 
                 0.593 
                 6.64 
               
            
           
           
               
            
               
                 ZXTN620MA; Temp = 0 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 111.6 
                 10254 
                 91.9 
                 0.598 
                 0.605 
                 2.85 
               
               
                 −1.6 
                 111.6 
                 10255 
                 91.9 
                 0.599 
                 0.604 
                 1.90 
               
               
                 −0.8 
                 111.6 
                 10255 
                 91.9 
                 0.599 
                 0.603 
                 1.43 
               
               
                 0 
                 111.6 
                 10255 
                 91.9 
                 0.600 
                 0.600 
                 0.98 
               
               
                 0.8 
                 113.3 
                 10254 
                 90.5 
                 0.603 
                 0.591 
                 2.22 
               
               
                 1.6 
                 115.2 
                 10253 
                 89.0 
                 0.604 
                 0.589 
                 3.63 
               
               
                 3.2 
                 119.0 
                 10251 
                 86.2 
                 0.606 
                 0.583 
                 6.45 
               
            
           
           
               
            
               
                 ZXTN620MA; Temp = 85 C.; Min h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.5 
                 10264 
                 97.3 
                 0.600 
                 0.603 
                 3.30 
               
               
                 −1.6 
                 105.8 
                 10265 
                 97.0 
                 0.600 
                 0.602 
                 2.62 
               
               
                 −0.8 
                 106.2 
                 10265 
                 96.6 
                 0.601 
                 0.601 
                 2.57 
               
               
                 0 
                 106.7 
                 10265 
                 96.2 
                 0.601 
                 0.601 
                 2.56 
               
               
                 0.8 
                 107.5 
                 10264 
                 95.5 
                 0.601 
                 0.600 
                 2.84 
               
               
                 1.6 
                 109.2 
                 10264 
                 94.0 
                 0.602 
                 0.598 
                 4.05 
               
               
                 3.2 
                 112.8 
                 10261 
                 91.0 
                 0.603 
                 0.594 
                 6.74 
               
            
           
           
               
            
               
                 ZXTN620MA; Temp = 85 C.; Max h FE ; Cascode 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 −3.2 
                 105.2 
                 10264 
                 97.6 
                 0.599 
                 0.606 
                 2.95 
               
               
                 −1.6 
                 105.2 
                 10265 
                 97.6 
                 0.599 
                 0.604 
                 2.00 
               
               
                 −0.8 
                 105.2 
                 10265 
                 97.6 
                 0.600 
                 0.603 
                 1.53 
               
               
                 0 
                 105.3 
                 10266 
                 97.5 
                 0.601 
                 0.601 
                 1.10 
               
               
                 0.8 
                 106.9 
                 10265 
                 96.0 
                 0.604 
                 0.592 
                 2.29 
               
               
                 1.6 
                 108.8 
                 10264 
                 94.4 
                 0.605 
                 0.589 
                 3.68 
               
               
                 3.2 
                 112.5 
                 10261 
                 91.2 
                 0.607 
                 0.583 
                 6.47 
               
               
                   
               
            
           
         
       
     
     In general, the first embodiment, the “Schottky” configuration, offers much better current matching (+/−1.5% worse case) while the second embodiment, the “No Schottky” configuration, offers the lowest power consumption at about 1 W less than the first embodiment. The user will be able to select which of the two parameters (current matching or power) are most relevant for their application. 
     Optional Error Detection 
       FIG. 9  is a schematic of one branch of an error-detecting current splitter in a fourth embodiment of the invention. An error refers to any element failure which would cause an open circuit on an LED load line or an excessive voltage on NPN  908  collector. Referring to  FIG. 9 , in case of an open circuit on LED line  900 , leading from a load comprising a plurality of LED elements, the error detection circuit disables BJT  908  via MOSFET,  914 , preventing transistor  908  from conducting. 
     In turning MOSFET  914  off, the circuit also turns on MOSFET,  915 , allowing resistor R biasError    903  (R biasError  having the same value as R bias ,  904 ) to feed base current to the remaining active BJT.  FIG. 9  discloses one (1) branch of a circuit containing N-branches. The other referenced BJT refer to the BJT of the other remaining branches assuming the branch in  FIG. 9  is the one where the error occurred. The other branches are connected via  917 ,  916  and  901  This ensures enough base current to allow the total current to be divided by the remaining N−1 stages This is particularly useful for lighting application since this means almost no change in light output (although the LEDs will be operating at N/(N−1)*ExpectedCurrent which may be outside their maximum current rating). 
     Since an open circuit error on LED line  900  turns off  913 , observe that resistor  902  (of size ˜10 kΩ) is connected to the LED line  901  of the following stage which is presumably biased (assuming only one error per branch). Note that branch or string are used interchangeably in this document. This requires the Nth error detection circuit to be connected to the Nth+1 stage, the last stage then being connected to the first stage, such that the error detection circuits are connected in a circle. 
     An error can also be triggered if enough voltage (typically greater than approximately 6V) is built on LED line  906  via Zener diode  918 , resistor R biasZ ,  919 , of size ˜20 kΩ, and the threshold voltage of MOSFET,  920 ; i.e., when V 906 &gt;˜V th, 920 +V z, 918 . Other voltage values may be set with different Zeners or by using a resistive divider. 
     Errors can activate an ErrorOut line  924  (active low) or a red LED on the lamp itself. The active low line can also be paralleled allowing for several lamps in the same group to inform a master controller of an error condition. 
     This circuit is replicated for each string as required. It is likely better suited for an integrated circuit (IC) solution as the space may be limited in the lamp housing. For a discrete solution this application would cost about $0.30-$0.40 per string. 
     To ensure current-splitter performance is not significantly impacted,  914  and  915  should have voltage drops of preferably less than a few mV. This typically implies R dsOn &lt;1Ω, R dsOn  being the MOSFET drain-source on resistance. 
     Additional elements of  FIG. 9  include Schottky diode  905 , ExtCurSenseR  909 , IntCurSenseR  910 , source voltage line or ground V SS    917 , resistor  911 , resistor R bias, LED line 900    912 , additional stages are added at  916 , two error bias resistors  922 ,  923 , and MOSFET  921 . ExtCurSenseR refers to a hypothetical external emitter resistor for the case of an integrate (IC) implementation and IntCurSenseR refers to a hypothetical internal resistor for the case of an integrate (IC) implementation. 
     The error detection circuit allows for use in high reliability applications. In such cases for example, reliability could be further improved by arranging the LEDs connected to LED line  906  and LED line  900  each into 2 groups of 2 LEDs in parallel, connected in series. The rest of the string as seen in  FIG. 4  can be made of single LEDs or paralleled pairs, paralleled pairs further improving the mean time to failure. LEDs operating at current levels below their max current ratings exhibit increased lifetimes. Two in parallel would last ˜30% longer than one running at 50% I max . Combining such redundant LED arrangements with the error-detection circuit of the fourth embodiment greatly improves reliability of the total light-emitting system. 
     Referring to  FIG. 10 , graph  1000  shows collector currents versus collector voltage at identically stepped base-currents for two (2) NPN transistors of different layout styles using BiCMOS technology. As can be seen, e that transistor of shown as style2 is better suited for the application herein as it shows a lower saturation voltage and higher V Early  while having comparable gain. Style_2 appears to be usable down to a collector voltage of about 0.3V up at 1.0 A. 
     SPICE Models Used 
     SPICE (Simulation Program with Integrated Circuit Emphasis) was used to simulate the various embodiments of the invention and obtain results listed above. Computer code used to generate the relevant models is provided below. 
     
       
         
           
               
             
               
                   
               
             
            
               
                 .subckt NSS1C301ET4G c b e NGNgain=0 
               
            
           
           
               
               
            
               
                 *Use BF={287/1.73} 
                    for minimum HFE 
               
               
                 *Use BF=287 
                    for nominal HFE 
               
               
                 *Use BF={287*1.73} 
                    for maximum HFE 
               
            
           
           
               
            
               
                 Rb b b1 0.01 
               
               
                 Q1 c b1 e Qnss1c301t4g2 
               
               
                 * Model generated on Sep 21, 11 
               
               
                 * MODEL FORMAT: PSpice 
               
               
                 .MODEL Qnss1c301t4g2 npn 
               
               
                 +IS=1.21674e−11 
               
               
                 +BF=287 
               
               
                 *+IS=1.21674e−11 
               
               
                 *+BF=287 
               
               
                 +NF=1.13047 VAF=14.6607 
               
               
                 +IKF=4.31072 ISE=3.25335e−12 NE=3.53101 BR=5.00076 
               
               
                 +NR=1.19574 VAR=6.23931 IKR=5.86862 ISC=6.25001e−13 
               
               
                 +NC=3.9375 RB=1.8106 IRB=0.1 RBM=0.1 
               
               
                 +RE=0.000711316 RC=0.0436544 XTB=0.786033 XTI=1.10401 
               
               
                 +EG=1.05 CJE=7.68935e−10 VJE=0.99 MJE=0.387949 
               
               
                 +TF=1.13993e−09 XTF=1000 VTF=1327.51 ITF=95.3145 
               
               
                 +CJC=9.37254e−11 VJC=0.95 MJC=0.450276 XCJC=1 
               
               
                 +FC=0.8 CJS=0 VJS=0.75 MJS=0.5 
               
               
                 +TR=1e−07 PTF=0 KF=0 AF=1 
               
               
                 .ends 
               
               
                 .subckt ZXTN619MA 1 2 3 
               
            
           
           
               
               
            
               
                 *Use BF={465/2} 
                   for minimum HFE 
               
               
                 *Use BF=465 
                     for nominal HFE 
               
               
                 *Use BF={465*2} 
                   for maximum HFE 
               
            
           
           
               
            
               
                 Q1 1 2 3 ZXTN619MA 
               
               
                 *ZXTN619MA Spice model 
               
               
                 *SIMULATOR=SIMETRIX 
               
               
                 *ORIGIN=PH 
               
               
                 *DATE=09April2019 
               
               
                 *VERSION=2 
               
               
                 *#SIMETRIX 
               
            
           
           
               
               
            
               
                 .Model 
                  ZXTN619MA NPN 
               
            
           
           
               
               
               
            
               
                 + 
                  IS = 
                 5.8032E−13 
               
               
                 + 
                  NF = 
                 1.02 
               
               
                 + 
                  ISE = 
                 1.5933E−13 
               
               
                 + 
                  NE = 
                 1.4148 
               
               
                 + 
                  BF = 
                 465 
               
               
                 + 
                  IKF = 
                 8 
               
               
                 + 
                  NK = 
                 0.8 
               
               
                 + 
                  VAF = 
                 84 
               
               
                 + 
                  NR = 
                 1.0006 
               
               
                 + 
                  ISC = 
                 5E−12 
               
               
                 + 
                  NC = 
                 1.6 
               
               
                 + 
                  BR = 
                 110 
               
               
                 + 
                  IKR = 
                 1.4 
               
               
                 + 
                  VAR = 
                 51 
               
               
                 + 
                  RB = 
                 14.5 
               
               
                 + 
                  IRB = 
                 8.00E−06 
               
               
                 + 
                  RBM = 
                 0.2 
               
               
                 + 
                  RE = 
                 0.05 
               
               
                 + 
                  RC = 
                 0.0375 
               
               
                 + 
                  CJE= 
                 2.17E−10 
               
               
                 + 
                  VJE = 
                 0.75 
               
               
                 + 
                  MJE = 
                 0.33 
               
               
                 + 
                  CJC = 
                 4E−11 
               
               
                 + 
                  VJC = 
                 0.4347 
               
               
                 + 
                  MJC = 
                 0.3708 
               
               
                 + 
                  XCJC = 
                 1 
               
               
                 + 
                  CJS = 
                 0 
               
               
                 + 
                  VJS = 
                 0.75 
               
               
                 + 
                  MJS = 
                 0 
               
               
                 + 
                  TF = 
                 780.0E−12 
               
               
                 + 
                  XTF = 
                 0 
               
               
                 + 
                  VTF = 
                 1E+20 
               
               
                 + 
                  ITF = 
                 0 
               
               
                 + 
                  PTF = 
                 0 
               
               
                 + 
                  TR = 
                 9.00E−09 
               
               
                 + 
                  XTB = 
                 1.3 
               
               
                 + 
                  XTI = 
                 3 
               
               
                 + 
                  RCO = 
                 0 
               
               
                 + 
                  TRB1 = 
                 0 
               
               
                 + 
                  TRB2 = 
                 0 
               
               
                 + 
                  TRC1 = 
                 0 
               
               
                 + 
                  TRC2 = 
                 0 
               
               
                 + 
                  TRE1 = 
                 0 
               
               
                 + 
                  TRE2 = 
                 0 
               
               
                 + 
                  TRM1 = 
                 0 
               
               
                 + 
                  TRM2 = 
                 0 
               
            
           
           
               
               
            
               
                 * 
                  T_ABS = 
               
               
                 + 
                  T_MEASURED =27 
               
               
                 * 
                  T_REL_GLOBAL = 
               
               
                 + 
                  QUASIMOD = 1 
               
            
           
           
               
               
               
            
               
                 + 
                  CN = 
                 2.42 
               
               
                 + 
                  D = 
                 0.87 
               
               
                 + 
                  FC = 
                 0.5 
               
               
                 + 
                  EG = 
                 1.11 
               
               
                 + 
                  GAMMA = 
                  1E−11 
               
               
                 + 
                  ISS = 
                 0 
               
               
                 + 
                  NS = 
                 1 
               
               
                 + 
                  QCO = 
                 0 
               
               
                 + 
                  AF = 
                 1 
               
               
                 + 
                  KF = 
                 0 
               
               
                 + 
                  VG = 
                 1.206 
               
               
                 + 
                  VO = 
                 10 
               
            
           
           
               
               
            
               
                 * 
                   (c) 2019 Diodes Inc 
               
            
           
           
               
            
               
                 * 
               
            
           
           
               
               
            
               
                 * 
                 The copyright in these models and the designs embodied belong 
               
               
                 * 
                 to Diodes Incorporated (“ Zetex ”). They are supplied 
               
               
                 * 
                 free of charge by Zetex for the purpose of research and design 
               
               
                 * 
                 and may be used or copied intact (including this notice) for 
               
               
                 * 
                 that purpose only. All other rights are reserved. The models 
               
               
                 * 
                 are believed accurate but no condition or warranty as to their 
               
               
                 * 
                 merchantability or fitness for purpose is given and no liability 
               
               
                 * 
                 in respect of any use is accepted by Diodes Incorporated, its distributor 
               
               
                 * 
                 or agents. 
               
            
           
           
               
            
               
                 * 
               
            
           
           
               
               
            
               
                 * 
                 Diodes Zetex Semiconductors Ltd, Zetex Technology Park, Chadderton, 
               
               
                 * 
                 Oldham, United Kingdom, OL9 9LL 
               
            
           
           
               
            
               
                 .ends 
               
               
                 .subckt ZXTN620MA 1 2 3 
               
               
                 Q1 1 2 3 ZXTN620MA 
               
            
           
           
               
               
            
               
                 *Use BF={480/1.5} 
                    for minimum HFE 
               
               
                 *Use BF= 480 
                    for nominal HFE 
               
               
                 *Use BF={480*1.5} 
                    for maximum HFE 
               
            
           
           
               
            
               
                 *DIODES_INC_SPICE_MODEL 
               
               
                 *ORIGIN=DZSL_DPG_GM 
               
               
                 *SIMULATOR=PSPICE 
               
               
                 *DATE=27JAN2011 
               
               
                 *VERSION=1 
               
               
                 * 
               
               
                 .MODEL ZXTN620MA NPN IS =6.5E−13 BF ={480*1.0} NF=1.003 VAF=150 IKF=1.5 
               
               
                 +ISE=2.00E−13 NE=1.42 BR=180 NR=1.0015 VAR=55 IKR=1 ISC=4.00E−12 
               
               
                 +NC=1.3 RB=0.04 RE=0.048 RC=0.065 CJE=2.13E−10 CJC=3.30E−11 VJC=0.48 
               
               
                 +MJC=0.41 TF =9E−10 TR=3.5E−8 
               
               
                 * 
               
               
                 * 
               
               
                 .ends 
               
               
                 .subckt ZXTN25100DG 1 2 3 
               
            
           
           
               
               
            
               
                 *Use BF={550/1.5} 
                    for minimum HFE 
               
               
                 *Use BF= 550 
                    for nominal HFE 
               
               
                 *Use BF={550*1.5} 
                    for maximum HEE 
               
            
           
           
               
            
               
                 Q1 1 2 3 ZXTN25100DG 
               
               
                 .MODEL ZXTN25100DG NPN IS=6E−13 NF=1 BF=550 IKF=4 VAF=117 ISE=1.3E−13 
               
               
                 + NE=1.42 NR=1 BR=35 IKR=1 VAR=36 ISC=5E−13 NC=1.18 RB=0.2 RE=0.0013 
               
               
                 + RC=0.0016 CJC=28E−12 MJC=0.3 VJC=0.4 CJE=182E−12 MJE=0.39 VJE=0.78 
               
               
                 + TF=7.5E−10 TR=5.3E−8 XTB=1.4 TRC1=.005 TRB1=.005 TRE1=.005 QUASIMOD=1 
               
               
                 + RCO=7 GAMMA=8.3E−8 
               
               
                 * 
               
               
                 * 
               
               
                 .ends 
               
               
                 .subckt FZT855 1 2 3 
               
               
                 Q1 1 2 3 FZT855 
               
            
           
           
               
               
            
               
                 *Use BF={240/2.0} 
                    for minimum HFE 
               
               
                 *Use BF= 240 
                    for nominal HFE 
               
               
                 *Use BF={240*2.0} 
                    for maximum HFE 
               
            
           
           
               
            
               
                 *ZETEX FZT855 Spice Model v2.0 Last Revised 24/2/05 
               
               
                 * 
               
               
                 .MODEL FZT855 NPN IS =7.5E−13 BF ={240} NF=0.995 VAF=350 ISE=4E−13 
               
               
                 +NE=1.42 GAMMA=8E−8 RCO=2 XTB=1.4 BR=27 NR=1.0015 VAR=140 ISC=8E−12 
               
               
                 +NC=1.3 RB=0.15 RE=0.018 RC=0.018 CJE=4.2E−10 CJC=6.6E−11 VJC=0.48 
               
               
                 +MJC=0.41 TF =1.5E−9 TR=18E−8 QUASIMOD=1 
               
               
                 * 
               
               
                 .ends 
               
               
                 .subckt ZXT1053AK 1 2 3 
               
               
                 Q1 1 2 3 ZXT1053AK 
               
               
                 *ZETEX ZXT1053AK Spice Model v1.0 Last Revised 08/03/06 
               
            
           
           
               
               
            
               
                 *Use BF=500 
                   for minimum HFE 
               
               
                 *Use BF=763 
                   for nominal HFE 
               
               
                 *Use BF=2800 
                   for maximum HFE 
               
            
           
           
               
            
               
                 .MODEL ZXT1053AK NPN IS=2.1E−12 NF=1.0 BF=760 IKF=2.2 VAF=100 
               
            
           
           
               
               
            
               
                 + 
                   ISE=0.9E−13 NE=1.25 NR=0.99 BR=150 IKR=2.5 VAR=15 
               
               
                 + 
                   ISC=5.0E−10 NC=1.76 RB=0.1 RE=0.028 RC=0.016 
               
               
                 + 
                   CJC=75.1E−12 CJE=520E−12 MJC=0.415 MJE=0.367 
               
               
                 + 
                   VJC=0.512 VJE=0.766 TF=550E−12 TR=22E−9 
               
            
           
           
               
            
               
                 * 
               
               
                 * 
               
               
                 .ends 
               
               
                 * RB501 Schottky diode 
               
               
                 * 
               
               
                 .model RB501VM-40 D(Is=825.5n N=1.059 Rs=1.187 Ikf=13.61 Xti=2 Eg=.55 Cjo=20.268p 
               
               
                 M=442.8m Vj=579.28m Isr=200.54n Nr=1.1 Bv=45 tt=14.7n Iave=0.1 Vpk=45 mfg=Rohm 
               
               
                 type=Schottky) 
               
               
                 * DS186 Lumiled LED 
               
               
                 * 
               
               
                 .model DS186 D(Is=4e−13 Rs=.125 N=3.8 Eg=3.0 Cjo=1.2n Xti=13 Iave=1.6 Vpk=5 
               
               
                 + mfg=Lumileds type=LED) 
               
               
                   
               
            
           
         
       
     
       FIG. 13  discloses an equivalent circuit of the previous disclosed embodiments (one branch shown only)  1300  using a Darlington configuration made with Q1  1301  driving the base of Q2  1302 . The Darlington approach offers the benefit of elevated gains (typically HFE1×HFE2) and if the speed of the transistors is sufficient, no penalty is seen in switching. In this configuration it is best to connect Q1&#39;s  1301  collector to the Nth LED instead of Q2&#39;s  1302  collector in order to reduce Q2&#39;s  1302  collector voltage, thus the DC power consumed by Q2  1302 . As seen in  FIG. 13 , it is connected above the second LED  1305  as an example. As long as the collector voltage tolerance of Q1  1301  is maintained, any appropriate higher voltage than V c (Q2)  1302  can be used. D1  1303  and D2  1304  can be used instead of a single transistor following the same principle because when the worst case forward current (i.e., worse voltage matching) flows through D1  1303  and D2  1304 , the collector voltage of Q2  1304  is still in the plateau region, away from saturation. Typically, this would be on the order of 0.3V but can be adjusted generally between 0.050V-0.60V either for a Darlington configuration or a single transistor configuration. 
     The graphs  1401  to  1404  of  FIG. 14A-D  shows the voltage and current performance of a single branch of the circuit of  FIG. 13 . The graphs of  FIGS. 14A-D  shows the typical performance of an integrated 2-branch circuits of  FIGS. 13 and 17 . In an exemplary embodiment, the invention uses DS186 white LEDs and was target for 600 mA/string (1200 mA total). The internal resistors were selected for optimal operation near 350 mA such that and additional parallel (R parallel ) resistor was used at 600 mA. Graph  1401  shows the collector voltage on branch 2 as an additional offset voltage is added to branch 2. If that additional voltage is negative then it results in a proportional increase in branch 2 voltage as the collector voltage in Branch 1 is fixed around 0.25V. Similarly, when the offset voltage is positive, branch 2&#39;s collector voltage is pinned at around 0.25V. Branch 1 voltage is complementary to Branch 2 voltage meaning that it is mirrored on the Y-axis. An ideal current mirror would should show 0V on the positive offset voltage and would increase linearly on the negative voltage axis with a slope of 1:1. The invention of  FIG. 13  shows ideal behavior but for an offset of about 0.25V across the entire range of voltages shown. 
     Graph  1402  shows the total power dissipated by the invention of  FIG. 13  is about 0.75 W when balanced and symmetrically increases at a rate of about 0.6 W/V (0.6 A/branch). An ideal current splitter would start at (0,0) and increase linearly with a slope of 0.6 W/V. As noted, the disclosed invention is only consuming 0.75 W more than an ideal linear current splitter. 
     Graph  1403  shows the actual branch 2 current on a linear scale so that the current mirroring performance can be seen. 
     Graph  1404  shows the fraction of the total ideal current (600 mA) passing through branch 2 as the circuit reacts to variable voltage imbalance from −5V to +5V. The average slope is about 0.24%/V (1.2%/5V) so this system is typically performing within 1% of expect current when dividing. 
       FIG. 15  discloses a similar Darlington configuration but uses an additional (cascode) transistor (Q3)  1501  to help in the case where the collector voltage of Q1  1502  could be exposed to higher voltages than desired. Resistors R2  1503 , R3  1504  and R4  1505  are appropriately chosen to ensure that both Q3  1501  and Q1  1502  are properly biased across temperature and gain extremes. 
       FIG. 16  shows a further similar Darlington configuration where an NMOS transistor  1601  ensures sufficient base current to Q3  1602  without impeding on the base current requirements for Q1  1603  now covered by resistors R3-R4  1604 ,  1605  and R2  1606 . In the circuit of either  FIG. 15 or 16  the ratio of resistors R3/(R3+R4) is chosen to ensure proper voltage across Q1  1603  and Q3  1602  collectors. 
       FIG. 17  discloses an embodiment where the current dividing circuit (one leg shown) is formed in an integrated circuit and external resistors  1701 ,  1702  (R parallel  and R series ) are used to bias the Darlington base of Q1  1703  with an appropriate current allowing the circuit to offer optimized operation for set currents as typically expected in PWM applications. For example, if the use of R2  1704  in parallel with R3  1705  and R4  1706  is optimal for a certain Q2  1707  collector current, the optimal current can be increased by adding R parallel    1701  with some chosen value such as to increase the base current in Q2  1707 . Likewise, if the optimal current needs to be decreased an appropriate R series  resistor  1702  can be selected such that the Q2&#39;s  1707  collector is constant across the range of expected operating and/or manufacturing conditions. As can be seen,  FIG. 17  is a superset of the circuit of  FIG. 13  which is embedded therein. 
     The disclosed invention can also be implemented in a system of M strings if instead of tying resistors to the Nth LED of each string, those resistors (or a single one of parallel equivalent value) are tied from a fix power supply (e.g., 2-8 Volts) in order to generate a bias current sufficient to ensure operation across the entire condition range (low/high HFE, low/high temperature). 
     The embodiments shown and described above are only exemplary. Even though numerous characteristics and advantages of the invention have been set forth in the foregoing description, the disclosure is illustrative only and changes may be made within the principles of the invention to the full extent indicated by the broad general meaning of the terms used herein. Various alterations, modifications and substitutions can be made to the disclosed invention and the system that implements the invention without departing in any way from the spirit and scope of the invention