Abstract: The present invention discloses a modulation method for inverter AC waveform. The detailed steps of the modulation method comprise: generating an AC waveform which includes at least three time periods, wherein a middle time period corresponds to a peak segment of the AC waveform, and the remaining time periods are averaged corresponding to the rise and decline segments of the AC waveform; and during the at least three time periods, a duty ratio modulated driving signal is generated according to different duty ratios, so as to modulate the AC waveform and generate a stepping AC waveform converted from the AC waveform. The stepping AC waveform generated by the modulation method of the present invention will have a longer dwell time at zero potential, so as to turn on the AC electric tool more efficiently.

Abstract: A method for determining capacitance values of capacitances of a photovoltaic system including a multiphase inverter which includes an output current filter on an alternating current side thereof and is connected to a multiphase energy supply network via a switching element and is associated with at least one intermediate circuit capacitance on the direct current side thereof is provided.

Abstract: A digitalized double-excitation uninterrupted switching power supply comprises a main transformer provided with a primary coil and a secondary coil, a main loop, a synchronous rectification output loop, a synchronous direct-current converter and a digital control unit, wherein the main loop comprises a high-voltage switching network, a resonant inductor, the primary coil and a resonant capacitor. The synchronous rectification output loop comprises a current-doubler rectifier formed by connecting two synchronous rectifier tubes in series oppositely and the secondary coil in parallel, and a filter circuit connected to two output ends of the current-doubler rectifier. The synchronous direct-current converter comprises two low-voltage switching tubes, an isolator and a low-voltage direct-current source.

Abstract: A power semiconductor package includes a first group of semiconductor dies attached to a first side of a substrate and evenly distributed over a width of the substrate and a second group of semiconductor dies attached to the first side of the substrate and evenly distributed over the substrate width. Each die in the first and second groups has all terminals at one side which is attached to the first side of the substrate and an insulated or isolated face at a side opposite the side with the terminals. A first intermediary metal layer of the substrate forms a first DC terminal. A second intermediary metal layer of the substrate forms a second DC terminal. These intermediary metal layers are insulated from one another and form a parallel plate waveguide. Additional power semiconductor package embodiments are described.

Abstract: A resonant type high frequency power supply device provided with a power semiconductor element that performs a switching operation at a high frequency exceeding 2 MHz, the resonant type high frequency power supply device including a variable inductor that makes an adjustment to the amplitude of a device output voltage.

Abstract: A power supply startup system activates a power supply of a device provided with a battery or the like at high speed by a wireless signal while suppressing current consumption on standby. The power supply startup system includes a battery, a device supplied with a power from the battery, and a controller which performs wireless communication with the device. The device includes a power supply section which generates a power supply from the battery, a startup section which receives a wireless startup signal transmitted by the controller and outputs a startup signal to the power supply section, a control section which controls the power supply section and the startup section, and a wireless communication section which performs wireless communication with the controller. The wireless startup signal includes at least two signal regions of a first stage and a second stage.

Abstract: The present invention discloses an interleaved LLC convertor with current sharing.

Abstract: A power generation apparatus includes a power calculation unit configured to receive voltage information and temperature information from a power generation module, and calculate power generation information of the power generation module based on the received voltage information and temperature information.

Abstract: A method and apparatus for multiplexing an electrical contact interface between two electrical devices uses a time differentiated enablement of two or more different circuit elements in a first electrical device that are accessed via the multiplexed contact by a second electrical device. A timing control circuit in the first electrical device enables and disables circuit elements in the first electrical device coupled to a shared information contact over time. The second electrical device interacts with a first circuit element during an initial period upon connection to the first electrical device, and then interacts with a second circuit element after the initial period.

Abstract: There is provided a solar power generation system including a solar cell, an inverter converting a direct current power generated by the solar cell into an alternating current power, a system voltage measurement unit measuring a system voltage, a voltage drop detector detecting a voltage drop of a power system, based on the system voltage, a first direct current voltage controller controlling a direct current voltage of the inverter to enhance a power generation efficiency of the solar cell, when the voltage drop is not detected, and a second direct current voltage controller controlling the direct current voltage of the inverter to suppress a current output from the inverter, when the voltage drop is detected.

Abstract: Exemplary embodiments are directed to a method for controlling a switching branch of a three-level converter to enter a stop state. The switching branch including a first semiconductor switch and a second semiconductor switch, a first diode and a second diode, a third semiconductor switch and a fourth semiconductor switch, a third diode, and a fourth diode, a fifth semiconductor switch and a sixth semiconductor switch, a fifth diode, and a sixth diode, and a manner of controlling the semiconductor switches. When the switching branch is set to enter a stop state, current flowing in a main circuit of the switching branch is transferred in a controlled manner to diodes that conduct the current, when all the semiconductor switches of the main circuit of the converter are turned OFF.

Abstract: A power conversion apparatus includes a power-conversion circuit unit that includes at least two voltage-type bridge circuits of an upper and lower arm configuration including switching elements connected in series, each of the switching elements including a transistor and a free wheel diode connected to the transistor in inverse parallel. Each of the voltage-type bridge circuits is configured to include, as the free wheel diodes: a SiC-SBD (SiC-Schottky-Barrier Diodes) in both upper and lower arms; a SiC-SBD only in the upper arm; a SiC-SBD only in the lower arm; or a diode other than the SiC-SBD in both the upper and lower arms; and the power-conversion circuit unit is configured by combining at least two configurations among the four configurations for the voltage-type bridge circuits.

Abstract: Disclosed herein is a direct current to direct current (DC-DC) converter. The DC-DC converter includes a first bridge and a second bridge. The first bridge includes a first switch and a second switch, whereas the second bridge includes a third switch and a fourth switch. The second bridge is in parallel connection with the first bridge. The second switch is in series connection with the first switch, and the fourth switch is in series connection with the third switch. The DC-DC converter switches between a first mode and a second mode based on a detection signal. Further, a method for controlling the DC-DC converter is also disclosed herein.

Abstract: A power converter topology is adapted for efficiency according to input voltage, output voltage or output current conditions. Topology adaptation is achieved by control responsive to the input and output operating conditions, or to one or more external control signals. Transition between any two topologies is implemented by pulse width modulation in the two switches in one of two bridge legs of a full bridge converter. When transitioning from full-bridge to half-bridge topology, the duty ratio of one switch in one leg of the full bridge is increased, while simultaneously the duty ratio of the other switch in the same leg is reduced until one switch is continuously on, while the other switch is continuously off. The transition from the half-bridge to the full-bridge topology is accomplished by modulating the same switches such that, at the end of the transition, both switches operate with substantially the same duty cycle.

Abstract: A converter for an electrical machine having a plurality of phase lines for connecting the electrical machine. For each phase line the converter has a half-bridge with a first semiconductor switch is configured to electrically connect at least one of the phase lines intermittently to a first supply line of the converter, and a second semiconductor switch configured to electrically connect the phase line intermittently to a second supply line of the converter. The converter is configured for operation in a first energy recovery limiting mode in which at least two of the first semiconductor switches are at least intermittently on simultaneously.

Abstract: A switching element of a power converter generates a low voltage, using a current flowing in the power converter, and supplies a power to drive itself. A switching element of a power converter for conversion from direct current into alternate current or from alternate current into direct current includes: a terminal and a terminal which are used in building the switching element itself in the power converter; a capacitor, a high-side controllable switch and a low-side controllable switch enabling outputting the voltage of the capacitor, the voltage being output between the terminal and the terminal, and a self-supply power source for supplying a power to drive the bi-directional chopper switching element itself, using a current flowing in the capacitor.

Abstract: A DC link is provided, which includes a capacitor connected in parallel to an output of a converter circuit, and outputs a pulsating DC link voltage. An inverter circuit is provided, which converts an output of the DC link to AC by switching, and supplies the AC to a motor connected thereto. A controller is provided, which controls switching of the inverter circuit so that motor currents pulsate in synchronization with pulsation of a power-supply voltage. The controller controls the switching of the inverter circuit in accordance with a load of the motor or an operational state of the motor, and reduces pulsation amplitude of the motor currents.

Abstract: Systems and methods are provided for controlling an uninterruptible power supply (UPS) to transition between three- or higher-level operation and two-level operation in a neutral-point-clamped (NPC) inverter. In an example, a UPS system includes an NPC inverter and a controller. The NPC inverter may supply power to a load. The controller may control the inverter to operate in a three-level mode or higher when the load is substantially balanced and to operate in a two-level mode when the load is substantially unbalanced.

Abstract: A switching power supply device includes: a positive voltage output circuit connected to a direct-current power supply, the positive voltage output circuit including a first switching element, a voltage boosting inductor, a first rectifying element and a first capacitor; a negative voltage output circuit connected to the power supply, the negative voltage output circuit including a second switching element, a voltage dropping inductor, a second rectifying element and a second capacitor; and an adder circuit configured to add switching currents flowing when the first and the second switching elements are operated. The circuit elements of the positive voltage output circuit are symmetrical with those of the negative voltage output circuit. The first switching current of the positive voltage output circuit and the second switching current of the negative voltage output circuit are generated in mutually opposite directions and are inputted to the adder circuit.

Abstract: The invention relates to a static converter connected between an electrical voltage source and an electrical load, said converter including a main static conversion arm comprising an output electronic switching cell and a backup conversion arm having identical structures. The static converter includes a pair of fuses connected on either side of the main arm, and a switching circuit comprising a connection element connecting the backup arm to the connection points between the fuses and the input terminals of the main arm, such that, when a fault occurs on one of the switching cells forming the main arm, a stable conductive link is established between the two fuses, the main arm is isolated by the two fuses, and the backup arm is spontaneously connected to the output of the main arm via the conductive line and replaces the main arm.

Abstract: A power module is disclosed having a first module block defining a first rectifier and including a first rectifier switch having a first FET and connected in parallel with a first diode, a second module block including a second FET connected in parallel with a second diode, a third module block including a third FET connected in parallel with a third diode, wherein the second and third module blocks are positioned between first and second terminal interfaces of the power module, and wherein two serially connected diodes are on the first interface side of the power module in parallel with the serially connected second and third module blocks, and a fourth module block defining a second rectifier and including a second rectifier switch having a fourth FET and connected in parallel with a fourth diode.

Abstract: Apparatus and method for controlling inductor current in a switch mode power supply. In one embodiment, a switch mode power supply includes an inductor, a high-side switch coupled to the inductor, a low-side switch coupled to the inductor, and a controller. The controller is coupled to at least one of the high-side switch and the low-side switch. The controller includes a first capacitor and a current source. The controller is configured to control timing of current switching to the inductor by enabling current flow through the at least one of the high-side switch and the low-side switch based on time to charge the first capacitor via the current source. The time is a function of voltage across the inductor.

Abstract: A method of synchronously operating a power converter in a series of converter operating cycles includes providing an oscillator for generating clock signals at an oscillator frequency, and generating timing control signals for each of multiple events based upon the clock signals. The method further includes to: (i) turn a primary switch ON and OFF at times when essentially zero voltage is impressed across the primary switch and essentially zero resonant current is flowing in the primary switch; and (ii) turn a secondary switch ON and OFF at times when essentially zero current is flowing in the secondary switch and essentially zero voltage is impressed across the secondary switch. The oscillator frequency is preset, and the timing of the timing control signals for one or more selected events may be set independently of other timing control signals and events.

Abstract: In a power converter, a deviation calculator calculates, in each cycle, a deviation between a value of an input electrical parameter of a switch circuit and a target value selected by a selector in a previous cycle. The input electrical parameter depends on the input power to the switch circuit. A second calculator calculates, in each cycle, a value of a second feedback controlled variable such that the value of the second feedback variable approaches the value of the input electrical parameter. A controller controls, in each cycle, the selector to select one of the value of the first feedback controlled variable and the value of the second feedback controlled variable as the target value for the next cycle according to the deviation calculated by the deviation calculator.

Abstract: The invention relates to an operating state circuit for driving an inverter with half-bridges having respective switching devices, which inverter supplies an n-phase supply voltage to an n-phase electrical machine via phase connections associated with the respective half-bridges, where n?1.

Abstract: A power supply device that is applicable to both 200 V and 400 V series input power by switching the operation of an auxiliary switching circuit with a switching switch. When a relatively large output is requested, PWM control is performed to adjust the on pulse width of a control pulse signal provided to switching elements of an inverter circuit and an auxiliary switching circuit, which is operated in cooperation with the inverter circuit. When a relatively small output is requested, PSM control is performed to adjusting a phase difference of two control pulse signals provided to the same set of switching elements in the inverter circuit.

Abstract: A measurement circuit in a motor circuit generates signals for use in a motor control strategy for an electric motor. The measurement circuit comprises a first current sensing means which produces an output signal indicative of the current flowing in a di/dt path connecting the phases of the motor to a ground or a common positive supply voltage, and further comprises a second current sensing means which produces an output signal indicative of the rate of change of current flowing in the ground line, and in which the second current sensing means comprises a Rogowski coil.

Abstract: In a process of changing an AC voltage from zero to +Ed (or negative to positive) or from zero to ?Ed (or positive to negative), a control method in accordance with some aspects of the invention detects voltage across the capacitors and when the detected voltage is lower than a predetermined voltage value, switching operation pattern capable of charging the capacitor is given to the switching elements during a short period of time; when the detected voltage is higher than the predetermined voltage value, a switching operation pattern capable of discharging the capacitor is given to the switching elements during a short period of time. Thus, the width of voltage variation of the capacitors is limited within a specified variation range.

Abstract: A method of performing space vector modulation for PWM control for creating AC waveforms includes generating and sampling a reference signal to generate reference samples and performing a reference vector approximation to synthesize a reference vector associated with at least one of the reference samples. The reference vector approximation employs active vectors, one or more zero vectors, and one or more pseudo zero vectors in the formation thereof. Another method of performing space vector modulation (SVM) includes generating a reference signal and sampling the reference signal at a sampling frequency to generate a plurality of reference samples. The method also includes performing a reference vector approximation to synthesize a reference vector associated with at least one of the reference samples, wherein the reference vector approximation has a first portion that employs two adjacent active vectors and a remaining portion that employs two non-adjacent active vectors in the formation thereof.

Abstract: A load drive control device is provided, which includes a pulse generator for generating pulse signals with a duty ratio to drive an inductive load, a feedback setting section for setting the duty ratio for feedback, a detection setting section for setting the duty ratio for detection of a natural vibration frequency of the inductive load, a natural vibration frequency setting section for setting the natural vibration frequency of the inductive load based on an actual current value detected at setting the duty ratio for detection, and a selection section for selecting the feedback setting section as a duty ratio setting section at a normal time and for selecting the detection setting section as the duty ratio setting section when a condition for detecting the natural vibration frequency is satisfied.

Abstract: A discharge controller carries out discharge control by determining a voltage to be applied to a conduction control terminal of each of switching elements such that a current in a non-saturation region of one of the switching elements is lower than a current in a non-saturation region of the other thereof, and applying the voltage to the conduction control terminal of each switching element with an opening-closing member opening an electrical path to turn on the switching elements, resulting in short-circuit of both electrodes of a capacitor so that a discharge current is outputted from the capacitor based on the discharge control. A manipulator manipulates, based on a value of the discharge current, how to apply the voltage to the conduction control terminal of the one of the switching elements, thus controlling an amount of heat to be generated in the one of the switching elements.

Abstract: The present invention discloses an inverter and a control method thereof. The inverter includes a first bridge leg having a series of first switch, second switch, third switch, fourth switch and fifth switch, and a second first bridge leg having a series of sixth switch, seventh switch, eighth switch, ninth switch, tenth switch. The control method includes steps of synchronously turning on or off the first switch, second switch, ninth switch and tenth switch, controlling that an on/off state of the third switch or eighth switch is complementary to an on/off state of the first switch, second switch, ninth switch and tenth switch, and synchronously turning on or off the fourth switch, fifth switch, sixth switch and seventh switch.

Abstract: A control system includes a fundamental control unit, first and second compensation control units, a switch control unit, and a switch implementation unit. The fundamental control unit generates fundamental commands to implement fundamental power conversion operation for a converter. The first compensation control unit generates a first compensation signal for injection into the fundamental command to balance neutral point voltage when the converter is in operation in a first state. The second compensation control unit generates a second compensation signal for injection into the fundamental command to balance neutral point voltage when the converter is in operation in a second state. The switch control unit detects first and second states of the converter and provides first and second switch signals respectively.

Abstract: A transformerless inverter that serves to feed electricity from a DC current source into an AC power grid, has an inverter bridge and a DC/DC converter connected upstream of the inverter bridge. The DC/DC converter converts an input DC voltage that is present between two input lines of the inverter into a DC link voltage present between two input lines of the inverter bridge. The inverter bridge converts the DC link voltage present at the input lines thereof into an output AC voltage. The DC/DC converter includes at least one resonant circuit that has a resonance inductance and a resonance capacitance and is connected on its input side via at least two clocked switches to one of the two input lines of the inverter or an intermediate potential line carrying a potential in between. The input lines of the inverter and the input lines of the inverter bridge are galvanically isolated from one another by a capacitive method.

Abstract: A switching power supply apparatus includes a transformer having a primary winding, a secondary winding, and an auxiliary winding, a switching element coupled in series to the primary winding; an output circuit section generating a voltage output from power transferred from the primary winding to the secondary winding in response to a switching operation of the switching element, a feedback signal generation circuit section configured to, during a secondary side conduction period in which an electric current flows through the secondary winding, generate a feedback signal having a signal level corrected based on a length of the secondary side conduction period, from an auxiliary winding voltage induced in the auxiliary winding, and a control circuit section driving the switching element based on the feedback signal.

Abstract: There is provided an even-level inverter, including: a voltage-dividing circuit dividing input DC power into an even number of voltage levels; a plurality of switching devices connected to individual nodes of the voltage-dividing circuit having the even number of voltage levels; and a bidirectional switching device connected to the individual nodes of the voltage-dividing circuit through at least one of the plurality of switching devices and including at least two transistors. According to the present invention, the bidirectional switching device is implemented without a diode to thereby reduce conduction loss caused due to an anti-parallel diode included in the related art bidirectional switching device, and a neutral point of the voltage-dividing circuit is electrically separated from the switching devices to thereby control reactive power.

Abstract: The invention discloses a voltage source converter and a voltage source converter system. The voltage source converter comprises: a multi-level voltage source converter, being adapted to output a multiple levels of a first voltage at one of two first output terminals through a multiple of first conducting paths; a first energy store; and a first switching element, being arranged to directly connected with the first output terminal, and being adapted to switch the first energy store in or out of the first conducting path so as to combine a level of the voltage of the first energy store with the level of the first voltage as a second voltage output at a second output terminal. By having the topology as above, the voltage class of each of the power semiconductors can be kept lower with the number of the power semiconductors unchanged. Besides, VDRM is lowed as compared to conventional topology. This renders the reduction of the cost and the increase of the liability.

Abstract: The invention relates to a H-bridge inverter and a method for controlling a H-bridge converter. The H-bridge inverter (1) comprises first and second DC terminals (Tdc1, Tdc2), first and second AC terminals (Tac1, Tac2), a first switch (S1), a second switch (S2), a third switch (S3) and a fourth switch (S4). The inverter further comprises a control circuit for controlling the switching of the first, second, third and fourth switches (S11, S2, S3, S4).

Abstract: An exemplary method and an apparatus implementing the method for an arrangement having a three-phase, multi-level inverter, an output LCL-filter connecting the inverter to a grid, and a virtual-ground connection between the LCL-filter and the neutral point of the DC-link. The method includes determining a zero-sequence component of an LCL-filter inverter-side current, calculating a zero-sequence damping and balancing voltage term based on the LCL-filter inverter-side current zero-sequence component and voltages over the two halves of the DC-link, and adding the zero-sequence damping and voltage balancing term to the output voltage reference.

Abstract: A power conversion device according to the aspects of the present technique is presented. The device includes a first converter and a second converter operatively coupled to the first converter. Moreover, the device includes a phase leg operatively coupled between the first converter, the second converter, where the phase leg includes a first unidirectional switch, a second unidirectional switch operatively coupled to the first unidirectional switch, and a first bidirectional switch, where a first end of the first bidirectional switch is operatively coupled to at least one of the first unidirectional switch and the second unidirectional switch.

Abstract: A power converter is configured to transfer energy from a photovoltaic (PV) array to a DC bus internal to the power converter. The power converter executes a modulation module to selectively connect one or more switching devices between the output of the PV array and the DC bus. The power converter is configured to operate in multiple operating modes. In one operating mode, the converter operates with a fixed modulation period and a variable on time, and in another operating mode, the converter operates with a variable modulation period and a fixed on time. The improved power converter provides highly efficient low power energy capture, improving power efficiency and enabling energy capture in low light conditions with reduced converter losses.

Abstract: A DC-to-AC power conversion system is provided to convert a DC input voltage into an AC output voltage, which mainly includes a bridge switching circuit, an auxiliary switch circuit, and a control circuit. The bridge switching circuit has a first power switch, a second power switch, a third power switch, and a fourth power switch. The auxiliary switch circuit has a fifth power switch, a sixth power switch, a seventh power switch, and an eighth power switch. The control circuit produces a complementary switching signal pair to control the first and fourth power switches and the second and third power switches, respectively. In addition, the control circuit produces a complementary level signal pair to control the sixth and seventh power switches and the fifth and eighth power switches, respectively.

Abstract: The present invention provides an electric circuit wherein a multi-phase bridge is connected in series with a plurality of single-phase bridges. The multi-phase bridge is composed of a plurality of 3-level diode clamped legs, while the single-phase bridges each is composed of two 3-level diode clamped legs. The present invention also provides control strategy for synthesizing multi-level voltage waveforms from output voltages of the multi-phase bridge and the plurality of single-phase bridges.

Abstract: There is provided a power controller including a drive circuit connected to a DC power supply to apply a first voltage to the drive circuit and configured to supply power to an external load, a current detection circuit configured to detect a current flowing in the drive circuit by converting the current into a second voltage corresponding to the current, and a current-voltage control unit configured to generate a reference voltage corresponding to a limit value of the current flowing in the drive circuit when the first voltage is applied to the drive circuit, and configured to control the drive circuit to operate in a desired current according to the first voltage, based on a comparison result of the reference voltage and the second voltage.

Abstract: A DC to AC converter includes a first switch, a second switch, a first half bridge inverter, and a second half bridge inverter. The first switch includes a first terminal and a second terminal. The second switch includes a first terminal and a second terminal. A portion between the first terminal of the first switch and the first terminal of the second switch is operable to receive a direct current power source. The first half bridge inverter includes a first terminal, a second terminal, and an output terminal. The second half bridge inverter includes a first terminal, a second terminal, and an output terminal. A portion between the output terminal of the first half bridge inverter and the output terminal of the second half bridge inverter is operable to output an alternative current.

Abstract: Systems and methods are provided for regulating the state of charge of a battery. An exemplary electrical system includes a fuel cell coupled to a bus and a battery coupled to the bus via a switching arrangement coupled to a capacitor. An exemplary method for operating the electrical system involves operating the switching arrangement such that a voltage of the battery is substantially equal to a voltage of the fuel cell when a state of charge of the battery is greater than a lower threshold value and less than an upper threshold value, and operating the switching arrangement to couple the capacitor electrically in series between the battery and the bus when the state of charge of the battery is not between the lower threshold value and the upper threshold value.

Abstract: Cascade H-Bridge inverters and carrier-based level shift pulse width modulation techniques are presented for generating inverter stage switching control signals, in which carrier waveform levels are selectively shifted to control THD and to mitigate power distribution imbalances within multilevel inverter elements using either complementary carrier or complementary reference modulation techniques.

Abstract: A circuit includes a full-bridge converter circuit coupled to a transformer for converting a first voltage level to a second voltage level. A sensing circuit is coupled to the transformer for sensing a size of a load coupled to the transformer. A digital feedback circuit is coupled to the full-bridge converter and to the sensing circuit for adjusting a rate at which the full-bridge converter is switched based on a signal received from the sensing circuit.

Abstract: An inverter configured for use within a vehicle to power consumer electronic devices and other types of devices requiring single-phase, AC energy. The inverter may include a network interface or other type of the connection to a vehicle data bus or other message exchange system in order to communicate with an electronic control unit (ECU) or other feature included within the vehicle to monitor and control energy consumption by one or more vehicle subsystems.

Abstract: Techniques for performing DC to DC power conversion in switch-mode converter circuits include combinations of dynamic switch shedding, phase shedding, symmetric phase circuit topologies, and asymmetric phase circuit topologies. In at least one embodiment of the invention, a method of operating a power converter circuit includes operating a first phase switch circuit portion using a first number of switch devices when the power converter circuit is configured in a first mode of operation. The first number is greater than zero. The method includes operating the first phase switch circuit portion using the first number of switch devices when the power converter circuit is configured in a second mode of operation. The method includes operating a second phase switch circuit portion using a second number of switch devices when the power converter circuit is configured in the second mode of operation. The second number is greater than the first number.