Patent Publication Number: US-9413568-B2

Title: Method and apparatus for calibrating an input interface

Description:
BACKGROUND 
     Many memory interfaces employ single-ended receivers to receive data from a corresponding memory or other memory interfaces. A single-ended receiver typically includes a differential amplifier having a reference DC voltage and a data signal usually applied as inputs. 
     SUMMARY 
     According to at least one example embodiment, a two phase calibration approach is employed for calibrating an input/output interface having multiple single-ended receivers. During a first phase, amplifier offset calibration is applied to each of the multiple single-ended receivers. During a second phase, reference voltage calibration is applied to a single-ended receiver of the multiple single-ended receivers to determine a calibration reference voltage value. The calibration reference voltage value is then employed in each of the multiple single-ended receivers during an active phase, e.g., a data reception phase, of the input/output interface. 
     In applying amplifier offset calibration, an input value is applied to both input leads of each amplifier associated with a corresponding single-ended receiver of the multiple single-ended receivers, the amplifier including one or more digital-to-analog converters (DACs) used to calibrate an offset of the amplifier. Control logic associated with input/output interface updates, over a number of iterations, a digital value based on an output of the amplifier. The digital value updated is provided as input to a DAC of the one or more DACs in the amplifier. The final value of the digital value, e.g., associated with a last iteration, is employed as input to the DAC of the one or more DACs in the amplifier for calibrating the offset of the amplifier during the active phase of the input/output interface. The one or more DACs are coupled to at least one gain circuit in the corresponding amplifier. In updating the digital value at a first iteration, the DAC for which the corresponding input digital value to be updated is determined. The DAC is determined based on the output of the corresponding amplifier and a coupling of the DAC to a gain circuit in the amplifier. 
     According to at least one example embodiment, the digital value is updated based on an indication of whether the output of the amplifier is logic 1 or 0. The digital value is represented by multiple bits. The total number of iterations is equal to the number of bits representing the digital value. 
     According to at least one example embodiment, in applying reference voltage calibration, a clock signal and a reference voltage signal are applied as inputs to an amplifier of the single-ended receiver. An indication of a duty cycle associated with an output signal of the amplifier is evaluated. Control logic associated with input/output interface adjusts a level of the reference voltage signal based on the evaluated indication of the duty cycle. The evaluating and adjusting processes are repeated over a number of iterations. 
     In adjusting the level of the reference voltage, the control logic, for example, updates over the number of iterations an input digital value to a digital-to-analog converter (DAC), the DAC providing a reference voltage level value to the amplifier. The input digital value is represented by multiple bits. The number of iterations is equal to the number of bits representing the input digital value minus one. 
     According to at least one example embodiment, the input/output interface is associated with a memory interface, such as, double data rate 2 (DDR2) memory interface, double data rate 3 (DDR3) memory interface, double data rate 4 (DDR4) memory interface, low power double data rate 2 (LP DDR2) memory interface, low power double data rate 3 (LP DDR3) memory interface, low power double data rate 4 (LP DDR4) memory interface, graphical double data rate 3 (GDDR3) memory interface, graphical double data rate 4 (GDDR4) memory interface, graphical double data rate 5 (GDDR5) memory interface, wide input/output (Wide I/O) memory interface, wide input/output 2 (Wide I/O 2) memory interface, or the like. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments of the present invention. 
         FIG. 1  is a diagram illustrating an overview of a memory system, according to at least one example embodiment; 
         FIGS. 2A and 2B  are block diagrams illustrating single-ended receivers associated, respectively, with DDR3 and DDR4 memory interfaces, according to at least one example embodiment; 
         FIG. 3  is a set of plots illustrating the effect of a reference voltage shift on a corresponding DQ signal; 
         FIG. 4A  is a diagram illustrating a system, or circuit, for reference voltage calibration; 
         FIG. 4B  is a diagram illustrating an example scheme of updating the input of the digital-to-analog converter as part of reference voltage calibration, according to at least one example embodiment; 
         FIG. 5  is a tree illustrating an algorithm for adapting the input of the digital-to-analog converter as part of reference voltage calibration, according to at least one example embodiment; 
         FIG. 6A  is a diagram illustrating a system, or circuit, for amplifier offset calibration; 
         FIG. 6B  shows a circuit of two digital-to-analog converters coupled to a gain stage of a differential amplifier, according to at least one example implementation; 
         FIG. 7  is a tree illustrating a scheme according to which a digital input for a DAC, within a differential amplifier of a single-ended receiver, is iteratively updated, according to at least one example embodiment; 
         FIG. 8  shows a set of plots illustrating different operation phases of a differential amplifier of a single-ended receiver, according to at least one example embodiment; and 
         FIG. 9  is a flowchart illustrating a method of calibrating an input interface having multiple single-ended receivers, according to at least one example embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     A description of example embodiments of the invention follows. 
     One of the commonly performed operations by a microprocessor is memory access. While microprocessors are getting faster and faster, latency associated with memory access usually results into a performance bottleneck. In fact, memory bottleneck represents a real challenge with respect to improving the performance of a processing system. One way to reduce latency associated with memory access operations is to enhance performance and accuracy of the memory interface associated with the accessed memory. 
     Many memory interfaces make use of single-ended receivers. Examples of such memory interfaces include double data rate 2 (DDR2) interface, DDR3 interface, DDR4 interface, low power double data rate 2 (LPDDR2) interface, LPDDR3 interface, LPDDR4 interface, graphical double data rate 3 (GDDR3) interface, GDDR4 interface, GDDR5 interface, wide input/output (Wide I/O) interface, and Wide I/O 2 interface. 
       FIG. 1  is a diagram illustrating an overview of a memory system according to at least one example embodiment. The memory system includes a memory controller device  100  and a memory component  90 . The memory controller device is typically implemented within a microprocessor. In response to a read operation, the memory component  90  outputs eight data signals, also referred to as DQ signals, representing eight bits of a data byte, and at least one pair of data strobe signals, also referred to as DQS signals. In the example shown in  FIG. 1 , each four DQ signals are associated with a corresponding DQS signal. The memory controller device  100  includes a bidirectional input/output memory interface  110 , a unidirectional command interface  120 , and a local memory controller LMC  150 . The command interface is an output-only interface for sending commands from the LMC  150  to the memory component  90 . The input/output memory interface  110  is a bidirectional I/O interface for sending data, in both directions, between the memory component  90  and the LMC  150 . The I/O memory interface  110  includes eight single-ended receivers, each having a differential amplifier, e.g.,  101   a - 101   h . For the sake of simplicity, the single-ended receivers  101   a - 101   h are shown with respect to one direction of data transfer between the memory component  90  and the LMC  150 . For each of the differential amplifiers  101   a - 101   h , associated with the single-ended receivers, the corresponding inputs include a reference voltage (V ref ) and one of the DQ signals, e.g., provided by the memory component  90 . The I/O memory interface  110  also includes at least one other differential amplifier, e.g.,  102   a and  102   b . Each of the differential amplifiers  102   a and  102   b is coupled to one pair of DQS signals as inputs. Output of the I/ 0  memory interface  110  is provided to a microprocessor, e.g., to a level-2 cache (L2C) of the microprocessor, through the local memory controller  150 . The output-only command interface  120 , receives input signals from the local memory controller  150  and provides corresponding output signals to the memory component  90 . 
       FIGS. 2A and 2B  are block diagrams illustrating single-ended receivers associated, respectively, with DDR3 and DDR4 memory interfaces, according to at least one example embodiment. In the DDR3 memory interface shown in  FIG. 2A , each input node of a differential amplifier  201   a  of the single-ended receiver is coupled to two resistors. Also, each input node of a differential amplifier  202   a , receiving a pair of DQS signals, is coupled to two resistors. The output of the differential amplifier  202   a  is shifted by 90 degrees. The shifted output of the differential amplifier  202   a  and the output of the differential amplifier  201   a  are provided to a sampler  205   a . The sampler  205   a  is configured to sample the output of the differential amplifier  201   a  based on the shifted output of the differential amplifier  202   a . The output of the sampler  205   a  is provided to the local memory controller  150 . 
     In the DDR4 memory interface shown in  FIG. 2B , the DQ input node of a differential amplifier  201   b  of the single-ended receiver is coupled to a single resistor. Also, the DQS_P input node of a differential amplifier  202   b , receiving a DQS_P signal, is coupled to a single resistor. The reference voltage input to the differential amplifier  201   b  is defined by a digital-to-analog converter (DAC)  215 . Similar to the DDR3 memory interface, the output of the differential amplifier  202   b  is shifted by 90 degrees. The shifted output of the differential amplifier  202   b  and the output of the differential amplifier  201   b  are provided to a sampler  205   b . The sampler  205   b  is configured to sample the output of the differential amplifier  201   b  based on the shifted output of the differential amplifier  202   b . The output of the sampler  205   b  is provided to the local memory controller  150 . 
     Degradation in the performance of a memory interface, e.g., DDR I/O memory interface such as  110 , may be due to a shift in the reference voltage V ref  or amplifier offset. Amplifier offset within a differential amplifier, e.g.,  101   a ,  101   b , . . . , or  101   h , results in an internal potential difference between the two input nodes of the differential amplifier even when the same voltage is applied to both nodes. The shift in the reference voltage and/or the amplifier offset within one or more differential amplifiers may be caused, for example, by Process-Voltage-Temperature (PVT) variation, design of the board on which the integrated circuit(s) (IC) resides, or other factors. 
       FIG. 3  is a set of plots illustrating the effect of a reference voltage shift on a corresponding DQ signal. Plot (a) shows DQS signals while plot (b) shows the same DQS signals shifted by 90 degrees. The plot (c) shows a DQ signal associated with the DQS signals in the plots (a) and (b). The DQ signal in plot (c) and the DQS signals shown in plot (a) are edge-aligned with each other. By shifting the DQS signals as shown in plot (b), the fall and rise phases of the shifted DQS signals become aligned with the middle of the pulse duration of the DQ signal in plot (c). The DQ signal in plot (c) has a reference voltage V ref  equal to half of the corresponding supply voltage, i.e., V dd /2, therefore resulting in equal pulse durations for distinct DQ pulses as shown in plot (d). Plot (e), however, shows a shift in the reference voltage equal to V ref-shift  with respect to half the supply voltage, e.g., V ref-shift =V ref −(V dd /2). The shift in the reference voltage may result in non-equal pulse durations for distinct DQ pulses. A person skilled in the art should appreciate that an offset in internal amplifier voltage may lead to similar effects as the ones caused by a shift in the reference voltage but with relatively smaller range. That is, an offset in internal amplifier voltage may potentially cause non-uniform pulse duration across distinct DQ pulses, increased duty cycle distortion, and/or potentially higher sampling error rate by the sampler  150 . However, the effects of an offset in internal amplifier voltage are typically less severe in magnitude than the effects of a shift in the reference voltage. 
     In typical memory interfaces, amplifier reference voltage is addressed through amplifier reference voltage calibration that is usually handled by the software of the microprocessor which causes the local memory controller  150  to take specific actions. Specifically, the software causes the LMC  150  to instruct the memory component  90  to send one or more patterns of DQ bits, e.g., eight bits, to the I/O memory interface  110  over a number of iterations. The corresponding outputs from the I/O memory interface  110  are compared to expected data patterns and an estimate of the reference voltage is evaluated based on comparison results over the iterations. For an eight-bit reference voltage calibration, the number of iterations is equal to 256 iterations to cover the entire code range. 
     According to at least one example embodiment, a scheme of reference voltage calibration is performed within the I/O memory interface  110 . According to at least one other example embodiment, a scheme of amplifier offset calibration is performed within the I/O memory interface  110 . The reference voltage calibration process and the amplifier offset calibration process are not handled by the local memory controller  150 . Specifically, the reference voltage calibration and/or the amplifier offset calibration may be triggered by the LMC  150 , however, the calibration processes, e.g., adjustment of calibration parameters, are performed within the I/O memory interface  110  with no control interference from the LMC  150 . According to further example embodiment(s) a two-phase amplifier calibration is performed. During a first phase, amplifier offset calibration is applied to each single ended receiver of the I/O memory interface  110 . In a second stage, a reference voltage calibration is applied to at least one single-ended receiver of the I/O memory interface  110 . 
       FIG. 4A  is a diagram illustrating a system, or circuit,  400  for reference voltage calibration. The system  400  includes a differential amplifier  401  of a single-input receiver, integrator circuit  410 , comparator  420 , control logic  430 , and digital to analog converter (DAC)  440 . The DAC  440  converts a digital value into an analog voltage value that is applied to the differential amplifier  401  as a reference voltage. The digital value, e.g., an eight-bit digital value, is provided by the control logic  430 . A clock signal  405  is applied to the differential amplifier  401  as a second input besides the reference voltage. The output of the differential amplifier is fed to the integrator  430 . The integrator circuit  410  is configured to provide one or more values indicative of the duty cycle associated with the output signal of the differential amplifier  401 . 
     According to an example implementation, the integrator circuit  410  may generate two signals from the output signal of the differential amplifier  401 ; a first generated signal consisting of high-voltage pulses of the amplifier&#39;s output signal, and a second generated signal consisting of low-voltage pulses of the amplifier&#39;s output signal. The integrator circuit  410  then integrates each of the generated signals over a time interval and provides two corresponding integral values to the comparator  420 . The comparator compares the two values and provides an indication of the result of comparison to the control logic  430 . Alternatively, the integrator may compute an estimate of the duty cycle based on the computed integral values and provide the duty cycle estimate result to the comparator  420 . The comparator then compares the estimated duty cycle to a reference duty cycle value, e.g., 50%, and provides the result of the comparison to the control logic  430 . The control logic  430  is a hardware logic, or logic circuit. 
     According to another example implementation, the integrator circuit  410  may simply integrate the amplifier&#39;s output signal over a period of time equal to a number of clock cycles, and provide an indication of the integration result to the comparator  420 . The comparator  420  compares the indication of the integration result to zero or to its inverted value, and provides an indication of the comparison result to the control logic  430 . 
     Based on the received indication of the comparison result, the control logic  430  is configured to determine whether the reference voltage is to be increased or decreased. For example, an indication that the duty cycle is less than 50%, e.g., the duration of a high voltage pulse is smaller than the duration of a low voltage pulse in the output signal from the differential amplifier, suggests that there is a positive shift in the reference voltage and that the reference voltage needs to be decreased. However, an indication that the duty cycle is greater than 50% suggests that there is a negative shift in the reference voltage and that the reference voltage is to be increased. Based on the determined type of shift in the reference voltage, e.g., positive or negative, the control logic  430  updates the digital value representing the reference voltage and provides the updated digital value to the DAC  440 . The DAC  440  converts the digital value to an analog DC voltage. The DC voltage is fed to the differential amplifier  401  as an updated reference voltage. Such process is repeated for a number of iterations before reaching a final value of the reference voltage. 
       FIG. 4B  is a diagram illustrating an example scheme of updating the input of the digital-to-analog converter  440  as part of reference voltage calibration, according to at least one example embodiment. The control logic  430  applies a binary, or half-interval, search. Assuming that the digital value is an eight-bit number, the control logic  430  starts with the binary number 10000000, or 128, to initialize the digital value. When applying the reference voltage corresponding to the initial digital value, the control logic  430  detects that the duty cycle is greater than 50%, and increases the digital value to 11000000. With the new digital value, the duty cycle is determined to be less than 50% and the digital value is decreased to 10100000. The process continues until a final value of the digital value, e.g., 10100101, is achieved after seven iterations. In general, if the number of bits representing the digital value is n, the binary search algorithm takes only n−1 iterations to achieve a final result. 
       FIG. 5  is a tree graph illustrating an algorithm for adapting the input of the digital-to-analog converter in reference voltage calibration, according to at least one example embodiment. In the tree graph shown in  FIG. 5 , only eight paths out of a total of 128 potential paths of the binary search algorithm for an eight-bit binary number are shown. Each node of the tree represents a digital value indicative of a corresponding analog reference voltage value. Each edge in the tree is either marked with “U,” indicating that a current reference voltage value suggests a shift up, or positive shift, and that the reference voltage value is to be decreased in the next iteration, or marked with “D,” indicating a down shift, or negative shift, of the current reference voltage and that the current reference voltage value is to be decreased. 
     A person skilled in the art should appreciate that a reference duty cycle value other than 50% may also be used, e.g., if the clock signal  415  fed to the differential amplifier has a duty cycle different from 50%. In other words, the reference duty cycle value considered when performing the comparison at the comparator  420  is equal to the duty cycle of the clock signal  415 . Also, it should be appreciated that reference voltage calibration is applied to at least one single-ended receiver among the multiple single ended receivers, for example, within the I/O memory interface  110 . For example, reference voltage calibration may be applied to one single-ended receiver. At the end of the reference voltage calibration process, the final reference voltage is applied to all differential amplifiers, e.g.,  101   a - 101   h , associated with multiple single-ended receivers within the I/O memory interface  110 . 
       FIG. 6A  is a diagram illustrating a system, or circuit,  600  for amplifier offset calibration. The system  600  includes multiple differential amplifiers  601  associated with multiple single-input receivers. According to at least one example embodiment, amplifier offset calibration is applied to each amplifier of the multiple single-ended receivers within the I/O memory interface  110 . For each differential amplifier associated with a corresponding single-ended receiver, the same DC voltage is applied to both input nodes of the differential amplifier during the process of amplifier offset calibration. The system  600  also includes at least one multiplexer  610  and a comparator  620 . According to at least one example implementation, outputs from multiple differential amplifiers  601  are multiplexed serially by the multiplexer  610 . Each output is then inverted by an inverter  615 , and both the output and its inverted value are passed to the comparator  420 . The comparator  420  compares both values and provides an indication of the comparison result to control logic  630 . The control logic  630  is hardware logic, or logic circuit, and is configured to update a digital value for sending to a DAC within a differential amplifier  601  based on the comparison result. The DAC is within the differential amplifier  601  whose output is used to generate the indication of the comparison result. In other words, given an indication of the result of comparison corresponding to a given differential amplifier  601 , the control logic  630  determines whether a digital input value, associated with a DAC within the same differential amplifier  601 , is to be increased or decreased based on the indication of the comparison result received from the comparator  620 . The control logic  630  then sends an updated value of the input digital value to the DAC with the differential amplifier  601 . The process of using the output of the differential amplifier  601  to update the input digital value associated with a DAC within the same differential amplifier  601  is repeated for a number of iterations. 
       FIG. 6B  shows a circuit  605  of two digital-to-analog converters coupled to a gain stage of a differential amplifier  601 , according to at least one example implementation. According to the example implementation shown in  FIG. 6B , each DAC is a four-bit DAC. A first DAC  606  is coupled to one side of the second stage gain  607  of the differential amplifier  601 , and a second DAC  608  is coupled to a second side of the second stage gain  607  of the differential amplifier  601 . By updating the digital input value of a DAC, e.g.,  606  or  608 , the control logic  630  is configuring the switches, e.g.,  609   a - 609   d  or  609   e - 609   h , associated with the same DAC. 
     A person skilled in the art should appreciate that one or more DACs, within a given differential amplifier  601 , may be configured by the control logic  630 . For example, assuming that the differential amplifier has a number of gain stages, The one or more DACs may be arranged in a way to be coupled to any of the gain stages of the differential amplifier  601 . For example, a total of two DACs may be configured by the control logic  630 . The two DACs may be both coupled the second gain stage of the differential amplifier, as shown in  FIG. 6B , or any other gain stage of the differential amplifier. Alternatively, each DAC may be couple to a distinct gain stage. According to another example implementation, more than two DACs may be configured by the control logic  630 . In such case different coupling patterns between the two or more DACs and gain stages of the differential amplifier  601  may also be considered. According to yet another example implementation, only a single DAC, coupled to a gain stage of the differential amplifier  601 , may be configured by the control logic. 
       FIG. 7  is a tree  700  illustrating a scheme according to which a digital input for a DAC, within a differential amplifier  601  of a single-ended receiver, is iteratively updated, according to at least one example embodiment. The tree  700  corresponds to a scenario where two DACs, e.g., as shown in  FIG. 6B , are configurable by the control logic  630 . Initially, e.g., at the first iteration, the digital value associated with each of the DACs is initialized to 0000. Upon receiving an indication of the comparison result associated with the output of the differential amplifier  601 , the control logic determines which DAC is to be configured based on the received indication. 
     For example, if it is determined that the differential amplifier  601  has a negative voltage offset initially, e.g., the output of the differential amplifier  601  is negative, and the output voltage is to be increased, the DAC  606  in  FIG. 6B  is the one selected for configuration. Specifically the digital input value applied to DAC  606  is updated to be 1000 while the digital input value applied to the DAC  608  is kept 0000. The selection of the DAC  606  is illustrated in the tree  700  by the node  715   a . However, if it is determined that the differential amplifier  601  has a positive voltage offset initially, e.g., the output of the differential amplifier  601  is positive, and the output voltage is to be decreased, the DAC  608  in  FIG. 6B  is the one selected for configuration. The digital input value applied to DAC  608  is updated to be 1000 while the digital input value applied to the DAC  606  is kept 0000. The selection of the DAC  608  is illustrated in the tree  700  by the node  715   b.    
     Once a DAC is selected, the digital input value for the selected DAC is updated in the following iterations. For example, the digital input value for the selected DAC is updated according to a binary, or half-interval, search algorithm as illustrated in the tree  700 . In other words, at each iteration, the digital input value is updated by a half of an interval representing a range of update values. In the tree  700 , an edge marked as “U” indicates an update towards increasing the offset voltage, and an edge marked as “D” indicates an update towards decreasing the offset voltage of the differential amplifier  601 . A person skilled in the art should appreciate that the updating of the digital input value may be performed according to a different scheme other than the binary search approach. 
       FIG. 8  shows a set of plots illustrating different operation phases of a differential amplifier  601  of a single-ended receiver, according to at least one example embodiment. According to at least one example embodiment, the offset calibration is performed when power is turned on, as shown by the offset phase plot “ph_offset,” so that offset of each receiver amplifier due to the non-uniformity and PVT variation is compensated. Offset calibration is performed to each differential amplifier of a single-ended receiver within the I/O memory interface  110 . Once amplifier offset calibration is completed, reference voltage calibration is performed, as shown in the reference voltage calibration phase plot “ph_V ref ,” for at least one single-ended receiver, e.g., within the I/O memory interface  110 . Upon completion of the reference voltage calibration, the final reference voltage is applied, e.g., to all differential amplifiers associated with single-ended receivers within the I/O memory interface  110 . After reference voltage calibration is complete, data read operations are performed. According to at least one example implementation, the reference voltage calibration process may be repeated during idle phases of the single-ended receivers. Also, during offset calibration, the enable read signal “ena_read” may be employed as the clock signal fed to control logic  630  and comparator  620 . 
     A person skilled in the art should appreciate that embodiment of the amplifier offset calibration and the reference voltage calibration described above may also be applied in I/O interfaces that are not memory interfaces. 
       FIG. 9  is a flowchart illustrating a method  900  of calibrating an I/O interface having multiple single-ended receivers, according to at least one example embodiment. At block  910 , amplifier offset calibration is applied to each of the multiple single-ended receivers in the I/O interface. The amplifier offset calibration is achieved through an iterative approach as described with respect to  FIGS. 6A, 6B, and 7 . Specifically, the same DC voltage is applied to both inputs of the differential amplifier of each single-ended receiver. Based on the sign of the output, a control logic  630  configures switches associated with a DAC within the differential amplifier. Configuring the switches of the DAC is achieved by updating a digital value provided as input to the DAC. According to an example embodiment, more than one DACs within each differential amplifier may be configurable by the control logic  630 . For example, in a first iteration, the control logic determines one of the DACs to be configured. In the following iterations, a digital value provided as input to the DAC determined is updated. 
     Once amplifier offset calibration is complete, reference voltage calibration is applied, at block  920 , to at least one single-ended receiver of the multiple single-ended receivers to determine a calibration reference voltage value. Reference voltage calibration is performed iteratively as illustrated above in the description of  FIGS. 4A, 4B, and 5 . In other words, a DC voltage signal and a clock signal are applied as inputs to the differential amplifier of the single-ended receiver. The output of the differential amplifier is analyzed to determine an indication of the corresponding duty cycle, e.g., greater or less, than a reference value. Based on the determined indication of the duty cycle, a control logic  430  updates a digital value provided as input a DAC  440 . The digital value represents an updated value of the reference voltage level, and is converted to an analog DC voltage by the DAC  440 . The DC voltage is applied as the reference voltage to the differential amplifier. The analyzing and updating process is repeated over a number of iterations, e.g., equal to the number of bits representing the digital number minus one, and a final reference voltage level is achieved at the last iteration. 
     At block  930 , the final reference voltage level is applied within each of the multiple single-ended receivers during a data reception mode. According to an example implementation, the reference voltage calibration may be repeated at a later time during an idle mode of the input/output interface. The amplifier offset calibration is performed after starting the chip associated with the input/output interface. 
     A person skilled in the art should appreciate that the amplifier offset calibration and the reference voltage calibration embodiments described above may also be applied in systems/circuits other than input/output interfaces and memory interfaces. 
     While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.