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Understanding And Using PMBus™ Data Formats Robert V. White bob.white@ieee.org Daniel Durant dan.durant@artesyn.com Artesyn Technologies 1401 West 122nd Avenue, Suite 180 Westminster, Colorado 80234, USA and supply Abstract—The Power Management Bus (PMBus™) in an open standard protocol for power system management that was introduced in 2005. The reception has been enthusiastic with adoption by both power semiconductor manufacturers. A key part of the specification, which took more than 250 person-hours to define, is the formats for sending and receiving data to and from a PMBus device. One format, called the Literal Format, exchanges data in user friendly units like volts and amperes. This format uses a floating-point like format with an eleven bit signed mantissa and a five bit signed exponent. The Literal Format minimizes the burden on the host or master device at the expense of greater complexity in the PMBus device. The Direct Format provides an alternative that minimizes or eliminates the computation in the PMBus device at the expense of more bus communication and being more computation intensive for the host or master device. This paper explores both formats, showing examples of how data is exchanged with PMBus devices. Particular attention is paid to the Direct Format, including a rigorous derivation of the equations needed to define the coefficients of the equation used by the host to encode and decode information exchanged with PMBus devices. I. INTRODUCTION for language configuring, The PMBus™ is an open standard protocol for power system management. It defines both the transport (how to get the bits and bytes to and from a PMBus device) and a command controlling and monitoring PMBus devices [1][2]. The PMBus can be used to configure, control and monitor a wide variety of power converters and other devices. One of the goals of the PMBus Specification Working Group was to create a standard that could be used with isolated dc-dc converters, point-of-load converters, microprocessor powering VRMs and offline ac-dc power supplies. The wide range of voltages, current and temperatures in these devices was a major problem for the Working Group. It was important to find the fewest possible data formats that could represent values over six orders of magnitude and with resolution requirements for some applications as tight as 0.025%. II. CONVENTIONS Before proceeding with the discussion, it will be helpful to establish the conventions used in this paper, which are the same as those used in the PMBus specifications. First, all PMBus commands are in all capital letters. An example: VOUT_COMMAND. MSB always means “most significant bit” and LSB always means “least significant bit.” In any diagram of a byte or bytes, the LSB will always be on the right and the MSB will always be to the left. Numbers are generally presumed decimal unless otherwise indicated or obvious from context. For example, the string 1101001101 is assumed to be binary. Binary numbers are indicted by a suffix of the letter “b” (Example: 11000b). Explicitly decimal numbers have a suffix of “d” (Example: 100d for the decimal value one hundred.). III. PMBUS COMMANDS PMBus commands are transmitted in a packet that contains at least an address byte followed by a command code byte. There may be one or more data bytes with a given command code. The packet may also include a byte length checksum (the Packet Error Checking (PEC) byte). An illustration of the packet used to send a command code and two data bytes to a PMBus device is shown in Figure 1. The details of the SMBus based transport used by the PMBus can be found in [1] and [3]. This paper is concerned with the format of the contents of the data bytes. IV. PMBUS DATA FORMAT CONCEPTS To accommodate the wide range of needs, the PMBus Specification Working Group chose to create two main groups of data formats. The first format, called the Literal format, can be thought of in either of two ways: • As scientific or floating point notation with a mantissa This paper explains the data formats that were created to and an exponent or address this need. • As the number of least significant bits (LSBs) with the size of the LSB also included in the data. 0-7803-9547-6/06/$20.00 ©2006 IEEE. 834

Address Byte Command Code S 7 6 5 4 3 2 1 W r A 7 6 5 4 3 2 1 0 A Data Byte Low Data Byte High 7 6 5 4 3 2 1 0 A 7 6 5 4 3 2 1 0 A Optional PEC Byte 7 6 5 4 3 2 1 0 A P S A START Condition From Host To Device Acknowledge (ACK) From Device To Host W r P Read/Write Bit Set For Write (0) STOP Condition From Host To Device Figure 1. PMBus Packet Construction The Literal format allows the host to send values that are independent of the PMBus device implementation, such as 3.3 to command an output voltage. The other format is the Direct format. Direct format data can be thought of as “raw” and in the native format of the PMBus device. For example, the output voltage is not commanded by sending a value such as 3.3 but a binary value corresponding to a value between the minimum and maximum rated output voltages. The Literal and Direct formats are explained in depth below. The Working Group also created variations of each format depending on whether or not the data was related to setting the output voltage (or a related parameter such as the output overvoltage fault limit) or not. The data formats for the output voltage related commands were given the ability to command a much smaller resolution. In addition, there is a mode for output voltage related commands that sends the manufacturer specified VID code for specified microprocessors. This gives a total of five different ways that data can be formatted for a PMBus device. The Working Group struggled with this more than any other topic and decided this was the minimum possible to cover all the desired applications and the needs of those applications. V. SETTING THE OUTPUT VOLTAGE The output voltage of a PMBus device is set in two steps. The first step uses the VOUT_MODE command to tell the device the format of the output voltage related commands that will be used to send commands to the device. This is usually only done once or as needed. PMBus devices may also be manufactured so that they accept output voltage and output voltage related commands in one or a fixed subset of the possible VOUT_MODE values. The second command, VOUT_COMMAND, sends the actual value. The data bytes for VOUT_COMMAND are a sixteen bit unsigned binary integer. The output voltage command instructs the device to set the voltage between the positive and negative output terminals. Whether these terminals are connected to ground to make a positive voltage output, connected to make a negative voltage output, or left flowing do not matter when commanding the output voltage. More information on setting the output voltage and output voltage related parameters can be found in Part II of the PMBus Specification [2][4]. VI. GENERAL PURPOSE LITERAL FORMAT The general purpose Literal format [2][4], as mentioned above, can be thought of as a floating point number. The mantissa, Y, is an eleven bit two’s complement binary integer. The exponent, N, is a five bit two’s complement binary integer. The value to be transmitted over the bus, X is represented as: X = Y · 2N (1) The combination of an eleven bit signed mantissa and a five bit signed exponent allows for a wide range of values with excellent resolution. The range of the values that can be represented using the PMBus general purpose Literal format is shown in Table I. TABLE I. Range of values for Literal format data Maximum Positive Minimum Value Maximum Negative 33.52 × 106 (1023 × 215) ±15.26 × 10–6 (±1 × 2-16) –33.55 × 106 (–1024 × 215) Another way of thinking of the Literal format is as a combination of the number of LSBs (Y) and the size of the LSB (2N). For example, if N = –10, 2N = 977 × 10–6, or about 1 mV/bit. The value of 3.3 could then be thought of as 3,379 LSBs, where each LSB = 2–10. When transmitted over the PMBus, Y and N are placed into the two data bytes as shown in Figure 2. Note that the Data Byte Low is transmitted before the Data Byte High. Figure 2. General Purpose Literal Mode Data Bytes A common question is that for a given value X to be transmitted over the PMBus, what value of Y and N gives the maximum resolution while staying within the allowed values of Y and N? The maximum resolution is with the maximum value of Y and the smallest value of 2N. Noting that the maximum value 835

of Y, YMAX =1023, it is possible to solve directly for N in terms of X and YMAX as shown in (2) (where int(x) is the function that returns the integer portion of x). 1. Separate the 16 bit value (1100001101001101) into Y (01101001101) and N (11000). 2. Decode N to a decimal value (–8) and compute 2N N = int = int ⎛ ⎜ ⎝ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ log 2 ⎛ ⎜ ⎝ X Y MAX ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ln X ⎛ ⎜ ⎝ ln 2 Y MAX ⎞ ⎟ ⎠ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (2) So for the example value of 3.3, then for maximum resolution N = –8. Y is calculated as follows: (1/256). 3. Decode Y to a decimal value (845). 4. Multiply Y (845) by 2N (1/256) to get 3.30078. Note the introduction of the 780 µV error due to rounding and quantization errors. Also, it is important that the multiplication by 2N not be done in the binary domain by right shifting the value of Y by 8 bits. If so, the result is simply 11b or 3.0 in decimal! VII. LINEAR FORMAT FOR OUTPUT VOLTAGE COMMANDS Y = X − 2 i N = 3.3 2 i − − ( 8) = 844.8 ⇒ 845 However, for most of the embedded microprocessors used for system maintenance and control, the calculation in (2) is overly complex. To find Y and N for a given X in a simpler, but somewhat longer calculation, start by dividing YMAX by X. Assuming X = 3.3: Then find the largest value of 2–N that is less than or equal to that result: max(2 ) 310.0 < − N ⇒ 256 ⇒ = − = N 8 11000b To find Y, multiply X by 2–N: 3.3 2 × N− 8 3.3 2 × = = 3.3 256 × = 844.8 ⇒ 845 ⇒ 01101001101b (5) (6) As transmitted over the PMBus, the two data bytes would be: Y MAX = 1023 X 3.3 = 310.0 (4) A. Motivation For The Direct Format The Linear format for output voltage related commands is the same as the Literal format for general purpose values except: (3) • The mantissa (V) is 16 bits and is unsigned (only positive related parameters are for output voltage values permitted) and • The exponent (N) is delivered as part of the VOUT_MODE command. VIII. DIRECT FORMAT The Direct Format, which is the same for all commands, is used for one of two reasons. First, it minimizes or eliminates the need for the PMBus device to do the “floating point arithmetic” required by the Literal format. Consider how many digitally controlled devices actually sense the output voltage (Figure 4). It is often more economical to sense, and digitize, only the error voltage than the full range of output voltage. In this case, the binary value transmitted over a bus to program an output voltage is sent to a D/A converter. The output of the D/A converter then serves as the reference voltage for an analog error amplifier. VOUT Error Amp V_ERROR PMBus Binary Number N D/A + OFFSET Figure 3. Maximum resolution literal mode representation of the value 3.3 as transmitted over the PMBus Thinking in terms of floating point, the transmitted value (3.3 in the example being used) is the 11 bit binary number (01101001101) with the binary point shifted by N places (N < 0 means shift left) to get the binary number 011.01001101 To decode a value received from a PMBus device, let’s work with the binary value found above. Figure 4. How Direct format data can be used to eliminate the “floating point” calculations required by the Literal format It would make the device’s task much simpler if the device were designed such that the: 836

• Minimum value transmitted over the bus (Ymin) set the C. Using Direct Format Data device output to its minimum rated output value, and the • Maximum value transmitted over the bus (Ymax) set the device output to its maximum rated output value. interest is when Another case of the range being commanded, such as a device’s output voltage, has a substantial offset from zero. For example, rectifiers used in telecommunications applications typically have output voltages that can be varied from about 44 Vdc to 58 Vdc. Another requirement is that the output voltage be controlled with a resolution in the range of 10-20 mV. And often, to minimize cost, the D/A converters used for controlling the output voltage have a resolution of only 10 bits. However, to control the output voltage from 0 V to 58 V with a resolution of even 20 mV requires at least 12 bits of resolution (and 10 mV requires at least 13 bits). However, the range from 44 V to 58 V can be controlled with a 10 bit D/A with a resolution of 13.4 mV–which is good enough for most applications. This is made possible by the Direct format. In the Direct format, the host sends a value of 0 over the bus to command the output to 44 V and the maximum binary value the device can use (such as 1023 for a device that has a 10 bit D/A) to command the output to 58 V. B. Direct Format Equations The Direct Mode actually uses an equation to define the encoding of information sent to a PMBus device [2][4]. This equation based encoding was inspired by the format used in the Intelligent Peripheral Management Interface specification [5]. The equation used to encode data being sent across the PMBus is: Where: Y mX b+ i =( ) 10 R (7) • • • • • X is the value to be encoded, m, the slope coefficient, is a 16 bit two’s complement integer, b, the offset coefficient, is a 16 bit two’s complement integer, R, the scaling coefficient is an 8 bit two’s complement integer, and Y, the value transmitted over the bus, is a 16 bit two’s complement integer. To decode values received from a PMBus transmission, the inverse of (7) is used: X = 1 m R − (10 −i Y b ) (8) The coefficients of the equation, m, b and R, are supplied by the PMBus device manufacturer. They can be made available from a data sheet or retrieved from the device itself with the COEFFICIENTS command [2][4]. 837 Before a host or master can send or retrieve Direct format data from a PMBus device, it must have the m, b and R coefficients used in (7) and (8). These values may either be programmed into the host from values supplied in a data sheet or they may be retrieved from the PMBus device using the COEFFICIENTS command. The details of using the COEFFICIENTS command are given in [2] and [4]. Two examples will illustrate the use of Direct format data for sending and receiving data from a PMBus device. In the first example, the host is to send a command to a PMBus device to set the output voltage to 3.30 V. In the second example, the host will read back the actual output voltage from the same device. The cycle to send the command for the output voltage starts with requesting the m, b and R coefficients for the VOUT_COMMAND command from the PMBus device. Suppose the device returns the values m = 3615, b = –2892 and R = –1. The host uses (7) to calculate the value to be sent over the bus (Y) using the desired output voltage of 3.3 for X. Y mX b + =( R ) 10 i = (3615 3.3 ( 2892)) 10 + − i i = 903.75 ⇒ 904 − 1 (9) The decimal value of 904 is converted to a 16 bit unsigned binary integer and sent over the bus to the PMBus device. Now suppose that the host wants to know the actual output voltage of the device whose output it just commanded to 3.3 V. The VOUT_COMMAND commands the nominal output voltage setpoint of the PMBus device. However, there are many factors that cause the actual output voltage to be different from the VOUT_COMAND values. These factors include tolerances within the PMBus, the effect of commands that adjust the output voltage (such as VOUT_TRIM), and the effect of current sharing circuits. The PMBus specification provides the READ_VOUT command that instructs the PMBus device to return the actual, measured value of the output voltage. When using Direct format data, the host starts the process of requesting the actual output voltage by requesting from the PMBus device the m, b and R coefficients for the READ_VOUT command. Suppose the device returns the values m = 10240, b = 0 and R = –1. The host then sends the PMBus device a READ_VOUT command. Suppose the device returned the value 3364d. The host then uses (8) to calculate the output voltage: X = 1 m − R (10 Y b − i ) 1 = = 10240 3.285 − − ( 1) (10 i 3364 0) − (10) From this calculation, the device’s actual, measured output voltage is reported as 3.285 V. It is important to note that the calculations (9) and (10) are not done in the PMBus device. These calculations are made

by the host device. The host presumably has much more computing power that the PMBus device and probably will perform these calculations using a high precision floating point format. D. Determining The Direct Format Coefficients Manufacturers of PMBus devices are required to supply the m, b and R coefficients, either in a data sheet or stored in the device. the coefficients. Users of PMBus devices do not need to calculate the coefficients but may find the process of interest. This section discusses how to calculate The problem in determining the coefficients is that there are three variables (m, b and R) but only two constraints. The two constraints are the mapping of the minimum value of X, Xmin, to the minimum value of Y, Ymin, and the mapping of the maximum value of X, Xmax, to the maximum value of Y, Ymax. The approach to solving this starts with assuming that R is fixed and known and then solving for m and b. Before starting this calculation, it is important to know the maximum value of Y that can be used or processed by the PMBus device. This is related to the maximum number of bits that the device can process (n). For example, 10 bits is common in cost effective devices. For calculating the coefficients, it is important to know how many bits the device will actually use. For example, if the device can only process 10 bits of information, then the maximum value of Y is 1023. The coefficients m, b and R must be chosen so that all Direct format data for values in the operating range of the PMBus device is less than or equal to Ymax. Starting with the constraints that the minimum value of X maps to the minimum value of Y and that the maximum value of X maps to the maximum value of Y: X min Y⇒ = 0 min X max Y⇒ = max 2 1n − Substituting these constraints into (7) gives: Y min = mX ( min + i ) 10R b Y max = mX ( max + i ) 10 R b (11a) (11b) (12a) (12b) Solving for m and b, assuming R is known and fixed, gives: m ⎛ = ⎜ ⎝ Y max X max − − Y min X min and − 10 R i ⎞ ⎟ ⎠ b = = ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ Y min − Y max − Y max X max Y max X max − − − − Y min X min Y min X min X min X max ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ (13) (14) − R 10 i − R 10 i The approach now is to work with the desired values of Xmin, Xmax , Ymin, and Ymax and use a tool such as Microsoft Excel to calculate m and b for various values of R. Any 838 results for which m and b are within their allowed values will work in the end system. E. Example: Calculating Direct Format Coefficients As an example, consider a telecommunications rectifier with a minimum output voltage of 44 V (Xmin = 44), a maximum output voltage of 58 V (Xmax = 58), and an internal D/A converter with 10 bits of resolution (n = 10 and Ymax = 1023). Using Microsoft Excel, (13) and (14) were solved for several values of R. The results are shown in Table II. TABLE II. Results of example calculation of Direct format coefficients R –3 –2 –1 0 1 2 3 4 m b m b (calculated) (calculated) (rounded) (rounded) 73071.42857 –3215142.857 73071 –3215143 7307.142857 –321514.2857 7307 –321514 730.7142857 –32151.42857 73.07142857 –3215.142857 7.307142857 –321.5142857 0.730714286 –32.15142857 0.073071429 –3.215142857 0.007307143 –0.321514286 731 73 7 1 0 0 –32151 –3215 –322 –32 –3 0 One of the first things to check is that the results are within the allowed values for m and b. These coefficients are both sixteen bit, two’s complement binary integers. The maximum positive value is 32,767 and the maximum negative value is -32,768. Also, fractional values less than 1 (or between 0 and –1) cannot be expressed. Examining Table II, any values out of range are in shaded cells. This leaves three possibilities for R: 1, 0 and –1. For maximum resolution, it is desirable to have the slope coefficient, m, as large as possible. Looking at Table II, the best choice for R is –1 giving m = 731 and b = –32151. To test these values, evaluate (12a) and (12b). The expected results are that Y(Xmin) = 0 and than Y(Xmax) = Ymax = 1023. Evaluating (12a): Y min = mX ( min + b ) 10 i R = = (731 44 ( 32151)) 10 + − i i 1 − 13 10 i = 1.3 0 ≠ 1 − (15) Evaluating (12b): Y max = mX ( max + b ) 10 i R = (731 58 ( 32151)) 10 + − i i 1 − (16) = 10247 10 i − 1 = 1024.7 1023 ≠ The evaluation of (12a) and (12b) in (15) and (16) does not yield the expected results. The difference between the calculated result and the expected result is due to the rounding of m and b. Increasing the D/A resolution to 16 bits does not correct the problem–rounding errors still exist. The choices available for dealing with this problem are:

• Live with it, • Adjust the slope (m), • Adjust the offset (b), • Adjust Xmax and Xmin, or • Adjust all of these. The easiest way to start is to keep m, b and R the same and adjust Xmin and Xmax. This is done by solving (8) for Xmax and Xmin starting with the previously calculated values of m, b and R. X = min 1 m − R i (10 Y min − b ) 1 − − ( 1) (10 = = 731 43.9822 i 0 ( 32151) − − better to start with a values of Xmax and Xmin that are slightly outside the desired control range. In this example, the desired control range is 44 V to 58 V. If the device being controlled uses 10 bits, then the resolution is approximately 13.67 mV. When calculating the Direct format coefficients, now start with values: X * max = X max + 2 LSB = 58.027 X * min = X min − 2 LSB = 43.972 (19a) (19b) (17) The results of using X * * max and X min for the desired control range and solving for m, b, and R are shown in Table IV. TABLE IV. Results of example calculation of Direct format coefficients * * using X min max and X X = max 1 m − R i (10 Y max − b ) 1 − − ( 1) (10 = = 731 57.9767 i 1023 ( 32151) − − (18) If these values of Xmin and Xmax are acceptable as the device’s specifications, then the exercise of finding the coefficients is complete. Suppose, however that the value of 57.9767 for Xmax is not acceptable as Xmax must be at least 58.0. Then coefficients m and b will need to be adjusted. Turning again to Excel and solving for a range of values of m and b (R was fixed at –1) gives the results in Table III. TABLE III. Results of search for workable values of m and b. 729 730 731 732 m R –3 –2 –1 0 1 2 3 4 m b m b (calculated) (calculated) (rounded) (rounded) 72785.48559 –3200523.372 72785 –3200523 7278.548559 –320052.3372 7279 –320052 727.8548559 –32005.23372 72.78548559 –3200.523372 7.278548559 –320.0523372 0.727854856 –32.00523372 0.072785486 –3.200523372 0.007278549 –0.320052337 728 73 7 1 0 0 –32005 –3201 –320 –32 –3 0 The shaded cells again show values that are out of bounds. Choosing the coefficient with the largest value of the slope coefficient gives the values m = 728, b = –32005 and R = –1. To test these values, evaluate (12a) and (12b). The expected results are that Y(Xmin) = 0 and than Y(Xmax) = Ymax = 1023. 44.058 43.997 43.937 43.877 Evaluating (12a) with these values of m, b and R: 58.091 58.011 57.932 57.852 44.059 43.999 43.938 43.878 58.092 58.012 57.933 57.854 44.060 44.000 43.940 43.880 Y min = mX ( min + b ) 10 i R = (728 43.972 ( 32005)) 10 + − i i = 6.6 10 i 1 − = 0.66 0 ≠ 1 − 58.093 58.014 57.934 57.855 Evaluating (12b) with these values of m, b and R: 44.062 44.001 43.941 43.881 58.095 58.015 57.936 57.857 44.063 44.003 43.943 43.883 58.096 58.016 57.937 57.858 Y max = mX ( max + b ) 10 i R = (728 58.027 ( 32005)) 10 + − i i = 10238 10 i 1 − = 1023.3 1023 ≠ − 1 (20) (21) b -32118 -32119 -32120 -32121 -32122 Shaded cells in Table III are values that are out of bounds. In the range of values explored, there are two combinations of m and b that yield X(Ymin) < 44.0 and X(Ymax) > 58.0: (m = 730 and b = –32118 or –32119), providing a solution that meets the requirements on to be commanded with realizable coefficients. the range output voltage F. Improved Method For Direct Format Coefficients Instead of creating a large Excel spreadsheet and hunting for values of m and b that yield the desired control range, it is 839 There is some small mismatch in the expected values of Ymin and Ymax. As was done in (17) and (18), keeping the calculated m, b and R, calculate the controllable range: X = min 1 m − R i (10 Y min − b ) 1 − − ( 1) (10 = = 728 43.9629 i 0 ( 32005) − − (22)

X = max 1 m − R i (10 Y max − b ) 1 − − ( 1) (10 = = 728 58.0151 i 1023 ( 32005) − − (23) From the results of (22) and (23), we see that the goal has been achieved–a control range of at least 44 V to 58 V and realizable value for the coefficients m, b and R. IX. SUMMARY A description of the data formats used by the PMBus is given along with examples of each format. Possible problems with quantization and rounding were shown and solutions presented. X. REFERENCES [1] [2] [3] [4] System Management Interface Forum (SMIF), “PMBus™ Power System Management Protocol Specification Part I – General Requirements, Transport And Electrical Interface”, Revision 1.0, 28 March 2005, Available at http://www/pmbus.org System Management Interface Forum, “PMBus™ Power System Management Protocol Specification Part II – Command Language”, Revision 1.0, 28 March 2005, Available at http://www/pmbus.org System Management Interface Forum, “PMBus™ Power System Management Protocol Specification Part I – General Requirements, Transport And Electrical Interface”, Revision 1.1, In press, To be available at http://www/pmbus.org upon release System Management Interface Forum, “PMBus™ Power System Management Protocol Specification Part II – Command Language”, Revision 1.1, In press, To be available at http://www/pmbus.org upon release [5] Intel et al, “Intelligent Platform Management Specification”, V2.0, 12 February 2004. 840

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