Abstract:
An rms converter accommodates incoming signals of large crest factor by using an amplifier having a transfer function of non-uniform slope. The amplifier has a lower gain for larger signals. The output of the amplifier is converted to digital voltage values. The non-uniform gain of the amplifier is compensated for in digital calculations of the rms value. The invention produces accurate rms measurements by accurately measuring lower incoming signal voltages while still accommodating high peak voltages. The invention also reduces the dynamic range requirements for the analog to digital converter.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to measurements of electrical voltages and in particular to measurement of rms values of time-varying voltages. 
     When measuring the voltage of an electric signal, it is useful to represent the voltage value by a single number, even though the voltage may be varying rapidly in time. One common measurement is the “peak” voltage, which represents the maximum magnitude present in the signal. In a sinusoidal signal, for example, the peak voltage is one half the voltage difference between a minimum and a maximum of the sine curve. 
     It is often more useful to represent a time-varying voltage by some type of average value that would correspond to an equivalent direct current (DC) voltage, because the equivalent DC current determines the energy loss or heating caused by applying a voltage across a resistor. A simple arithmetic average of the voltage over time is typically not useful because time varying signals, such as an alternating current (AC) signal in which the voltage varies sinusoidally between positive and negative values, often have an average voltage over time of approximately zero. A more useful value to represent the time varying voltage is the root mean square (“rms”) value, which is the square root of the integral of the square of the voltage over time. The ratio of the peak voltage to the rms voltage of a signal is known as the “crest factor.” 
     Systems for determining an rms voltage from a time-varying incoming signal are known as rms converters, a common type of which is the log-antilog rms converter described in U.S. Pat. No. 4,389,708, which is assigned to the assignee of the present invention. 
     Electrical measurement instruments are typically accurate over a limited range, in part because circuit components in the instruments are linear over only a limited range. Thus, measuring devices have difficulty measuring signals that have a high crest factor, that is, signals that include peak voltage values that are significantly larger than the rms value. Inaccurate measurement of the high peak voltages adversely affects the accuracy of the calculated rms value. 
     The ratio of the highest peak that can be accurately measured to the maximum rms value is called the crest factor limitation of the measuring device. Known methods for increasing the crest factor limitation by shrinking the incoming signal to fit the device capability do so by sacrificing measurement accuracy at lower voltages. The signal being measured, however, typically has a low voltage over most of the measurement interval and low voltages, therefore, contribute the most to the rms calculation. 
     Analog gain correction methods are known for extending the crest factor limitation, but such methods require switching the gain at the front end of the analog rms converter. This gain switching creates problems with settling time, overshooting, and accuracy at the lower voltages. Extending both range and accuracy of a measuring device requires more complex and costly components and circuits. 
     Another method is to use two rms converters, one to process high incoming voltages and one to process receive low voltages. The outputs of the two rms converters are then combined in an analog adder with appropriate scaling. The use of two rms converters increases expense and size of the resultant device. 
     The crest factor limitation problem is particularly acute in rms converters that convert the incoming signal to digital values before determining the rms value. The additional capacity required for digitally processing a high peak and converting it from an analog signal into a digital value is costly, and is seldom used, because the majority of the signal is well below the maximum anticipated peak. 
     SUMMARY OF THE INVENTION 
     In accordance with the invention, a high crest factor, time-varying signal can be easily and accurately converted to an rms value. 
     Accordingly, it is an object of the present invention to provide an improved method and apparatus for determining an rms value of an incoming signal. 
     It is a further object of the present invention to provide such an improved method and apparatus that can accurately measure incoming signals having high crest factors. 
     It is yet another object of the present invention to provide such a method and apparatus that can utilize components having limited dynamic range. 
     The present invention is a method and apparatus for processing an incoming signal at the front end of an rms converter and a method and apparatus for determining an rms value of a time-varying electrical signal. In accordance with the present invention, an incoming, time-varying signal is processed by an amplifier having a transfer function of non-uniform slope. Higher voltage portions of the incoming signal are amplified less than lower voltage portions, thereby reducing the maximum voltage of the signal output from the amplifier. 
     When the output signal is processed to determine an rms value, the processing includes compensating for the known non-uniform slope of the transfer function. By using a transfer function of non-uniform slope and compensating for the non-uniformity in the processing step, the crest factor of the measuring device is increased without the necessity of increasing the dynamic range of the components following the amplifier. 
     In a preferred embodiment, the transfer function comprises a line having a change in slope at a voltage of a predetermined magnitude. The slope of the line decreases above the predetermined magnitude, thereby reducing the amplifier output voltage value for large signals. The amplifier output is fed into an analog to digital converter and is then digitally processed to produce an rms value. The digital processing includes weighting the signals in accordance with the appropriate gain factor, so that each part of the time-varying signal contributes appropriately to the rms calculation. 
     The invention thus accommodates the infrequent peaks of high crest factor signals while still maintaining accuracy at the lower voltages levels of the preponderance of the incoming signal. The simplicity and low cost solution to high crest factor rms measurement provided by the present invention makes it particularly suitable for application in hand-held or small bench top multimeters. 
     The subject matter of the present invention is particularly pointed out and distinctly claimed in the concluding portion of this specification. However, both the organization and method of operation, together with further advantages and objects thereof, may best be understood by reference to the following description taken in connection with accompanying drawings wherein like reference characters refer to like elements. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a measuring instrument that incorporates the present invention; 
     FIG. 2 is a block diagram of a circuit used in the present invention; 
     FIG. 3 is a flowchart showing the steps of a preferred embodiment of the present invention; 
     FIG. 4 is an example of a transfer function of a preferred amplifier used in an embodiment of the present invention; 
     FIG. 5 is a circuit diagram that demonstrates the principles of the present invention; 
     FIG. 6 is a functional but simplified circuit diagram of a circuit that could be used in the present invention; 
     FIG. 7 shows an ideal transfer function of the circuit in FIG. 6; 
     FIG. 8 is a block diagram of one embodiment of the measurement instrument in FIG. 1; 
     FIG. 9 is a block diagram of an alternative embodiment of the measurement instrument in FIG. 1; and 
     FIG. 10 is a simplified block diagram of the rms converter used with the present invention. 
    
    
     DETAILED DESCRIPTION 
     A preferred embodiment of the present invention comprises a system for determining an rms voltage value of a time varying electrical signal. 
     FIG. 1 is a drawing (not to scale) of a measurement instrument  4  coupled via test leads  6   a  and  6   b  to a voltage source  8  to obtain an input signal. The measurement instrument  4  is designed to be used in service, installation, and maintenance environments in which a variety of input signals having a variety of waveshapes may be encountered. Skilled persons will recognize that the input signal source need not be a voltage source, but could be any signal source, for example, a current source, provided that the input signal is appropriately conditioned. The measurement instrument  4  may be implemented in the form of a digital multimeter, an oscilloscope, or other measurement instrument for measuring input signal voltages. 
     FIG. 2 shows a block diagram of a portion of a measurement device  4  that includes an amplifier circuit  14 , an analog to digital converter  16 , a compensator circuit  18 , an rms converter calculator  20 , and a display  22 . 
     FIG. 3 is a flowchart showing the steps of a preferred embodiment of the method of the present invention. Step  30  shows that a time varying electrical signal is applied to an input of amplifier circuit  14 . Step  32  shows that the time varying electrical signal is amplified in accordance with the transfer function of amplifier  14 . Steps  32 A,  32 B, and  32 C show in more detail how the time varying electrical signal is amplified in accordance with a preferred transfer function. 
     Step  32 A shows that the voltage value of the time varying signal is compared to a predetermined value, V pre . Step  32 B shows that if the magnitude of the signal voltage is less than V pre , the signal is amplified by a first gain factor, G 1 . Step  32 C shows that if the magnitude of the signal voltage is greater than V pre , the signal is amplified by a second gain factor, G 2 , and the magnitude increased by a constant, K. 
     FIG. 4 shows a transfer function  34  of a preferred amplifier  14 . For input voltages having an amplitude less than the predetermined voltage V pre , the transfer function has a slope m 1  equal to the amplifier gain factor, G 1 . For positive input voltages having a magnitude greater than the predetermined voltage V pre , the transfer function is an affine function having a slope m 2  equal to the second amplifier gain, G 2 , and y-axis intercept equal to a constant, K, which is calculated by multiplying V pre  by the difference in the slopes (m 2 −m 1 ). The constant chosen in this way ensures that the transfer function is continuous and has an inverse function, that is, each output value from the amplifier corresponds to one and only one input value. The transfer function is symmetrical for positive and negative voltages, so the y-intercept of the portion of the transfer function for negative incoming voltages less that −V pre  is −k. 
     In one embodiment, the predetermined voltage V pre  is 1.0 V, the first amplifier gain is 1.0, the second amplified gain is 0.2, and the constant can be calculated to be 0.8 V. In this example, for an input voltage of 0.5 V, which is of lesser magnitude than the predetermined voltage of 1.0 V, the amplifier output voltage is equal to 0.5 V multiplied by 1.0, the first amplifier gain, for a resultant output of 0.5 V. If the input voltage is 3.0 V, which is greater in magnitude than the predetermined voltage, the output voltage is 3.0 V multiplied by the second amplifier gain, 0.2, plus the constant, 0.8 V, to produce an amplifier output voltage of 1.4 V. If the input voltage is exactly the predetermined voltage, 1.0 V, the output can be determined to be 1.0 V, using either of the two calculations. 
     Step  40  shows that the output of the amplifier circuit  14  is converted into a digital signal by analog-to-digital converter (ADC)  16 . ADC  16  samples the output from amplifier circuit  14  and converts it to digital values representing the voltage value of the amplifier output during small sampling time intervals. 
     Step  50  shows that compensator  18  uses an inverse of the amplifier&#39;s transfer function to digitally convert the amplifier output values back into the values that accurately represent the actual values of the time varying signal being measured. Steps  50 A,  50 B, and  50 C show in more detail how step  50  is accomplished. Step  50 A shows that a determination is made as to whether the incoming signal was greater than V pre . If the incoming signal was less than V pre , step  50 B shows that the digital value is divided by the first amplifier gain. If the incoming signal was greater than V pre , step  50 C shows that the constant is subtracted from the digital value and the result is divided by the second amplifier gain. 
     In the example above, incoming voltage values that were less than the V pre  were unchanged by the transfer function (which had a slope of 1.0), so the compensator merely divides by 1.0 and makes no changes to those digital values. For time-varying signal values that were greater than V pre , the values were changed by amplifier circuit  14 , and compensator  18  digitally converts the changed values back to the original values of the time-varying signal. In the example, compensator converts the values by subtracting the constant (0.8) and then dividing by the second amplifier gain factor (0.2). 
     For example, if the ADC stores a digital value of 1.4 V for a sampling interval of the amplifier output, the actual incoming signal voltage value would 1.4 V minus the constant, 0.8 V, and divided by the second amplified gain factor, 0.2, to yield an actual incoming voltage of 3.0 V. Step  58  shows that the incoming voltage value is then used in the calculations of the rms value. Step  60  shows that the calculated rms voltages is presented, for example via a display to a user. 
     The peak values that can be measured are limited by the input range of the ADC  16 . The present invention expands the peak values that can be used in determining the rms value by lowering the voltages input to the ADC. In the example above, assuming the ADC had a maximum input voltage of 2.0 V, actual peak values of up to 6.0 V could be measured, without exceeding the maximum input voltage of the ADC. 
     FIG. 5 shows an idealized circuit that demonstrates the principles of the present invention. Skilled persons will recognized that the simplified circuit of FIG. 5 is not itself functional, but presents principles from which skilled persons will be able to create a functional circuit. Amplifier circuit  14  includes an input resistor R in  an operational amplifier  80  having three feedback paths to the inverting input. 
     A first feedback path  82  includes a first feedback resistor R f1 . A second feedback path  86  includes a second resistor R f2  and a breakdown diode  84 . A third feedback path  88  includes a third feedback resistor R f3  and a second breakdown diode  92 . Breakdown diodes  84  and  92  conduct in opposite directions. As a small positive or negative voltage is applied to input resistor R in , neither breakdown diode will conduct, so only feedback path  82  will allow current flow. The amplifier gain will, therefore, be −R f1 /R in . When V in  exceeds a predetermined threshold positive voltage, breakdown diode  84  will begin to conduct, and the amplifier gain will be −1/R in ×(R f1 ×R f2 )/(R f1 +R f2 ) 
     Similarly, when V in  exceeds a predetermined negative voltage value, the voltage across breakdown diode  92  cause it to conduct and the amplifier gain will be −1/R in ×(R f1 ×R f3 )/(R f1  +R f3 ). Points  96  and  98  on transfer function curve  34  show the points where breakdown diodes  84  and  92 , respectively, begin to conduct. 
     FIG. 6 shows a functional, but simplified amplifier circuit  120  that further demonstrates the principles of the present invention. FIG. 7 shows the transfer function of the amplifier of FIG.  6 . Skilled persons will recognized that the circuit of FIG. 6 will be modified by a circuit designer depending upon the requirements of a particular application. 
     Amplifier circuit  120  includes a circuit  124  that controls the negative breakpoint and a circuit  126  that controls the positive breakpoint. Circuit  124  includes an operational amplifier  130  having a diode  134  between its output and its inverting input. Resistors  136 ,  138 , and  140  all have the same resistance value, R 1 , and one terminal of each is connected to the summing node of operational amplifier  130 . The second terminal of resistor  136  is connected through a diode  144  to the output of operational amplifier  130 . The second terminal of resistor  138  is connected to the incoming signal, and the second terminal of resistor  140  is connected through the center terminal of a variable resistor  146  connected between voltage source, −V c  and ground. The voltage drop across the portion of resistor  146  between resistor  140  and −V c  determines the negative breakpoint  146  on the transfer function  148 . 
     Circuit  126  includes an operational amplifier  149  and is similar to circuit  124 , but the voltage source is +V c  and diodes  150  and  152  are reversed in direction from diodes  134  and  144 . Resistors  154 ,  156 , and  158  have a resistance value of R 1 , the same value as resistors  136 ,  138 , and  140 . A variable resistor  162  determines the positive breakpoint  166  of transfer function  148 . Alternatively, rather than adjusting variable resistor  162  to produce a predetermined breakpoint, a fixed resistor having a resistance within a prespecified range can be used. The actual breakpoint of the circuit with the fixed resistor is then measured and stored for later use in calculations involving the breakpoint. 
     The output of circuit  120  is taken from the output terminal of a third operational amplifier  168 . Connected to the summing node of operational amplifier  168  is a feedback resistor R F  that connects to the output of operational amplifier  168  and a resistor  160  that connects to the incoming signal voltage. Resistor  160  also has a resistance of R 1 . 
     A variable resistor R 4  between circuit  124  and the summing node of operational amplifier  168  determines the slope of a segment  174  of transfer function  148  after the breakpoint  164 . The slope of segment  174  is (R F /R 1 )−(R F /R 4 ). A variable resistor R 3  between circuit  126  and the summing node of operational amplifier  168  determines the slope of a second segment  184  of transfer function  148  before the breakpoint  166 . The slope of segment  184  is (R F /R 1 )−(R F /R 3 ). The slope of a center segment  190  of transfer function curve  148  is (R F /R 1 ). 
     Amplifier circuit  120  provides precise breakpoints and slopes and is relatively insensitive to temperature changes. Resistors  146 ,  162 , R 3 , and R 4  are shown as variable resistors to emphasize that c,hanging the value of these resistors changes the slope of segments  174  and  184  and breakpoints  164  and  166 . These variable resistors are preferably replaced with fixed resistors once desired properties of the circuit are specified and resistance values calculated. Alternatively, as described above with respect to variable resistor  162 , rather than using resistors having the exact values required to produce predetermined breakpoints and slopes, fixed resistors having resistances within limited ranges of values can be used. The actual circuit properties are then measured to characterize the transfer function, and the measured slope and breakpoint values are stored for use in later calculations. 
     Rms calculator  20  is preferably implemented using a squaring circuit followed by an rms digital filter and a square root circuit. Each digital sample from the ADC is squared and then presented to a digital filter where it is filtered in a continuous fashion to produce rms values. 
     The transfer function of the rms digital filter is modeled after the thermodynamic principles of applying a signal to a temperature sensitive resistor in the manner of the thermal rms converter. In this way, the rms value may be obtained using a stream of digital samples from a signal without regard to the period of the signal while avoiding the difficulties of providing thermally isolated matched resistors or in having to choose an integration period to calculate the rms value. 
     According to the thermodynamic model, the resistor heats up according to the power in the signal applied across it such that the power dissipated in the resistor is proportional to the square of the signal voltage. The resistor heats to an equilibrium point where the energy added is equal to the energy lost. The rms value of the signal at this equilibrium point is the same as the amplitude of a d.c. signal that heats the resistor to the same temperature. As such, the resistor acts as filter for the energy applied to it and the signal period is not relevant to its operation. There is no requirement that the signal be periodic because this filtering action takes place continuously. 
     In modeling the thermodynamic behavior of the resistor, the rms digital filter may be implemented in its simplest form as an infinite impulse response (IIR) filter according to the following general equation 
     
       
         
           Y 
           n 
           =aX 
           n 
           2 
           +bY 
           n−1 
         
       
     
     in which the filter constants a and b are chosen so that 
     
       
           a+b= 1 
       
     
     The rms digital filter is then implemented according to following equation: 
     
       
           Y   n   =a ( x   n ) 2   −aY   n−1   +Y   n−1   
       
     
     where: 
     Y n  is the present filtered digital sample 
     Y n−1  is the past filtered digital sample 
     X n  is the present digital sample 
     In an equilibrium state, Y n =Y n−1  and added energy, represented by a(x n ) 2 , equals energy lost, represented by aY n−1 , making Y n  and X n  steady values. Therefore, X n  is equivalent to a steady d.c. value which is the square root of Y n  and thus represents the rms value. 
     The rms digital filter within the rms converter extends this fundamental concept by having a transfer function that is essentially a low pass filter that extracts the rms value from the stream of digital samples in a continuous manner thus requiring no knowledge of the period of the signal. The squaring and rms digital filtering operations take place in real-time using each digital measurement value as it arrives. Next, a square root of the digital measurement values is taken, preferably only when a display update is made, to obtain the present rms value from the rms filter. In addition, the rms digital filter is optimized in terms of settling time, stop band frequency and attenuation, pass band ripple, and other filter parameters using optimization techniques known in the art. For a given accuracy and resolution, the rms digital filter can be optimized to provide faster responses than prior art rms converters. 
     A measurement bandwidth, which is typically determined as a design requirement for the measurement instrument, determines the minimum sample rate needed for the sampling system. Frequency components in the input signal beyond the measurement bandwidth would not be measured. The sampling system may comprise a sigma-delta converter followed by a decimation filter or alternatively a conventional ADC. The sampling system samples the input signal having an arbitrary waveshape to provide the digital samples at a sample rate to the rms converter. The rms values developed as described above from the rms converter are provided to a display on the measurement instrument, typically at an update rate determined by a microprocessor. 
     The input signal provided by the voltage source  8  may be an alternating current (a.c.) signal, a direct current (d.c.) signal or a combination of a.c. plus d.c. on the same waveform. The input signal may have a sinusoidal waveshape with a stable period or it may simply be random noise with no period or discernible waveshape. It is desirable that the measurement instrument  4  be capable of displaying the rms (root-mean-square) value of the input signal without any knowledge of its period or waveshape within a desired measurement bandwidth. 
     FIG. 8 is a simplified block diagram of the measurement instrument  4  (shown in FIG. 1) according to the preferred embodiment of the present invention. The voltage source  8  is coupled via the test leads  6   a  and  6   b  to a front end  216  within the measurement instrument  4 . The front end  216  includes amplifier  14  having a non-uniform transfer function and may contain over-voltage and over-current protection circuits, other amplifiers, attenuators, and filters in order to provide a scaled input signal of suitable amplitude level and bandwidth for conversion into digital samples. 
     Sigma-delta converter  218  is an over-sampling type analog to digital converter (ADC) which generates raw sample data at a sample rate substantially higher than the Nyquist rate for a selected measurement bandwidth, as is known in the art. The raw sample data may be converted to digital samples at base band using a decimation filter  220  as is also known in the art. In the preferred embodiment, the measurement bandwidth was chosen to be 500 kilohertz, with the sigma-delta converter  218  operating at a sample rate of ten megasamples per second (10 MS/s) for a 20:1 ratio. The sigma-delta converter  218  generates the raw sample data with a resolution of 5 bits which is supplied to the decimation filter  220  which low-pass filters the raw sample data to provide digital samples at 2.5 MS/s with a resolution of 13 bits (along with an additional sign bit). 
     The decimation filter  220  may be implemented as a finite impulse response (FIR) filter, as a infinite impulse response (IIR) filter, or as a hybrid of FIR and IIR filters, with the filter constants and structure chosen to obtain a desired transfer function. The sigma-delta converter topology is desirable because no precision components are needed in the converter, thus allowing for the circuitry to be implemented easily as a monolithic integrated circuit as is known in the art. The sigma-delta converter  218  and decimation filter  220  collectively comprise a sampling system  221  which converts the input signal to a stream of digital samples according to a sample rate. 
     The digital samples are provided as a continuous data stream at a rate of 2.5 MS/s to an rms converter  222 . The function of compensator  18 , which rescales the digital samples to compensate for the non-linear output of amplifier  14  of front end  216 , is performed in rms converter  222 . The rms converter  222  processes each of the digital samples in the continuous data stream as they arrive with no knowledge of the periodicity or waveshape of the input signal, as explained in more detail below. A microprocessor  224  receives rms values produced by the rms converter and selectively provides the rms values to a display  226  where they may be displayed in numerical or graphical format as desired. The rms values may be provided continuously or in response to an update signal from the microprocessor  224 . 
     The rms converter  222  offers a number of advantages over the prior art particularly when applied in the measurement instrument  4  as a handheld, battery-operated package. The sigma-delta converter  218 , the decimation filter  220  and the rms converter  222  may all be implemented as monolithic integrated circuits, with a minimum of external precision components, thus reducing cost, board space, power consumption, and manufacturing complexity. 
     The rms converter  222  further offers substantial performance advantages over the prior art. The crest factor, a substantial limitation in monolithic rms converters, is limited in the present invention only by the sampling system  221  and word length of the rms digital filter  232 . At the same time, the a.c. bandwidth of the rms converter  222  is constant, being defined according the filter constants applied in the rms digital filter  232 . Furthermore, the performance of the rms converter  222 , defined in terms of transfer function and a.c. bandwidth, are substantially constant over a wide range of amplitudes of the input signal. The rms digital filter  232  may have as many poles and zeros as needed to achieve adequate stopband rejection of a.c. ripple components while maintaining a desired settling time and no overshoot in its pulse response characteristic. 
     FIG. 9 is a simplified block diagram of the measurement instrument according to an alternative embodiment of the present invention in which a sampling system  225  consists of an analog-to-digital converter (ADC)  228 . The voltage source  8  is coupled via the test leads  6   a  and  6   b  to a front end  216  within the measurement instrument  210 . The front end  216  includes amplifier  14  having a non-uniform transfer function and may contain over-voltage and over-current protection circuits, amplifiers, attenuators, and filters in order to provide the input signal of suitable amplitude level and bandwidth to the sampling system  225 . 
     The ADC  228  generates digital samples at a sample rate higher than the Nyquist rate which is twice the measurement bandwidth, as is known in the art. Because the measurement bandwidth was chosen to be 500 kilohertz, the ADC  228  must operate at a sample rate exceeding 1 MS/s and preferably at 10 MS/s, with the actual sample rate driven by considerations of conversion accuracy. Other ADC technologies may be readily substituted for the ADC  228 , with consideration given to component cost, maximum sample rate, power consumption, as well as converter accuracy and resolution, to provide digital samples representative of the input signal to the rms converter  222 . 
     The digital samples are provided as a continuous data stream from the ADC  228  to the rms converter  222 . The rms converter  222  processes each of the digital samples in the continuous data stream as they arrive with no knowledge of the periodicity or waveshape of the input signal, as explained in more detail below. The rms converter  222  compensates for the non-uniform transfer function of amplifier  14 . A microprocessor  224  receives the rms values produced by the rms converter and selectively provides the rms values to a display  226  where they may be displayed in numerical or graphical format as desired. The rms values may be provided continuously or in response to an update signal from the microprocessor  224 . 
     FIG. 10 is a simplified block diagram of the rms converter  222  according to the present invention. Digital samples from the sigma-delta converter  218  and decimation filter  220  as shown in FIG. 8 or the ADC  228  as shown in FIG. 9 arrive at the rms converter  222 . The digital samples are rescaled as necessary in compensation circuit  18  to compensate for the non-uniform transfer function of amplifier  14 . Each digital sample is then squared in the squaring circuit  230  to produce squared digital samples  231 . Alternatively, the samples could be squared before resealing. Each squared digital sample is provided to an rms digital filter  232  which has filter coefficients chosen to allow the rms digital filter  232  to operate as a low pass filter. The filter coefficients and digital filter topology may be designed according to known IIR and FIR techniques, or a combination of FIR and IIR techniques, to provide a low pass filter having desired characteristics. In the preferred embodiment, the rms digital filter  232  has the following characteristics: 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 measurement bandwidth 
                 500 kilohertz maximum 
               
               
                   
                 stopband of −123 decibels 
                 49.9 hertz maximum 
               
               
                   
                 settling time to 0.001% 
                 0.5 seconds maximum 
               
               
                   
                 of final value 
               
               
                   
                 step response overshoot 
                 0.0% maximum 
               
               
                   
                 acquisition rates 
                 0.125, 0.5, 2, 
               
               
                   
                   
                 and 1000 hertz 
               
               
                   
                   
               
             
          
         
       
     
     In the digital rms filter  232 , it was important that there be no overshoot in the step response along with a high stopband rejection of 50/60 hertz ripple from power line frequencies. Filtered rms values produced by the digital rms filter  232  are provided as filtered digital samples  233  to a square root circuit  234  which produces the rms value by taking the square root of the present filtered rms value, either continuously or as needed in response to the update signal received from the microprocessor  224 . 
     The squaring circuit  230 , the rms digital filter  232 , and the square root circuit  234  may be implemented in hardware, in software, or a combination thereof according to the requirements of the application. The transfer function of the rms digital filter  232  is readily adaptable to a different sample rates and accuracy requirements. The sampling system  221  may comprise any of a variety of converter technologies suitable for generating digital samples of the input signal at a desired sample rate and accuracy. 
     While a preferred embodiment of the present invention has been shown and described, it will be apparent to those skilled in the art that many changes and modifications may be made without departing from the invention in its broader aspects. For example, a transfer function having more than two sections of differing slopes can be used. The transfer function does not need to be linear or affine, and could be, for example, logarithmic. Moreover, the functions of the invention need not be accomplished in separate. circuits. For example, the compensator could be combined with the rms converter. The appended claims are therefore intended to cover all such changes and modifications as fall within the true spirit and scope of the invention.