Correcting for a gain error resulting from the position of a pole of zero in a transfer function of a system

Abstract

The response of a Rogowski coil based current measuring circuit is often proportional to frequency. To correct for this a low pass or integrating function is applied to the response to linearize it. The low pass filter is made from real resistors and capacitors, and tolerances in their values significantly affect the estimate of current. This disclosure relates to a way of addressing such problems. This allows consumers of electricity to have confidence in the accuracy of, for example, their electricity meter.

Claims

1. An apparatus for estimating a gain error resulting from a position of a pole or a zero in a transfer function of a filter having at least one of a pole or a zero in a filter transfer function of the filter, the apparatus comprising: a characterization circuit comprising resistor (R) and capacitor (C) components matched to the filter to provide a characterization circuit transfer function such that there is a predictable relationship between a position of at least one pole or zero in the characterization circuit transfer function and the filter transfer function, and wherein the characterization circuit and the filter share at least one of a temperature or a manufacturing process variation; and a processing circuit arranged to interrogate a performance of the characterization circuit and to estimate a correction value for a filter response of the filter based on an attenuation factor of the filter at a particular frequency as determined using a time constant of the R and C components of the characterization circuit.

2. The apparatus as claimed in claim 1, in which the filter is a low pass RC filter.

3. The apparatus as claimed in claim 1, in which the filter is a leaky, integrator.

4. The apparatus as claimed in claim 1, in which the characterization circuit comprises an oscillator formed of at least one RC stage.

5. The apparatus as claimed in claim 1, in which the characterization circuit comprises a further filter, and a signal generator to provide a test signal to the further filter.

6. The apparatus as claimed in claim 5, in which the signal generator is one of a) a free running oscillator providing an oscillator signal set to a nominal oscillation frequency such that a comparison of the oscillator signal and an output of the further filter allows the frequency of a pole or zero of the further filter to be identified with a desired accuracy; b) a digital to analog converter driven so as to provide the test signal.

7. The apparatus as claimed in claim 1, in which the filter comprises R and C components, where a fabrication process is the same for the R and C components of the characterization circuit and are notionally identical.

8. The apparatus as claimed in claim 1, in which the filter comprises R and C components, where a fabrication process is the same for the R and C components of the filter and the R and C components of the characterization circuit and the respective R and C components are scaled versions of each other.

9. The apparatus as claimed in claim 8, further comprising a swap circuit for swapping the filter and the characterization circuits.

10. The apparatus as claimed in claim 1 coupled to a responsive variable gain amplifier, variable attenuator or multiplier for estimating gain error to apply a correcting gain.

11. The apparatus of claim 1, included in or in combination with an electricity monitoring or measurement system.

12. A method of correcting for a gain error resulting from a position of a pole or a zero in a transfer function of a signal processing first circuit to process an input signal, the method comprising: providing a characterization circuit including RC, RL, or LC circuits formed therein respectively having identical or scaled versions of corresponding RC, RL or LC circuits in the first circuit such that transfer functions of the first circuit and the the characterization circuit are related; providing a second circuit for interrogating a performance of the characterization circuit, to determine a time constant of the characterization circuit; and using the determined time constant of the characterization circuit, determining or adjusting a transfer function of the first circuit.

13. The method as claimed in claim 12, wherein adjusting the transfer function of the first circuit comprises calculating a deviation of the transfer function of the first circuit from a nominal transfer function, and making said calculation available for correcting an output of the first circuit.

14. The method as claimed in claim 12, further comprising driving the characterization circuit with a known test signal and monitoring an output of the characterization circuit so as to estimate a transfer function of the characterization circuit.

15. A current measuring circuit for characterizing a low pass RC filter, the current measuring circuit comprising: an air-core current transducer; an apparatus for estimating a response of the RC filter, for calculating an attenuation provided by the filter at a frequency; a second circuit comprising at least one RC circuit matched to the RC filter to share at least one of a temperature or manufacturing process variation; and a circuit for interrogating a performance of the second circuit so as to characterize an RC time constant within the second circuit and to use a result of the characterization to calculate or modify an output of the filter.

16. The current measuring circuit as claimed in claim 15, further comprising a surge detector, and a processor arranged to monitor an evolution of voltage over time, using the characterization of a transfer function of the RC filter to estimate a magnitude of a surge.

17. The current measuring circuit as claimed in claim 16, in which the surge detector is connected upstream of the RC filter.

18. A surge estimator comprising: a transient event detector, for measuring an output voltage or a current, the transient event detector connected to a comparator configured to provide a time stamp indicating a start of a surge event; a filter for filtering an output of the transient event detector, the filter having a filter circuit transfer function; a characterization circuit for estimating the transfer function of the filter, wherein the characterization circuit comprises matched components to the filter to provide a characterization circuit transfer function such that there is a predictable relationship between a position of at least one pole or zero in the characterization circuit transfer function and the filter circuit transfer function; a circuit for interrogating a performance of the characterization circuit associated with an air-core current transducer to determine a time constant of the characterization circuit; and a processor responsive to the output of the filter and the characterization circuit for estimating a magnitude of a surge event.

19. The surge estimator as claimed in claim 18, wherein the filter is an RC filter, and the characterization circuit further comprises additional R and C components scaled by a known scaling factor to the R and C components component of the RC filter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Example embodiments of the present disclosure will now be described, by way of non-limiting example only, with reference to the accompanying figures in which:

(2) FIG. 1 schematically illustrates a Rogowski coil encircling a current carrying conductor;

(3) FIG. 2 is a plot of the voltage developed across a Rogowski coil as a function of frequency for a constant magnitude alternating current;

(4) FIG. 3 is a circuit diagram of a single pole Butterworth RC filter;

(5) FIG. 4 is a circuit diagram of a Rogowski coil in association with and an analog integrator;

(6) FIG. 5 is a graph illustrating how a change in the break-point (−3 dB frequency) of the filter can affect the measured amplitude of a current at a specific frequency;

(7) FIG. 6 is a plot of the magnitude of the filter as a function of frequency on a linear-linear scale for a filter having a cut-off frequency of 8 Hz;

(8) FIG. 7 is a plot of the output voltage of a Rogowski coil (in arbitrary units) on a linear-linear scale;

(9) FIG. 8 is a plot combining the data shown in FIGS. 6 and 7, and showing the product thereof as a function of frequency;

(10) FIG. 9 shows an embodiment of an apparatus in accordance with the teachings of the present disclosure;

(11) FIG. 10 shows a further embodiment;

(12) FIG. 11 illustrates a further embodiment of an oscillator;

(13) FIG. 12 illustrates the evolution of voltage across the capacitor as a function of time in response to a surge event; and

(14) FIG. 13 illustrates a further embodiment of the present disclosure.

DESCRIPTION OF SOME EMBODIMENTS

(15) FIG. 1 is a schematic illustration of the current measuring circuit in the form of a Rogowski coil 2. Such a current transducer can be used to measure a wide range of alternating currents, such as current supplied to a domestic dwelling or the currents around a distribution grid from electricity generation stations to users. The Rogowski coil comprises a coil 2 of cross sectional area A which encircles a current carrying conductor 4 which, in use, carries an alternating current I. The alternating current I in the conductor 4 induces a voltage a the output of the Rogowski coil

(16) $\begin{array}{cc}V\left(t\right)=\frac{\mathrm{AN}}{2\pi R}{\mu }_o.Math.\frac{dI}{dt}& \mathrm{Equation}1\end{array}$
where A is the cross sectional area of the coil (see FIG. 1) N is the number of turns of the coil R is the radius of the coil around the conductor μ.sub.o=4τ×10.sup.−7 Hm.sup.−1 I=current

(17) A consequence of this is that if the conductor 4 were to carry an alternating current of a constant peak-to-peak or RMS value but the frequency of that current was swept from low frequency to high frequency then the voltage V developed across the Rogowski coil would increase linearly with frequency, as schematically illustrated in FIG. 2.

(18) This property of the Rogowski coil can be unhelpful since mains born load currents are generally quite low frequency, say 50 or 60 Hz whereas noise components can be at much higher frequencies, possibly running into the hundreds of kHz or above. It can therefore be seen that such a response gives a disproportionate amount of weight to a noise signal of low magnitude but high frequency compared to a response of the desired load current having a much higher magnitude but a much lower frequency.

(19) Ideally the output voltage of the Rogowski coil 2 would depend only on the magnitude of the current I through the conductor 4 and not on the frequency of the current.

(20) The person skilled in the art is aware of low pass filters. FIG. 3 is a circuit diagram of a first order Butterworth low pass RC filter 15 comprising a resistor 20 and a capacitor 26. The filter comprises a pair of input nodes 22a and 22b and a pair of output nodes 24a and 24b. The resistor 20 extends between the input node 22a and the output node 24a. The capacitor 26 extends between the output node 24a and the conductor connecting nodes 22b and 24b.

(21) It is known that Butterworth filters can be provided in a number of “orders” and that text books show the magnitude function for an N.sub.th order Butterworth low pass filter as

(22) $\begin{array}{cc}\frac{V_o}{V_I}=\frac{1}{\sqrt{1+{\left(\frac{\omega }{{\omega }_C}\right)}^{2n}}}& \mathrm{Equation}2\end{array}$
where ω=angular frequency ω.sub.c=cut off frequency 2πf.sub.o V.sub.O=output voltage V.sub.I=input voltage

(23) The first order Butterworth response is an integrator-like response which can be coupled to the output of a Rogowski coil to linearize the response of such a circuit as a function of frequency. The Butterworth filter 15 is often implemented as a “leaky” integrator as shown in FIG. 4. The integrator comprises an RC filter combination formed by resistor 30 and capacitor 32 around an operational amplifier 34. In order to stop the integrator integrating endlessly and thereby risking running into its supply rails a further resistor 36 (shown in dotted line) is provided in parallel with the capacitor 32 that causes it to leak some of its charge away.

(24) A problem with the circuit is that the magnitude of the output signal depends critically on the value of the RC product of resistor 30 and the capacitor 32. In order to understand this, consider FIG. 5 which shows an idealized response from the Rogowski coil current transducer as represented by chain line 40 which increases as function of frequency. Suppose, for example that we team this response up with a first order Butterworth filter having a cut-off frequency which is nominally F.sub.0. The frequency responses are routinely represented on a log-log plot where the skilled person knows that for a first order low pass filter the frequency response falls off at 20 dB per decade. In simplistic terms, the graph is constructed such that the frequency response of the filter stays flat with zero insertion loss until the break point, and then falls at 20 dB per decade of frequency increase. We will come back to this simplification later. However, it can be seen that if process or temperature variation causes the RC product to vary such that the cut off frequency moves from F.sub.0 to F.sub.1 then the attenuation introduced by a filter at a given frequency decreases. For example, if we wish to measure the amplitude of a frequency at frequency F.sub.m, for example 50 Hz, then the cut of frequency of F.sub.0, the gain (or really the attenuation) introduced by the filter can be represented by G.sub.0 at F.sub.m. However, if the filter cut off frequency increases to F.sub.1, then the gain of the filter increases to G.sub.1 at frequency F.sub.m (or more intuitively the attenuation inserted by the filter has reduced). Similarly, if the RC components vary such that the break point decreases in frequency from F.sub.0 to F.sub.2 then the filter response at frequency F.sub.m is represented by gain G.sub.2.

(25) It's worth considering the effect of these numbers in detail.

(26) Current measuring circuits often specified to a certain degree of decision. For example, a circuit may be specified to measure to within 0.1% accuracy, i.e. 1 part in 1000.

(27) If rather than using the graphical approach of the log-log plot of FIG. 5 we calculate the frequency response for a first order low pass filter and plot it on a linear-linear scale as shown in FIG. 6 by curve 50 it becomes apparent that the gradient of the filter changes more rapidly near the break-point and then changes less rapidly as the frequency moves further away from the break-point. FIG. 6 was plotted for a first order filter having a nominal break-point at 8 Hz. For such a filter the gain of the filter at 50 Hz can be calculated using Equation 2 and corresponds to 0.157991. However, if R or C were to vary such that the break point moved from 8 Hz to 9 Hz, then the gain at 50 Hz would be 0.177153. This corresponds to a change of 12% in the magnitude response of the filter at the measurement frequency. Where the resistor and capacitor components are fabricated using integrated circuit technologies, the components could be matched to great accuracy. However the absolute values of the resistor and capacitors can vary wildly from wafer to wafer, with changes of 20% or more having to be tolerated which gives rise to changes in the magnitude response of the filter much larger than the permissible measurement tolerance limit. It may be possible to calibrate at manufacture the response of the signal chain, either by trimming the components or calculating and storing a correction factor to be applied, but this may only be useful if the system remains stable forever. Furthermore, packaging stress and ambient temperature can also cause component values to change. Thus, whilst it may be possible to integrate all or part of an RC filter onto an integrated circuit it is exceptionally difficult to actually set it to a particular value without having to undertake expensive trimming. Even then, the circuit value in terms of the RC product is liable to drift with temperature. It should be noted that part of the filter may be implemented using off-chip (discrete) components.

(28) FIG. 7 schematically illustrates a response of the Rogowski coil 2 as line 52 on a linear-linear scale and FIG. 8 reproduces the information of FIG. 6 and FIG. 7, and also plots their product, indicated by curve 60. It can be seen that the product 60 of the low pass filter response as represented by line 50 and the Rogowski coil response as line 52 becomes relatively constant with frequency, especially so once the frequency has moved a reasonable distance from the cut off frequency of the low pass filter.

(29) It can be seen that it would be desirable to be able to accurately characterize the RC product of the low pass filter. FIG. 9 schematically illustrates a circuit where RC component combination, this time represented by resistor 70 and capacitor 72 act as a low pass filter, and then the output of the filter is digitized by an analog to digital converter 74 before being passed to a processing block 76 in order to output an estimate of a measured current as detected by the Rogowski coil 2. As noted before, the problem exists that the estimate of current depends on the transfer function of the RC filter. It is therefore highly desirable to know the RC product of the resistor 70 and capacitor 72. The Rogowski coil may be replaced by an air-cored current transformer with a burden resistor.

(30) As noted before, capacitors and resistors can be matched exceptionally well within an integrated circuit or reasonably well when collocated as discreet passive components from the same manufacturer outside the IC Therefore, one approach is to form replica copies of the capacitor 72 and the resistor 70 in a circuit which is intended to characterize the RC response. As such the circuit, here generally designated 100, can be regarded as a characterization circuit. In the embodiment shown in FIG. 9 the characterization circuit comprises three replica capacitors 72a, 72b and 72c and three replica resistors 70a, 70b and 70c arranged to introduce phase shifts within a feedback loop of an operational amplifier 102. Each stage in this network is required to insert a phase shift of 60°, and it can be shown, either by analysis or by reference to text books that

(31) $\begin{array}{cc}{F}_r=\frac{1}{2\pi \mathrm{RC}\sqrt{2N}}& \mathrm{Equation}3\end{array}$
where all the resistors 70a to 70c=R all the capacitors 72a to 72c=C N=number of stages F.sub.r=resonance frequency

(32) Thus the self-sustaining oscillator within the characterization circuit 100 has a frequency which is reliably related to the RC time constant of the capacitors 72 and resistors 70 within the filter 15. An output from the oscillator can be digitized by an analog to digital converter 110 and then processed by the processor 76 to accurately determine the frequency of operation. The values of the capacitors in the characterization circuit 100 do not necessarily need to be the same as the values of the capacitors in the filter circuit 15. Thus smaller capacitors may be used resulting in a higher oscillation frequency which takes less time to accurately characterize. Similarly the resistors can also be smaller. Thus the characterization circuit need not take up such a significant amount of die area as the filter.

(33) As an alternative, both the filter 15 and the characterization circuit 100 may be fabricated to have identical R and C components, as shown in FIG. 10. Here the filter components are designated as R.sub.f and C.sub.f and the corresponding filter in the characterization circuit is designated R.sub.c and C.sub.c with the intention that R.sub.F=R.sub.c and C.sub.F=C.sub.c. The filter within the characterization circuit 100 may be driven with an oscillating signal with a digital to analog converter 150 and the output of the filter may be provided by way of a multiplexer 160 to an analog to digital converter 170. The control signals to the digital to analog converter 150 and the results from the analog to digital converter 170 may stem from and be provided to a processor 200. As a consequence the processor 200 can accurately characterize the response of the RC circuit within the characterization circuit 100. Additionally, if required, an array of switches acting to form a swapping circuit 210 may be provided such that the input signal can be swapped to the filter formed by R.sub.c and C.sub.c and that the DAC 150 may be used to drive the filter formed by R.sub.f and C.sub.f. Thus, from time to time functionality of the filter 15 and the characterization circuit 100 can be swapped such that each can be accurately characterized and then drift in one of the circuits can be used to compensate for a corresponding drift to the other one of the circuits. By knowing the correct RC time constant then the gain/attenuation and phase shift provided by the filter, irrespective of the filter configuration or number stages can be quickly calculated thereby allowing a circuit, such as a current measuring circuit, to be characterized to a required accuracy even though the absolute values of the resistors and capacitors used within the filter may vary by 20 or more percent from product to product.

(34) The characterization need not require multiple copies of the RC filter to form an oscillator. FIG. 11 shows an oscillator circuit where a resistor 210 and a capacitor 220 are provided in a feedback loop around a Schmidt inverter 230 so as to form an oscillator. The output of the inverter 230 is a square wave which as a logic signal can be monitored directly by a processor 240 so as to estimate the frequency of the square wave. Alternatively the output of the inverter may be provided to an ADC to digitize it, or to a logic circuit, such as a divide by two counter, to clean its edges and equalize the mark-space ratio thereof prior to having the frequency of the signal estimated.

(35) Once the data processor can determine the actual response of the low pass filter it can apply a gain correction. Thus supposing that the RC component as measured by the oscillator drifted upwardly by 1% as a result of ambient or other temperature change, and that corresponded to the measured output being X % higher at the measurement frequency (mains frequency) then a corresponding attenuation can be introduced into the signal chain to compensate for the RC drift.

(36) Thus the estimate of current can be corrected.

(37) In the context of Rogowski coil (or air-cored current transformer) based current consumption meters (or watt-hour meters) this approach can be used to improve their performance. Thus approach may be used in conjunction with techniques described in WO2013/038176, “current measurement”, which is incorporated herein by reference, where a known additional current can be superimposed on a load current, and then the response of the measurement transducer and associated signal processing chain is examined to deduce the transfer function of the measurement transducer and signal processing chain, or at least to monitor for changes in the transfer function.

(38) The teachings disclosed herein can be used with an

(39) $\frac{dI}{dt}$
based transducer and integrator combination to monitor for response changes due to heating or aging, and/or to allow correction factors to be calculated and applied, or component values to be electronically trimmed where, for example, the capacitor is made of a plurality of smaller capacitors and associated switches for selectively removing or adding capacitors into a group of capacitors.

(40) The monitoring of the integrator response by a replica characterization circuit can be applied in many areas of technology, such as motor control, automotive, aerospace and medical systems, metering and protective systems (relays and circuit breakers) and the like.

(41) The filter 15 (see FIG. 9) by its nature introduces a delay in processing the input signal, and this can be disadvantageous if some remedial action needs to be taken on an urgent basis, for example to apply protective measures in the event of an overcurrent or overvoltage event. In such an arrangement the signal from the air core current transformer or Rogowski coil may be provided directly to a protection circuit without passing through the low pass filter such that the protection circuit can make a decision about initiating a protective action as quickly as possible.

(42) Once a filter response is characterized the filter can be used to help estimate other parameters such as a magnitude of a surge current or surge voltage. The RC filter provides a linearization of the frequency response from the Rogowski coil or similar inductor based current transducer. In normal operation the output of the filter will be a sinusoid. However in the event of an electrostatic discharge event, such as a lightning strike on a power distribution system, current surges may be caused to flow. The magnitude of a current surge at any point in the distribution system may vary as a function of distance from the point of the lightning strike, and may also depend on the number of intervening current splitting nodes or devices such as transformers. The surge current will be a largely unidirectional event and hence the voltage on the capacitor may become elevated, and then decay away in an exponential manner as set out by:
V(t)=Vs exp(−t/RC)  Equation 4
Where V(t) is the voltage at time t after the surge event at T.sub.0, and Vs is the surge voltage at time T.sub.0

(43) By examining the evolution of V(t) as a function of time, and with some estimate of elapsed time since the surge event occurred, it becomes possible to estimate the magnitude of the surge current. This requires knowledge of the RC time constant of the filter, but this information becomes available as a result of the operation of the present disclosure. The value Vs may also depend on the duration of the surge event. The duration may be measured by a circuit that runs a counter-timer to time the duration for which the signal exceeds a threshold, or the duration of the surge event, such as lightning strike, may be assumed to be constant.

(44) FIG. 12 shows the evolution as a function of time of the voltage stored on the capacitor 26 of FIG. 3 following the occurrence of a surge current and as the voltage decays away. For the purposes of illustration the sinusoidal response from the filter has been omitted but if a mains-borne current is being detected then the sinusoidal response thereof will be superimposed on the exponential decay, represented by line 250 of the voltage across the capacitor.

(45) If the time T.sub.0 of the surge event can be captured by a detector, such as by a voltage monitoring circuit that connects directly to the sensor or to some other arrangement that detects the voltage or current spike of the surge (or the occurrence of its peak value within the filter) and the elapsed time to T.sub.1, where the voltage is measured is known, then by knowledge of the RC time constant the surge voltage V.sub.s at time T.sub.0 can be calculated. The accuracy of timing can be verified or improved by taking further voltage measurements, such as V2 at time T.sub.2. The measurements can then be fitted to an appropriate function, such as an exponential delay or to a sync function. Thus an estimate of the energy in the surge event may be made.

(46) If desired, multiple RC filters having different time constants could be used to the evolution of their respective decay voltages as a function of time should intersect at the time of the surge event.

(47) FIG. 13 schematically illustrates a further embodiment of the present disclosure. As with the earlier Figures, a current carrying conductor 4 is associated with an inductive sensor 2, such as a Rogowski coil. A voltage developed across the Rogowski coil is filtered by a low pass filter comprising the resistors 20, 20′ and the capacitor 26. The low pass filter is, in this embodiment, provided as a differential filter at the input to a difference amplifier 280. An output of the difference amplifier 280 is provided to a differential ADC 290 which converts the differential output of the difference amplifier 280 into a digital code. Thus, the operation of this circuit is analogous to that described with respect to FIG. 9 except that it is fully differential. The time constant of the filter 15 can be estimated by a data processor 300 responsive the output of the characterization circuit 100. The characterization circuit may be formed as described hereinbefore.

(48) In normal use the data processor 300 is responsive to the output of the ADC 290 so as to estimate the alternating current carried by the conductor 4.

(49) The arrangement shown in FIG. 13 is further modified by the inclusion of a transient event detector, generally designated 320 which acts to monitor the output voltage across the Rogowski coil and if it exceeds a target value, as set by voltage source 325 outputting the voltage V.sub.t, then a digital signal is output by a comparator 330 indicating that the transient event may be occurring. This gives a timing reference equivalent to time stamping the time T.sub.0 of FIG. 12, and may also allow the duration of the surge event to be estimated. The data processor 300 can then monitor the evolution of the voltage across the capacitor 26 as a function of time. Based on the evolution of this voltage, together with an estimate of the RC time constant the data processor 300 can estimate the magnitude of the surge. This is useful as it is indicative of whether components in, for example, an electricity distribution system are likely to have been damaged by the surge event or whether the surge event was within their current handling capability. The comparator 330 may be protected by way of a voltage clamp, schematically illustrated by way of zener diode 332. The transient detector 320 may also include a DC blocking capacitor 334 to provide further protection against transient events.

(50) The circuits have been described with respect to characterizing an RC filter, but the teachings apply equally to characterizing RL or LC filters.

(51) Although the teachings have been presented with respect to inductive current transducers, the teachings relating to estimating the transfer function of a filter or circuit, and using this to estimate the magnitude of a surge current can be applied to estimating the size of over-voltage events or any other measured exception that is converted into the electrical domain by a suitable transducer.

(52) It is thus possible to provide a method and apparatus for accurately characterizing the filter response where the values of the filter are not well known, but the change in their value can be accurately matched to the change in values in a corresponding interrogation circuit.

(53) The techniques discussed herein are applicable components formed in integrated circuits where components can be matched with great accuracy. The techniques can also be applied to discrete components, but some form of preselection to find appropriately matched components may be required.

(54) The claims presented herein are in single dependency format suitable for filing at the USPTO. However it is to be understood that the claims are intended to depend on any preceding claim of the same type except where that is clearly technically infeasible. Thus converting these claims from single dependency to multiple dependency format is not intended to introduce any added matter.