# Patent

## Title
Filter for switched mode power supply

## Abstract

There is provided a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter including means arranged to determine the output voltage in dependence on the frequency components of the source voltage within the filter passband, and independent of output current drawn.

## Background
BACKGROUND TO THE INVENTION
1. Field of the Invention
The present invention relates to the filtering of a voltage in an arrangement in which the voltage is a stepped or rectangular voltage. The invention is particularly but not exclusively concerned with the filtering of a supply voltage in a switched mode power supply.
2. Description of Related Art
Modulated power supplies are used, for example, for providing a supply voltage to an amplification stage, typically a radio frequency (RF) amplification stage. An example of a particularly advantageous modulated power supply stage can be found in United Kingdom Patent No. 2398648.
In general, modulated power supplies provide a technique for tracking the supply voltage to an RF amplifier in dependence upon the RF input signal to be amplified by the amplifier. Such modulated power supply stages may typically be provided with a plurality of power supply voltages, one of which is selected in dependence upon a current level of the signal to be amplified. Thus there is provided a switching block which switches between one of a plurality of available power supplies to deliver a suitable power supply voltage to the RF amplifier.
In typical applications the output of the switching block is provided with a filter for filtering the selected voltage supply.
This filter gives rise to certain problems. Losses in the switching device may occur as a result of the filter input current being drawn through the “on” resistance of the switching devices. This input current comprises an unavoidable DC term due to the output load (e.g. the RF amplifier) being driven through the filter, and a “ripple” current determined by the filter input impedance.
In addition to these losses which occur in a switching device as a result of the connection of its output to the filter, there are also losses as a result of the filter itself.
These losses incurring in the filter and as a result of the filter cause variations to the output voltage delivered to the load from the filter. This is disadvantageous.
It is thus an aim of the present invention to provide an improved arrangement for filtering a stepped or rectangular voltage such as found in a modulated power supply.
SUMMARY OF THE INVENTION
A key performance metric for a dynamically modulated switch mode power supply is voltage tracking accuracy, i.e. the difference between a desired and an actual output voltage. This is directly influenced by the output impedance/load current combination. A typical filter results in large voltage resonances in the filter transition region as a consequence of output impedance peaks. In accordance with the invention there is provided a means for reducing the impedance peaks to thereby control the resonances.
The invention provides a filter for receiving a rectangular or stepped source voltage to be filtered, the filter being arranged to provide a reduced output impedance whilst maintaining an appropriate input impedance. The output impedance is preferably reduced across the full frequency range, the input impedance being maintained across the full frequency range. In particular the input impedance may be increased above a level which would otherwise be achieved as a result of reducing the output impedance.
In accordance with the invention there is provided a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter including means arranged to determine the output voltage in dependence on the frequency components of the source voltage within the filter passband, and independent of output current drawn.
The means may be arranged to provide reduced impedance at the output of the filter across the filter transition band.
The means may be arranged to provide an impedance at the output of the filter at the filter transition band which approximates to the impedance at the output of the filter at the passband.
The means may be arranged to provide a low impedance at the output of the filter at the passband, transition band, and stop band.
The means may include a lossy resistance means. The means may include a resistor connected in parallel across part of the input inductor of the filter. In other words, the input inductor may be split into two parts, with the resistor connected in parallel across one part. The filter may be a jth order filter, and a further resistor may be placed across the inductor of each further order of the filter.
The impedance of all elements within the filter may be reduced by a factor n, in order to further reduce the output impedance of the filter stage.
The filter may be a jth order filter, and the means may be arranged to reduce the impedance of the inductor and capacitor in one or more orders of the filter. To achieve the reduction, the inductance of the inductor may be divided by a value n and the capacitance of the capacitor may be multiplied by a value n.
This modification to the filter, however, also reduces the filter input impedance and hence increases the static losses in the switching devices. This effect may be counteracted, in a preferred modification, by splitting the input inductor into several sections to create parallel resonance circuits at the switching frequency and its odd harmonics. This may be achieved in the preferred arrangement by splitting the input inductor into k sections. Each of the k sections preferably includes a parallel arrangement of an inductor, a capacitor and a resistor.
Where the means is arranged such that if part of the input inductor is split into a series of parallel resonant circuits, the input impedance is increased relative to the value it would have had if the elements of each stage of the filter where not split.
The means may include at least one output trap at the output of the filter, each output trap including an inductance having a low Q factor. The at least one output trap may include an inductor and a capacitor connected in series.
Advantageously the invention suppresses output impedance peaks which occur in the transition band of conventional filters. These impedance peaks result in voltage peaks at the filter output when the load current frequency lies in the filter transition band. The impedance peak suppression is achieved in accordance with the invention without unduly comprising other filter design parameters such as input impedance, loss, and transfer function.
In accordance with embodiments invention provides a filter topology which allows simultaneous attainment of the following design goals for a switched mode power supply output filter:

    
    
        a low output impedance across pass band, transition band and stop band;
        b high input impedance at the fundamental and odd harmonics of the switching frequency;
        c low pass band amplitude and group delay ripple;
        d low dissipation when driven with switching waveform; and
        e low output voltage ripple at the switching frequency.
    
    


The filter topology contains several features, in a particularly preferred implementation, to permit simultaneous attainment of the design goals. A first feature is the use of resistors to introduce loss at selected frequencies. A second feature is parallel resonant input sections to raise input impedance at the fundamental and odd harmonics of the switching frequency. A third feature is the use of low Q-factor series resonant output sections to reduce output impedance at selected frequencies.
The invention also provides a filter for receiving or filtering a rectangular or stepped source voltage and for providing an output voltage, the filter including at least one lossy resistance means. The filter may be arranged to provide a reduced output impedance whilst maintaining an appropriate input impedance.



BRIEF DESCRIPTION OF THE FIGURES
The present invention in now described by way of example with reference to the accompanying Figures, in which:—
FIG. 1 illustrates a block diagram of an RF amplification stage embodying the concept of the present invention;
FIG. 2 illustrates a conventional filter arrangement;
FIG. 3 illustrates a conventional multi-stage filter arrangement;
FIG. 4 illustrates an improved filter arrangement according to a first embodiment of the invention;
FIG. 5 illustrates an improved filter arrangement according to the first and a second embodiment of the invention;
FIG. 6 illustrates an improved filter arrangement according to the first and a third embodiment of the invention;
FIG. 7 illustrates a modification to the filter arrangement of FIG. 6; and
FIG. 8 illustrates a preferred filter implementation.



DESCRIPTION OF PREFERRED EMBODIMENTS
The present invention is described herein by way of particular examples and specifically with reference to preferred embodiments. It will be understood by one skilled in the art that the invention is not limited to the details of the specific embodiments given herein. In particular the invention is described herein by way of reference to an RF amplification stage including a switched mode voltage supply. However more generally the invention may apply to any arrangement where it is necessary to filter a rectangular or stepped drive signal.
Referring to FIG. 1, there is illustrated an RF amplification stage 100 in accordance with an exemplary application for describing the present invention. The RF amplification stage 100 includes an RF amplifier 102, a supply voltage selection block 106, an envelope detector 104, and a filter 108.
In the illustrated example of FIG. 1, the supply voltage selection block 106 receives four supply voltages V1-V4 on respective input lines 1321-1324. In general, however, a supply voltage selection block may select between any number of levels, four being a non-limiting example. The selected supply voltage is output from the supply voltage selection block 106 on line 120. The RF amplification stage 100 receives an RF input signal RFIN on line 110. The envelope detector 104 has an input 114 coupled to line 110 to thereby detect the RF input signal. The envelope detector provides an output on line 118 to the supply voltage selection block 106 to provide the necessary information for the supply voltage selection to take place. The filter 108 receives the output of the supply voltage selection block on line 120. The filter 108 provides a filtered supply voltage on line 122 for the RF amplifier 102. The RF amplifier 102 provides on line 112 the RF output signal RFOUT.
The example arrangement of FIG. 1 is illustrative, and the invention is not limited to any details shown. For example elements of the illustrative RF amplification stage of FIG. 1, specifically the envelope detector 104, the supply voltage selection block 106 or the filter 108, may be implemented in the digital domain in an alternative arrangement.
In general, given a selection of the desired supply voltage for the RF input signal to be amplified, the supply voltage selection block 106 connects the selected supply voltage to its output on line 120. The filter 108 functions to filter the supply voltage on line 120 to the RF amplifier 102.
FIG. 2 illustrates an equivalent circuit for the supply voltage selection block 106 and a conventional arrangement for the filter 108. The filter 108 receives a rectangular drive voltage, as represented by the voltage waveform 210, which is provided by voltage source 202 in the equivalent circuit arrangement of FIG. 2. The rectangular drive voltage is provided by semiconductor switches with low “on” resistance, represented by resistance RSW in FIG. 2 and denoted by reference numeral 204. The filter circuitry is provided by an inductor 2061, having an inductance value L1 and a capacitor 2081 having a capacitance value C1. The filter substantially removes frequency components at the switching frequency and the associated harmonics, leaving only the DC components of the input waveform. The output DC voltage provided on output line 212 is then determined by the duty cycle of the input switching waveform.
Dynamic modulation of the output voltage provided on the output line 212 may be obtained by varying the duty cycle of the input waveform. The duty cycle of the input waveform may be varied by varying the pulse width of the input waveform, the repetition rate of the pulse, or both. The modulation bandwidth and switching frequency residual ripple are both determined by the design of the output filter 108.
The maximum tracking bandwidth for a given switching frequency and output ripple may be increased by adding additional sections to the filter, as shown in FIG. 3. As shown in FIG. 3, additional inductor-capacitor pair arrangements are added to the filter arrangement of FIG. 2, in order to provide a higher order filter. As shown in FIG. 3 a second stage or section comprising an inductor 2062 having an inductance value L2 and a capacitor 2082 having a capacitance value C2 are added, and in general a jth stage is added by an inductor 206j having an inductance value Lj and a capacitor 208j having a capacitance value Cj.
The input switching waveform may in general be regarded as a m-level quantised representation of the desired output waveform. High order quantisation results in reduced quantisation noise and hence reduced filtering requirements.
The efficiency of the supply voltage selection stage 106 is determined by losses in the switching devices within the selection stage 106 and losses in the output filter 108, as set out in the background section above. The losses within the switching devices may further be classified into “static” and “dynamic” or switching losses. The static losses occur as a result of a filter input current being drawn through the “on” resistance of the switching devices. The input current comprises an unavoidable DC term due to the output load and a “ripple” current determined by the filter input impedance. The ripple current is determined by the filter input impedance at the switching frequency and its odd harmonics. Hence for high efficiency the filter should present high impedance at these frequencies.
Ideally, it is desired for the voltage provided at the filter output to be determined solely by the source voltage and to be independent of the output current drawn. To approach this ideal, in accordance with embodiments of the present invention, a filter arrangement is provided in which the output impedance is low across the filter pass band, transition band, and stop band.
Achieving low output impedance at the transition band is more difficult than in the pass band and stop band. Typically the transition band shows large impedance peaks due to resonances within the filter. If the spectrum of the load current is a white noise spectrum, then large errors in output voltage will occur at the frequencies of resonance.
There is now described three embodiments for implementing the present invention. Each embodiment, on its own, offers a solution to reduce the output impedance of the filter in the transition band, and thereby make the output voltage of the filter less dependent on the output current drawn. The embodiments may be utilised individually or in any combination.
The first embodiment of the invention is shown in FIG. 4. In this first embodiment the magnitude of the impedance peaks is reduced by introducing at least one lossy resistive element into the filter. The lossy resistive elements are chosen so as to introduce loss at the resonance peaks without significantly increasing the passband loss of the filter, or the loss at the switching frequency and its harmonics.
A resistor is preferably provided for each inductor in each order of the filter.
Whilst the filter of FIG. 4 is adapted to achieve a reduced output impedance, it is important to ensure that the input impedance of the filter is not adversely affected, and particularly that the input impedance is not reduced. A reduction in the filter input impedance increases the static losses in the switching devices, which is undesirable.
To ensure the input impedance is not reduced, for the first section of a jth filter, or in a first order filter, the inductor is split such that the resistor is connected in parallel across only a part of the inductor. Thus as shown in FIG. 4 the inductor 2061 of FIG. 3 is split into a first part 2061a having an inductance value L1a and a second part 2061b having an inductance value L1b. A lossy resistor 5021 having a value R1 is connected in parallel across the inductor 2061b. The inductor 2061a ensures that the input impedance of the filter, Zin, remains high at the switching frequency and its harmonics.
As also shown in FIG. 4 for a jth order filter each inductor of each filter stage, other than the inductor of the first stage, has a resistor connected in parallel across it. The inductor 2062 is thus shown to have a resistor 5022 having a resistance value R2 connected across it, and the inductor 206j is shown to have a resistor Rj 502j having a resistance value Rj connected across it.
In this first embodiment, when applied to a jth order filter, advantages are obtained by connecting a lossy resistor across the inductor of one or more stages. It is not essential to connect a lossy resistor across all stages.
Using the exemplary technique of FIG. 4, the output impedance is maintained low across the passband, transition band and stopband of the filter, i.e. across the full frequency range.
A second embodiment is described with reference to FIG. 5. The embodiment of FIG. 5 is shown by way of additional modification to the embodiment of FIG. 4. It should be understood, however, that the embodiment of FIG. 5 does not require to be implemented in combination with the embodiment of FIG. 4. The principles of the embodiment of FIG. 5 offer an improvement in themselves when implemented without the features of the first embodiment.
In accordance with the second embodiment, the impedance of all elements within the filter is reduced by a factor n, to further reduce the output impedance of the filter stage. This is illustrated in FIG. 5 by the notation of the values of all the inductors shown therein being divided by n, and similarly the values of the lossy resistors 502 in a multiple-order arrangement being divided by n. The capacitance values are multiplied by n.
This modification to the filter, however, whilst reducing the output impedance also reduces the filter input impedance.
This effect may be counteracted, in a preferred modification, by splitting the input inductor into several sections to create parallel resonance circuits at the switching frequency and its odd harmonics. This may be achieved in the preferred arrangement of FIG. 5 by splitting the input inductor 2061b into k sections. As shown in FIG. 5 each of the k sections includes a parallel arrangement of an inductor 502, a capacitor 504 and a resistor 506.
The inductors 5021, 5022, 502k in total have an inductance value equivalent to the value of the inductor 2061b.
This second embodiment is shown as an arrangement in combination with features of the first embodiment, where only a portion of the input inductance is modified.
Where the arrangement to implement counteraction of static losses is desired, i.e. to avoid a reduction of input impedance, and the arrangement of the first embodiment is not implemented, the input inductance 2061b of FIG. 5 may still be split up into parallel resonance circuits as shown for the inductance 2061b of FIG. 5.
Using the exemplary technique of FIG. 5, the output impedance is maintained low across the passband, transition band and stopband of the filter, i.e. across the full frequency range.
A third embodiment is illustrated with reference to FIG. 6. The principles of this third embodiment are again illustrated in combination with the principles of the first embodiment described hereinabove, but they need not be implemented combination with the first embodiment.
In the third embodiment as illustrated by FIG. 6, a plurality p of “output traps” are utilised, each output trap including an inductor and capacitor connected in series to ground. Thus there is shown a first output trap comprising an inductor 5021 and capacitor 5041 connected in series; a second output trap comprising an inductor 5022 and a capacitor 5042 connected in series; and a pth output trap comprising an inductor 502p and capacitor 504p connected in series.
The output traps each have a low Q factor. The Q factor of each inductor 502 in the output traps may be deliberately reduced through use of series and parallel resistors as shown in FIG. 7. Thus, for example, with reference to FIG. 7 the inductor 5021 may be implemented by an inductor 510 and resistor 512 in series, with a further resistor 514 connected across in parallel.
The output traps reduce the output impedance of the filter. The number of output traps, p, provided is dependent upon the number of frequency regions over which traps are required: each trap lowers the output impedance for a given frequency region.
In the above there is described a first embodiment with reference to FIG. 4, a second embodiment described in combination with the first embodiment with reference to FIG. 5, and a third embodiment described in combination with the first embodiment with reference to FIG. 6. Each embodiment may be utilised on its own or with any combination of the other embodiments. For completeness, a particularly preferred arrangement in which all three embodiments are combined is illustrated in FIG. 8.
This preferred arrangement of FIG. 8 offers a particularly advantageous reduced output impedance. It should be noted that in the arrangement of FIG. 8 the principle of the second embodiment, in which the impedance values of the elements in the Figure are divided by a factor n, is only illustrated as implemented in the input stage of the filter, and not in subsequent orders of the filter. Thus each of the inductors 5061, 5062, 506k combine to provide an inductance value which is an nth of the value of the inductor 2061b of FIG. 4.
There is thus described three embodiments, exemplified by FIGS. 4, 5 and 6 respectively. The second embodiment is described with reference to FIG. 5, in combination with the first embodiment. Each embodiment may be implemented independently or in combination with any other embodiment.
However, whilst advantages in accordance with the invention can be achieved by implementing only the techniques of the second embodiment, it is preferable to implement the second embodiment in combination with either the first or third embodiment. The first and third embodiments have in common the provision of at least one lossy resistor. In the first embodiment the lossy resistor is provided in combination with the inductor of each order of the filter. In the second embodiment the lossy resistor is provided by one or more output traps. Thus in the preferred embodiment at least one lossy resistor is provided.
The present invention has been described herein by way of reference to particular preferred embodiments, and particularly by way of reference to an application in a modulated voltage supply. This description is, however, only illustrative of examples. In particular the invention may be implemented more broadly.

## Claims

1. A modulated power supply including a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, and wherein the filter is configured to provide reduced impedance at the output of the filter across a filter transition band.

2. The modulated power supply of claim 1 wherein the filter is configured to determine the output voltage in dependence on frequency components of the source voltage within the filter passband.

3. The modulated power supply of claim 1 further including a lossy resistor connected in parallel across at least part of an inductor of a first stage of the filter.

4. The modulated power supply of claim 3 wherein the inductor of the first stage of the filter is split into a first part and a second part, the lossy resistor being connected across the second part.

5. The modulated power supply of claim 1 wherein the filter is configured to include a lossy resistance.

6. An RF amplification stage including the modulated power supply according to claim 1.

7. The modulated power supply of claim 1 wherein the filter comprises at least one series resonant output trap at the output of the filter, each output trap having a low Q factor.

8. The modulated power supply of claim 7 wherein the at least one output trap includes an inductor and a capacitor connected in series.

9. The modulated power supply of claim 1 wherein the filter is configured to reduce the output impedance of an input inductor and an input capacitor.

10. The modulated power supply of claim 9 being a jth order filter, wherein the filter is configured to reduce the output impedance of the input inductor and the input capacitor in one or more orders of the filter.

11. The modulated power supply of claim 9 wherein the inductance of the input inductor is divided by a value n and the capacitance of the input capacitor is multiplied by a value n to reduce the output impedance.

12. A modulated power supply including a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, and wherein the filter is configured to provide a low impedance at the output of the filter at a passband, a transition band, and a stop band.

13. A modulated power supply including a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, wherein the filter is configured to include a lossy resistance, and wherein the filter is configured to include a resistor connected in parallel across part of an input inductor of the filter.

14. The modulated power supply according to claim 13 being a jth order filter, wherein a further resistor is placed across an inductor of at least one order of the filter.

15. The modulated power supply of claim 14 wherein the filter is configured such that part of the input inductor is split into a series of parallel resonant circuits.

16. A modulated power supply stage including a filter for receiving a rectangular or stepped source voltage to be filtered and for providing an output voltage, the filter including an inductor having an inductance value L1 and a capacitor having a capacitance value C1, and arranged to remove frequency components at a switching frequency and the switching frequency's associated harmonics of the modulated power supply, wherein the filter is arranged such that the impedance of the inductor and capacitor is reduced by a factor n, such that the inductor has an inductance value L1/n and the capacitor has a capacitance value C1*n in order to reduce the output impedance of the filter and wherein the inductor is implemented as a plurality of resonant circuits resonating respectively at the switching frequency and the switching frequency's odd harmonics, each of the plurality of resonant circuits comprising a parallel arrangement of a parallel inductor, a parallel capacitor and a parallel resistor, the inductance values of each parallel inductor, combined, corresponding to L1/n, wherein the plurality of resonant circuits prevent the reduction of the input impedance of the inductor and the capacitor at the switching frequency and the switching frequency's odd harmonics.

17. The modulated power supply stage of claim 16 wherein the filter is arranged to provide the reduced impedance at the output of the filter at a passband, transition band, and stop band.

18. The modulated power supply stage of claim 16 wherein the filter is arranged to provide the reduced impedance at the output of the filter across a filter transition band.

19. The modulated power supply stage of claim 16 wherein the filter includes at least one series resonant output trap at an output thereof, each output trap having a further parallel resistor to reduce a Q factor thereof.

20. The modulated power supply stage of claim 19 wherein the at least one output trap includes an inductor and a capacitor connected in series.

21. The modulated power supply stage of claim 16 wherein the filter is arranged to determine the output voltage in dependence on the frequency components of the source voltage within the filter passband.

22. The modulated power supply stage of claim 16 wherein the filter is a jth order filter.

23. The modulated power supply stage according to claim 22, wherein a resistor is placed across a further inductor of at least one further stage of the jth order filter.

24. A modulated power supply including a filter for receiving a source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, wherein the filter is configured to provide reduced impedance at the output of the filter across a filter transition band.

25. The modulated power supply of claim 24 wherein the filter is configured to reduce the output impedance of an input inductor and an input capacitor.

26. The modulated power supply of claim 25 being a jth order filter, wherein the filter is configured to reduce the output impedance of the input inductor and the input capacitor in one or more orders of the filter.

27. The modulated power supply of claim 25 wherein the inductance of the input inductor is divided by a value n and the capacitance of the input capacitor is multiplied by a value n to reduce the output impedance.

28. The modulated power supply of claim 24 wherein the filter comprises at least one series resonant output trap at the output of the filter, each output trap having a low Q factor.

29. The modulated power supply of claim 28 wherein the at least one output trap includes an inductor and a capacitor connected in series.

30. An RF amplification stage including the modulated power supply according to claim 24.

31. The modulated power supply of claim 24 wherein the filter is configured to determine the output voltage in dependence on frequency components of the source voltage within the filter passband.

32. The modulated power supply of claim 24 wherein the filter is configured to include a lossy resistance.

33. The modulated power supply of claim 24 further including a lossy resistor connected in parallel across at least part of an inductor of a first stage of the filter.

34. The modulated power supply of claim 33 wherein the inductor of the first stage of the filter is split into a first part and a second part, the lossy resistor being connected across the second part.

35. A modulated power supply stage including a filter for receiving a source voltage to be filtered and for providing an output voltage, the filter including an inductor having an inductance value L1 and a capacitor having a capacitance value C1, and arranged to remove frequency components at a switching frequency and the switching frequency's associated harmonics of the modulated power supply, wherein the filter is arranged such that the impedance of the inductor and capacitor is reduced by a factor n, such that the inductor has an inductance value L1/n and the capacitor has a capacitance value C1*n in order to reduce the output impedance of the filter and wherein the inductor is implemented as a plurality of resonant circuits resonating respectively at the switching frequency and the switching frequency's odd harmonics, each of the plurality of resonant circuits comprising a parallel arrangement of a parallel inductor, a parallel capacitor and a parallel resistor, the inductance values of each parallel inductor, combined, corresponding to L1/n, wherein the plurality of resonant circuits prevent the reduction of the input impedance of the inductor and the capacitor at the switching frequency and the switching frequency's odd harmonics.

36. The modulated power supply stage of claim 35 wherein the filter is a jth order filter.

37. The modulated power supply stage according to claim 36, wherein a resistor is placed across a further inductor of at least one further stage of the jth order filter.

38. The modulated power supply stage of claim 35 wherein the filter is arranged to provide the reduced impedance at the output of the filter at a passband, transition band, and stop band.

39. The modulated power supply stage of claim 35 wherein the filter is arranged to provide the reduced impedance at the output of the filter across a filter transition band.

40. The modulated power supply stage of claim 35 wherein the filter includes at least one series resonant output trap at an output thereof, each output trap having a further parallel resistor to reduce a Q factor thereof.

41. The modulated power supply stage of claim 40 wherein the at least one output trap includes an inductor and a capacitor connected in series.

42. The modulated power supply stage of claim 35 wherein the filter is arranged to determine the output voltage in dependence on frequency components of the source voltage within the filter passband.

43. A modulated power supply including a filter for receiving a source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, wherein the filter is configured to include a lossy resistance, and wherein the filter is configured to include a resistor connected in parallel across part of an input inductor of the filter.

44. The modulated power supply according to claim 43 being a jth order filter, wherein a further resistor is placed across an inductor of at least one order of the filter.

45. The modulated power supply of claim 44 wherein the filter is configured such that part of the input inductor is split into a series of parallel resonant circuits.

46. A modulated power supply including a filter for receiving a source voltage to be filtered and for providing an output voltage, the filter configured to reduce the output impedance of the filter without adversely affecting the input impedance of the filter, wherein the filter is configured to provide a low impedance at the output of the filter at a passband, transition band, and a stop band.