US2153857A - Phase-correcting low-pass filter - Google Patents

Phase-correcting low-pass filter Download PDF

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US2153857A
US2153857A US208513A US20851338A US2153857A US 2153857 A US2153857 A US 2153857A US 208513 A US208513 A US 208513A US 20851338 A US20851338 A US 20851338A US 2153857 A US2153857 A US 2153857A
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phase
filter
circuit
network
shunt
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Harold A Wheeler
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BAE Systems Aerospace Inc
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Hazeltine Corp
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B3/00Line transmission systems
    • H04B3/02Details
    • H04B3/04Control of transmission; Equalising
    • H04B3/14Control of transmission; Equalising characterised by the equalising network used
    • H04B3/146Control of transmission; Equalising characterised by the equalising network used using phase-frequency equalisers
    • H04B3/147Control of transmission; Equalising characterised by the equalising network used using phase-frequency equalisers fixed equalisers

Description

A ril 11, 1939. A. WHEELER v PHASE-CORRECTING LOW-PASS FILTER Filed May 18, 1938 R FIG. la.
FIG.4.
INVENTOR HAROLD A. WHEELER ATTORNEY Patented Apr. 11, 1939 Pl ATENT OFFICE PHASE-CORRECTING LOW-PASS FILTER Harold A. Wheeler, Great Neck, Y., assignor to Hazeltine Corporation, a corporation of Delaware Application May 18, 1938, Serial No. 208,513
12 Claims.
This invention relates generally to low-pass wave-filter circuits and particularly to a low-pass filter section utilized as a phase-linear filter, as a phase-correcting section in a confluent network, or as a phase-correcting filter co-operating with other filters having phase distortion.
In many electrical circuits it is desirable to translate signals of a wide range of frequencies through an electrical network with a predetermined frequency phase-shift characteristic or, in the case of distortionless transmission, with a phase shift in the network directly proportional to the frequency. For instance, in the translation and amplification of a video-frequency signal in a television apparatus, it is required to translate signals comprising a wide band of frequencies and including frequencies very low as compared with the cutoff frequency. The circuits have the characteristics of low-pass filters, even though they do not pass signals quite down to zero frequency. While it is desired to translate such signals with no distortion in any stage of the signal-translating channel, this may not be practicable so that it may be necessary to provide phase-correcting circuits in the signal-translating channel. Such phase-correcting circuits may be utilized for the purpose of providing a distortionless over-all characteristic for the signal-translating channel or for providing a given frequency phase-shift characteristic for one part of the signal-trans1ating channel which is complementary to such characteristic of some other part of the channel.
Certain phase-correcting networks have heretofore been utilized for the purpose discussed above. In designing a phase-correcting section fora particular form of correction, it is necessary to select a type of filter section whose phase shift varies in the desired manner over the entire pass band of thesystem in which it is to be utilized. It is highly desirable, therefore, to have available a phase-correcting network whose phase shift filter sections do not tolerate a shunt capacitance of any appreciable magnitude across the terminals, of the section. The normal characteristics of such filters are disturbed by any inherent capacitance of the circuit elements connected across the terminals at either end of the phasecorrecting section.
Also, since the requirement for distortionless transmission over a band of frequencies is a straight-line frequency phase-shift characteristic for the network, it is particularly desirable to obtain in a low-pass network having generally the desired characteristic, a phase-correcting section capable of further correcting the phase shift of the system to its theoretically correct value at one or more points in the pass band. With a plurality of such phase-correcting networks, any desired degree of correction of the over-all transmission characteristic of the system is possible.
It is an object of theinvention, therefore, to provide an improved low-pass phase-correcting network for use in a filter system, the phase shift of which can be predetermined as desired at one or more frequencies within the pass band. 20
It is another object of the invention to provide an improved low-pass filter for substantially distortionless transmission of a wide band of frequencies, the frequency phase-shift characteristic of which passes through a straight line through the origin at several points in the pass hand, one of the points being the origin.
, It is another object of the invention to provide a phase-correcting filter section for the purposes described above which includes substantial shunt capacitance across either or both terminals.
It isstill another object of the irivention to provide a phase-correcting filter section of the type described requiring a relatively small coefficient of inductive coupling between inductance elements of the filter circuit.
In accordance with one embodiment of .the invention, there is provided a low-pass filter section comprising a transformer, the windings of which are connected as series arms of a ladder network whose shunt arms comprise capacitance elements. Input and output terminals of the section are across the terminal shunt capacitance elements. The reactive elements of the section are so proportioned 'as to provide a low-pass filter circuit having constant-hmid-shunt image impedanceat each end, a predetermined. cutoff frequency, and a phase shift which is a multiple of Ir at selected critical frequencies within the pass band. In other words, the frequency phase-shift characteristic of the filter section of this embodiment of the invention can be utilized, in a lowpass signal-translating channel, to compensate l for the usual forms of phase distortion over the major part of the pass band.
In another embodiment of the invention there is provided a filter section comprising three or more inductance elements inductively coupled in pairs, the individual elements being connected in the series arms of a ladder network, the shunt arms of which are capacitance elements. The
reactive elements of the circuit are so proportioned as to provide a low-pass filter circuit having constant-k mid-shunt image impedance at each end, a predetermined cutoff frequency, and a phase shift which is a multiple of 1r at two or more independent selected critical frequencies within the pass band. In other words, the frequency phase-shift characteristic of this embodiment of the invention can be utilized in a system to provide a greater degree of phase correction. In a variation of this embodiment of the invention, the three above-mentioned inductance elements are bridged by an additional inductance element. This bridged ladder circuit has the advantage that a complete freedom of choice of critical frequencies is procured in a symmetrical filter section with only one inductive coupling.
For a better understanding of the invention, together with other and further objects thereof, reference is had to the following description taken in connection with the accompanying drawing and its scope will be pointed out in the appended claims.
Referring now to the drawing, Fig. 1a is a circuit diagram of the filter composition of one embodiment of the invention and is utilized to explain the general theory of the invention; Figs. 1b and 1d are circuit diagrams of ladder networks utilized, respectively, to obtain one-point and two-point phase correction within the pass band; Fig. 1c is a graph illustrating certain operating characteristics of the circuits of Figs. la and 11); Fig. 2a is a circuit diagram of a network providing phase correction at two predetermined frequencies within the pass band; Fig. 2b is a graph illustrating an operating characteristic of the circuit of Fig. 2a; Fig. 3a is a combination of the circuits of Figs. 1d and 211; Fig. 3b is a modification of the circuit of Fig. 3a with self-inductances substituted for mutual inductances; and Fig. 4 is a circuit diagram of a vacuum-tube amplifier utilizing a phase-correcting filter in accordance with the invention.
Referring now more particularly to Fig. is, there is shown a phase-correcting network comprising an m-derived filter section interposed between two constant-k half-sections so that the image impedances of the network are those of mid-shunt terminations of a constant-k filter. The terminating impedances or resistors to which the input and output pairs of terminals of the circuit of Fig. la are coupled are represented by resistors R, R shown in dotted lines. The inductance of the shunt arm of the m-type section; in this case the filter having an m greater than unity, is negative. It is not possible, therefore, to construct this inductance as a separate element. However, in the circuit of Fig. 1b there is shown an equivalent network utilizing a transformer as an equivalent to the three inductance elements of the circuit of Fig. 1a. This network comprises inductances L, L having a coefficient of coupling k therebetween and connected in the series arms of a ladder network having shunt arms comprising condensers C1, C1 connected across the terminal circuits thereof, and shunt arm C1 interposed between inductances L, L.
Fig. 1c shows the frequency phase-shift characteristic of the circuits of Fig. la and Fig. 1b.
The shape of the phase characteristic may be determined by the choice of the value of m in Y the formulae hereinafter given. In other words, the intersection of each curve with the r phaseshaft line occurs at frequency I1, I: being the cutofl frequency, and x1 being determined by the first of the following formulae which are applicable to the circuits of Figs. 1a and 1b:
where u: is the angular frequency corresponding to f1, and R is the image impedance at zero frequency. The value of m in the above equations may be determined from the curves of Fig. 10. It will be seen that the curve m=l is concave upwardly over the major portion of the pass band, while the curve m=3 is convex upwardly over the major portion of the pass band.
It will be seen from the above description and formulae that each of the circuits of Figs. 1a and 1b may be utilized as a phase-correcting filter network having a phase shift which is a multiple of 1r at one preselected critical frequency within the pass band and that such a filter presents a'constant-k mid-shunt image impedance across each of its pairs of terminals.
The circuit of Fig. 1d is similar in some respects to the circuit of Fig. 1b and similar circuit elements have been given identical reference numerals in the two figures. The filter composition of the circuit of Fig. 1b is shown in Fig. 1a and comprises a single m-type section; the filter composition of the circuit of Fig. id is not shown but is similar except that it comprises two mtype sections. These may or may not have the same value of m. The circuit of Fig. 1d is effective to provide a phase shift which is a multiple of r at each of two critical frequencies in the pass band, while presenting a constant-k midshunt image impedance across each of its pairs of terminals. Formulae for the circuit of Fig. 1d may be derived on filter principles from the equivalent network comprising two m-derived sections.
The circuits described above illustrate the utility of the phase-correcting networks of the invention in securing a linear frequency phase-shift characteristic or for partially compensating for the curvatures of the characteristics of other networks towhich the phase-correcting network is coupled. The same general utility is found in the circuits of Figs. 2a, 3a, and 312, but these have greater freedom of design.
The circuit of Fig. 2a comprises inductors L1, L2 and L1 connected in the series arms of a ladder network and condensers C3, C4, C4, connected as shunt arms thereof. Pairs of input and output terminals are connected, respectively,
across condensers C3, C3 to which are coupled resistors R, R which may be actual terminating resistors or may represent the image impedances of the circuits to which the filter of the invention is coupled. Inductor L5 is connected to bridge inductors L1, L2, L1 while inductors L1, L1 have amass? a coefficient of inductive coupling In therebetween. as represented in the drawing by the dotted line M.
The following are the formulae applicable to the circuit of Fig. 2a:
" where the subscripts on the angular frequencies or identify the angular frequencies with the corresponding frequencies 14, f5, and is at which the filter has a phase shift of 1r, Zr, and 311-, respectively, is being the cutoff frequency.
The circuit of Fig. 2a is thus effective to provide a phase-correcting circuit having a phase shift which is a multiple of 1r at each of two predetermined independent critical frequencies within the pass band and which presents a constunt-k mid-shunt image impedance at its terminals. The frequency phase-shift characteristic of the circuit of Fig. 2a is represented by the graph of Fig. 2b.
The inductance L5 as determined by Formula 12 becomes infinite, and may then be omitted from the circuit without altering its characteristics, if the following relation between the critics. frequencies is satisfied:
The operation of the circuit thus modified is essentially unchanged except that the two critical frequencies within the pass band, .at which the phase shift is a multiple of 1r, are interdependent.
Also, the circuit of Fig. 2a may be so proportioned as to secure a frequency phase-shift characteristic which is substantially linear over the major portion of the pass band. It is, however, impossible to provide a linear phase characteristic near the cutoff'frequency. The maximum phase shift of the circuit of Fig. 2a. is 311-, there being four critical frequencies as shown in Fig. 2b. these being fa, f4, f5, and ft. The cr tical frequencies may be so related that the curve between is, or zero frequency, and is is v bstantially linear by choosing equal frequency; differences between successive critical frequencies except the last two andmaking the difference Between the last two approximately half that between the acteristic in a network of the ty 'e of the inven-' tion having a maximum phase shift n1r and hav-.
ing a number of critical frequencies equal to (11+ 1),is:
The spacing of the critical frequencies in such a,
between inductances capacitance element 20 which takes the place of design is uniform except that the space just inside the cutoff frequency is only one-half the uniform value.
In Fig. So there is shown a filter-correcting circuit in accordance with the invention which has the features of both Fig. 1d and Fig. 2a, similar circuit elements being given identical reference numerals. The only difference between the circuits of Figs. 2a and 3a is that there is, in the case of Fig. 3a, inductive coupling between the inductance La andeach of inductances L1, L1., It will be understood, however, that Equations 6-12, inclusive,; given above as being applicable to Fig. 2a, are not applicable to the circuit of Fig. 3a inasmuch as they do not take into account the added mutual inductances. Comparable formulae may be derived utilizing well-known principles of filter design.
.The circuit of Fig. 3b is the run equivalent of Additional self-inductances in the circuit of Fig.
3b have been added in place of mutual inductances in the circuit of Fig. 3a; thus, inductance element Le replaces the mutual inductance between inductance Le and one of inductances L1 in Fig. 3a, and inductance L7 replaces the mutual inductance between inductances L1, L1 of Fig. 3a. Fig. 3b is given mainly for explanatory purposes, since one or more of Le, L6, L7 would be negative in a phasecorrecting filter, so that mutual inductance would be needed.
In Fig. 4 there is shown a filter in accordance with the invention which is utilized as a coupling circuit between the output electrodes of a vacuum tube l0 and the input electrodes of a vacuum tube II. .The inherent capacitance of the output circuit of vacuum tube i0 is represented by capacitance means I! and I3 in parallel, while the inherent capacitance of the input circuit of vacuum tube II is represented by capacitance means I and IS in parallel. These inherent capacitances tend to limit the response of the systems of the prior art as a wide band amplifier. filter circuit comprising an inductance l6, condenser and resistor 2b is coupled across capacitance l2, l3 to maintain a high impedance across the output terminals of vacuum tube I II over a wide band of frequencies in a manner which is fully described in applicant's copending application, Serial No. 203,597, filed April 22, 1938. The filter circuit between the tubes l0 and I I, which is in all respects equivalent to the circuit of Fig. lb, comprises inductances l8 and I9 which are widely separated from each other and adjacent, respectively, to vacuum tube l0 and vacuum tube ll. These l inductances comprise series arms of the filter, being the equivalent of inductances L, L of the circuit of Fig. 1b. A shunt arm interposed l8 and I9, comprises a In order to provide a coupling.
A dead-end vided comprising an inductance 2| inductively coupled to inductance II and tapped on inductance ll. A grid-leak resistor 22 is provided for vacuum tube ll while blocking condensers 23, 24 serve to confine direct currents to their proper paths.
In considering the operation of the circuit of Fig. 4, it will be seen that the dead-end filter, comprising capacitance elements l2 and H, inductance l6, and resistor 26, serves to maintain a high value of impedanceacross the output circuit of vacuum tube It in a manner fully described in the above-mentioned copending application. The filter circuit of the present invention operates in the manner described in detail with respect to the circuit of 'Fig. 1b to provide a circuit in which a predetermined phase shift, equal to a selected multiple of r, is obtained at a selected critical frequency within the pass band of the system for any of the purposes outlined in detail above.
While there have been described what are at present considered to be the preferred embodiments of the invention, it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the invention, and it is, therefore, aimed in the appended claims to cover all such changes and modifications as fall within the true spirit and scope of the invention.
What is claimed is:
1. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of one or more preselected frequencies within said band comprising, a ladder network including a plurality of inductances as series arms, at least one pair of said inductances having negative mutual inductance therebetween, a plurality of capacitance elements included as shunt arms, and input and output pairs of terminals across different ones of said shunt arms, the reactive constants of said filter network being so proportioned as to present constant-k mid-shunt image impedance across each of said pairs of terminals.
2. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is r at a preselected frequency within said band comprising, a ladder network including two negatively inductively coupled inductances as series arms, three capacitance elements as shunt arms, and input and output pairs of terminals across difl'erent ones of said shunt arms, the reactive constants of said filter network being so proportioned as to present constant-k mid-shunt image impedance across each of said pairs of terminals.
3. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of two preselected frequencies within said band, comprising, a ladder network including two negatively inductively coupled inductances and a third inductance as series arms, four capacitance elements as shunt arms, and input and output pairs of terminals across different ones of said shunt arms, the reactive constants of said filter network being so proportioned as to provide constant-k mid-shunt image impedance across each of said pairs of terminals.
4. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of two or more independent preselected frequencies within said band comprising, a ladder network including at least three inductances as series arms, at least one pair of said inductances having negative mutual inductance therebetween, a plurality of capacitance elements as shunt arms, input and output pairs of terminals across diflerent ones of said shunt arms, and an additional inductance connected to bridge said" plurality of inductances, the reactive constants of said filter network being so proportioned as to provide constant-k midshunt image impedance across each of said pairs of terminals.
5. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of two independent preselected frequencies within said band comprising, a ladder network including three negatively inductively coupled inductances as series arms and four capacitance elements as shunt arms, input and output pairs of terminals across different ones of said shunt arms, and an additional inductance connected to bridge said three inductances, the reactive constants of said filter network being so proportioned as to provide con stant-k mid-shunt image impedance across each of said pairs if terminals.
6. A low-pass wide band amplifier comprising first and second vacuum tubes comprising input and output electrodes having shunt capacitance, a phase-correcting filter network coupled between the output electrodes of said first tube and the input electrodes of said second tube for procuring a phase shift which is a multiple of 1r at each of one or more preselected frequencies within said band, said filter network including a ladder network having a plurality of inductances in series arms of said network, said inductances comprising at least one pair having negative mutual inductance therebetween, said filter network elements having inherent capacitance included as shunt arms, the output circuit capacitance of said one of said tubes being included in one of said shunt arms and the input circuit capacitance of the other of said tubes being included in another of said shunt arms, said inherent capacitances of said network elements comprising substantial portions of the total capacitances of said shunt arms with which they are associated, and the reactive constants of said filter network being so proportioned as to provide constant-k mid-shunt image impedance across each of said circuits.
'7. In a low-pass wide band amplifier, first and second vacuum tubes comprising input and output circuits having appreciable capacitances, a phase-correcting filter network coupled between the output circuit of one of said tubes and the input circuit of the other of said tubes for procuring a phase shift which is a multiple of r at each of one or more predetermined frequencies within said band, said filter network including a ladder network having two remotely separated inductances as series arms adjacent to said tubes, a link circuit comprising inductance coupling said inductances to provide a negative mutual inductance therebetween, and shunt arms comprising said capacltances, the reactive constants of said filter network being so proportioned as to provide constant-k mid-shunt image impedance across each of said capacitances.
8. A low-pass phase-correcting filter network for procuring a phase shift of Jr at a preselected frequency within said band, said filter network including a transformer comprising primary and secondary windings providing negative mutual inductance, shunt capacitance elements for each of said windings comprising a common portion, and input and output pairs of terminals across the remaining portions of said shunt capacitance elements, the reactive constants of said filter section being so proportioned as to provide constant-lc mid-shunt image impedance across each of said pairs of terminals.
9. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of one or more preselected frequencies within the pass band comprising, a ladder network including a plurality of inductances as series arms, at least one pair of said inductances having negative mutual inductance therebetween, a plurality of capacitance elements as shunt arms, and input and output pairs of terminals across different ones of said shunt arms, the reactive constants of said filter network being so proportioned as to present constant-k mid-shunt image impedance across each of said pairs of terminals.
10. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of Jr at a preselected frequency within the pass band comprising, two constant-k half-sections with adjacent mid-series terminations, an m-derived filter section interposed between said half-sections, said m-derived section having a value of m greater than unity, 4nd input and output pairs of terminals across said half-sections, wherefore said network presents constant-1c image impedance across each of said pairs of terminals.
11. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of: at each of one or more preselected frequencies within the pass band comprising, a ladder network including a plurality of inductances as series arms, at least one pair of said inductances having negative mutual inductance therebetween, a plurality of capacitance elements as shunt arms, and input and output pairs of terminals across different ones of said shunt arms, the reactive constants of said filter network being so proportioned as to provide a phase-frequency characteristic which is convex upwardly over the major portion of the pass band and to present constant-k image impedance across each of said pairs of terminals.
12. A low-pass phase-correcting filter network for procuring a predetermined phase shift which is a multiple of 1r at each of one or more preselected frequencies within the pass band comprising, a ladder network including a plurality of inductances as series arms, at least one pair of said inductances having negative mutual inductance therebetween, and a plurality of capacitance elements as sh'unt arms, and input and output terminals across diflerent ones of said shunt arms, said filter having a mardmum phase angle of mand having n-l critical frequencies within the band, the spacing between the critical frequencies being uniform to provide nearly linear phase-frequency characteristic over the fraction 211-2 fln-l of the pass band and to present constant-k midshunt image impedance across each of said pairs of terminals.
HAROLD a.
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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2598683A (en) * 1946-02-05 1952-06-03 Marcel J E Golay Corrected delay line
US2676308A (en) * 1947-12-05 1954-04-20 Hartford Nat Bank & Trust Co Device for deriving phase-shifted voltages from an input voltage of varying frequency
US2930005A (en) * 1956-06-27 1960-03-22 Philips Corp Network for frequency-modulated signals
US2988713A (en) * 1956-03-26 1961-06-13 Kokusai Electric Co Ltd Connection system of multiple-tuned coupled circuits
US3155927A (en) * 1960-09-12 1964-11-03 Gen Electric Bridged-t termination network
US20040135651A1 (en) * 2001-03-08 2004-07-15 Dirk Heumann Filter arragement
US20050206470A1 (en) * 2004-03-16 2005-09-22 Yo-Shen Lin Lumped-element transmission line in multi-layered substrate
US20050219011A1 (en) * 2004-04-02 2005-10-06 Yo-Shen Lin Lowpass filter formed in a multi-layer ceramic
US20060038635A1 (en) * 2004-08-17 2006-02-23 Dominick Richiuso Integrated passive filter incorporating inductors and ESD protectors
US20160272345A1 (en) * 2015-03-17 2016-09-22 Airbus Operations Sas Method And Device For Assisting The Piloting Of An Aircraft During A Parabolic Flight

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2598683A (en) * 1946-02-05 1952-06-03 Marcel J E Golay Corrected delay line
US2676308A (en) * 1947-12-05 1954-04-20 Hartford Nat Bank & Trust Co Device for deriving phase-shifted voltages from an input voltage of varying frequency
US2988713A (en) * 1956-03-26 1961-06-13 Kokusai Electric Co Ltd Connection system of multiple-tuned coupled circuits
US2930005A (en) * 1956-06-27 1960-03-22 Philips Corp Network for frequency-modulated signals
US3155927A (en) * 1960-09-12 1964-11-03 Gen Electric Bridged-t termination network
US20040135651A1 (en) * 2001-03-08 2004-07-15 Dirk Heumann Filter arragement
US7002434B2 (en) * 2004-03-16 2006-02-21 Chi Mei Communication Systems, Inc. Lumped-element transmission line in multi-layered substrate
US20050206470A1 (en) * 2004-03-16 2005-09-22 Yo-Shen Lin Lumped-element transmission line in multi-layered substrate
US20050219011A1 (en) * 2004-04-02 2005-10-06 Yo-Shen Lin Lowpass filter formed in a multi-layer ceramic
US6970057B2 (en) * 2004-04-02 2005-11-29 Chi Mei Communication Systems, Inc. Lowpass filter formed in a multi-layer ceramic
US20060038635A1 (en) * 2004-08-17 2006-02-23 Dominick Richiuso Integrated passive filter incorporating inductors and ESD protectors
US7808752B2 (en) * 2004-08-17 2010-10-05 Semiconductor Components Industries, Llc Integrated passive filter incorporating inductors and ESD protectors
US20160272345A1 (en) * 2015-03-17 2016-09-22 Airbus Operations Sas Method And Device For Assisting The Piloting Of An Aircraft During A Parabolic Flight
US9828118B2 (en) * 2015-03-17 2017-11-28 Airbus Operations Sas Method and device for assisting the piloting of an aircraft during a parabolic flight

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