US2054794A - Wave filter - Google Patents

Wave filter Download PDF

Info

Publication number
US2054794A
US2054794A US729733A US72973334A US2054794A US 2054794 A US2054794 A US 2054794A US 729733 A US729733 A US 729733A US 72973334 A US72973334 A US 72973334A US 2054794 A US2054794 A US 2054794A
Authority
US
United States
Prior art keywords
band
phase
frequency
impedances
frequencies
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
US729733A
Other languages
English (en)
Inventor
Robert L Dietzold
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
AT&T Corp
Original Assignee
Bell Telephone Laboratories Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Bell Telephone Laboratories Inc filed Critical Bell Telephone Laboratories Inc
Priority to US729733A priority Critical patent/US2054794A/en
Priority to GB15511/35A priority patent/GB451527A/en
Priority to NL73806A priority patent/NL44376C/xx
Priority to FR791876D priority patent/FR791876A/fr
Priority to DEG90629D priority patent/DE683708C/de
Application granted granted Critical
Publication of US2054794A publication Critical patent/US2054794A/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Images

Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/01—Frequency selective two-port networks
    • H03H7/17—Structural details of sub-circuits of frequency selective networks
    • H03H7/1741—Comprising typical LC combinations, irrespective of presence and location of additional resistors
    • H03H7/1783—Combined LC in series path
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/01—Frequency selective two-port networks
    • H03H7/0115—Frequency selective two-port networks comprising only inductors and capacitors
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
    • H03H7/01—Frequency selective two-port networks
    • H03H7/17—Structural details of sub-circuits of frequency selective networks
    • H03H7/1741—Comprising typical LC combinations, irrespective of presence and location of additional resistors
    • H03H7/1791—Combined LC in shunt or branch path

Definitions

  • This, vinvention relates to frequency selective networks and more particularly to the control of the phase characteristics of broad band selective systems.
  • FIG. 1 shows schematically a general type of network of the invention
  • Fig. 2 is a reactance characteristic used in the explanation of the invention.
  • Figs. 3 and 4 illustrate vtlfiecharacter of the impedances in a particular embodiment of the network of Fig. l;
  • Fig. 5 illustrates certain characteristics of the networks of the'inventio'n.- i
  • the network illustrated comprises a symmetrical lattice having series and diagonal impedances Za and Zb respectively, connected between equal terminal resistances, R in series Vwith' one of which-is a Wave source E.
  • the branch impedances may be 4of any degree of complexity;A but should be' substantially free ⁇ from dissipation.
  • the resonance and anti-resonance frequencies of the branch impedances hereinafter designated critical frequencies
  • certain advantageous frequency characteristics of the image impedance and the transfer constant may be provided.
  • the characteristics discussed in the Bode patentV are those of the lattice per se, namely, its image impedance and transfer constant,as distinguished from the overall properties of the lattice plus the impedances between which it is connected.
  • the transmission characteristic Vof the system is not represented by the transfer constant alone but by this factor together with modifying factors representing the reection effects at the junctions of the lattice and the eX- ternal impedances.
  • The'total effect which is a measure of the ratio of the currents at the re ⁇ ceiving end of the system before and after the' insertion of the lattice is termed the insertion transfer factor.
  • the present invention is concerned with the phase component of the insertion transfer factor, that is, with the sum of al1 the phase shifts in the system including those produced by reflection effects.
  • the terms insertion phase shift and insertion phase characteristic are used to designate the phase component of the insertion transfer factor.
  • this phase shift is made to have a linear variation' with frequency not only within the transmission band but also through the attenuating ranges by Va particular allocation of the critical frequencies of the branch impedances. This allocation is such that, except at each side of the cut-off frequencies, the critical frequencies are separated by a uniform interval both in the transmission band and in the attenuating ranges, the separation at each side of the cut-olf frequencies being reduced to three quarters of the interval else- Where.
  • the determination is further subject tothe-f condition that the impedance arms be physically-V s PATENT OFFICE realizable. This condition imposes a certain functional form for the dependence upon the, fr quency, which may be quickly ascertained.
  • Za and Zb are reactances unlike in sign, that is, reactances of which the alternating resonances and anti-resonances correspond, a resonance in Za to an anti-resonance in Zb and so son.
  • Equation (l) the network attenuates in a frequency interval in which Za/Zb is positive, for then 0 is real. This ensues if Za and Zh are alike in sign, or if resonances in Za correspond to resonances in Zb, and so for antiresonances. Since a condition for the physical realizability of a reactance is that its resonances and anti-resonances alternate, between an interval of transmission and an interval of suppression there must occur a critical frequency, the cut-off, in one impedance arm only.
  • the impedances Za and Zt by their frequency variations and magnitudes completely determine the transmission properties of the network and for that reason may be termed characterizing impedances.
  • filter properties are obtainable from a physically realizable lattice network if only the arms are reactances having the appropriate type of correspondence between their respective natural frequencies. This is illustrated in the case of the low-pass ⁇ lter, in which the branch impedances Za and Zb are of the types shown in Figs. 3 and 4 respectively, by the reactance ex- 1Where Ka and Kb are constants and where f1 and f2 are critical frequencies in the transmitting band, fc a cut-01T intermediate between f2 and f3, and f4 and f5 critical frequencies in the attenuating band. For convenience the critical frequencies representing resonances are termed zeros and those representing anti-resonances are termed poles.
  • Equation 4 represents the repeated reflection of the initially reflected part of the current or wave as it passes back and forth betweenY the terminal. impedances and infinite number of times.
  • the convenience of this form of expression becomes manifest when one eX- amines the variation in the phase shift separately in the three intervals, the transmitting band, the attenuating band, and the transition band. In so doing is established the distribution of the critical frequencies j.,i and f i corresponding to linear phase shift.
  • Transition band-It remains to determine the frequency spacings adjoining the cut-off so that the phase curves in the transmitting'and .attenuating bands are joined through the transition band by a chord of the same slope.
  • this interval which we suppose to be bounded by theV last uniformly spacedY critical frequencies in the transfer constant and impedance controlling chains and to contain only the cut-olf frequency, neither the reflection nor interaction effects are negligible. In fact, for this method of decomposing the total insertion loss, these components become op-positely infinite at the cutfoff.
  • the interaction factor introduces no net change of phase over the interval, since it vanishes at one edge in virtue of Z1 equal to R very nearly and at the other in virtue of e2e being very small. It may therefore be ignored in evaluating the total change in phase through this interval.
  • the phase of. the transfer constant increases by 1f.
  • the phase ⁇ of the reflection factor increases by 1r.
  • the reflection factor in-Y troduces 'an abrupt change in phase of jto represented by the first term of (6). Therefore the net change in the transition interval is radians, and the interval must contain 3/2 uniform spaces if the average slope is to be correct. Considerations of symmetry require that the cutoif be the center of the interval, which thus comprises two three-quarter spaces.
  • the discontinuity in l at the cut-off is asV required to remove the discontinuity at this point introduced by the reflection effect.
  • CurveV I2 represents the transfer phase shift that is, the phase component yof the transfer constant of the lattice per se, in the transmission range from zero frequency to the cut-o.
  • This component increases by 1r in each of the intervals between the critical frequencies, including fc, and undulates about the straight line I5 departing therefrom by 1r/4 at the cut-olf.
  • the undulations of this curve, as well as those of the other curves are somewhat exaggerated in order that their character may be exhibited.
  • Curve I3 represents the reflection phase shift r in the attenuating range, this component being zero in the transmission band.
  • Virtue of the critical frequency spacing the general slope of this curve is that of the line I5 but it is characterized first by a departure of 1r/4 at the cutoff and a sudden change of 1r at the critical frequency f3. amounts to a reversal of phase its effect in general is not material.
  • Curve I4 represents the interaction phase shift. This curve is characterized by undulations of half the period of those of the other curves and by a sudden change of 1r/2 at the cut-off.
  • the total phase shift in the system is obtained by adding the three curves togetherin which case it will be noted that the discontinuity of curve I4 at the cut-off just neutralizes that at th-e junction of curves I2 and 32.
  • the resultant phase shift will therefore show a smooth variation which is very close to linear through the whole range from zero to ,f3 and which continues at the same slope, subject to reversals at the critical frequencies, in the higher range.
  • the pattern for the transfer constant and impedance controlling frequencies which has been found is suflicient to insure only that the phase shift has its linear value at each critical frequency, or that the average slope in each space be the same. In order that the slope may closely approximate to the average at every intermediate point, it is further necessary to ⁇ determine the multipliers K1 and K2 of the transfer constant and image impedance expressions. We have already seen that K2 should be taken equal tothe terminating impedance, R, so as to obtain impedance match and vanishing interaction effects in the pass band.
  • the effect of dissipation on the phase characteristic in the transition interval A may be otherwise corrected for by small variations in the ide-al frequency pattern.
  • the non-dissipative phase slope may be caused progressively to increase through the band so that change due to parasitic dissipation displaces the characteristic toward, rather than away from, the ideal straight line.
  • the lattenuation characteristic is improved by increase of dissipation in the impedances together with compensating modification of the frequency spacing in this way.
  • the appropriate variations of vthe critical frequencies from their theoretical locations are best determined by trial.
  • the loss may be increased at the cost of some degradation of the phase Vproperty by varying the constants K1 and K2.
  • the spacing of impedance controlling frequencies must be uniform over that portion of the attenuating band in which the phase slope is to be uniform, the extension of this condition over the infinite attenuating band of a lowpass filter would result in an infinite network.
  • the phase slope is seldom of interest very far into the attenuating band, so that the chain of uniformly spaced impedance controlling frequencies may be soon terminated.
  • uniform spacing must be maintained through fd.
  • the infinite chain of uniformly spaced critical frequencies greater than fd may be replaced by one or more critical frequencies so located that the corresponding factors approximate in the range below fd to the factors associated with the omitted infinite sequence.
  • the numerical determination of the terminating critical frequencies is simple, since a close approximation is obtained by use of one, or at most two, of them at somewhat extended spacings.
  • the theoretical constant multiplier is unity.
  • the multiplier of the image impedance expression is determined to make the impedance R at the mean of the cut-E frequencies.
  • the high-pass filter may be regarded as the limiting case of the band-pass filter as the upper cut-off recedes toward infinity.
  • the preservation of linear phase shift over this infinite pass band would require an infinite network on account of the necessity of uniform spacing of transfer constant controlling frequencies, but if there is a frequency, fd, beyond which the phase shift is not of interest, the high-pass filter may be realized in a nite'netwcrk by terminating the chain of critical frequencies beyond this point in the manner described above for impedance controlling frequencies.
  • a broad band selective system comprising a symmetrical reactance network having multiple resonant characterizing impedances Za. and Zh, and equal resistive terminal impedances connected to the input and the output terminals of the network
  • the method of producing a linear phase shift throughout the band and beyond the limits thereof which comprises spacing the critical frequencies of the characterizing impedances at uniform intervals throughout the greater portion of the transmission band and in a-portion of an attenuation range beyond a band limit and spacing the critical frequencies on each side of said band limit at intervals therefrom substantially equal to three-quarters of the uniform interval elsewhere.
  • a broad band selective system comprising a symmetrical four-terminal reactance network having characterizing impedances Za and Zb, and equal resistive terminal impedances connected to the input and the output terminals of said network, said characterizing impedances each having a plurality of critical frequencies which are spaced at uniform intervals throughout the greater portion of the transmission band and in an attenuation range beyond a cut-off frequency, and which on each side of the cut-off frequency are spaced at intervals substantially equal to three-quarters of the uniform spacing elsewhere whereby the insertion phase characteristic is linear throughout the band and a portion of the attenuation range.
  • a broad band selective system comprising a symmetrical four-terminal reactance network having characterizing impedances Za and Zb,
  • said characterizing impedances having a plurality of critical frequencies certain of which lie within the transmission band and others of which lie outside the band and one of which determines a band limit, said critical frequencies being spaced at uniform intervals throughout the transmission band and in a portion of the attenuation range beyond said band limit and having a spacing on each side of said band limit substantially equal to three-quarters of the uniform .spacing elsewhere whereby the insertion phase characteristic of the network is a substantially linear Yfunction of the frequency throughout the band and through the cut-off frequency.
  • poles and zeros of the impedance Za are inversely coincident with the poles and zeros of the impedance Zb within the band and are directly coincident with the poles and zeros of impedance Zh outside the band.

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Measurement Of Resistance Or Impedance (AREA)
  • Networks Using Active Elements (AREA)
US729733A 1934-06-09 1934-06-09 Wave filter Expired - Lifetime US2054794A (en)

Priority Applications (5)

Application Number Priority Date Filing Date Title
US729733A US2054794A (en) 1934-06-09 1934-06-09 Wave filter
GB15511/35A GB451527A (en) 1934-06-09 1935-05-28 Electric wave filters
NL73806A NL44376C (enrdf_load_stackoverflow) 1934-06-09 1935-06-06
FR791876D FR791876A (fr) 1934-06-09 1935-06-08 Perfectionnements aux filtres d'ondes électriques
DEG90629D DE683708C (de) 1934-06-09 1935-06-12 Verfahren zur Regelung der Phasencharakteristik eines symmetrischen Wellenfilters mit grossem Durchlassbereich, welches durch jeden seiner Reaktanzzweige bei einer Mehrheit von kritischen Frequenzen Resonanz und Antiresonanz zeigt

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US729733A US2054794A (en) 1934-06-09 1934-06-09 Wave filter

Publications (1)

Publication Number Publication Date
US2054794A true US2054794A (en) 1936-09-22

Family

ID=10060415

Family Applications (1)

Application Number Title Priority Date Filing Date
US729733A Expired - Lifetime US2054794A (en) 1934-06-09 1934-06-09 Wave filter

Country Status (5)

Country Link
US (1) US2054794A (enrdf_load_stackoverflow)
DE (1) DE683708C (enrdf_load_stackoverflow)
FR (1) FR791876A (enrdf_load_stackoverflow)
GB (1) GB451527A (enrdf_load_stackoverflow)
NL (1) NL44376C (enrdf_load_stackoverflow)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2681391A (en) * 1950-08-11 1954-06-15 Philco Corp Interstage coupling network having improved phase response
US2711516A (en) * 1949-10-29 1955-06-21 Rca Corp Frequency discriminatory systems
US2760167A (en) * 1952-10-29 1956-08-21 Hogan Lab Inc Wave transmission network
US3122716A (en) * 1961-08-24 1964-02-25 Seg Electronics Co Inc Electrical filter consisting of frequency discriminating section concatenated with all-pass complementary phase correcting section
US4885562A (en) * 1987-07-20 1989-12-05 Electronique Serge Dassault Microwave delay circuit having a bridge-T circuit

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2711516A (en) * 1949-10-29 1955-06-21 Rca Corp Frequency discriminatory systems
US2681391A (en) * 1950-08-11 1954-06-15 Philco Corp Interstage coupling network having improved phase response
US2760167A (en) * 1952-10-29 1956-08-21 Hogan Lab Inc Wave transmission network
US3122716A (en) * 1961-08-24 1964-02-25 Seg Electronics Co Inc Electrical filter consisting of frequency discriminating section concatenated with all-pass complementary phase correcting section
US4885562A (en) * 1987-07-20 1989-12-05 Electronique Serge Dassault Microwave delay circuit having a bridge-T circuit

Also Published As

Publication number Publication date
NL44376C (enrdf_load_stackoverflow) 1938-11-15
DE683708C (de) 1939-11-17
GB451527A (en) 1936-08-07
FR791876A (fr) 1935-12-18

Similar Documents

Publication Publication Date Title
US2530691A (en) Wave filter
US2816270A (en) Microwave channel dropping filter pairs
US2266658A (en) Electrical frequency-selective system
FR858308A (fr) Filtres d'ondes électriques
US2531419A (en) Hybrid branching circuits
US2054794A (en) Wave filter
US2639326A (en) Electromagnetic wave microwave frequency structure using hybrid junctions
US2052703A (en) Coupled circuits
US2768351A (en) Multipole network
US2342638A (en) Wave transmission network
US1828454A (en) Transmission network
US1955788A (en) Transmission network
US2249415A (en) Wave filter
US1781469A (en) Wave filter
US3449696A (en) Dual section all pass lattice filter wherein nonlinearities of two sections cancel
US2238023A (en) Equalizer
US2667622A (en) Coaxial cable attenuator matching device
US3573674A (en) Tailored response microwave filter
US1557229A (en) Terminating network for filters
GB495815A (en) Improvements in or relating to electric signal transmission systems
US2216937A (en) Wave filter
US2988713A (en) Connection system of multiple-tuned coupled circuits
US2914737A (en) Transmission line tap-off
US2760167A (en) Wave transmission network
US2199221A (en) Wave filter