US 3761846 A
An impedance-matching resistor connected between two transmission paths of different characteristic impedances Zo and (Zo + Rg) by the use of a series-impedance Rg, in which the impedance-matching resistor is formed into a transmission line, such as a coaxial line or a strip line, and a characteristic impedance Zch of the transmission line is varied so as to meet with a condition (Zo + x/L .Rg) at a medium point spaced by a distance x from the input of one of said two transmission paths, the above mentioned one of the two transmission paths having the characteristic impedance Zo.
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n O a United States Patent [1 1 [111 3,7 Tsuboi Sept. 25, 1973 IMPEDANCE-MATCHING RESISTOR 3,452,302 6/1969 Hayany 333/34 x 1 Inventor: Kiyoshi Tsuboi, setagaya-ku, 512331;? 21133? kiiTiLijiji.................111:1 iii/332 Tokyo-to, Japan  Assigneei Iwasaki Tsushinki Kabushiki Kaisha, P i Examiner-Rudolph V. Rolinec Tokyo-to, Japan Assistant Examiner-Saxfield Chatmon, Jr.  Filed: May 3, 1971 Attorney-Robert E. Burns and Emmanuel J. Lobato Appl. No.: 139,326
 ABSTRACT An impedance-matching resistor connected between two transmission paths of different characteristic impedances Z and (Z Rg) by the use of a seriesimpedance Rg, in which the impedance-matching resistor is formed into a transmission line, such as a coaxial line or a strip line, and a characteristic impedance Zch of the transmission line is varied so as to meet with a condition (Z x/L 'Rg) at a medium point spaced by a distance x from the input of one of said two transmission paths, the above mentioned one of the two transmission paths having the characteristic impedance Z 5 Claims, 5 Drawing Figures IMPEDANCE-MATCHING RESISTOR This invention relates to impedance-matching resistors used in high frequency circuits.
An impedance-matching resistor is usually employed to connect an output of a high frequency circuit, such as a pulse generator, to a load impedance. However, since impedance-matching realized in accordance with conventional techniques is incomplete, distortion of a wave form occurs in a transmitted pulse if the pulse is transmitted in a high frequency circuit.
An object of this invention is to provide an impedance-matchingyresistor employed for theoretically providing impedance-matching in a high frequency circuit so as to eliminate distortion ofa transmitted wave form.
The principle and construction of the invention will be understood from the following detailed discussion in conjunction with the accompanying drawings, in which the same or equivalent parts are designated by the same reference numerals, characters, and symbols, and in which:
FIG. 1 is a circuit diagram illustrating an example of a conventional pulse generator using an Esaki diode (tunnel diode);
FIG. 2' is a wave form of an output of the pulse generator shown in FIG. 1;
FIG. 3 is a schematic section illustrating an embodiment of this invention applied to a coaxial cable; and
FIGS. 4A and 4B are respectively a schematic plane view and a schematic side view, illustrating an embodiment of this invention applied to' a strip line on a printed wiring board.
With reference to FIGS. 1 and 2, defects of conventional impedance-matching techniques are described. In a conventional pulse generator using an Esaki diode, an impedance-matching resistor Rg is usually inserted between an Esaki diode D'and a load ingpedanq e Z as in FIG. 1. A high impedance source and a trigger pulse source are connected across terminals 8 and 8,. If a coaxial cable having acharacteristicimpedance of 50 Ohms is connected as the load impedance Z,,, a single registor of 50 Ohms is usually employed as the inserted resistor Rg. Howevensince an'impedance looking into the load impedance 2, from the pulse generator is not matched witha high impedance of the pulse generator, "overshoot La appears at a rear 'end of a pulse as shown in FIG. 2. v
In this case, an impedance lookinginto the load impedance 2, from two terminals of the Esakidiode D assumes values Z or (Rg Z,) if the inserted resistor Rg is equal to zero or is not equal to zero respectively; As a matter of fact, the Esaki diode D and the load impedance 2,, are connected to each other by a transmission line, such as a coaxial cable or a strip line etc. Accordingly, the above mentioned overshoot cannot be eliminated if impedance matching is not performed between the Esaki diode D and the load impedance Z, so that the output of the pulse generator cannot be employed for a pulse device, such as a sampling oscilloscope.
In view of the situation, an impedance-matching resistor of this invention is proposed to be used for inserting between two high frequency circuits having different characteristic impedances (Z and Z +Rg). For example, an impedance-matching resistor of this invention is inserted between a Esaki diode D and an input (usually an connector) of a connection line (e.g.; a coaxial cable or a strip line). In this case, the characteristic impedance of the impedance-matching resistor of this invention defines a transmission line having a characteristic impedance Zch and assumes an impedance (Rg Z at the connection-side to the Esaki diode D, while the characteristic impedance of the impedancematching resistor assumes an impedance Z, at the connection-side to the connection line. Moreover, at a medium point of the impedance-matching resistor, an impedance looking into the connection line is equal to a characteristic impedance Zch of the impedancematching resistor at the medium point as mentioned below.
Accordingly, the impedance-matching resistor of this invention is so designed that the characteristic impedance Zch is gradually varied along the longitudinal direction of this impedance-matching resistor. In this case, many types of the impedance-matching resistor can be realized in accordance with distribution types of a substance causing a series-resistance (generally a series-impedance). Examples of the impedance-matching resistor of this invention are shown in FIGS. 3, 4 and 4A. Before detailed description for the examples, theoretical principles for the characteristic impedance of the impedance-matching resistor of this invention are described below.
A characteristic impedance Zch of a transmission line is generally given as a value Zch V L/C, if an inductance for a unit length and a capacitance for a unit length are defined as values L and C respectively. Moreover, assuming the inductance L and the capacitance C between two conductors of a transmission line are given, the characteristic impedance Zch of the transmission line can be also obtained.
A characteristic impedance Zch of a coaxial cable can be indicated as follows:
Zch I38 vuie log b/a In this case, references a, b, u and e are defined as a diameter of an inner conductor, one half the inner diameter of an outer conductor, and a specific permeability and a specific dielectric constant of an insulator between the inner con ductor and the outer conductor respectively.
A strip line belongs to either two possible types which are the balanced type and the unbalanced type. A characteristic impedance Zch of a strip line of the balanced type can be defined as follows if the width of the inner conductor, the thickness of the inner conductor and the space between outer conductors are respectively given as values W, t and b respectively and if a value W/(bt) is equal to or more than a value 0.35:
Zch 2, 138 u/-log ib/1rd,,
In this case, a reference d is a diameter ofa center conductor of the strip line, the section of which is equivalently deemed as a circle.
A characteristic impedance Zch of a strip line of the unbalanced type can be defined as follows, if the space against an outer co nductor is assumed as a value It, and if a value t is substantially equal to zero:
Accordingly, if a desired value of the characteristic impedance Zch is given, respective values a, b, h, W and t can be determined in accordance with the above equations (1), (2), (3) and (4).
In embodiments shown in FIGS. 3 and 4, since an impedance-matching resistor Rg is inserted between a diode D and a connector CT connected to a coaxial cable or a strip line. It is deemed that the diode D is connected, at the input of the impedance-matching resistor Rg, to a coaxial cable having a ratio a/b defined by the following relationship:
Z, Rg I38 V u/e'log b/a In a case of a strip line, respective values W etc. can be obtained by replacing the characteristic resistance Z, by a value (Zch Rg) in the equations (2), (3) and (4).
An impedance-matching resistor Rg of this invention is inserted between two center conductors in the generality of cases. In a case of insertion in a coaxial cable, ifa whole length L of an internal resistor is divided into a number of very short sections, and if respective resistances from each division point to another end of the impedance-matching resistor are assumed as values R,, R respective impedances looked into the load Z, from each division point can be indicated by values (R 2,), (R Z ..Accordingly, respective values b /a b /a of a ratio b/a of respective diameters of the inner and outer conductors at each division point can be determined so as to meet with the following relationship:
Moreover, the whole outside pattern of the impedancematching resistor can be corrected under the above 7 conditions.
In an example shown in FIG. 3 in which the resistance material is uniformly distributed along the whole length having a rectangular section, the following relationship is met with respect to a characteristic impedance Zch Z,+Rg x/L if the inner diameter of an outer conductor at a division point is assumed as a value 2bx,
if a distance from the division point to an input of a connector CT is assumed as a value x, and if the whole effective length of the impedance-matching resistor is assumed as a value L:
Zch Z Rgx/L K-log V bx/a Accordingly, an outside pattern 2 of the impedancematching resistor shown in FIG. 3 can be obtained by calculating the value bx in response to the value x varied in a region from zero to the value L.
On the other hand, if the inner diameter of the outer conductor is constant while the width 2a of the resistor is varied for impedance matching, a pattern of the width W, is determined as shown in FIG. 4A so as to meet with the following relationship:
Zch Z, R -x/ g T,
In other words, the width W, is varied along a logarithmic curve if the value b is constant.
In a case of a strip line, equations obtained by replacing the left side Zch of equations (2), (3) and (4) by a value (Z Rg-x/L) are also satisfied. Accordingly, a required impedance-matching can be performed by adjusting the width W, the thickness 1, and the distance h against the outer conductor (Le; a metal ground plate), and moreover the space b between the outer conductors for the balanced type only.
With reference to FIGS. 4A and 4B, an embodiment of this invention comprises an insulating board 3 usually used for printed wiring, a resistive film 1 printed or evaporatively deposited on the insulating board 3, a diode D connected to a conductor 5 on the highimpedance side of the resistive film l, a metal terminal 4 connected to another end of the resistive film l, and a metal ground plate 6 spaced by a space h from the insulating board 3.
As mentioned above, an impedance-matching resistor of this invention is suitable for impedance-matching two transmission paths of different impedances and useful for reliably transmitting pulses without distortion.
1. An impedance matching resistor comprising a transmission line of predetermined length L, having an axial portion comprising one end having a characteristic impedance Z and another axial portion integral with the first-mentioned portion comprising the opposite end and having a characteristic impedance (Z +R,) to jointly define a relationship, (Z,,+xR,/L) defining a characteristic impedance at a point it along a length L of said length of transmission line.
2. An impedance matching resistor comprising a first conductor of predetermined length comprising a material having a constant resistance per unit length and a second conductor, said conductors having a configuration wherein the ratio of the transverse dimensions of said conductors at any point along the length thereof defines an exponential function, thereby jointly defining a transmission line having a linear characteristic series impedance variation linear in both directions along the length thereof, and each of said conductors having means for connecting alternatively thereto a bidirectional input and output.
claim 2, wherein said second conductor has a uniform width and wherein said first conductor has a configuration whereby the ratio of the transverse dimension second conductor and the transverse dimension of said first conductor define an exponential function.
5. An impedance matching resistor according to claim 2, wherein said first conductor and said second conductor define a strip line transmission line.
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