US 3890589 A
A resistive element has a gradient of resistivity extending along its length. It is held in slidable contact with two or more brushes spaced-apart from each other. The resistance between the brushes can be varied by changing their position relative to the resistive element and the gradient or resistivity. The resistive element may have an arcuate configuration and the relative position may be changed by rotating the element. Two such variable resistors having a logarithmic resistance gradient may be combined in a variable resistance attenuator.
Description (OCR text may contain errors)
United States Patent Kogo et a1.
1 1 VARIABLE RESISTOR  Inventors: Masanori Kogo; Hisashi Honda,
both of Tokyo, Japan  Assignee: Nippon Electric Company, Limited,
Tokyo, Japan Notice: The portion of the term of this patent subsequent to Sept. 18, 1990, has been disclaimed.
 Filed: June 20, 1973  Appl. No.: 371,620
Related US. Application Data  Continuation-impart of Ser. No. 267,630, June 29,
1972, Pat. NO. 3,760,322.
 Foreign Application Priority Data June 30, 1971 Japan 46-48316  US. Cl. 338/89; 338/137; 338/142; 338/150; 333/81 R  Int. Cl. 1101C 10/04; HOIC 10/26  Field of Search 338/89, 137, 138-142, 338/150; 333/81 R  References Cited UNITED STATES PATENTS 1,731,772 [0/1929 Greenewalt 338/141 X 1*June 17, 1975 2,005,922 6/1935 Stoekle 338/140 2,096,027 10/1937 Bode H 333/81 X 2,681,967 6/1954 Harrison et a1... 338/89 2,798,140 7/1957 Kohring 338/137 2,854,643 9/1958 Wigan et a1 333/81 2,881,295 4/1959 Brown 338/137 X 3,657,688 4/1972 Casey et a1. 338/150 Primary Examiner-J. V. Truhe Assistant Examiner-D. A. Tone Attorney, Agent, or FirmHopgood, Calimafde, Kalil, Blaustein & Lieberman 1 7 1 ABSTRACT A resistive element has a gradient of resistivity extending a1ong its length. It is held in slidable contact with two or more brushes spaced-apart from each other The resistance between the brushes can be varied by changing their position relative to the resistive element and the gradient or resistivity. The resistive element may have an arcuate configuration and the relative position may be changed by rotating the element. Two such variab1e resistors having a logarithmic resistance gradient may be combined in a variable resis tance attenuator.
3 Claims, 13 Drawing Figures PATENTEDJUN 17 ms SHEET [IMAM/451D;
(PR/0R ART) FIG. la WWW? 5 FIG. 26
(PRIOR ART) Fl GI b PMENTEDJUN 17 1975 3' 8 SHEET 3 '43 (=IZII/IZII) VARIATION 0P4; f y/ w/ru RESPECT r0 THE LENGTH ,r(4r 100 MH FIG. 8
DJ Du TD fi CV Cu PATENTEDJUN 17 I975 SHEET 2a ea 90 100616) MOVEMENT RATE OF BPUSHFS 0F VAfi/AHLE kfslsraks FIG. II
1 VARIABLE RESISTOR RELATED APPLICATIONS This is a continuation-in-part of an application entitled Variable Resistor Ser. No. 267.630 filed June 29, I972 now US. Pat, No. 3,760,322 and the benefit of the filing date of that application is claimed.
BACKGROUND OF THE INVENTION This invention relates to a variable resistor for use in electrical circuits and, more specifically, to a variable resistor including a film of resistive material having a gradient of resistivity in a predetermined direction.
In a conventional variable resistor, terminals are provided at the ends of the resistive film and a brush is held in slidable contact with the film to provide a variable resistance between one of the terminals and the brush. The resistance then depends on the position of the brush with respect to the film.
One of the shortcomings of this type of variable resistor is that the inductance component appearing in parallel with the variable resistance undergoes a considerable change depending on the resistance selected. A principal object of the present invention is therefore to provide a variable resistor capable of resistance variation without causing a change in the inductance component.
SUMMARY OF THE INVENTION The variable resistor of the present invention comprises a resistive element having a gradient of resistivity that varys in a predetermined manner along its length and at least two brushes separated by a predetermined interval and held in slidable contact between the resistive element. The desired gradient of resistivity can be given to the resistive element by tapering its width or gradually changing its composition. More than two slidable brushes may be used as required When more than two brushes are used, a different variable resistance can be obtained across every two brushes. The brushes are interconnected so that the distance between them remains constant.
In the variable resistor of this invention, a desired variable resistance is provided between the slidable brushes, while maintaining the accompanying inductance component at a fixed value.
Another feature of the present invention is that the variable resistance never takes the value zero ohms. This contributes to the simplification of a circuit including a finite minimum resistance.
BRIEF DESCRIPTION OF THE DRAWINGS The present invention will now be described with reference to the accompanying drawings, in which:
FIGS. la and b show equivalent circuits of a conventional variable resistor for the direct-current and extremely low frequency region and for the high frequency region, respectively;
FIGS. 2a and b show equivalent circuits of an embodiment of the invention for the direct-current and low frequency region and for the high frequency re' gion, respectivelyf FIG. 3 is a cross-sectional view of a first embodiment of the invention;
FIG. 4 shows a circuit diagram of a bridged-T type variable resistance attenuator to which this invention is applicable;
FIG. 5 shows a cross-sectional view of a second embodiment of this invention adapted to the attenuator of FIG. 4;
FIG. 6 is an equivalent circuit of a third embodiment of the invention;
FIG. 7 is an equivalent circuit of a fourth embodiment of the invention;
FIG. 8 shows diagramatically, the impedance variation characteristics of the invention as compared to those of a conventional variable resistor;
FIG. 9 shows diagramatically, the frequency charac teristics of the conventional bridged-T type variable attenuator and those of the attenuator of FIG. 4 in comparison with the second embodiment of the invention shown in FIG. 5;
FIG. 10 shows diagramatically, the attenuation values of a conventional attenuator and the attenuator of FIG. 4 and the resistance values of variable resistors Rs and Rp used therein, as a function of the movement of brushes of the variable resistors; and
FIG. 11 shows diagramatically, the resistance variation of the variable resistors Rs and Rp which are used in the variable resistance attenuator of FIG. 4, with respect to the movement of the brushes of the variable resistors.
DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. la shows an equivalent circuit for conventional variable resistor comprising a resistive film 10 having terminals 1 and 3 at its ends, and a slidable brush 2 opcrating in the low frequency range. The desired variable resistance is obtained between the brush 2 and the terminal 3. The resistive film 10 has a uniform specific resistance, and its inductance component is proportional to the length, but negligibly small when a direct current or extremely low frequency signal is applied. Likewise, the capacitive component is also negligible. Generally, the impedance Z between the terminals 1 and the brush 2 is given by:
Z =x R'+w"-L (2 where R stands for the resistance per unit length of the resistive film 10; L, for the inductance per unit length of the film 10; x, for the length of the section of the film 10 lying between the terminal I and the brush 2; and w, for the angular frequency. Differentiating Eq. (2) with respect to x and w,
dIZ I/dx= W I III =WL XI JRE'I'WELI 4 From Eqs. (3) and (4), it is apparent that I Z, I increases linearly with each successive increment of the length x, and non-linearly with each successive increment of the angularfrequency w.
The impedance Z of an ideal variable resistor having neither a capacitance component nor an inductance component may be expressed as follows:
0 I oI (5) where resistive film is assumed to have a uniform specific resistance R. The ratio A of I 2 I to I Z is given by:
-Continued More specifically. the absolute value of impedance is always larger in the conventional variable resistor than in the ideal variable resistor. Also. the larger the angular frequency w. or the smaller the specific resistance R of the resistive film. the greater the ratio A of Eq. (6) becomes.
In other words. with the increase of the frequency. the impedance has a greater effect on the variable resistance. making the deviation from the ideal variable resistor g eater. An equivalent circuit for a conventional variabl resistor at high frequency is shown in FIG. lb.
In the equivalent circuits of the variable resistor of the invention shown in FIGS. and 2b, slidable brushes 5 and 6 are in contact with a resistive film 30. The film (resisti've element) has a nonlinear gradient of resistivity with respect to its length. Two brushes 5 and 6, spaced apart by a predetermined interval. are held in slidable contact with the resistive film 30. The interval between the brushes and the nonlinear gradient in the resistivity of the film 30 are selected so that the resistance between the brushes 5 and 6 exhibits an increase in linear proportion to the lengthwise movement of the brushes. It will be appartent, however. that the invention is not limited to this resistive film arrangement. In general. the gradient may change continuously. linearly or nonlinearly. For simplicity in this explanation. it is assumed here that the incremental change in the gradient. in other words. the rate of the change of the resistivity of the film 30. is in linear proportion to the position selected along its length.
Assuming that the distance from the lefthand end of the resistive film 30 to the brush 6 is x, the resistance therebetween is .rR. and the spatial interval between the brushes 5 and 6 is unity. then the impedance Z between the brushes 5 and 6 can be expressed as:
|Z,|= .r R+ x where .r g l and the variables are the same as those in Eqs. (I) and (2). The ratio AQof the impedance 1 Z of the present variable resistor to the impedance I Z.,\ of the ideal variable resistor is given by:
where x g I.
As in the case of Eq. (6), Eq. (9) indicates that the impedance of the present variable resistor is always larger than that of the ideal variable resistor. and that the value of A, is increased with the increase in the angular frequency w. Also. as the resistance .rR is increased, the present variable resistor approaches the ideal variable resistor in its characteristics.
Derived from Eqs. (2) and (3), the ratio A of the absolute value of the impedance of the present variable resistor to that of the conventional one is given by:
It follows that A l.O where .l 2 l.
In other words. in the range ofx ll). the variable impedance Z of the present variable resistor is smaller than that Z, of the conventional resistor and closer to that of the ideal resistor. FIG. 8 shows the value of A; given in Eq. (IO) with respect to the length x.
In such a variable resistor. the resistance obtained across the brushes 5 and 6 cannot take the value zero ohms even under the state of unity thus maintaining a certain minimum resistance value. The variable resistor of this invention is therefore highly desirable for those circuits which require a minimum constant resistance.
Referring now to FIG. 3, the first embodiment of the invention, an equivalent circuit of which is shown in FIG. 2, two brushes 106 and 107 are attached to a cylindrical housing 105 and held in contact with an arcuate resistive film 102 attached to a disc-shaped base 103. The film 102 may form a complete circle. The resistive film 102 has a nonlinear gradient of resistivity in the circumferential direction. This gradient is attained by tapering the thickness or the width of the film I02. Alternatively, it may be attained by varying the composition of the material of which the film is made. By the expression gradient of resistivity it is meant that the resistance per unit length of the film varies in a predetermined manner as it is measured at different points along its length. The base 103 is pressed downwardly by a spring 104 thus permitting rotation under the control of a rotatable disc 101. The desired variable resistance value is thus obtained between the brushes 106 and 107. by changing the relative position of the brushes and the film 102.
Referring now to FIG. 4, a bridge-T type variable attenuator using the variable resistors of the present invention permits a variation in the attenuation depending on the selected resistance of two resistors Rs and Rp. A variable resistor Rs is connected across the input terminal 41 and the output terminal 43, and two fixed resistors R0 and R0 are connected in parallel with the variable resistor R A variable resistor Rp is connected across the connection point 44 of the two fixed resistors R0 and R0 and the input-output common terminal 42. In each of the variable resistors Rs and Rp. the interval between the brushes 45 and 46 (47 and 48) and the nonlinear gradient in the resistivity of the film 49 (50) are selected so that the resistance between the brushes 45 and 46 (47 and 48) exhibits an increase in logarithmic proportion to the lengthwise movement of the brushes 45 and 46 (47 and 48). Moreover, the variable resistors Rs and Rp are interlocked to operate so that when one resistance is increasing, the other is decreased. When conventional variable resistors are used in this attenuator, the voltage standing wave ratio (VSWR) is unavoidably increased with an increase in the frequency. This tends to cause an increase in the impedance 2..
Referring now to FIG. 5, a second embodiment is shown which is adapted to the variable attenuator of (ill FIG. 4 and has a dual variable resistor which may be viewed as two separate variable resistors. Each of these variable resistors is the equivalent to one resistor of the circuit shown in FIG. 2. The dual variable resistor has two brushes H6 and II7 fixed to a base 119 which also serves as a cover. Two arcuate resistive films I12 and "2' having nonlinear resistivity gradients are attached to bases I13 and 114 and kept in slidable contact with the brushes I16 and 117. The resistive films H2 and I12 are moved as a disc 101 on which the bases I13 and 114 are mounted is rotated. These elements are contained in a cylindrical housing 105 and a closure including a base 119. A pair of brushes are provided for each of the resistive films 112 and H2.
With the dual variable resistor of FIG. 5 used as the resistors Rs and Rp of the bridged-T type variable attenuator of FIG. 4, the impedances of the resistors Rs and Rp exhibit virtually no change in the inductive components, as indicated by Eq. (7). Therefore, the voltage standing wave ratio (VSWR) can be kept unchanged as shown in FIG. 9, which illustrates two groups of curves showing the attenuation vs. frequency and the voltage standing wave ratio (VSWR) vs. fre quency characteristics of the present variable attenuator as compared with those of a conventional variableresistor-based attenuator.
In the bridged T type variable attenuator of FIG. 4, the resistances r, and r, of the resistors Rs and Rp can be expressed as a function of the attenuation value e as follows:
r e (e" I) r, e (e" l) where a is given in neper.
The zero attenuation value is achieved by making the resistance r, and r, zero and infinity, respectively. Con versely, infinite attenuation is achieved by making r, and r, inifinity and zero, respectively. Practically, however, these requirements cannot be met, because infinite impedance is difficult to achieve with a conventional variable resistor. This results in a residual attenuation which causes a high voltage standing wave ratio. Therefore, to achieve a satisfactorily low voltage standing wave ratio with the conventional device, at least one resistor must be in series with either Rs or Rp or both. In contrast, the variable resistor of the invention never takes the value zero ohms. This makes it possible to dispense with any additional resistance elements and consequently to simplify and miniatuarize the attenuator as a whole. This applies to any apparatus or device in which the present invention finds application.
Now, other advantages of the variable attenuator of FIG. 4 will be explained.
It is required for the purpose of inserting a bridged-T type variable resistance attenuator into a transmission line without changing the characteristics of the transmission line that resistors of the attenuator satisfy the following equation "l "n "o (I3) where r, stands for a resistance value of each fixed resistor R0. In general, an attenuation value of the bridge- T type attenuator is adjusted by changing the resistances r, and r, of the variable resistors Rs and Rp. Therefore, the above equation I3) should be satisfied regardless of the adjusted attenuation value, for the mention purpose. In order to meet equation (13), the conventional bridgedT type attenuator employs a variable resistor Rs of such a type that the resistance increases in linear proportion to the movement of the brushes and a variable resistor Rp of such a type that the resistance increases in inverse proportion. In such conventional attenuators. it is difficult to provide a variable resistor Rp having the desired inverse resistance variation, because strict controls are needed for the area resistance and width of the resistance film thereof. Therefore. the yield and manufacturing efficiency are small. and the manufacturing cost is usually about two or three times higher than that of the variable resistor Rs having a linear resistance variation. Also, since variable resistors Rs and Rp have different resistance variations, it is not possible to interchange the variable resistor Rs with Rp or vice versa, where attenuation value or characteristic impedance is changed.
In contrast, both the variable resistors Rs and Rp of the attenuator of FIG. 4 have a structure such that resistanee increases or decreases in logarithmic proportion to the movement of brushes. Therefore, the variable resistors Rs and Rp can be interchanged, and, moreover, the attenuator of FIG. 4 always satisfies equation (13).
FIG. 10 shows the attenuation values (ATT) of a conventional attenuator and the attenuator of FIG. 4 and the resistance values of variable resistors Rs and Rp used in the conventional attenuator and in the attenuator of FIG. 4, all as a function of the movement of the brushes of the variable resistors Rs and Rp. As will be understood from FIG. II], the variable resistor Rp having the logarithmic variation of the resistance value r,, (dotted line) has a smaller variation gradient of the resistance than that of the resistor having the reciprocal variation of the resistance value r, (solid line). This reveals the ease of manufacture of the resistor Rp of the invention.
In designing electronic equipment such as transmission equipment, it is preferable, to avoid the use of variable resistance attenuators. If the use of such attenuators is not avoidable, they should be used in a region where the attenuation value thereof is small. In this respect, as will be apparent from comparison of the ATT curves of FIG. 10, the variable resistance attenuator of this invention is more suited for selecting a small attenuation value than the conventional attenuator. Hence the attenuator or this invention is suitable for use in transmission equipment.
FIG. II shows the resistance variation of the resistors Rs and Rp of the attenuator of this invention; the move ment of the brushes of the variable resistors is presented along the abscissa and the resistance value is represented along the ordinate on a logarithmic scale to show the resistance values r,, and r, of the variable resistors Rp and Rs. Both the resistances r, and r are selected to vary logarithmically with respect to the movement of the brushes, but their variations are in opposite directions. Hence, in FIG. 11, resistances r and r, are shown as straight lines declining in opposite directions.
In FIG. 11, three pairs of resistances r and r,,, r,, and r,,, and r,,; and r are shown. However, for resistances r and r, belonging to either the same pair or different pairs the value of r,,,- X r (both i and j stand for 1,2 or 3) is always equal to the second power of the resistanee value at an intersection of the straight lines r,,,- and r,;. In effect, for a variable resistance attenuator having a characteristic impedance of ohms (corresponding to r,, of equation 13 variable resistors Rs and Rp having resistance values r and respectively. may be selected. In the same way. for the characteristic impedance of 50 ohms, variable resistors Rs and Rp having resistance values r and r 2. respectively. may be selected. and for the characteristic impedance of 300 ohms, variable resistors Rs and Rp having respectively resistances r and r... may be selected.
An additional advantage of the resistance attenuator of FIG. 4 is that one variable resistor may be used as either Rs or Rp. It can be pointed out as another advantage that one variable resistor can be used in a variable resistance attenuator having any characteristic impedance. These advantages are attributed to the fact that the variable resistors having a logarithmic resistance variation are used as both variable resistors Rs and Rp of the variable resistance attenuator. This allows mass production of variable resistance attenuators having one or more characteristics with fewer kinds of variable resistors and contributes to reduced losses.
Referring now to FIG. 6, a third embodiment of this invention has four brushes 202, 203, 204, and S spaced at predetermined intervals and held in slidable contact with a resistive film 201. This variable resistor makes it possible to obtain two desired variable resistance values from one resistive film 201, one from the brushes 202 and 203 and the other from the brushes 204 and 205. In other words. a dual variable resistor can be constructed using one resistive film 201. Brushes 203 and 204 may be connected to each other when these two brushes are to be at an equal potential. It will be apparent that more than four brushes can be used.
Referring now to FIG. 7, the fourth embodiment of the invention includes a resistive film 301 having terminals 304 and 305 at its ends, respectively, and brushes 302 and 303 held in slidable contact with the resistive film 301 with a voltage is applied between the terminals 304 and 305, the desired voltage is derived from the brushes 301 and 303. In this variable resistor, the inductive component of the output impedance is small and constant. Therefore, the use of this variable resistor in a high frequency device will contribute substantially to better performance.
In the foregoing description. we have explained the present invention with reference to several exemplary embodiments and their application. However it will be apparent to those skilled in the art that other modifications are possible without departing from the spirit and scope of the invention.
I. A variable resistance attenuator comprising an input terminal. an output terminal. a common terminal. a first variable resistor connected between said input terminal and said output terminal. first and second resistors connected in series between said input terminal and said output terminal. and a second variable resistor connected to the series connection between said first and second resistors and connected at its opposite terminal to said common terminal, said first and second variable resistors each comprising an electrically resistive element. the incremental resistance of which varies along its length, to form a gradient of resistivity. and two brushes spaced apart by a constant distance in slidable contact with each said resistive element. said gra dient being such that the resistance between the brushes varies logarithmically. but the inductance between them remains substantially constant as they are moved with respect to the gradient.
2. A variable resistor comprising an electrically resis tive element the incremental resistance of which varies along its length to form a gradient of resistivity. and two moveable brushes spaced apart by a fixed distance and in slidable contact with the resistive element, the resistive element providing a substantially constant inductance and a linearly variable resistance as the position of the brushes with respect to the gradient is varied.
3. A variable resistor comprising an electrically resistive element the incremental resistance of which varies along its length to form a gradient of resistivity, and two moveable brushes spaced apart by a fixed distance and in slidable contact with the resistive element, the resistive element providing a substantially constant inductance and a logarithmically variable resistance as the position of the brushes with respect to the gradient is varied.