DE2040550C - Changeable high-ohmic precision resistor for high frequency applications - Google Patents

Description

_Rx

i _S (r, + /,) J

can be measured.

2. Variable high-ohmic precision resistor for high-frequency application according to claim I. characterized by two parallel plate capacitors C ₁ and C ₂ . which are formed by two fixed plates and a sliding plate in between, so that there are two gaps f, or / _, with a small capacitance Co, which is in series with each of the parallel-plate capacitors C ₁ and C ₂ and with a standard Fixed resistance Rs which is connected in parallel to the parallel plate capacitor C ₂ , the capacitance value of the parallel plate capacitor C ₂ being changeable by changing the air gap t ₂ so that the relationship

2.T / C ₂ · Rs ^ 10

between the parallel plate capacitor C ₂ , the standard resistor Rs and a supply frequency / can be fulfilled, so that a combination of the parallel plate capacitors C ₁ and C ₂ and the standard resistor Rs is formed by a parallel connection of an equivalent resistor Rx, in which the resistor Rx continuously variable and the capacitance C _{AB is} kept constant.

The invention is based on variable high-value precision resistors for use in ) high frequency ranges.

Recently, for various reasons, it has become more important when measuring a dielectric constant #, filled and the intermediate capacitor formed from thin parallel _plates with the dielectric of the thickness f l2 and the dielectric constant e _{s is designed to} be displaceable in such a way that a small displacement by means of a device can be achieved that holds the capacitor formed by thin parallel plates parallel to the two opposite * sides of the electrodes, and wherein a capacitance C ₂ between an electrode of the displaceable capacitor against the air gap t ₂ and the grounded electrode is respected and through the expression

C ₂ =

A / t ₂

can be represented and wherein a standardized high-frequency fixed resistor with a resistance value Rs is connected in parallel with the capacitance C ₂ and the resistance value of this resistance Rs has the relationship 2.-τ / C ₂ Rs 2; 10 satisfied (/ = frequency of a Spasequeüe) and where an unknown resistance Rx of a sample to be examined is connected in parallel to the aforementioned capacitor group and can be replaced by a small shift Ir of the displaceable capacitor and the unknown high value of the resistance Rx via the relationship

2i ₂

1
1 - 1/2 /,

Rs

Loss angle in the range of high frequencies can also be used to measure very small dielectric losses The frequency band swept becomes wider and wider by the so-called wireless frequencies, for example in Long or medium wave range up to very high, even ultra-high frequencies. A changeable commercial one Resistor with a high resistance value that is very reliable over such wide frequency bands is, very small loss angles are primarily required for precise measurement.

Recently, among the synthetic insulating materials, those with excellent properties have been developed one after another and made usable in practice. It is a fact, however, that to date there has been no device for accurately measuring 1 and λ for isolators with a Q of IC ⁴ to 10 ⁵ over a frequency range between 100 kHz and 1000 MHz.

The object of the invention is to provide a standardizable, variable resistor with a high resistance value for use in high frequency ranges to provide excellent reliability

d. H. Reproducibility with high precision over a wide frequency range, all the more so to be able to meet the requirements briefly outlined above.

The object is achieved by the invention specified in claim 1.

The invention offers the advantage that a commercially available variable resistor with a high resistance value and high accuracy for a wide frequency range and great variability of the resistance value can be produced by a relatively simple Aufbai.

Several exemplary embodiments of the invention are explained in more detail with reference to drawings.

15th

Fig.! A, IB and IC show a combination of parallel plate capacitors and a resistor to illustrate the principle of a changeable and standardizable resistor with high resistance value for high frequency application according to the invention;

2A and 2B illustrate equivalent circuits of the construction according to Fig. IB;

3A and 3B show equivalent or equivalent circuits the combination shown in Fig. IC;

F i g. 4 illustrates a first embodiment of the invention for measuring an unknown resistance Rx, the high-resistance variable standard resistance suitable for high-frequency applications being used;

F i g. 5 A shows a second AusruhrüngsiOrm discovery. where the one suitable for high frequencies high-ohmic and changeable resistance according to the invention for measuring purposes with a matched door Tuning or oscillating circuit ve; bundcn Jt;

Fig. 5B illustrates the equivalent circuit wing of the variable resistor shown in Fig. 5 \ and F i g. 6 A and 6 B illustrate a third embodiment of the invention, according to which the variable resistor suitable for high frequencies is connected for measurement purposes to a tuning circuit, with a common ground connection, like the auxiliary circuit belonging to this circuit structure.

With reference to the drawings, exemplary embodiments of the invention are explained in detail below. In Fig. 1A, electrode plates of circular parallel plate capacitors 1 and 2 with the same plate area A and intervening dielectric substance with a dielectric constant t _s and corresponding thicknesses rs and is ₂ are arranged parallel to one another, with gaps r, and I ₁ on both Sides of the capacitor 2 are provided. A fluid dielectric substance (air or liquid) with the dielectric constant I ₁ fills the gaps f _{1 and t 2} . Let the relation r "= f, + r ₂ and is = rs, + rs" apply, and it is further assumed that is »I ₀ . For example, the value for ts lies between 10 and 20 mm, and J ₀ has been ordered, is mounted so that it can be displaced in such a way that a small displacement can be achieved, while the parallel position to the capacitor 1 and the plate E is made by means of a suitable device, such as a micrometer. Very thin metal plates are provided as electrodes on the Uater-Brooks of the capacitor 1, both surfaces of the capacitor 2 and the surface of the plate E. A disk-shaped insulator of suitable thickness is inserted between the top and bottom plates of the plate E. As mentioned, a very thin metal plate is bonded to the surface of the disc insulator, and a metal plate between 0.5 and 1 mm thick is attached to the bottom surface of this insulator, the top and bottom plates usually being electrically connected to each other, as shown in FIG Fig. 1B can be seen. As FIG. 1B shows, a fixed resistor Rs suitable for high frequency applications is connected between the lower electrode of the capacitor 2 and the upper electrode of the plate E. If the capacitance value between the lower electrode of the capacitor 2 and the upper electrode of the plate E is designated as C ₂ , then the following applies:

where> ₀ corresponds to the absolute dielectric constant of the vacuum. The capacitor arrangement of Fig. 1B is represented by the equivalent circuit shown in Fig. 2A, and the following relationship holds:

J
Cr

+ fsh

where: t _s = t _d + t _ü .
For the angular frequency

we have ω = 2π /, where /

corresponds to the frequency of the feeding source. In Fig. 2 A applies under the condition

mCRs ^ lO (2)

that the substitute image according to FIG. 2A into the

the value lmm. The intermediate capacitor 2, which can be transformed 45 Fig. 2B. For Fig. 2 B The following relationships apply between the capacitor 1 and a plate £ an-:

1
Cp

O's'

r, _

Ό's

^<! - - const.
I ₁ A

+ 'J. ^f ._ ± .'iLi \ _Rs _ ₍₃₎

As shown in FIG. 1 C can be seen, the intermediate capacitor 2 shifted by "a small amount 1f to the plate E , the representation shown in FIG. 3A results as a substitute image, for which the following applies:

Cr '

Ό 'ι ^A

'1,' - Tt

Furthermore, the equivalent circuit of FIG. 3 A are transformed into the dor Fig. 3 B. For Fig. 3 B then the expression applies:

_J_ _ J__ ₊ J ₌ _____ ₊ ... J Cp 'Cr' C ₂ ' 'o's-4> n '\ A

Ό's

ΌΊ-4

The value Cp in FIG. 2 B corresponds to the value Cp ' in FIG. 3 B. That is to say, Cp = Cp applies. The capacitance Cp visible from the terminals T _x and T ₂ is therefore constant for small displacements of the capacitor 2. On the other hand, Rpx can be represented by the following expression:

Rpx = (l

> \ h 4-

+ If) V

Rs.

From the above results it can be seen that a high-resistance variable standard resistance door can produce high frequencies by changing the size If.

F i g. 4 shows a first embodiment of the invention, in which the variable standard resistance for high frequencies, as described above, is used in connection with a measuring circuit, a sample of a dielectric substance with a capacitance Cx and a resistance Rx being firstly used via a switch S. is separated from the circle. In this state, the circuit is controlled by an adjustable capacitance Ct? Voted. Let the tuning value of Cv be Cr ₁ and the current flowing through the display device be Igo. Then after clamping the sample of dielectric substance (Cx, Rx) parallel to the terminals T ₁ and T ₂ by closing the switch S, the circuit is again tuned by readjusting Cv. The following relationship applies:

Cx = Cv ₁ - Cv ₂ .

Here, Cv _{2 is} the tuning value for Cr when the sample is clamped. In this case the current flowing through the display device decreases from the value Igo due to the connection of Rx . however, this current can be readjusted to the same value Igo by adjusting the capacitor 2 of the variable resistor for high frequencies by a small displacement against the plate E. If the current flowing through the display device reaches the value Igo, then after connecting the sample to the circuit, the shift amounts to the value If, and the following can be derived:

of the high resistance Rx from the following Determine relationship (7):

Ix = (\ + AV J »· ■ -; - Rs.

For example, if the various parameters are selected as follows: diameter of the electrodes = 40 mm, to = 1 mm, f, = f ₂ = 0.5 mm, f ₂ = 10 mm, Rs = 40 kil, f _S = 5 (for a Glass plate) and / = 2 χ

10 ⁶ Hz, so that IuC ₂ R ₅ = 10, it follows from equation (7), if If = 10 μ: Rx = 36 mil. If a liquid with t _t = 10 is used as the fluid dielectric, then for / If = 10 μ: Rx = '^ 64 MU, ie. it turns out that the resistance value of the high-value resistor Rx can be measured over a very wide resistance range.

The second and third modified embodiment of the invention, in which the changeable standard or reference resistance for high frequencies according to

the invention is applied to measuring circuits,

will be described below with reference to FIG. 5 A and

5 B or 6 A and 6 B explained in more detail.

In Fig. 5A, parallel plate capacitors are C ₁

and C _{2 are shown} with air gaps fj and f ₂ , respectively. A metal plate therebetween is grounded, and the capacitance values of the capacitors C ₁ and C ₂ are given by the relationship

40 or C ₂ = *

Rx Rpx Rpo '

45

it follows:

Rx - Rpo

- Rpo / Rpx '

(5)

If Rpo and Rpx in equations (3) and (4) are substituted by relationship (S), the following equation (6) results:

Rx = (l + ^ -f) -j: 'JT

- lf / 2t ₂

Case (6) given. Therein, A is the area of each electrode plate of the capacitors C ₁ and C ₂ that are not connected to ground, and r ₀ denotes the permittivity of free space, ie for vacuum The intermediate grounded PIaUe can mitteli a micrometer screw with small displacement »amounts to up and to be moved. If, based on the assumption that J ₀ = r, = t ₂ , the intermediate electrode lying at Mass is shifted slightly upwards or downwards to If, then the capacitance values of the capacitors C _{1 and C 2 change} accordingly. In this case, however, the capacitance value C _AB, which can be measured via the two connection terminals A and B of the capacitors C and C _2, remains unchanged, ie the following applies:

55

In the equation (6), the values for r _u r _s , h * h and Rs are all known, so that the resistance value of the high-resistance resistor Rx can be obtained by measuring the value At . Furthermore, the quality value Q of the sample can be obtained from the relationship Qx = fuCxRx .

_{In the special case that the relationship f 1} = f 2 initially applies to the capacitor 2 and the fluid dielectric substance is air, that is to say r is equal to or approximately equal to 1, the resistance value can be

± if

-AWAY

fl + h

C ₂ S ₀ A

- —9— = constant

If according to FIG. 5 A, a standard fixed resistor Γ for high frequencies (for example a carbon film resistor) _{happened in parallel with the capacitor C 2} , so with C _AB and Rx the one in FIG. 5

indicate the equivalence circuit shown, where the following relationships (8) and (9) apply to the expressions Rx and C _AB:

c, {ι +,., ² Q (C ₁ + C ₁ ) RfI ~ "7 (cjTc) ² A ^

(cj

Milm = 2.-T / as the angular frequency of a supply source and assuming that the resistance value of the fixed resistor Rs is chosen so that the relationship

1,, _{C 2 Rs}

1 or m C ₂ Rs

C ₁ C ₂

(10)

(11)

Using the relationships

C ₁ =

and C ₁ =

Rx =

C _AB =

Rs

= const.

(10) '

(11) '

This means that the resistance value Rx can be changed arbitrarily and continuously between Rs and infinity, while the capacitance value for C _AB remains unchanged.

In order to achieve a very high resistance value as the variable resistor Rp , which is an equivalent representation of the variable resistor according to the invention, as occurs at the terminals T ₁ and T ₂ when the value door t _{2 is} not zero, the capacitors Co, which the _{Satisfy the} relationship Co -c C _AB , inserted in series with the capacitor C ΛΒ. The following expression (12) can thus be given for Rp:

■ +

Back (12)

is satisfied, equations (8) and (9) can be simplified as follows, taking into account the relationship ,,, ² C ₂ ² Rs ^{2 »1 :.}

This makes a variable standard resistor with a very high resistance value for high frequency applications obtained, whereby loss resistances of very low-loss dielectrics by a substitution process become measurable.

The resistance Rx of the sample is given by the following equation:

'ix

_4th Co

in the above expressions, the following Bc drawings be derived

where r ₂₀ corresponds to the gap in capacitor C ₂ at the beginning of the measurement and t _2x corresponds to the gap assigned to this resistance value. A resistance value of the variable resistor according to the invention can be substituted or determined as the value Rxs of the sample in the course of the measurement.

In principle, the circuits dci FIGS. 6A and 6B completely correspond to the circuits dci FIGS. 5A and 5B. Only the shifting intermediate plate between the parallel plate capacitors is modified to the extent that this plate is isolated from ground and the lower electrode plate of the capacitor C _{2 is connected} to ground. because dci tuning circle for measurement on a continuous! Ground line is laid.

1 sheet of drawings 209640/3

Claims (1)

Patent claims: 1. Variable, high-precision resistor for high-frequency applications, characterized by a capacitor formed by thin parallel plates with thin metal film electrodes on both sides and a dielectric with a dielectric constant f _s and a thickness t _s2 , the thin metal film electrodes of which are parallel to the electrode plates of a parallel plate -Capacitor are arranged with the plate surface A and which has an intermediate dielectric with the dielectric constant e _s and a thickness t _sl , the adjacent electrodes of the two capacitors being separated from one another by a gap 1, and with a dielectric formed as a parallel plate Element of any thickness which is provided on both sides with metal electrode plates and is arranged parallel to the capacitor with the thin plates, an intermediate gap f _{2 being} provided and the metal electrode plates to form a Ground electrodes are connected to one another and connected to ground, the gaps f, and t, with a fluid dielectric substance with a dielectric