DE19533002A1 - High-frequency voltage and current measurement device for conductor - Google Patents

Abstract

The device measures voltages and currents of any amplitude on a line of any wave impedance by means of a voltage pick-up and current transformer respectively. The pick-up has a coupling plate (2) of larger diameter than the feeler head, which is surrounded by a metallic tube (V26). An amplifier with high input impedance (1) is connected to the plate for a high transformation ratio. The transformer is set into the pocket-shaped outer conductor. The plate may be replaced by a pin in direct contact with the inner conductor. The ratio is determined by choice of the diameter of the plate and its distance from the inner conductor.

Description

State of the art (general)

One of the most widely used feedthrough power meters is the directional coupler. With this a signal is output at one output which is proportional to the incoming power and at the other output a signal that is proportional to the returning power.

Voltage and current values are often required in HF measurement technology. The voltage measurement in Today, conductors are made with amplifiers that have high-impedance input resistances. Active Probe heads are such amplifiers, for example. Their amplitude measurement range is 4 to 5 Orders of magnitude limited. The amplifier is used to expand the amplitude measurement range (Probe) upstream voltage divider. Also used to measure very high voltages capacitive voltage divider used, the reduction ratio is determined by the Ratio of the coupling capacitance to the input capacitance of the amplifier. Not yet available however, a voltage tap, in which one can replace the component by Reduction ratio 1 can come to a large reduction ratio. A more precise one A description of the prior art can be found in the "Voltage tap" chapter. The high frequency Current in conductors today is usually converted into equivalent using feedthrough current transformers Voltage converted. As described in more detail in the chapter "Current transformers", such conditions in a line introduced current transformer that this line is no longer RF-tight. Furthermore is by the structure requires that such current transformers have a different earth potential than the outer conductor of the lead through line, with which fault converted voltage is faulty. As another Limitation is the maximum measurable current of such current transformers limited by the saturation of the used cores. These limitations and problems are compounded by the present invention Device eliminated or bypassed.

The voltages supplied by the device must be measured by a measuring device, which is able to simultaneously measure two voltages according to their absolute value and their Measure phase difference. This meter can be a digital oscilloscope or a Be a digital vector voltmeter that sends the readings to a computer, where it processes and are displayed. The device itself consists of a short, low reflection and low attenuation Line section with a voltage tap and a current transformer. He is designed that at the same time currents and voltages over a large frequency and a high dynamic range can be tapped or converted.

Ways of Carrying Out the Invention

The invention relates to a device for measuring high-frequency voltages and currents. Fig. 1 shows an embodiment of the device. The current is converted in the area shown in dashed lines and designated by the letter C (Current). The voltage is tapped in the area shown in dashed lines and designated by the letter V (voltage). In area D, the coaxial conductor with the associated plug contacts is delimited. This coaxial conductor consists of the inner conductor with the diameter d _i and the outer conductor with the diameter d _a . The detailed numbering performed later on the individual components lead as group characters the area designations z. B. V1 or C2. In the following, the voltage tap, the current conversion and the lead-through are dealt with in three separate chapters.

Voltage tap

There is a time-variable voltage between the inner conductor and outer conductor in the line carrying out the device, which voltage has to be tapped. A signal should come out, the voltage of which is proportional to the voltage on the inner conductor. By means of this voltage tap, however, the disturbances on the line passing through should be as small as possible. Small disturbances are achieved by tapping the signal with very high impedance. This is e.g. B. possible in that the inner conductor of the lead is connected to an ohmic voltage divider. The resistors used for this can be very high-impedance, making the current flowing to earth very small. However, ohmic resistors for high frequencies are no longer purely ohmic, they have a series inductance and a parallel capacitance, which makes the transfer function frequency-dependent. An RF voltage can be tapped with a passive probe almost independent of frequency. These usually have a reduction ratio of 1/10 and have a high-resistance input with a resistance in the mega-ohm range. However, such a probe has a certain input capacity, ie a capacity of the live conductor to earth. However, this capacitance causes a displacement current to flow from the inner conductor to earth, which changes the voltage of the inner conductor. With passive probes, the input capacitances are in the order of 10 pF to 15 pF. Active probes have lower input capacities. The input capacitances of these are in the range of 2-3 pF. Such active probes usually have a frequency-independent transfer function over a very wide bandwidth range (e.g. the P6202A from Tektronik goes from DC to 500 MHz) [TekPr]. This has a reduction ratio of V _u = 1/10. A disadvantage of such active probes proves, however, that they can only tolerate a limited maximum input voltage, and this maximum input voltage is also frequency-dependent. With Tektronik's P6202A, the maximum voltage from DC to 15 MHz is 200 volts peak, at higher frequencies the maximum input voltage becomes smaller and has a value of 12 volts peak at 500 MHz. An attenuator can be connected upstream of the probe to increase the maximum input voltages. This means that the peak-to-peak voltage can be 200 volts for frequencies from DC to 180 MHz. This becomes smaller towards higher frequencies and has a value of 60 volts peak-peak at 500 MHz. When using such an attenuator, the total reduction ratio of the probe V _u = 1/100. By using an AC coupler, the maximum input voltage for the P6202A can be increased to 200 volts peak-to-peak in the frequency range from 16 Hz to 500 MHz.

The practical task now is to have such an active probe; possibly with an attenuator or an AC coupler to connect to the inner conductor of the lead. For this purpose, a hole is drilled into the outer conductor of a coaxial tube, the probe is inserted into it, the probe tip is connected to the inner conductor, and the outer conductor is electrically well connected to the earthing ring of the probe. This is how lead-through measuring heads are constructed with which voltage and level measurements are made. The crucial limitation of such a device is the z. B. Maximum input voltage limited to 200 volts peak-peak. Another disadvantage of a device constructed in this way is that the direct electrical connection of the probe tip to the inner conductor means that the inner conductor cannot be easily replaced by another with a larger or smaller diameter. Both of these disadvantages are eliminated by a hollow tube voltage divider with capacitive coupling. Such hollow tube voltage dividers have been known in RF technology for a long time and are used, for. B. described in [MeiHF p. 1620]. One of these is shown in Fig. 3 to illustrate the basics. A tube V3 is attached to the outer conductor on a coaxial conductor with the outer conductor V1 and the inner conductor V2. In this there is a displaceable metal piston V4, through the center of which a coaxial cable V5 passes, the inner conductor V6 of which comes out of the cable a little and ends as a measuring tip V7. The coaxial conductor V5 is terminated at its other end with a resistor Z _w . Field lines meet the measuring tip V7 from the inner conductor V2. The inner conductor and the measuring tip have a capacitance to one another, the coupling capacitance C _cop . The ratio of the voltage at the measuring tip U _s to the inner conductor voltage U _in gives the behavior of a high pass, which means that the reduction ratio V _u = U _s / U _{in is} frequency-dependent. In addition, the reduction ratio is quite small for low frequencies.

The reduction ratio becomes frequency-independent if a purely capacitive voltage divider is built instead of the capacitive / ohmic voltage divider. This means that there must be a capacitor between the measuring tip and earth, which means that the impedance is essentially capacitive, which is the case, for example, with the active P602A probe from Tektronik, which has an input capacitance of 2.0 pF and an ohmic resistance of 10 MΩ [TekPr] , is satisfied. The consequence of this is that the impedance to earth C _{earth is} determined by the probe input capacitance C _t , ie C _earth = C _t . This calculates the voltage divider ratio

The coupling capacitance C _kop and the earth capacitance C _earth must be chosen so that V _{u is} suitable. The coupling capacitance C _kop should be as small as possible so that the line impedance of the lead-through line is only minimally disturbed. However, this also means that, given a reduction ratio V _u , the capacitance to earth C _earth should also be minimal.

The structure of this hollow tube voltage divider looks like this: As Fig. 4 shows, a tube is attached to the coaxial outer conductor. The diameter of this tube must be the same as the diameter of the probe. A metal piston V11 is pushed onto the ground ring of the probe V10, which is shown enlarged in Fig. 5. A good electrical contact must be made between the tube and the grounding ring of the probe by means of this metal piston. For this purpose, the inner bore of the metal piston V12 is made to match the diameter of the earthing ring of the V10 probe. As shown in Fig. 5, the outside of the metal piston is made so that it widens conically from the inside diameter of the tube by a few tenths of a millimeter. This expanded part is slit. The remaining webs V13 press against the inner wall of the tube. In order for the electrical contact to occur at the tip of the metal piston, the tube is somewhat thinner at point V14, so that the contact surfaces V15 remain, which then press against the tube. So that this widened metal piston V10 can be inserted into the tube V16, it must be widened conically at the point V17, at least by the amount by which the metal piston ends up tapering apart. The coupling capacitance C _{kop is} present between the inner conductor and the probe _tip . This configuration is difficult to calculate in this configuration because the electric fields going from the inner conductor to the probe tip are inhomogeneous. A largely homogeneous electric field can be achieved by using a flat probe tip instead of the pointed probe tip. This can be put into practice as follows: The probe tip is pulled out of the probe and a self-made probe tip with a plate at the end is inserted. The probe is then inserted into the opening of the coaxial tube as described above. The coupling capacitance for this configuration is determined by the area A of the plate and by the distance k _{i of} this plate from the inner conductor.

With a given reduction ratio V _u , known earth capacitance C _earth and a preselected distance k _i , the platelet area A is calculated. The distance k _i must be set when the probe is inserted into the outer conductor of the coaxial tube. However, this is practically very difficult since the probe has to be pushed into the tube, which is only possible with imprecision. In addition, the coupling capacity and thus the reduction ratio will change if the probe is shaken slightly. This problem is solved in that the probe tip with the plate at the end passes through an insulator which is screwed into the tube. Fig. 6 shows this structure. The probe tip with the plate at the end is identified by V19 and the isolator by V20. The insulator is fastened with the thread V21 in the tube V1 and the probe tip V19 is held in the insulator by the thread V22. With a special screwdriver, the tip of which is shown in Fig. 7 in a side view, the distance k _{i of} the plate V19 from the inner conductor V2 can be set very easily and precisely. The probe with the slid-on metal piston is pushed into the tube, in such a way that the measuring tip with the plate V19 goes into the input connector of the probe V23.

It proves to be disadvantageous that the longer pin creates an additional capacitance to earth through the isolator V20, which capacitance is also increased by the dielectric constant of the isolator. To keep this additional grounding capacitance small, the length of the pin should be as short as possible and the dielectric constant of the dielectric should be minimal. The most suitable for this is Teflon, which has sufficient strength and a low dielectric constant with ε _r = 2.05. If the probe tip with the coupling plate is replaced by the probe tip shown in Fig. 8, a reduction ratio V _u = 1 can be set. Even very small voltages can be tapped. This probe tip tip can be adjusted depending on the diameter d _{i of} the inner conductor by making the tip V24 in the appropriate length. By screwing this probe tip in and tightening this screw, the probe tip is pressed against the inner conductor, so that good electrical contact is created.

The Teflon insulator has a certain elasticity. Therefore, by screwing in and tightening this measuring tip build up a certain compressive stress, which ensures that small Shocks the probe tip always presses against the inner conductor.

Fig. 1 shows how the voltage tap is installed in the device. The part previously referred to as the pipe in which the probe is located is here part of the device itself. The pipe V25 screwed onto the device serves only to hold and guide the probe.

Fig. 2 shows a configuration for the voltage tap, in which the coupling plate has a larger diameter d _pa than the probe. In this version, to adapt the diameter of the probe to the diameter of the outer tube, the metal piston is guided in a tube around the probe V26.

The earth capacitance C _earth is thus a parallel connection of the earth capacitance of the probe C _t and the individual capacitances C _{k of} the metal pin and the plate against earth. So that will

The capacitance of a cylindrical metal pin within a bore can be described by the model of a cylindrical capacitor. Its capacitance depends on the diameter of the bore d _a, the diameter of the pin d _i , the length l of this piece and the dielectric constant ε of the insulator. Since the diameters, lengths and the dielectric constant change, must l _k for each section with the length, the outer diameter d _ak, the inner diameter d _ik and the dielectric constant ε are calculated _{k k,} the capacitance C, namely by the formula

Instead of a simple cylindrical capacitor, there is a cylindrical capacitor in two places, the dielectric of which consists of an inner cylinder, the material of which has the dielectric constant ε _k , the inner diameter d _i and the outer diameter d _ad , and an outer cylinder whose dielectric constant ε _k = , whose inner diameter is d _ad and whose outer diameter is d _a . The capacitance of this capacitor is calculated for the kth section

The coupling capacitance C _{kop of} the plate in the coaxial tube is determined by the plate area A and the distance of the plate from the inner conductor k _i . For the coaxial tube, the capacitance C _{coax is described} by a cylindrical _capacitor with the inside diameter d _i , the outside diameter d _a and the length l as well as the dielectric constant ε.

First, it is assumed that the plate is flush with the surface of the outer conductor and thus the distance of the plate from the inner conductor is equal to the distance of the inner conductor from the outer conductor in coaxial tube, d. H.

As many field lines end on this plate per unit area as on a surface element of the outer conductor. A coaxial tube with the surface O has the total capacity C _coax . From this a surface _element with the area A has the capacity C _cop = C _coax A / O. The plate with the diameter d _p can be regarded as part of the coaxial surface of an outer conductor piece with the length d _p . The outer conductor surface is thus O = πd _a d _p and the area of the plate is

Is the distance of the tile from the Inner conductor different from the distance of the outer conductor to the inner conductor, d. H.

the capacitance C _{kop changes} . For the model description it is assumed that the field lines now end on the cylinder surface O ', the cylinder having the diameter d = d _i + 2k _i . However, this also changes the capacitance of the coaxial conductor assigned to the cylinder _surface O 'to C _coax '. But that means for the coupling capacity

An example is to be used to calculate which diameter d _p the coupling plate must have so that the predetermined reduction ratio V _{u is} established at a predetermined distance k _i . To simplify the coupling plate should end with the surface of the outer conductor, ie k _i = (d _a - d₁) / 2. In addition, _u should be 1/100. The dimensions otherwise required for the calculation can be seen in Fig. 9. The diameters of the screw threads are set so that they go to the middle of the threads. By this measure, the normally changing diameters are averaged out. The calculation gives the diameter d _p = 0.0035 m.

The transfer function is measured for a practical check of the functioning of the voltage tap. The network analyzer HP4195A from Hewlett-Packard is used for this. The block diagram of the measurement is shown in Fig. 10. The signals from the source V23 are split with the power divider V24 into two voltages of the same size, one of which voltage via the cable V25 to the reference input of the network analyzer and the other voltage via the cable V26 on the device V27 and via the voltage tap V28 and the Cable V29 goes to the measurement input of the network analyzer. The line leading through the device V30 is terminated with its characteristic impedance. In order to achieve the highest possible accuracy, which is also necessary to determine the large reduction ratios, the network analyzer is calibrated with the built-in calibration method "Thru &Isolation" [HPNet]. With the "Thru" measurement, the lines V26 and V29 are connected directly. In the "isolation" measurement, line V26 is terminated with its characteristic impedance and line V27 remains open.

Fig. 11 shows the overall frequency-dependent transfer function recorded with the calibrated network analyzer from 1 MHz to 500 MHz. The ratio of the voltage U _t at the probe to the voltage U _ref at the output of the lead conductor is measured.

In Fig. 11 the amount of this ratio is | U _t / U _ref | shown as a function of frequency f. It can be seen from this diagram that this ratio | U _t / U _ref | at 1 MHz is 0.00084. This ratio then rises steadily up to a frequency of 200 MHz and has the value 0.00087 at 200 MHz. If the frequency continues to increase, this ratio then drops again and has the value 0.00070 at 500 MHz. This averaged ratio is superimposed on changes which, with a frequency change of a few megahertz at frequencies up to 100 MHz, amount to approximately 1% of the averaged ratio and towards higher frequencies approximately 2%. These higher frequency changes in the ratio are essentially determined by the measurement inaccuracies of the calibrated network analyzer and are due to the large reduction ratio. The course of the averaged transfer function is determined by the active probe. This has a specified bandwidth of 500 MHz, ie the -3 dB point is approximately 500 MHz, but this explains the steady decrease in the average transmission ratio from 200 MHz to 500 MHz. If one takes into account the reduction ratio of the P6002 probe from Tektronik, with V _utast = 1/10, there is a reduction ratio between the inner conductor and the probe tip at z. B. 1 MHz of V _u = 0.0084.

Inductive coupling does not falsify the voltage tap

Up to this point, the capacitive coupling from the inner conductor into the measuring tip has been discussed. It stays still to be clarified whether this is the only coupling into the probe. It could also be that a voltage is inductively coupled into the probe tip. If this were the case, it would be on Probe applied voltage is no longer just a function of the inner conductor voltage, but also of Inner conductor current, which falsifies the voltage tap. Whether inductive coupling it is necessary to check. It is so that a between the coupling plate V2 and the outer conductor Gap is present. Through this, the alternating magnetic field H in the space between the Pen and housing penetrate.

However, this can induce a voltage in the probe tip, since U _ind ∼H. Fig. 12 shows the equivalent circuit diagram for such an inductive coupling. It can be seen that there are two conductor loops which run via the tactile copying capacitance C _t the outer conductor and the capacitances left C _l and right C _r . The capacitances C _l or C _r are the capacitances seen from the center of the measuring tip to the left or right side towards the outer conductor. The voltages U _indl and U _{indr are} induced in these two conductor loops. In the event that the measuring tip with the coupling plate is completely symmetrical, C _t = C _r . However, this also makes U _indl = U _indl, which means that the resulting voltage U _ind = U _indl - U _indr = 0 V disappears. In the event that the measuring tip with the coupling plate is not completely symmetrical, C _l ≠ C _r , which means that U _ind ≠ 0 V. However, this voltage will be very small, since very little magnetic field lines can penetrate the space between the measuring tip and the outer conductor. In addition, the very small voltages U _indl and U _indr are largely compensated for by the approximately identical capacitances C _l and C _r . There is therefore no inductive coupling that falsifies the voltage tap. Such an inductive coupling cannot be seen from a simple measurement of the transfer function.

Disturbance of the wave resistance of the lead through the voltage tap

Every real measurement falsifies the size to be measured. This voltage tap is also annoying the voltage on the lead line. By opening the outer conductor for the Voltage tap changes both the inductance and the capacitance of this line piece, what a change in the line impedance causes. But this means that the incoming wave is reflected. The size of this reflection factor has to be determined. Furthermore, by a Reflection at the voltage tap causes the measured voltage to overlap the incoming and the returning voltage wave is, but this is the voltage tap itself adulterated.

The change in inductance in the coaxial line is due to the fact that the current I at the open point can no longer flow over the entire outer conductor surface, but has a course, as indicated by the current lines in Fig. 13. For the description, the direction of propagation of the coaxial tube is designated by χ. The circumference of the conductor is designated Umf (χ). At the undisturbed point this circumference is just Umf = 2π · r _a , where r _{a is} the outer conductor diameter. The opening width of the hole at point χ is b (χ), which is related to the angle seen from the central axis of the coaxial conductor by the relationship ϕ (χ) · r _a = b (χ). This opening width is subtracted from the circumference, with Umnf (χ) = (2π -ϕ (χ)) · r _a . This formula applies in general because b (χ) disappears outside the hole. With the Maxwell equation using Stoke's theorem we get for the field strength

That has to Consequence that the magnetic flux density increases at the point of interference. The magnetic flux density on the Length is l

The location-dependent inductance is thus

If one now approximately assumes that the hole with the diameter d _{b is} square instead of round, although the areas should be the same ie π · (d _b / 2) ² = b², the angle at the drilling point results

It is important to change the inductance L _s at the disturbed location compared to the conductor inductance L _l at the undisturbed locations. Both have the relationship

The data can be taken from Fig. 9 for an application example. Here d _{b is} the core diameter of the thread V21, it is d _b = 4.2 mm. The radius of the coaxial conductor is r _a = d _a / 2 = 4 mm. So S _Ll = 1.17.

On the other hand, opening the outer conductor changes the capacitance in this area. To calculate this changed capacitance, the fact is used that when the coupling plate is flush with the surface of the outer conductor, ie k _i = (d _a - d _i ) / 2, the conductor capacitance C _l is retained. This can be justified by the fact that the capacitance C in _{earth of} the inner conductor via the coupling plate and the measuring tip to earth is the series connection of the coupling capacitance C _kop and the earth capacitance C _earth . But since C _cop «C _earth the capacitance C _inerde ≅ C _cop . If the measuring tip is now screwed in or out, the coupling capacitance changes and thus the resulting conductor capacitance C _l '. This is determined by the equation C _l ′ = C _l - C _kop (k _i = (d _a - d _i ) / 2) + C _kop (k _i ). This results in the ratio of the conductor capacity at the disturbed point C _l 'to the conductor capacity C _l in the undisturbed area to S _Cl = C _l ' / C _l . For the special case above that k _i = (d _a - d _i ) / 2, S _Cl = 1.

Fig. 14 shows the simplified equivalent circuit diagram of a lossless line, which is terminated by its characteristic impedance Z _ab . This homogeneous lossless line is described by its inductances and capacities per unit length. In Fig. 14, these inductances and capacitances L _l1 , C _l1 , L _l2 , C _l2 and L _l3 , C _{l3 are given} for a certain length l₁, l₂ and l₃. At the point of the voltage _tap , the conductor inductance is represented by the series connection of the conductor _inductance L _l2 and the interference inductance L _ls . The conductor capacitance at the point of the voltage _tap is represented by the parallel connection of the conductor capacitance C _l2 and the interference capacitance C _ls . By interchanging the order of the interference inductance L _ls and the conductor capacitance C _l2 , the line is represented by a succession of several line elements in which the interference by the voltage tap is integrated as an additional concentrated component. Since the line is terminated with its characteristic impedance, this characteristic impedance will be present up to the point of failure, so that the line elements with the terminating resistance can be described as a concentrated component. This equivalent resistor is arranged in the equivalent circuit diagram in Fig. 15 according to the interference inductance L _ls and interference capacitance C _ls . Overall, these impedances can be combined to form the total terminating resistance Z ₁

The following generally applies to the reflection factor at the point of interference

In relation to the application, L _ls = (S _Ll -1) L _l = 0.11 nH and C _ls = (S _Cl -1) C _l = 0 pF, with which Z _l ′ = Z _l + jω · L _ls , which means for the reflection factor

For Z _l = 50 Ω

becomes. At 500 MHz this gives a value of | r _sp | ≈ 0.3%. This reflection factor is negligibly small.

Overall transfer function of the voltage tap

Fig. 16 shows the equivalent circuit diagram from which the overall transfer function can be calculated. On the far right of the terminating resistor Z is _from. There is a coaxial cable with the corresponding characteristic impedance between the point of the voltage tap and the terminating resistor. The length of this piece of coaxial cable l _sp is just from the center of the coupling plate to the measuring plane, which is also referred to as the calibration plane. In the standard notation, the calibration level is at the end of the inner conductor contact, as shown in Fig. 1. Between the location of the voltage tap V31 and the coaxial line V32 are the replacement elements L _ls and C _ls for the fault location. The replacement elements for the fault location must be at this point, because the voltage applied to the coupling plate is changed by the fault location. This is namely a superimposition of the incoming voltage wave U _l and the one reflected by the voltage tap, ie U _k = U _l · (1 + r _sp ).

For the general illustration, this equivalent circuit diagram is now described by the associated four-pole equations. The voltage U is found _from across the terminating resistor and the current flows _from I. The voltage U _l and the current I _{l are present} in front of the coaxial cable, the voltage U _ab and the current I _ab through the homogeneous, loss-free four-pole equation 9

The voltage U _cl and the current I _cl are with the voltage U _l and the current I _l through the four-pole equation

connected. The voltage U _k and the current I _k on the coupling plate on the inner conductor are with the voltage U _cl and the current I _cl through the four-pole equation

connected. The voltage at the probe tip U _s is connected to the voltage at the inner conductor U _in by the reduction ratio V _u , which is the four-pole representation

results. The voltage U _{t is present} at the output connector of the probe. This has a certain delay t _d compared to the voltage U _s . With the Tektronik P6202A probe, this signal delay is approximately 12 ns [TekPr]. In addition, the probe itself has a reduction ratio _t = | U _t / U _s |. This results in the complex amplitude in the four-pole display

The overall equation can now be established by recursive insertion. The individual matrices can be multiplied together and result in a new total four-pole

Power converter

Currents can be measured in different ways. The measurement of the voltage drop across a resistor is the most common. In high-frequency measuring technology, thermal transducers are used in which the temperature increase is measured by a heating wire, which is proportional to the current through the heating wire. Induction coils are used to measure high and high-frequency currents, which are named Rogowsky coils in honor of the inventor. Such a Rogowsky coil is shown in Fig. 17 [Coo63]. This is a uniformly wound solenoid C1, which is placed in a ring around the current-carrying wire C2. According to the law of induction, the voltage U _ind induced in N turns of the coil is equal to the change over time of the magnetic flux in this coil, ie

The magnetic flux is calculated using the formula

The magnetic flux density is determined with the help of the law on flooding

linked to the current I. If one chooses circles with the radius ρ around the z-axis as integration path for the calculation of the flux density, as can be seen in Fig. 18, then follows

Let S be any cross-sectional area of the coil with the surface element dS · = h _z dρ · The magnetic flux Φ through S in the direction of results from the following calculation [UnbTE]

Here AL is a constant in which Coil properties are included. For further considerations, it makes sense to use the Time domain representation f (t) to switch to the frequency domain representation F (ω). Of the Differential operator d / dt then merges into jω. So that for the angular frequency ω in the Rogowsky coil induced voltage

U _ind (ω) = -jωA _L I (ω) Eq. 2nd

The induced voltage is therefore frequency-dependent and phase-shifted from the current by -90 °. By terminating the coil with a resistor Z _i , a frequency-independent voltage U _i can be measured via this resistor. Fig. 19 shows the corresponding equivalent circuit diagram. The voltage U _{ind is present} at the coil with the inductance L and the resistance Z _i , which causes the current i _{s to} flow. The flow of this current i _{s is} impeded by the self-inductance L of the coil. The self-inductance L is in turn the proportionality constant of the magnetic flux generated by the current i _s in the ring coil, ie dh = Li _s . From the law of flooding follows for the magnetic flux density within the coil

With an analog calculation as above, for the magnetic flux of N current turns comprised Φ = A _L N²i _s . But this makes the inductance L = A _L N². Using the equivalent circuit diagram in Fig. 19, the voltage measured across the resistor Z is

If equation 2 of U _ind and L is used, the equation is transformed and it is assumed that the coil is wound in such a way that the phase is 0 ° at the operating frequency of 13.56 MHz, the result is

This voltage becomes frequency independent for frequencies with

In order to meet this condition, either the terminating resistance Z _i can be selected to be very small or the number of turns N very large. Both then leads to the transformation ratio

gets very small. It is better to make the A _L constant as large as possible. This can be done by winding the coil on a ferrite core, which then increases this constant by the permeability µ _{r of} this core. For toroidal cores, the inductance factor is defined by A _L = µ _o µ _r A / l. Here A / l is the core factor, which is given in the data manuals [DatPh, ComVo, AmiFe]. The relative permeability µ _r is usually a frequency-dependent, complex variable, which is defined by µ _r = µ _s ′ -jµ _s ′, in which µ _{s is} the real part and µ _s ′ is the imaginary part of the complex permeability. This complex permeability is shown in the data manuals as a function of frequency [DatPh, ComVo]. When choosing a ferrite core, it should be noted that the real part of the complex permeability is larger than the imaginary part of the complex permeability, since the latter describes the losses of a ferrite core.

Fig. 17 shows the basic shape of a Rogowsky coil. This is practically unusable, since electrical field lines end on the coil from the inner conductor, which cause a voltage to be capacitively coupled into this coil, which is superimposed on the inductively coupled voltage. This capacitive coupling can be reduced by electrically shielding the coil. Fig. 20 shows a coil with a ferrite core and a metal shield. This coil is referred to as a feedthrough current transformer and is described, for example, in [Pat74, Pat88, MeiHF S. 1547, RohSt]. In this feedthrough current transformer, the coil C4 is wound on a ferrite core C3. The metal jacket C5 is arranged around the coil and is electrically separated from the coil by the insulator C6. The metal jacket C5 must not completely surround the coil, because otherwise a ring current would flow through this metal jacket, the magnetic field inside the coil of which would just compensate for the magnetic field of the current-carrying conductor inside the coil, with which the current of the current-carrying conductor could no longer be measured . The metal jacket C5 is thus open on the outside, which is indicated in cross section through the openings C7. The openings C7 are arranged on the outside of the current transformer so that the path from the current-carrying conductor C2 to the coil is maximal and the coupling capacitance is minimal. The metal jacket C5 is grounded by the measuring line to be connected to the connector C8.

This feedthrough current transformer is used to convert the current I into the voltage U _i with a conductor lying in the room. So that the current I can flow, a circuit must be present, that is, there is a current flowing in and a current flowing back. In Fig. 20, the current transformer is placed around a single live conductor C2. The return conductor is not shown and can be anywhere. For high-frequency currents, such a routing would lead to large reflections, which is why it should be avoided. For the transmission of high-frequency currents, lines with defined characteristic impedances must be used, ie the outgoing and return conductors must have a defined and fixed distance from each other, as is the case for. B. is given with coaxial conductors. Fig. 21 shows a device with which the current in the inner conductor can be measured inside a coaxial line. This device was developed to calibrate feedthrough current transformers [Pat89]. This device is constructed in such a way that the inner conductor C2 continues to pass through the feedthrough current transformer C9 and the coaxial outer conductor is laid around this feedthrough current transformer C10. In order to largely maintain the line impedance, the coaxial conductor is widened in such a way that the inner diameter of the outer conductor d _w corresponds precisely to the inner diameter d _{w of} the feedthrough current transformer. The feedthrough current transformer is electrically isolated from the outer conductor of the leadthrough by the insulation C11. This is necessary because otherwise the current flowing back would run through the interior of the current transformer, with which the current in the inner conductor could no longer be measured. The necessity of isolating the outer conductor of the lead-through line from the current transformer means that the outer conductor must remain open at the point C12 where the connector C8 of the transformer is located. However, this has the consequence that the lead-through is no longer HF-tight, which means that electrical power can be radiated into the room through this opening, resulting in undetermined losses. An additional measurement error arises as follows: The current transformer C9 is grounded through the signal line which is connected to the measuring device. Since this signal line has a certain ohmic resistance, the potential of the current transformer will be different from the potential of the line carrying it through. However, this makes the measured voltage U _i incorrect.

These measurement errors cannot occur with the current transformer shown in Fig. 22. The outer conductor of this current transformer is bag-shaped. The measuring coil is inserted into this sack-shaped design. The measuring coil is shielded from the inner conductor by the grounded tube between the inner conductor and the coil. The remaining capacitive coupling is very small and can be estimated quite easily. The current coil has the same potential as the outer conductor and the entire current transformer arrangement is RF-tight, which enables reproducible and very precise measurements. Due to the shape and size of this sack-like design, the wave resistance of the line running through is only minimally disturbed, and the associated reflection factor can also be calculated. These properties finally allow the transmission quadrupole to be calculated. Due to the special shape of this sack-shaped design, it is also possible to build a coaxial current divider in which only part of the current flows through the current measuring coil. Such a current divider makes it possible to enlarge the measurable current measuring range as desired, which at the same time reduces the disturbances in the wave impedance of the line passing through.

Fig. 23 shows the sack-shaped widening of the outer conductor in a simplified manner. This line can be divided into three areas, which are delimited by dashed rectangles in the figure. In area C14, the coaxial line has an outer conductor jump [MeiHF], in which the diameter of the outer conductor is widened from D _ia to D _aa . In area C15, the coaxial line has a series branch point [MeiHF], at which the undivided line in area C16 with the outside diameter D _aa and inside diameter D _{ii is} divided into two coaxial lines in area C18 at division level C17, at which the outside line Outside diameter D _aa and the inside diameter D _ai and the inner pipe has the outside diameter D _ia and the inside diameter D _ii . In area C19 the outer coaxial line is short-circuited. The current runs through this sack-shaped widening as follows: from the current source, the current I _{h flows} on the surface of the inner conductor to the terminating resistor, passes through it and flows along the surface of the outer conductor as current I _r back to the generator. Here, the current I _{r flows} on the surface of the outer conductor with the diameter D _ia towards the surface of the outer conductor with the diameter D _aa . At the split level of the series branch point C17, the current continues along the surface of the outer outer conductor to the area C19 where the outer coaxial line is short-circuited. The current then flows from the outer conductor to the inner conductor of the outer coaxial line. The current then flows back along the inner conductor of the outer coaxial line to the division plane C17 and there passes into the outer conductor of the inner coaxial line, from where the current then flows back to the generator. The measuring coil is arranged in the outer coaxial line. The current flowing along the inner conductor of the outer coaxial line causes the alternating magnetic flux in the measuring coil, thereby inducing the voltage U _ind , which causes the current i _s via the resistor Z, which leads to the voltage U _i via the resistor. The voltage U _i generated is described by equation 2.

The current measuring unit consists of two cylindrical components. One component has the designation B1 and the other component has the designation B2. Both components are pushed together and screwed together, which can be seen in Fig. 1 and 2. The contact surfaces C20 and C21 are located on these two components, which ensure that these two components get optimal electrical contact. Fig. 24 shows a top view of component B2. This clearly shows the shape of the contact area C21, which is characterized in that the entire area is actually surrounded as a contact area, right down to the connector. By stepping these contact surfaces C23, which can be seen in Fig. 21, it is achieved that the two components are guided centrally into one another and that the current measuring unit becomes RF-tight. The only remaining opening is the inner conductor passage of the end connector, which is sealed by the line to be connected. Component B2 contains the area of the outer conductor jump. In order to avoid strong field changes, this outer conductor jump is a constant transition in practice, in which the outer conductor widens conically C24. For the same reason, the corners C25 are rounded and the short-circuited coaxial line is semicircular C26. In component B1, the tube C27 is attached, which on the inside is just the outer conductor of the inner coaxial line with the diameter D _ia and on the outside of the inner conductor of the outer coaxial line with the diameter D _ai . The end of this tube is semicircular C28 to avoid large field strength changes. All surfaces over which the current flows should be turned off to avoid unnecessarily high resistances and have a clean surface.

Inside the sack-shaped formation there is a ferrite or iron powder core C29, onto which one Coil is wound, the wire C30 is a silver wire, a enamelled copper wire or other Wire can be. One end of this wire is soldered into a cable lug C31. This Cable lug is securely connected to component B2 by screw C32. The other The end of the wire is soldered into a standard C33 end connector, here type N. Parallel to the coil is a low inductance and low capacitance resistor C34, e.g. B. a carbon film resistor, the one end is soldered to the end connector and the other to the cable lug. Of the The standard end connector C33 is in this configuration with one side on component B1 and with the screwed on the other side to component B2. So that the ferrite core C29 does not hang in the air this is held by an isolator C35. This insulator can be glued to the coil. At the On the inside, this insulator is adapted to pipe C27, so that the insulator is on the pipe can be easily moved.

Fig. 1 shows how this current transformer is integrated in the measuring head. For this arrangement the company Amidon [AmiFe] used the ferrite core FT82 - 67 with µ _s ′ = 40 with a core factor A / l = 1 / 507m. The ferrite core was wound with a coil with N = 15 turns. A resistor with a value Z _ia = 20 Ω was selected. This is parallel to the characteristic impedance of the closed line with Z _l = 50 Ω. The total resistance Z _i = 14.2 Ω. With equation 4, U _i / i = 0.95 V / 1A. In order to show the function of the current transformer, the transfer function is measured with the network analyzer HP4195A. The measurement setup is similar to that shown in Fig. 10. Here, the cable of the current transformer is connected to the measurement input of the network analyzer, which makes U _t = U _i , and the output of the lead-through line to the reference input. The network analyzer is calibrated using the implemented calibration procedure, "Thru &Isolation". Fig. 25 shows the measurement curves. For frequencies from 1 MHz to 500 MHz, the amount of the ratio U _t to U _ref and the phase difference between U _t and U _{ref are} plotted. The transfer function of | U _i / U _ref | calculated according to equation 3 is a straight line = 0.019 plotted. The diagram shows that between 10 MHz and 150 MHz the amount of the calculated transfer function approximates the amount of the measured transfer function quite well. The deviations become larger towards higher frequencies. At 250 MHz and at 430 MHz there are resonance phenomena. These resonance points cause the phase to drop from 0 ° at about 10 MHz to -80 ° at 250 MHz again to about 0 ° at 430 MHz and then to -40 ° at 500 MHz. This behavior of the transfer function can be explained as follows: Each ferrite core is described by a complex permeability. Towards higher frequencies, the real part of the complex permeability µ _s ′ (f) becomes smaller and the imaginary part µ _s ′ ′ (f) larger [DatPh]. Furthermore, the impedance of the resistance Z _ia = Z _ia (f) is frequency-dependent. In the equivalent circuit diagram this can be described by a series connection of a resistor with an inductance which is connected in parallel with a capacitor. Furthermore, the coil itself still has a certain winding capacity, a certain capacitance to ground and also has a certain ohmic conductor resistance. In order to make the transfer function independent of frequency towards higher frequencies, a ferrite core or iron powder core is selected in which the real part of the complex permeability at the correspondingly higher frequencies must be much larger than the imaginary part of the complex permeability. In practice, however, this means a reduction in the value of µ _s , so that the transfer function becomes frequency-dependent at low frequencies. Furthermore, by choosing other terminating resistors with a lower inductance and lower parallel capacitance, the resonance point can be shifted to higher frequencies. It is therefore possible to achieve a frequency-independent transfer function up to high frequencies by suitably selecting the number of turns of the ferrite or iron powder core and the resistance.

What is the maximum current I _max flowing in the lead conductor without overloading the transducer? The maximum current I _max is essentially determined by the maximum power that the resistors Z _ia and Z _l can absorb. If standard resistors are used, then P (z _l ) = 2 W and P (Z _ia ) = 0.5 W, which makes the maximum secondary current i _max = 0.16 A and thus I _max = 3.2 A. The maximum power to be transmitted through the toroid is thus about 2.5 W. This is far below the power consumption of the ferrite core used, which is approximately 100 W [AmiFe]. The temperature rise in the coil wire is also still small with these outputs. These two effects therefore do not help to reduce the estimated value for.

Capacitive coupling falsifies current conversion

In the above derivation it was stated that a simple Rogowsky coil cannot work because a capacitance U _{kap is} capacitively coupled into the coil due to the coupling capacitance. This voltage is superimposed on the inductively U _in coupled voltage, so that U _i = U _in + U _cap . When measuring the voltage U _i , it is therefore not possible to say exactly which part of the inductive U _in coupling and which part of the capacitive coupling U _{kap is} attributable. In the construction shown in Fig. 22, the sack-shaped design of the outer conductor provides shielding, which means that the coupling capacity is very small. But even a small coupling capacity can mean considerable measuring errors. It is therefore necessary to calculate this coupling capacitance and to estimate the influence of this on the voltage U _i .

Some field lines from the inner conductor meet the coil. As a very simple model, it is assumed here that only those field lines reach the coil wire that lie directly on the line of sight. In Fig. 22 the replacement element for this coupling capacitance C _ik is drawn in such a way that the wires ending on the coil wire and on the inner conductor lie directly on a line of sight. However, this can be used to describe the coupling capacitance using the model of a spherical capacitor. The capacity is for such an air ball condenser

Here r _{ka is} the radius of the outer sphere and r _{ki is} the radius of the inner sphere. The radius r _ki thus corresponds exactly to the distance between the point of intersection of the line of sight with the axis of symmetry C36 and the point of intersection of the line of sight with the surface of the inner conductor C37. The outer radius r _ka is the distance from point C36 to the surface of the wire. Since the wire is wound as a coil, this distance is different for every point on the surface of the wire. To make the calculation as simple as possible, it is assumed at this point that the distance to the center of the core at point C38 approximates the distance to the individual surface elements of the wire sufficiently well.

Furthermore, for this simple estimation, it is assumed that the increase in capacitance caused by the dielectric of the ferrite core is negligible. A wire of length l _wire thus appears at a distance r _ka from point C36 and is thus located on a spherical surface. With the width d _{wire of} the wire, this results in a certain surface area O _wire = 1 _wire · d _wire . The coupling capacitance C _ik can hereby but by the ratio of the given through the wire surface O _line to the entire spherical surface O _ball multiplied by the capacitance C of the capacitor _ball of the ball, so

be calculated. The spherical surface is calculated as O _sphere = 4 π · r _ka ².

As an example, the coupling capacitance is calculated for the arrangement shown in Fig. 1. It is l _wire = 290 mm, d _wire = 0.5 mm, r _ka = 32 mm, r _ki = 6.7 mm, with which the coupling capacitance is approximately C _ik ≈ fF.

The simple equivalent circuit diagram in Fig. 19 is expanded to estimate the error caused by the injected voltage and results in the equivalent circuit diagram in Fig. 26. The voltage on the inner conductor U _in can now have an additional current i _c in the secondary coil via the coupling capacitance C _ik produce. So the voltage across the terminating resistor U _i '= (i + i _c ) Z _i = U _i + U _cap . The capacitively coupled voltage is determined by the voltage divider ratio, that is

The inductively coupled voltage by equation 4, thus U _i = Z _i / N I. The relationship between the capacitive and the inductively coupled voltage is important, since this represents the error

Consequently, this ratio is proportional to the ratio between the voltage on the inner conductor U _i to the flowing primary current I. This ratio is greatest when the voltage U _{i is} maximum and the current I is minimal. However, this is the case if the lead-through has no terminating resistor - if it is open. In this case, the current I is the displacement current in the line section of the line to be carried out, where I = jω C _l U _i . Here, C _{l is} the capacity of the lead-through line, specifically for the line section that lies between the coil and the open end. For a coaxial conductor, this capacitance is described by a cylindrical capacitor. Overall, it will

the ratio of the coupling capacitance C _ik to the conductor capacitance C _l multiplied by the number of turns N. In the arrangement of Fig. 1 there is a 50 ohm cable and the length between the coil and the end is approximately 5 cm, which makes C _ik = 5 pF . With N = 15 and C _ik = 11 fF, U _kap / U _i = 3.3%. This means that the maximum error due to capacitive coupling during current conversion is just 3.3%, regardless of the frequency.

By suitably shaping the sack-like design of the outer conductor, it can be achieved that the capacitive coupling is considerably reduced. Such a configuration is shown in Fig. 2. In this, the expansion of the coaxial line is divided into two areas. The first expansion goes up to the diameter D _wa . This is followed by a piece of length l _ü in which the diameter remains constant. Then the outer conductor is flared up to the diameter D _aa . The tube C27 is made so long that it protrudes into the first expansion. The diameter D _wa must be chosen so that an air gap remains between the tube with the diameter D _ai and the first expansion. The smaller this air gap and the longer the overlap area l _ü , the lower the capacitive coupling. However, this tube has opposite the widened portion of the outer conductor a certain capacitance C _concert, via which a displacement current I _v, flows directly to the tube with which this current is no longer flowing through the measuring coil and thus can not be measured. For the construction of this sack-shaped design, this has the consequence that the air gap between the tube and the widening of the outer conductor and the length l _{ü have to be} a compromise between the capacitive coupling and the capacitive crosstalk.

Disturbance of the wave resistance of the lead through the current transformer

The outer conductor is opened by the current measuring unit and shaped into the bag-shaped configuration described. However, this has the consequence that the line wave resistance is changed at this point, which is equivalent to the fact that the incoming wave is reflected at this point. The parameter important for HF technology is the input reflection factor r _St , which is to be calculated in the following.

The sack-shaped design of the outer conductor can be described by the model shown in Fig. 23. Coming from the right, when the outer conductor _jumps in the area C14, the coaxial characteristic impedance goes from Z _l to Z _l2 . In the divided area C18, the inner coaxial line has the characteristic impedance Z _l and the outer coaxial line has the characteristic impedance Z _l2 . The characteristic impedance of the outer, coaxial line is determined by the diameters D _ai and D _aa and is calculated using the formula

If you consider this line as damping-free, the voltage and the current for the angular frequency ω are calculated at the point with the distance L₂ before the end of the line through the four-wire equation

This line is short-circuited, whereby the voltage U _l disappears at the end of the line. This results in the impedance

The tangent can be developed for small angular frequencies ω and small distances L₂. In first approximation then results

Z₂ = Z _l2 · j · (ω L₂ / c). Eq. 5

In the expanded area, the line with the characteristic impedance is very short, so that its influence can be neglected. If the coaxial line is terminated at the end with its terminating resistor Z _l , the entire line element can be described by a resistor Z _l . As shown in Fig. 27, the incoming line, which is completed by the series connection of the resistors Z₂ and Z _l , has the characteristic impedance Z _l . This results in the amount of the input reflection factor

The approximation in the second part of the formula was justified by the fact that 2Z₁ »Z Z₂ applies. It can be seen that the reflection factor is proportional to the angular frequency ω. A measuring bridge is connected upstream of the HP4195A network analyzer to measure the input reflection factor. Due to the built-in full calibration with the terminating resistors "Short", "Load" and "Open", the network analyzer was calibrated with the measuring bridge. "Reflection factor" was selected as the output variable. Fig. 28 shows the measured input reflection factor as a function of the frequency f from 1 MHz to 500 MHz. It can be seen that | r _St | increases linearly with frequency f. For the structure according to Fig. 1, the length L₂ = 2 cm, the inner diameter of the outer line is d _ai = 10 mm and the outer diameter of the outer line is d _ai = 28 mm. So Z _l2 = 62Ω. The characteristic impedance of the lead-through line is Z₁ = 50Ω. This results in the reflection factor | r _St | at a frequency of 500 MHz = 0.13, which agrees quite well with the measurement. This shows that the model used is correct.

Current divider

The measuring head is to be used later in a setup in which the current flowing through the measuring head will be greater than the permissible maximum current of I _max = 3.2 A. In the measuring head now used, the "short" is used for calibration Almost reached maximum current. In order to be able to measure currents larger than I _max with the measuring head, the maximum measurable current nm could be increased by a factor of 10 or 100 by a measuring transducer arrangement with two magnetic cores [Pat82]. The expansion of the measuring range is further pursued here by means of a coaxial current divider, since the line impedance is less disturbed by this. A known current divider is shown in Fig. 29 [Pat77]. In this, the line in which the current I flows is split into two lines, in which one flows the current I _measure and in the other the current I _sh . The measuring line has the impedance Z _l2 and the line parallel to it has the shunt resistance R _sh . The two partial currents I _measure and I _sh are calculated from the model of two resistors connected in parallel. Hereby will

The coaxial current divider works on the same principle. Fig. 30 shows the series junction without the inner conductor as a top view. In contrast to Fig. 23, the outer conductor is continuous at point C39, it looks like a bridge at this point. This bridge has a certain impedance R _sh . The impedance of the series junction was derived in the previous chapter and is Z₂. The current I _sh thus flows over the bridge and the current I _measure over the series _branch . Fig. 30 shows the associated current profiles.

The measuring head shown in Fig. 2 contains such a coaxial current divider. The tube C27 is made so that the webs C40 remain at its end. When the two components are pushed together, these webs press on the contact surfaces C41 of the counterpart. This creates a bridge at this point over which the current I _sh can flow.

When manufacturing these webs and the contact surfaces, it is important that the contact resistances between the webs and the contact surface are as small as possible. This can be achieved by silvering the webs on their contact surface side and the contact surfaces. In addition, the webs must have a certain tension with which they press against the contact surface. For this purpose, the end of the tube is made similar to the metal piston in Fig. 5. The only difference from the illustration is that here the areas are milled out in which there should not be any bars. In order to be able to insert the component with the tube into the counterpart, the area C43 is flared out over a length of a few millimeters and at least by the amount by which the webs are flared out. To ensure that the outer conductor does not jump at the contact point, component B3 is expanded at point C41 by the thickness of the webs. Fig. 31 shows the section through the section plane EF from Fig. 2. This shows the individual webs C40 that are in contact with the contact surface C41. These webs are evenly distributed over the circumference in order to obtain a field distribution that is as symmetrical as possible.

The webs C41 have an electrical resistance that has to be calculated. First of all is too say that for higher frequencies the dc resistance is much smaller than that frequency-dependent AC resistance. The cause of the AC resistance is Skin effect, in which the alternating currents flowing in the conductor due to the induction effect in the conductor to be pushed to the surface. The decrease in current density towards the inside of the conductor runs exponentially. For a simple description, the depth of penetration δ is used, that of the distance from the surface at which the amount of current density corresponds to 1 / e times the value of the amount has assumed the current density on the conductor surface. The penetration depth δ is calculated according to the formula

R _{spec is} the specific resistance of the conductor material, µ _r the relative permeability and f the frequency. The resistance value of the webs of length l _st is determined by the relationship

Here, A is the cross-sectional area of the webs through which the current flows, but which at The skin effect is given by the product of the penetration depth δ and the total web width bo. The Size bo is just the entire length of the arch on which there are webs, or it is the sum of Arc lengths of the individual webs

However, the radian α _b is just the entire arc length divided by the circumference πd _a , where d _{a is} the diameter of the outer conductor, that is

The shunt resistance thus results

The shunt resistance is therefore proportional to the reciprocal of the arc length.

The ratio between the measuring current I _meas and the shunt current I _sh , ie | I _meas / I _sh |, is of practical importance for the use of the current transformer = | R _sh / Z₂ |. The impedance Z₂ is given by equation 5. But this results in

If you put z. B. d _a = 100 mm, l _st = 20 mm, L₂ = 50 mm, Z _l2 = 190Ω, so with R _spec = 0.08 Ω mm² / m and µ _r = 1 a current reduction of

The ratio α _b is set according to the requirements. By using a current divider, the input reflection factor for the current measuring unit is reduced.

Overall transfer function

In order to determine the current as a function of the current at the output resistance, the overall transfer function is derived. As shown here, this overall transfer can be described by a single four-pole equation. The equivalent circuit diagram for this is shown in Fig. 32. The voltage U _from across the terminating resistance Z _from communicating with the current I _{ab ab} by Ohm's law in conjunction U _ab = Z _from I. Between the terminating resistor Z _ab and the sack-shaped opening of the outer conductor there is a homogeneous, coaxial line with the characteristic impedance Z _l and the length l _c . This length is entered in Fig. 1. When looking at Fig. 1 it can be seen that the voltage tap is located in this line element. The resulting disturbance in the line impedance is not taken into account in this calculation, since this disturbance is small in comparison with the disturbance in the line impedance due to the sack-like design of the outer conductor. The four-pole equation results in

The voltage U₃ is the series connection of the voltage U₂ and the voltage U _sh . The last voltage is calculated from the parallel connection of the bridge resistance R _sh and the resistance of the short-circuited line Z₂ ie U _sh = -I₂ (R _sh || Z₂). The current I₃ is equal to the current I₂. This results in the complete transformation

The current flowing in the short-circuited line I _{measured is} calculated from the current divider _{ratio of} the bridge resistance R _sh to the resistance of the short-circuited line Z₂

The current transformer is arranged in the middle of the short-circuited coaxial line. Actually, the current would have to be transformed there by the associated line equation. However, since this piece is very short and the wave impedance present there is constant and very small, the change in current will also be very small - the change at 500 MHz is of the order of 2%, which is why this element is treated here as a concentrated component becomes. If the capacitive coupling is neglected, the voltage _{i present} across the resistor Z _{c is} described by equation 2, in which the current i is replaced by the current I _meas and the impedance Z _{i is} the parallel connection of the resistor Z _c with the line impedance Z _lc , assuming that this line is terminated with its characteristic impedance.

Herein is the current that flows through resistor Z _c

By inserting equation 4 gives the summarized transformation equation

The voltage U _i and the current I _i at the end of the coaxial line with the characteristic impedance Z _lc and the length l _cc is thus

By multiplying all matrices, the total transfer can be calculated, which again is the form a four-pole equation

Executive management

As shown in Fig. 1 and 2, the duct is a coaxial air duct. This coaxial line consists of an inner conductor D1 which passes undisturbed through the measuring head and an outer conductor which is changed in shape at the point of the voltage tap and at the point of the current transformer. The topic of this chapter is to explain how the inner conductor is fixed in the measuring head and how the safe connection of the measuring head to a line can be accomplished.

In Fig. 1 it can be seen that the measuring head has an N-type connector D2 at both ends. The plugs attached here are standard end plugs. With these, the inside of the metal guide D3 is turned off, the inner conductor D4 is pulled out. There remains the outer conductor connector D2 and the isolator D5. The inner conductor D1 passing through the measuring head is a cylindrical metal rod, the ends of which have the same shape as the inner conductor D4 pulled out of the end plugs. The diameter d _{i of} the inner conductor corresponds exactly to the diameter of the inner conductor D4 at the point indicated. The diameter d _{a of} the outer conductor is chosen so that the wave resistance given by the connector, z. B. 50 ohms. This configuration then ensures that the inner conductor is firmly inserted into the measuring head.

According to this construction principle, it is possible to provide the measuring head with various connectors. In Fig. 2 the connection to cables is realized in a very simple way. Here there is only one contact surface D6 at the end of the measuring head, which is lowered into the measuring head. The corresponding counterpart is attached here and fastened with screws that are screwed into the threads D7. In this configuration, the inner conductor is attached to the measuring head itself. The inner conductor is held by the isolators D8 (e.g. made of Teflon). The snap rings D9 and D10 hold the insulators and the inner conductor [MeiHF] so that it can no longer move. The ends of the inner conductor D11 are constructed here like the ends of the inner conductor D4. They are drilled, slotted and compressed so that the corresponding counterpart can be pushed into them. The safe electrical contact is guaranteed by the pressure exerted by the webs. In this version, the characteristic impedance of the lead is high-resistance. If you choose an inner conductor with a larger diameter, the characteristic impedance of the lead-through cable becomes smaller. Overall, the lead through the measuring head can be realized with any wave resistance.

When assembling and using the measuring head, it should be noted that from the terminating resistor first seen the voltage tap and then the current transformer comes. The reason for this is: The disturbance of the wave resistance of the lead through caused by the voltage tap is much smaller than the disturbance of the wave impedance of the lead through the Power converter. From a resistance point of view, first the voltage tap and then the current transformer, the voltage and current are measured almost undisturbed. Is from the terminating resistor first seen the current transformer and then the voltage tap, the current was almost measured undisturbed, but the voltage measurement would be due to that on the current transformer reflected waves are relatively disturbed.

An important area of application for the measuring head is voltage and current measurement in high-resistance or low-resistance line systems, where directional couplers cannot measure due to their finite directional sharpness. Fig. 33 shows the basic circuit diagram of such an application: In this figure, D12 denotes the terminating resistor, which can have any impedance. This resistor can be an antenna or a plasma reactor, for example. High-frequency power generators D13 are used to generate the high-frequency power. These generally have output impedances R _i that correspond to those of standard line impedances, e.g. B. 50 ohms. In order to be able to feed the power into any impedance with maximum efficiency, the output impedance of the generator must be transformed to the impedance of the terminating resistor using a matching network D14. There should be a line D15 between the matching network and the terminating resistor, the characteristic impedance Z _{la of} which corresponds approximately to that of the terminating resistor. The voltage / current measuring head D16 can now be used in this line to measure the voltage and the current at the terminating resistor. The lead through the measuring head D17 should have the same characteristic impedance as the leads D15 to avoid unnecessary reflections.

Function of the measuring head in the measuring system

With the voltage tap, the voltages in the lead-through conductor can be tapped and converted into a proportional voltage. The current transformer converts the current flowing through the conductor into a voltage proportional to it. The resulting voltages must be measured with a suitable measuring device. This can be an oscilloscope, a vector voltmeter or any other device that can measure the amplitudes and the phase differences of these two high-frequency voltages. For practical measurements, it is advantageous if the voltages displayed can be converted very easily to the voltage present in the lead conductor. The easiest way to do this is to set a simple reduction ratio, e.g. B. V _u = 1/1 or V _u = 1/1000. It is the same with the current conversion. Here, for example, a conversion of V _i = 1 V / 1 A or 0.1 V / A is useful. Furthermore, it is also useful if the voltages to be read are in the correct phase relationship to one another. If the lead through is terminated with its characteristic impedance, the voltages indicated by the measuring device should have a phase difference of zero degrees. To achieve this, we consider Fig. 33. This shows how the measuring head D16 is connected to the measuring device D18 through the two lines D19 and D20. The length l _{u of} the cable D20 is determined by the length of the probe cable. The length l _{i of} the cable D19 is freely selectable. It is chosen so that when the line leading through the measuring head is terminated with the characteristic impedance, the phase difference indicated by the measuring device becomes just 0 °.

literature

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Claims (14)

1. Device for measuring high-frequency voltages and currents in a lead-through conductor, which consists of a voltage tap and a current transformer,
characterized in that

• a) an amplifier with a high-resistance input resistor is used for the voltage measurement, which is connected to a coupling plate,
• b) for the current measurement of the outer conductor is bag-shaped and in this bag-shaped configuration a current transformer is used.

2. Device according to claim 1), characterized in that the coupling plate is replaced by a pin that goes directly to the inner conductor. 3. Apparatus according to claim 1), characterized in that by closing in places bag-shaped formation at the upper end a current divider is created. 4. The device according to claim 1) characterized in that the reduction ratio by choice the diameter of the coupling plate and the distance of the coupling plate from the inner conductor can be. 5. Apparatus according to claim 1 or 2), characterized in that for the production of a good Outer conductor contact for the voltage tap is a metal piston in use, which has a bore, which is suitable for the external conductor contact of the amplifier used, the spring-loaded to the outside Has contacts that match the tube in which this amplifier is located. 6. Device according to claim 1 or 3), characterized in that one side of the wire of the current transformer is connected directly to the outer conductor and the other side of the wire the following measuring system goes. 7. The device according to claim 1, 2 or 3), characterized in that it consists of two components exists, which are joined together and have contact surfaces on the connecting sides. 8. The device according to claim 1, 2 or 3) and 7), characterized in that the contact surface is preferably stepped to have better guidance. 9. The device according to claim 1 or 3) and 6) characterized in that the Signal voltage of the current transformer can go to a standard end connector. 10. The device according to claim 1, 2 or 3) characterized in that the performing Line is coaxial. 11. The device according to claim 1,3) and 10), characterized in that for places Closing the sack-shaped formation with the tube passing through the current transformer Crosspieces, which are designed as spring contacts, are electrically connected to the further pipe becomes. 12. The device according to claim 1, 2 or 3) characterized in that standard end plug are used to loop the device into a line system. 13. The device according to claim 1, 2 or 3) characterized in that when connecting the device with a measuring device with lines by a suitable choice of line lengths The measuring voltage and current signals on the measuring device are in phase if the lead is connected their wave resistance is completed. 14. The device according to claim 1, 2 or 3) characterized in that the Input reflection factor and the entire four-pole transfer function for the voltage and Current measurement can be calculated.