The First All New Resonant Line in Thirty Years

NOTE: Submitted to CARTS 2014

Introduction

The resonant line technique began at MIT Electrical Insulation Laboratories during WWII. The method satisfies a basic need to measure low losses in large reactive loads. The technique is to cancel the reactance of the load with a known (calculable) reactance, leaving the losses of the load and the fixture. The fixture losses are assumed to be known, and thus can be separated from load loss. [1] [2] [3]

The device under test (DUT) is connected across the conductors of either a short circuited (SC) or open circuited (OC) resonant coaxial transmission line whose electrical length, characteristic impedance, and Q-factor as a function of frequency are assumed to be known. The in situ impedance of the DUT causes a change in the resonant frequency and Q-factor of the system. Using transmission line calculations, the resistance and reactance of the DUT are separated from the characteristics belonging to the line.

fig1

Fig. 1. Loosely coupled transmission lines may be configured as. (a) short-circuited termination with inductive loop coupling. (b) open circuited termination with capacitive probe coupling. [4]

As a practical measurement circuit, the transmission line must be connected to a signal source and a detector. As shown in Figure 1, this is accomplished by ‘loose coupling’ to the electric field (at the open circuited end) or the magnetic field (at the short circuited end).

The Need for an Update

The method began long before the age of printed circuitry, industrial automation and computerized test. At that time there was neither a need nor a desire to use any other transmission line configuration than coaxial. Furthermore, in a time before modern computer-aided engineering the exact contribution of second order effects to measurement uncertainty were not known or even calculable.

As DUTs get smaller and smaller, inserting them into a coaxial line becomes difficult. The test method was never intended to be automated and is in fact very inconvenient and time consuming. Finally, component engineering has improved to the point where the measurement uncertainty associated with the current design and test procedure obscures the observable characteristics of the DUT.

fig2

Fig. 2. A photograph of a commercially available resonant coaxial line (Boonton 34A) shows how the outer conductor must be modified to allow the DUT to be inserted and removed from the test equipment. [5]

                        Figure 2 illustrates the problem of inserting a DUT into a coaxial line. A slot has been cut into the outer conductor of the line to make it possible to insert the DUT into the test equipment with tweezers, but the slot is small and cramped and the inside of the line is dark.

The Resonant Slab Line (patent pending)

fig3

Fig. 3. The two cross-sections of transmission lines being discussed are (a) coaxial and (b) slab line.

Device Insertion

Fig. 3 illustrates how the proposed resonant slab line makes inserting the DUT easier. With the slab line configuration there is no need for a slot to be cut into the outer conductor, because there are full length slots on two sides. The configuration makes it much easier to automate the test procedure because there are pathways into and out of the instrument.

Comparing figs. 2 and 4 it becomes obvious that the DUT will be easier to insert, remove and even see, making the test procedure faster and easier.

Calibration/Standardization

fig4

Fig. 4 By using the open-sided geometry of a slab line, it becomes much easier to control the placement of the DUT.

The resonant line technique depends on the assumption that the electrical characteristics of the fixture are known so that they may be extracted from the measured electrical characteristics of the fixture with a DUT inserted. This process compares to measuring the mass of a beaker containing water and then subtracting the mass of the empty beaker to obtain the mass for the water. However, the analogy fails because inserting the DUT into the resonant line has the potential to change the electrical characteristics of the line.

 

 

Resonant lines have historically been calibrated by measuring their open- and short- circuited resonance properties and assuming that these characteristics may be interpolated to intermediate frequencies. This assumption can be shown to be incorrect if one understands the theory of coupled resonators. Unfortunately it is not convenient to perform a more accurate calibration technique using a coaxial resonant line. A more accurate calibration method is easily achieved using a resonant slab line if the center conductor and coupling probes are fixed in position relative to one another and the center conductor and probe assembly is made to move in a precise way relative to the ground plates of the slab line. In this case, calibration data points may be directly collected which allow a more accurate calibration of the resonant slab line and concomitantly more accurate measurements of DUTs.

Probe Coupling

Another advantage of employing the slab line configuration is that the coupling probes do not have to be inserted into the resonant line by drilling holes in the outer conductor, as shown in fig. 1. Using the slab line configuration, the center conductor can be excited by inserting probes through the full length slots on both sides of the slab line, fig 5.

fig5

Fig. 5. The location of coupling probes with respect to the center conductor and DUT is shown here with the upper plate of the slab line removed for illustrative purposes.

In fig. 5, one of the grounding plates has been omitted from the illustration to show the relationship between the coupling probes, the center conductor and the DUT. The DUT may be inserted into the line and clamped between the center conductor and ground without using a so-called “movable plunger” by moving the entire center conductor. As the center conductor moves the coupling probes may also be moved because they do not depend on holes drilled through the outer conductor for access to the interior of the resonant line.

The relationship between the center conductor and the coupling probes may be maintained with a carriage that fixes their relative positions and allows a lead screw to be used to precisely set the position of the center conductor and coupling probes in relationship to the rest of the fixture.

Simulated Results

fig6

Fig. 6. This simple loosely coupled circuit was used to study the change in Q-vs frequency of a resonant line (with losses) is terminated with a lossless capacitance.

 Consider the simple linear network shown in fig. 6. A “mathematical” 75 Ω transmission line model, with an electrical length of 180˚ and a specified loss of 0.01 dB at 900 MHz and increasing in proportion to the square root of frequency is terminated with a variable lossless “mathematical” capacitor-to-ground to form a tunable resonator. This resonator is then loosely coupled to 50 Ω input and output ports via vanishingly small lossless “mathematical” capacitors.

We would expect that, as the terminating capacitor, labelled ‘DUT’ in the figure, increases in value the resonant frequency of the network would decrease. We would also expect to see the Q-factor of the network increase roughly in proportion to the square root of frequency. Some of us might also expect to see the Q-factor “roll off” from f1/2 as the frequency increases, due to increased coupling of the source impedance (source-loading). But perhaps only experienced RF filter designers would anticipate the modeled behavior of the loaded resonator shown in fig. 7.

Note the following:

  • There are only three sources of loss in the model: (1 &2) the source and load resistances and (3) the finite loss ( f1/2) in the transmission line.

  • The variation in Q vs. f does not depend on “fixture resistance”.

  • The variation in Q vs. f does not go as .

  • The variation in Q vs. f clearly obeys some model, because it arose from a model.

  • The behavior of Q vs. f in a real resonant line is likely to be more complex than the modeled behavior.

Measured Results

To test out these ideas a simple slab line was constructed using a 1/8” dia. copper rod and two 1-1/2” wide copper plates. The center conductor was fixed to a probe carriage in a manner similar to that shown in fig. 5. The ground two plates were shorted together on both ends and at the probe carriage. The experimental setup was used to make Q vs. f measurements with different capacitive loads by creating a gap between the end of the center conductor and at one of the shorting connections between the two ground plates.

Measurements were made from ~650 – ~2800 MHz using a HP 8753 network analyzer and from ~0.9 – ~9 GHz using a HP8510. The results, fig. 8, clearly show that the modeled behavior of the simple circuit in fig. 6 corresponds to measured data taken with a capacitively loaded physical slab line.

fig7

Fig. 7. Modeled Q vs. f behavior of the loosely coupled resonator circuit shown in fig. 6.

fig8

Fig. 8. Measured Q vs. f behavior of a realized resonant slab line, capacitively loaded with a variable air gap capacitor.

Interpretation of Results

Taken together the simulation and experimental results show that using a power law to interpolate/extrapolate the Q-factor of an ‘empty’ resonant line fails to account for the actual behavior of a capacitively loaded resonant line. The consequence of this failure is a systematic error in reported ESR of a DUT. This systematic error tends to produce logically inconsistent results, such as varying ESR with respect to capacitance in similarly designed DUTs and even negative ESR values for low-loss DUTs.

By designing a resonant line that will enable its ‘empty’ Q-factor as a function of loading capacitance to be directly measured, the whole interpolation problem may be sidestepped completely – We simply observe the resonant frequency of the DUT and then measure (or look up) the Q-factor of the line when it has been tuned to that same frequency with a gap capacitance.

It may still be necessary to account for contact resistance when measuring DUTs. This and other work is ongoing.

Conclusions

A resonant slab line has been proposed and its Q vs. f properties investigated. It offers the potential for enhanced accuracy and logical consistency of measured ESR for component designers and users.

The slab line configuration, in addition to enabling a more accurate characterization of its Q vs. f properties, offers the possibility for improved labor efficiency because the slab line configuration enables easier access to the placement site of the DUT.

References

[1]

W. B. Westphal and A. R. Von Hippel, Dielectric Materials and Applications, Cambridge: MIT Press, 1959.

[2]

J. P. Maher, R. T. Jacobsen and R. E. Lafferty, “High-frequency mesasurement of Q-factors of ceramic chip capacitors,” IEEE Trans. Components, Hybrids, Manuf. Technol., Vols. CHMT-1, no. 3, 1978.

[3]

M. Ingalls and G. Kent, “Measurement of the characteristics of high-Q ceramic capacitors,” IEEE Trans. Components, Hybrids, Manuf. Technol., Vols. CHMT-10, no. 4, 1987.

[4]

M. Ingalls and H. Partel, “Resonant Lines for Device Measurement, 10 MHz – 3.5 GHz,” in 19th Capacitor and Resistor Technol. Symp., New Orleans, 1999.

[5]

“Boonton 34A Data Sheet,” [Online]. Available: http://www.ko4bb.com/Manuals/09)_Misc_Test_Equipment/1)_Brochures_and_Datasheets/BTN%2034A%20DATA%20SHEET.PDF. [Accessed 4 February 2014].

 

 

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