WO1999027647A2

WO1999027647A2 - Symmetrical biasing architecture for tunable resonators

Info

Publication number: WO1999027647A2
Application number: PCT/US1998/025373
Authority: WO
Inventors: David Galt; Zhiahang Zhang
Original assignee: Superconducting Core Technolgies, Inc.
Priority date: 1997-11-26
Filing date: 1998-11-24
Publication date: 1999-06-03
Also published as: AU1902499A; WO1999027647A3

Abstract

An extra symmetry is introduced into resonant circuits in order to make the location of voltage nodes (+Vdc, -Vdc) of the resonant waveform stationary. These stationary voltage nodes (+Vdc, -Vdc) are then used as the contact points of the bias circuitry to the resonant structure. Connecting the bias circuitry to the voltage nodes insures no resonant energy escapes the resonator into the bias circuitry thus ensuring no degradation of the resonant quality factor ('Q') and no interfering energy in the bias circuitry.

Description

SYMMETRICAL BIASING ARCHITECTURE FOR TUNABLE RESONATORS

FIELD OF THE INVENTION

The present invention is related to tunable resonators

and specifically to tunable resonators using dc bias voltage

circuitry.

SUMMARY OF THE INVENTION

The tunable resonating circuit of the present invention,

includes:

(a) a resonating element having first and second voltage

nodes ;

(b) an electrically tunable element (e.g., a voltage

tunable capacitor or varactor, a current tunable inductor, and

the like) in electrical communication with the resonating

element ;

(c) biasing means (e.g., a power source and bias lines

attached to the resonating element) for applying the bias

(voltage or current) to the electrically tunable element to

tune a characteristic of RF energy passing through the

resonating element; and

(d) maintaining means (e.g., a second electrically

tunable element) for maintaining the first and second voltage

nodes in first and second positions, respectively, when the biasing means applies the bias to the electrically tunable

element. The first and second positions are the positions of

the first and second voltage nodes relative to the resonating

element when the resonating element is free of a bias. As

will be appreciated, the application of the bias to the

resonating element alters the reactance ("Z") of the

electrically tunable element and therefore the characteristic

of the RF energy.

The electrically tunable element can include a dielectric material having an index of refraction that is a function of

the bias. The index of refraction can be dielectric permittivity for the capacitor (which is a function of bias voltage) cr magnetic permeability for the inductor (which is

a function of bias current) . By way of example, the dielectric material can be a bulk or thin film ferroelectric

or paraelectric material.

As noted, the maintaining means can include a second

electrically tunable element in communication with the

resonating element. The first and second voltage nodes are

maintained in their respective first and second positions over

a range of biases and in different resonant modes by

maintaining the reactances of the tunable elements substantially equal. By way of example, the elements could be

capacitors having dielectric materials of substantially

identical thicknesses and be subjected to substantially the

same bias voltage to produce substantially identically

capacitances.

In one configuration, the tunable elements are located

about 180 degrees apart on the resonating element. Preferably, the tunable elements are connected in series with the resonating element.

In yet another configuration, the biasing means includes first and second connections between the biasing means and the resonating element. Each of the first and second connections are located at a voltage node. A voltage node can be located between the electrically tunable elements on either side of

the resonating element. The voltage nodes are typically about

180 degrees apart.

In another configuration, the electrically tunable

element is attached to the resonating element at about ninety

degrees from a voltage node.

In another configuration, the resonating circuit,

includes :

(a) a resonating element for RF energy; (b) first and second electrically tunable elements

respectively having first and second reactances for altering

a characteristic of the RF energy, the first and second

electrically tunable elements being electrically connected to

the resonating element and the first and second reactances

being substantially the same reactances; and

(c) biasing means for biasing the first and second

electrically tunable elements in communication with the first

and second tunable elements. Preferably, the first reactance

is at least about 50%, more preferably at least about 75%, and

most preferably at least about 90% of the second reactance but

no more than about 150%, more preferably no more than about

125%, and most preferably no more than about 110% of the

second reactance.

In yet another configuration, the resonating circuit

includes :

(a) a resonating element for RF energy;

(b) first and second electrically tunable elements for

altering a characteristic of the RF energy, the first and

second electrically tunable elements being electrically

connected to the resonating element; and (c) first and second bias lines connected to the

resonating element at first and second points, respectively.

The resonating element is symmetrical about a line passing

through the first and second points.

In operation, the resonating element performs the

following steps:

(a) first applying a first bias to a tunable element in

the resonating element;

(b) second applying a second bias to the tunable element

wherein the first and second biases have different magnitudes;

and

(c) maintaining the positions of first and second

voltage nodes in the resonating element constant during the

first and second applying steps.

As noted, the resonating element can include a second

tunable element having a second reactance. The maintaining

step can include maintaining the reactance and the second

reactance substantially equal. This can be accomplished by

applying the same bias over time to the two tunable elements. BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 depicts an electrically tunable resonating element

according to a first embodiment of the present invention;

Fig. 2 depicts an electrically tunable resonating element

according to a second embodiment of the present invention;

Fig. 3 is a plot of RF voltage versus position along the

resonating element;

Fig. 4 depicts an electrically tunable resonating element

according to a third embodiment of the present invention; Fig. 5 is another view of the circuit of Fig. 4;

Fig. 6 is a plot of transmission resonance versus

frequency;

Fig. 7 depicts various plots of capacitance versus bias

voltage for a tunable capacitor as the tunable element; Fig. 8 is a plot of K- factor versus dc voltage; and

Fig. 9 is a plot of RF voltage versus inverse tunability.

DETAILED DESCRIPTION

Problems, difficulties, or circumstances giving rise lo the idea: When tunable circuit elements, e.g. voltage-tunable capacitors or current- unable inductors, are introduced inio resonant structures in order that the resonant frequency may be tuned, bias circuitry must be connected lo the rcson.anl structure lur the purpose of controlling the tunable elements. To ensure no resonant energy escapes the resonator into the bias circuitry the impedance (at the frequency of the resonator) of the bias circuitry as seen from the resonutor must be very lurge compured to the resonant mode impedance at the contact points. Towards achieving this goal, qu-aπcr-wavc impedance transformers are usually incorporated into the bias circuitry to make the bias circuits imped-ance iargc as seen from the resonator, and contact between the bias circuitry and resonator is made ut the resonutor's voltuge node where the resonunt mode's impedance is zero. These impedances, however, will vary when the bias circuitry is employed to lune the resonator, i.e. the location of the voltage-node will shift and the l.arge impedance of the quarter- wave transformers will drop.

The symmetrical biasing architecture ensures that the voltage nodes remain stationury when the resonator is tuned. These stationary voltage-nodes arc used as the contact points to the resonator for the bias circuitry to ensure that no resonant energy will escape the resonator into the bias circuitry. Two examples of the symmetrical bias architecture are drawn below, In the first example, a loop resonator has two identical, tunable capacitors inserted in series into it at positions 180° from pach other. This makes the frequency of the lowest order resonant mode (as well as all the odd ordered modes) dependent on the value of the tunable capacitors. The points 90° from the cupacitors axe voltage-nodes of the lowest frequency resona- nt mode (and for the next-to-lowest frequency mode which is even-ordered und thus non-tunable). These points remain voltage nodes regardless of the value of the capacitors as long as that value is the same for both capacitors. Bias circuitry may be connected to these voltage nodes without disturbing the resonunt mode. In the second example two identical, series capacitors arc placed together in scries with a loop resonator. The point between these capacitors and the point 180° from that point are vυllage-nodes and remain voltage nodes regardless of the value of the capacitors as long as that value is the same for both cnpacitors. The first example has the advantage that the microwave voltage gradient is less steep near the voltage nodes and thus is mode tolerant to dissimilarities between the two cap.acitors while the second example has the advantage of a smaller overall size.

Thin films of SrTiθ3 and Bao. Sro.fi i 3 have been pulse laser ablated onto LaΛlO.1 substrates. Normal metal coplanar capacitor electrodes were patterned on top of these films and the capacitors were incorporated into weakly coupled microstrip resonators. Resonant frequencies und Q's were measured as a function of bias at room temperature and at 77 K. The microwave frequency capacitance and loss is calculated from the resonant properties and compurεd with the simultaneously measured 1 MIJ7, capacitance and dis.sipation. Two-tone intermodular on distortion products were measured .and the third-order intercept is referenced to the microwave voltage across the capacitors. Commercially available semiconductor vαractors were tested in a similar manner. Tuning quality (the ratio of the relative capacitance tuning to dissipation), frequency dispersion, and power handling of these capacitors is compared. Although there appears to be no intrinsic power handling capability of the paraelectrics over the semiconductor varactors, the paraelectrics can offer tuning quality advantages.

INTRODUCTION

The nonlinear dielectric constant of paraelectric films such as SrTiO, and Ba,._xSr,TiO^ can be used to tune microwave signal processing components such as phase shifters,¹'^* rcsonators '¹'^5,6 filters,⁷⁸ and voltage controlled oscillators. Tunable capacitors mude from these films may offer some advantages over semiconductor vαractors for tunable microwave applications, especially at X band and higher microwave frequencies. Possible advantages include a better tuning to loss ratio and the possibility of designing for higher power handling capability. This paper directly compares the two technologies at frequencies near 1.5 GHz.

EXPERIMENT

Films of SrTiO, (STO) and Ba₀₄Sr₍,_.-_>TiO, (13 ST) were laser ablated from stoichiometric targets onto LaΛ10₃ (J.AO) substrates which were held at 775 °C in a partial pressure of 65 mTorr of O,. The 248 mτ> Kr-F excimer laser fluencc was approximately 2 J/cm² at the target, and the target to substrate distance was 8 cm. AUer growth, the films were cooled in an atmosphere of 0,, then annealed in flowing O₇ at 1200 °C for 7 hours. Coplanar, intcrdigital electrodes (separated by 1 μm) of e-beam^' evaporated normal metals (10 nm Ti / 100 nm Λu / 6 μra Ag / ] 50 nm Λu) were formed on top of these films by lift-off. The samples were then diced into individual capacitors. Abrupt junction varactors based on GαAs (cat. MΛ46506-1056) and Si (cut. it MΛ45234-1056) were purchased from M/A-COM, Inc. for comparison. Abrupt junction GaAs varactors were also purchased from MDT, Inc. (cat. U MV2008-36).

Capacitors were reflow soldered (52% In, 48% Sn) into a microstrip resonator oj^* characteristic impedance Z, depicted in Fig.5. Transmission resonances ( .. shown in Fig.β) were measured by connecting a vector network analyzer (HP8510C) to the resonator's ports 1 und 2 which are weakly coupled to the resonant line so that the measured, loaded Q, { , , is approximately equal to the unloaded Q. Tine resonator design is such that the lowest order mode is highly sensitive to the capacitance and dissipation of inserted capacitors (5- > 0.4 for C > 1.35 pF). In general, the sensitivity, S, of a resonator's properties to the capacitor properties is defined us the ratio of the average energy stored in the capacitor lo the total energy stored in the resonator⁰ (ξ = S in Rcf. 6) or equivalcntly as

where „ is the resonant frequency and C is the capacitance of one of the inserted capacitors. The relation between j, and C for the resonator of Fig. ^'(for the tunable, odd-ordered mode) is

where *₀ (= 2 r/„/v ) is the resonant wave number and L_fff is tiie effective length of the resonant line. L_eJ. is calibrated by measuring linear capacitors of normal metal, interdigital electrodes on AO and .assuming no frequency dispersion between the 1 MHz capacitance and the microwave frequency capacitance. The even-ordered, non-tunable mode (see Fig. 5) may also be used to calibrate _ttr . The phase velocity, v^, and Z₀ are calculated from the resonant line geometry and LΛO's dielectric constant⁹ using standard microstrip design equations.¹⁰ Using the resonator of Fig._f] its sensitivity as derived from Eq. 1 and Eq. 2, and the approach of Rcf. 11, the microwave voltage across the capacitor can be calculated as a reference point for the third order intercept of the power measurements. The capacitor dissipation (effective loss tangent), D, is calculated from O , . (i, is due to the losses of the resonant line, Q_lt>lit, -and to the losses of the capacitors, O . $ = &L + Q where

The resonant line is formed by lift-off of e-beam evaporated melals (10 nm Ti / 100 nm Λu / 6 μm Ag / 2 μm Λu) on LAO. The losses due to it are dominated by the conductor losses. We calculate these losses near 1.5 GHz to be Q_lne = 300 ± 75 (from σ ~ 6.2x10^,Ω^"'m^"1) at room temperature and Q_IIIH. = 600 ± 150 (from σ = 23^10' Q^m^"1 ) at liquid nitrogen temperature. Values of Q_m in this study range from 20 to 200 indicating they are dominated by the varactor loss.

The four-fold symmetry of the resonutor's electrical desicn (requiring two identical capacitors) ensures that the dc ports are located at voltage nodes of the tunable resonant mode regardless of the bias state. This is an alternative approach to the mechanically adjustable bias circuitry of previous work.⁵ An LCR meter (HP4275Λ) is connected to the dc ports to allow for the simultaneous measurement of the low frequency (1 MHz) cap.acitance and dissipation. The LCR ac excitation of 10 mV RMS is low enough to not interfere with microwave measurement.

Tuning quality, K, is the ratio of the element's "tunability" to loss.^{12, H} Equivalent differential forms of it can be defined as

_{κ m} øL 6SL. _lJS _{% Q (}4)

*' " ε_r tan* C D ^l f. * ^{' W}

This figure-of-merit is useful for displaying at what bias level the tuning quality is best, but device-lo-dcvicc comparisons arc best made by integrating K_Ϋ over the entire bias range from 0 V to breakdown (if possible).

In band, two-tone, third-order-interccpt (TOI) measurements were performed on the resonator loaded by the various varactors. Two signal generators (HP8643A's) were connect^ through 6 dB pads (for additional isolation between signal generators) to a power combiner (MA2090-6204-00), the output of which was connected to the resonator. The output of the resonator was, in turn, monitored by a spectrum analyzer (HP8594E). The power into the spectrum analyzer at the fundamental and third-ordcr-intcrmodulation frequencies versus the power produced by the signal generators was measured as a function of the bias state of the varactor.s. The linearity of the experimental set-up was investigated to ensure that the third- ordcr-intcrmodulation power was dominantly generated in the resonator and not in the spectrum analyser or signal generators.

RESULTS

The STO capacitors were measured at 77 K while the BST, Si, and GaAs capacitors were measured at room temperature. Their capacitance and dissipation near 1.5 GHz is displayed in Fig. 7. Data from the MDT, Inc. varactor is not shown here for brevity. (Raw resonant data for the MDT, Inc. varactor is displayed in Fig. B) The simultaneously measured 1 MHz capacitance is similar but not indistinguishable from the high frequency capacitance for all samples. Capacitance frequency dispersion is greater at low bias than at high bias for all samples. For the STO sample at zero bias the high frequency capacitance is 8% lower than the 1 Mlfo capacitance but the difference decreuses to less than 1% at biases greater than 15 V. (This trend has previously been observed in STO varactors.^5,15) The BST's high and low frequency capacitances are within 3% of each other at all biases. The ϋaAs sample's high frequency capacitance is 13% larger than the 1 Milz capacitance at zero bias decreasing to 11% at high biω. The Si sample's hi h frequency capacitance is 12% larger than the 1 MHz capacitance at .zero bias decreasing to a 10% difference at high bias. The apparent -10% . high frequency capacitance offset over the 1 MHz capacitance of the semiconductor varactors may be caused by an inappropriate value of ,_s . l_e„ was calculated from LAO calibration capacitors of the same shape and size as the paraclcctric varactors and is thus more appropriate for the pafaclectric vuractors on LAO than for the lurger semiconductor varactors. The 1 MHz dissipation significantly differs from the high frequency dissipation in all .samples and is ulso displayed in Fig.7. Dissipation error bars arc derived from the assumed 25% error in Q„,_μ mid 10% error in β_ .

Figure 8 is a comparison of the various varactors' integrated -factors where K. is plotted versus the bias range employed. Note that the x-axis is geometry dependent and that if the paraelectric capacitor gaps were reduced from, for example, 10 μm to 5 μm, then roughly the same K.-factor would be achieved at half the bias. The Si .and GaAs varactors from M/A-C M .are quoted to breakdown near 30 V which limits their maximum attainable K to -100 for the GaAs varactor and -80 for the Si varactor at the frequencies of these measurements. The MDT, Inc. varactor is quoted to break down near 48 V limiting its K to 55 at its measurement

frequencies. The paraclectric capacitors do not breakdown until well over 100 V (in vacuum), thus increasing the bias range (or reducing the capacitor gap size) could significantly increase the demonstrated K's of 125 for STO and 37 for BST.

We note that the semiconductor varactors' losses arc well described by D = ωRC in the GH/. regime¹⁰ while there is some evidence that the dissipation of STO capacitors is much less frequency dependent than this in the range from 6 to 20 GHz.⁵ A 10 GHz projection of the semiconductor varactors' K-factors (assuming D = ωRC) is included in Fig. ζ> This projection suggests that the maximum attainable K. for both GaAs samples tested is the same value of ~15 at their respective breakdown voltages and that the Si varactor's K is —11 at breakdown and 10 GHz. This further suggests that the difference between the GaAs varactors' measured K. values is simply due to the difference in their respective measurement frequencies. The MDT, Inc GaAs varactor is of a lower capacitance (0.35 pF < C < 1.13 pF) than the M/A-COM GaAs sample (1.4 pF < C < 6.27 pF) .and is thus measured at a higher frequency (2.1 GHz <f₀ < 3 GHz) than the M/A-COM GaAs sample (1.0 GHz <f_σ <1.9 GHz) resulting in a larger measured dissipation. Assuming no degradation of the BST's K-faέtor with iπcre-asing frequency, BST would provide significant tuning quality advjintagcs over the semiconductors at higiier microwave frequencies and STO would provide vastly better tuning quality if one is willing lo employ cryogenics. Higher frequency measurements arc needed to ascertain the accuracy of these speculations.

Since the nonlinearity which results in capacitance tuning should also result in signal distortion due to the self-biasing of the tunable capacitor by strong signals which pass though it, one would expect the TOl to be inversely related to the devices tunability.

where V_m/ is the TOl of the resonator referenced to the microwave voltage across the capacitor and g is a function independent of the material upon which the varactor is based. Figure 9 is a plot of V_lvl versus the inverse tunability of the various varactors. Error b.ars are derived from the deviation of the third order slope from 3 und they reflect the sign of the deviation. No other errors arc considered. (Fundamental slopes were always within 2% of the expected value of 1 while the third order slope deviated from the expected value of 3 by as much as 20%.) Although there is considerable scatter in the data, they are consistent with the idea that there is no intrinsic power handling capability advantage of one material over the others and that the nonlincarity which gives rise to the capacitance tuning also limits the TOl.

The absolute power handling of a voltage-tunable capacitor is determined by the voltuge bias required for tuning, i.e. the signal voltage level must be kept far below the voltage level required for significant tuning in order to avoid self-biasing by the signal and the associated signal distortion. Thus v* ^» a) where V_dc is the bias voltage and V_κ is the signal level. Althoug there appears to be no intrinsic power handling advantages of paraeleclric varactors, they are easily scaled-up to larger capacitor gap si.zes and thus can be made to handle more power if one is willing to employ larger biasing voltages. CONCLUSIONS

This study has directly compared two available tuning technologies - semiconductor varactors and paraelcctric varactors - at frequencies near 1.5 GHz and at 1 MHz. Capacitance and dissipation measurements of the various samples near 1.5 GHz and at 1 MHz show that the capacitance frequency dispersion is slight but die dissipation frequency dispersion is significant in ull samples tested. This exhibits the need to conduct microwave frequency testing on components for microwave devices and that low frequency LCR meter measurements are not sulTicicnt for such purposes. The 1.5 GHz tuning quality of STO is superior to that of the semiconductors but requires a cryogenic environment. A projection to 10 GHz suggests that the BST sample would display superior tuning quality over the semiconductor samples at higher frequencies. Two-tone, third-order-interccpt measurements suggest that there is no intrinsic power handling capability advantage of paraelectrics over semiconductor varactors but that the dynamic range of tunable elements is limited by their tunability regwdlcss of the material they are based upon. Tunable varactors based on GaAs and Si are a mature technology. Although the current quality of the purαelcctric varactors may offer some advantages over semiconductor varactors especially at higher microwave frequencies, material improvements are needed and expected. Specifically, hysteresis must be eliminated in the Ba,..Sr_xTiO_j varactors before they can be commercialized for microwave tuning applications since their semiconductor competition displays little to no hysteresis.

Claims

loWhat is claimed is:

1. A tunable resonating circuit, comprising:

(a) a resonating element having first and second voltage

nodes, the first and second voltage nodes having first and

second positions relative to the resonating element when the

resonating element is free of a bias;

(b) an electrically tunable element in electrical communication with the resonating element;

(c) biasing means for applying the bias to the

electrically tunable element to tune a characteristic of RF energy passing through the resonating element such that the

application of the bias to the resonating element alters the

reactance of the electrically tunable element; and

(d) maintaining means for maintaining the first and

second volcage nodes in their respective first and second

positions when the biasing means applies the bias to the

electrically tunable element .

2. The tunable resonating circuit of Claim 1, wherein

the electrically tunable element includes a dielectric

material having at least one of a dielectric permittivity and

magnetic permeability that is a function of the bias.

3. The tunable resonating circuit of Claim 1, wherein

the maintaining means includes a second electrically tunable

element in electrical communication with the resonating

element .

4. The tunable resonating circuit of Claim 3 , wherein

the electrically tunable element and the second electrically tunable element are located about 180 degrees apart.

5. The tunable resonating circuit of Claim 1, wherein the biasing means includes first and second connections between the biasing means and the resonating element, each of the first and second connections being located at a voltage

node .

6. The tunable resonating circuit of Claim 5, wherein the electrically tunable element is attached to the resonating element at about ninety degrees from a voltage node.

7. The tunable resonating circuit of Claim 3 , wherein

the reactances of the electrically tunable element and the second electrically tunable element are approximately the

same.

8. The tunable resonating circuit of Claim 3, wherein

a voltage node is located between the electrically tunable

element and the second electrically tunable element.

_

18

9. A tunable resonating circuit, comprising:

(a) a resonating element for RF energy;

(b) first and second elements respectively having first

and second reactances for altering a characteristic of the RF

energy, the first and second elements being electrically

connected to the resonating element and the first and second reactances being substantially the same reactances; and (c) biasing means for biasing the first and second elements in electrical communication with the first and second

tunable elements.

10. The tunable resonating circuit of Claim 9, wherein the first reactance is at least about 50% of the second reactance but no more than about 150% of the second reactance.

11. A tunable resonating circuit, comprising:

(a) a resonating element for RF energy;

(b) first and second elements for altering a

characteristic of the RF energy, the first and second elements

being electrically connected to the resonating element; and

(c) first and second bias lines connected to the

resonating element at first and second points, respectively,

wherein the resonating element is symmetrical about a line

passing through the first and second points.

12. A method for tuning RF energy passing through a

resonating element, comprising:

(a) first applying a first bias to an electrically

tunable element in the resonating element;

(b) second applying a second bias to the electrically

tunable element wherein the first and second biases have

different magnitudes; and

(c) maintaining the positions of first and second

voltage nodes in the resonating element constant during the

first and seco: d applying steps.

13. The method of Claim 12, wherein the resonating

element includes a second electrically tunable element having

a second reactance and the electrically tunable element has a

first reactance and the maintaining step comprises maintaining

the reactance and the second reactance substantially equal.

14. The method of Claim 12, wherein the resonating

element includes a second electrically tunable element and the

maintaining step comprises applying the same bias to the

element and the second element.

15. A method for tuning RF energy passing through a

resonating element, comprising:

(a) applying a first bias to a first electrically

tunable element in the resonating element to produce a first

95 reactance;

(b) applying a second bias to a second electrically

tunable element in the resonating element to produce a second

reactance; and

(c) maintaining the first reactance substantially equal

100 to the second reactance during the applying steps.

16. The method of Claim 15, wherein the first and second

biases are substantially the same.

17. The method of Claim 15, wherein the first and second

biases are one of voltage and current .

105