# High Tuning Sensitivity Dielectric Resonator Oscillator From Optimization of Dielectric Resonator TE_{01δ} Mode

In the design of a dielectric resonator oscillator to be used as a local oscillator, the objective of this study is to find a method to achieve a wide tuning range with a tuning sensitivity of 1 MHz/V or higher for the dielectric resonator oscillator operating at 3.6 GHz. The tuning structure dimensions of the dielectric resonator circuit were varied, in order to understand the resonator behavior and limitations to achieve the desired tuning sensitivity for the dielectric resonator oscillator. A practical method is proposed for dielectric resonator oscillators, which yield a high tuning sensitivity as well as a wide bandwidth. A dielectric resonator oscillator with tuning sensitivity of 1.9 MHz/V at 3.6 GHz has been developed using this method.

Dielectric resonators (DR) are widely used to construct microwave frequency filters and oscillators due to their temperature stability and high dielectric constant, ε_{r}, which enable miniaturization of the circuits. A high ε_{r} means that the electric field of the particular resonant mode is concentrated within the DR and the external field attenuates very rapidly with the distance from the surface, thus giving small radiation loss and high unloaded Q factor, QU, which is limited only by the dielectric loss (loss tangent, tan δ) of the DR material. The QU is approximately 1/tan δ.^{1} Various dielectric resonators are made from various titanate compounds ceramics^{2} and the DR used in this study is a zirconium titanate-based ceramic, which has an excellent temperature stability, that is a temperature coefficient, τ_{ƒ} ≈ 0 ppm and a QU > 9500 at 4.3 GHz.^{3,4}

### Typical Construction of DR Circuits for Oscillator Applications

**Setting the DR Resonant Mode**

The DR can be excited in various modes, but the principal transverse electric mode, TE_{01δ}, is employed because the magnetic field can be conveniently coupled to microstrip transmission lines. In these lines, a signal propagates in transverse electric magnetic mode, TEM. The DR comes in a cylindrical shape for ease of fabrication and assembly, as shown in **Figure 1**.

**Figure 1** A cylindrical DR for practical assembly.

The dimensions or the size of the DR determine its resonant frequency. But to resonate the DR in TE_{01δ} mode, the ratio of its outer diameter (OD) to its thickness (L), that is OD/L, must be greater than 1.42^{5} and, specifically, the ratio must be kept between 2 and 3.33 to minimize interference of spurious modes.^{6} With reference to the axis shown in the figure, the DR transverse electric resonant mode standing wave pattern has 0 wave variation in the circumferential, Φ direction, 1 wave variation in the radial, ρ direction and the δ indicates that the standing wave is not a complete half-sinusoid pattern along the z direction.

**Metal Enclosure Assembly**

The DR must be placed in a metal enclosure to avoid radiation loss and interference from external fields. The enclosure dimensions must be approximately twice of those of the DR dimensions (OD and L) to minimize the effect on Q_{U} from the current induced on the metal surface by the external field of the DR.^{1} Experimental studies have been done^{7} to determine the effect of ground plane distance (in the z-axis direction) to the DR, on several resonant frequencies of the DR. The results show that the TE_{01δ} mode resonant frequency increases as the distance gets closer because of the magnetic field perturbation by the ground plane.^{7,8} Thus, to compensate for variations in the DR material, a metallic tuning disc is added onto the top of the enclosure. The tuning disc height is adjustable mechanically to tune the resonant frequency. The enclosure height, L_{c} is made to be slightly more than twice the DR height, L. When the tuning disc is completely retracted, there is a gap, L_{2} between the tuning disc (ground plane) and the top of the DR. This mechanical frequency adjustment is very slow compared to electrical tuning and is meant for a one-time tuning to set the center frequency of the circuit.

**Figure 2** Typical assembly of the DR circuit for a TE_{01δ} mode oscillator.

In order to realize the high Q_{U} of the DR, it must be located away from the conducting shield or the ground plane.^{9} A cylindrical ceramic support with a low ε_{r} , that is below 10, is placed between the DR and the bottom ground plane. This seems like contradicting the earlier statement for having a metallic tuning disc in the top of the enclosure; in fact this is a compromise between the high Q_{U} and the accurate resonant frequency. The basic construction of the DR circuit described above is presented in **Figure 2**.

**Figure 3** DR TE_{01δ} resonant mode coupling to a TEM mode miscrostrip.

### Analysis of the Tuning Structure for DR

**Varactor-tuned DR Circuit**

As mentioned earlier, the DR circuit resonating in the TE_{01δ} mode can be conveniently coupled to a microstrip line, which is a TEM waveguide. This is the approach for the dielectric resonator oscillator (DRO) design, but before going into the oscillator, the DR will be first characterized as a passive circuit. A varactor coupled to a stub is introduced into the DR circuit for electrical tuning. The tuning stub is circular in shape, as opposed to a straight line stub used by Yom et al;^{10} this is to allow a locking screw insertion at the center of the DR. The main objective of the characterization is to find a method that will give the DRO a maximum tuning sensitivity, KV. There are many references describing varactor coupled techniques that achieve high tuning bandwidth for the DR circuits; some are impractical due to tuning complexity,^{11} cumbersome enclosure or assemblies as described by Virdee.^{8} However, one potential method described by Virdee^{12} will be the basis for this study, but with some modification.

**Figure 4** The varactor-tuned DR circuit for analysis.

The DR TE_{01δ} mode resonance coupling to the TEM microstrip line is depicted graphically in **Figure 3**, and the proposed varactor coupled tuning circuit, analogous to a band- pass filter circuit, is shown in **Figure 4**. Effectively, the varactor introduces a variable capacitance into the circuit. By varying this capacitance, the overall electromagnetic field of the DR circuit changes, thus varying the resonant frequency. The mechanism is similar to the tuning circuit proposed by Virdee,^{12} where the tuned resonant frequency of the DR is given by:

Where ω_{DR}^{2} = 1/L_{DR}C_{DR} is the untuned DR resonant frequency, L_{DR} being the equivalent DR inductance and C_{DR} being the equivalent DR capacitance, n is the turns ratio between the DR and the tuning circuit. Equation 1 shows the relationship of the tuned resonant frequency with the coupling n, the varactor capacitance, C_{v}, and the inductance of the tuning stub, L_{stub}.

**Designs of the Varactor-tuned DR Circuits for Analysis**

The final DRO is intended as a local oscillator in a spectrum analyzer, with the operating frequency specified as 3.6 GHz. The circuit was built on a RO4350B laminate, 20 mils thick, with a dielectric constant of 3.48. The microstrip lines characteristic impedance is Z_{0} = 50 Ω and the electrical length is λ/4 at 3.6 GHz, measured from the open end to the maximum coupling point to the DR, as marked by the dotted line. With the presence of these two coupling lines (ports 1 and 2), this configuration is identical to a narrow bandpass filter. The varactor was biased from a low noise voltage supply, where the narrow and winding V_{tune} bias line offers a high impedance at the microwave frequency, that is 3.6 GHz, so that it will not load the DR tuning circuit.

**Variation of the Tuning Stub Electrical Length**

The tuning stub length was varied arbitrarily; the lengths were set at λ/4 and Λ/2 at 3.6 GHz. For each variation, the V_{tune} was adjusted from 0 to 10 V at 1 V intervals and the resonant frequencies and the corresponding insertion loss (IL) were recorded. The results were compared for their tuning bandwidth and IL at resonant frequencies.

**Figure 5** Resonant frequency of the varactor-tuned DR circuit with different stub lengths.

**Figure 6** Insertion loss of the varactor-tuned DR circuit for different tuning stub lengths.

**Figures 5** and **6** show the resonant frequencies and ILs, respectively; the width of the tuning stub was kept at Z_{0} = 50 Ω. For the λ/4 stub length, the circuit ceased to resonate after V_{tune} = 6 V. Although λ/4 tuning stub gives wider tuning bandwidth, it is very nonlinear and beyond V_{tune} = 6 V, resonance ceases to exist, possibly because of a decrease in Q, due to strong coupling. Secondly, the IL is very high, from more than 4 dB and up to 14 dB. A nonlinear frequency tuning would complicate a PLL design and a high IL would demand a very high gain amplifier. On the contrary, the λ/2 tuning stub, though it gives a much smaller tuning bandwidth, offers an approximately linear tuning and a more consistent and very low IL across the tuning bandwidth.

**Figure 7** Resonant frequency of the varactor-tuned DR circuit with different stub impedances.

**Figure 8** Insertion loss of the varactor-tuned DR circuit for different stub impedances.

**Figure 9** H-field pattern for three DR circuits with different stub widths (a) Z_{o} = 28 Ω (b) Z_{o} = 34 Ω and (c) Z_{o} = 50 Ω.

### 3D EM Simulations of the Varactor-tuned DR Circuits

The varactor-tuned DR circuits with different tuning stub widths were simulated in a three-dimensional electromagnetic field (3D EM) simulator, using Agilent EMDS software, to understand how the K_{V} increases as the tuning stub width increases. The varactor-tuned DR circuit is more of a three-dimensional physical structure rather than a typical planar electrical circuit. To simulate it in a circuit simulator would be complicated considering the modeling of the cavity, the DR and its mounting, the electromagnetic field coupling and any other physical structure that may affect the resonance. As for the varactor, which is an active device, it can be modeled as a simple parallel plate capacitor shunted to ground. Its capacitance can be varied by changing the dielectric constant of the material in between the parallel plates. The DR resonates in the TE_{01δ} mode, so its magnetic field (H-field) is the one that couples to any microstrip lines on the circuit. Therefore, the 3D EM simulation was concentrating on the H-field distribution. In **Figure 9**, the H-field was observed on a vertical plane crossing the DR center marked by the dotted line shown in Figure 4. Note that the uniform circular lines are the input and output ports of the circuit.

The H-field pattern was monitored at the vertical plane that cuts across the center of the DR, the tuning stub and the microstrip lines, similar to that in Figure 3. In Figure 9, the H-field strength is displayed in two ways – first, by means of the contour lines, and secondly, by means of the color spectrum, with the red shade being the strongest H-field region and, following the rainbow colors sequence, dark blue is the weakest.

The simulation shows that the circuit with the widest stub (Z_{0} = 28 Ω) has the strongest H-field coupling between the DR and the tuning stub – the contour lines covering the widest region and stretching from the DR to the tuning stub. However, the H-field coupling to the microstrip is the weakest, with hardly noticeable contour lines. On the contrary, the circuit with the narrowest tuning stub of Z_{0} = 50 Ω, the H-field is the weakest in the vicinity of the DR and weak coupling to the tuning stub, but there are strong H-fields in the microstrip lines, indicating a strong signal.

Compared with the measurement results in Figures 7 and 8, there is a good correlation with the simulation. For the lowest Z_{0} tuning stub, where there is a strong H-field coupling between the DR and the tuning stub, the tuning bandwidth is the largest; it also has the highest IL at resonance. With the highest Z_{0} (50 Ω) tuning stub, where the simulation shows the weakest coupling between the DR and the tuning stub, the measurement shows it has the smallest tuning bandwidth. But on the other hand, it has the least IL at resonance as expected because the simulation shows strong H-field around the microstrip lines that couple the signal out to ports 1 and 2. This finding is summarized in **Table 1**.

**Figure 10** Final tunable DR circuit with only one port.

**Figure 11** Schematic of the circuit that generates the negative resistance.

### Implementation in DRO Circuit

**DRO Design**

Now that the varactor-tuned DR circuit has been characterized and the configuration that gives the biggest tuning bandwidth is identified, the DRO can be designed. The design is based on a negative resistance oscillator or a one-port oscillator. The strong H-field concentration around the DR and the tuning stub apparently reduces the H-field coupling to the microstrip, as can be seen in Figure 9a. Hence, the tunable DR circuit with tuning stub of Z_{0} = 28 Ω has a high IL, ~ 6 dB. To reduce this loss, the microstrip is slightly widened (to Z_{0} ≈ 37 Ω) to improve the field coupling between the DR and the microstrip. Only one microstrip line is used because it will be a one-port oscillator. The final varactor-tuned DR circuit is shown in **Figure 10** and the active device circuit, which is based on a Si bipolar transistor and provides the negative resistance, is shown in **Figure 11**. The varactor-tuned DR circuit is coupled at port 1. However, the negative resistance occurs over a wide frequency range and in this case more than 2.5 GHz wide. This will potentially cause instability within the range.^{11} The DR circuit and the active device were coupled together to form the DRO. When the DRO output was monitored, spurious signals were observed along with the DRO oscillation. A 50 Ω termination is then added to the open end of the λ/4 stub of the microstrip line that couples to the DR; this eliminated the spurs.^{13}

**Figure 12** Frequency sweep of the designed DRO showing a tuning bandwidth of 17 MHz.

**Figure 13** Phase noise of the DRO at 3.6 GHz with V_{tune} = 5 V.

**DRO Results**

At V_{tune} = 0 V, the oscillation frequency is f_{0V} = 3.591 GHz and at V_{tune} = 9 V, the oscillation frequency is f_{9V} = 3.608 GHz, giving a tuning bandwidth of 17 MHz or 0.47 percent. **Figure 12** shows the spectrum analyzer sweep of the DRO with V_{tune} swept from 0 to 9 V. The output power varies from approximately 0 dBm to about +4.5 dBm. The power is 16 dB lower, because the measurement was done using a directional coupler (16 dB coupling factor). The phase noise at 100 kHz, 1 MHz and 10 MHz offsets from the center frequency, is -125 dBc/Hz, -147 dBc/Hz and -161 dBc/Hz, respectively. This is shown in **Figure 13**. **Figure 14** shows the complete DRO. Notice that a 50 Ω resistor termination was added at the end of the λ/4 stub to eliminate spurs. The plastic screw holding the DR in place is also visible.

**Figure 14** Photograph of the complete DRO.

### Discussion and Conclusion

Experiments on a DR circuit excited in the TE_{01δ} resonant mode were carried out, with its tuning stub in circular shape. It is found that the tuning stub dimensions can affect the DR tuning range. A linear tuning pattern can be achieved by keeping the tuning stub electrical length at λ/2, and by reducing the tuning stub Z_{0}, that is increasing its width, the tuning bandwidth is increased. 3D EM simulation reveals that as the tuning stub width is increased, the H-field coupling between the DR and the tuning stub increases, which explains the increase in K_{V}. Based on this finding, a DR tuning method that offers wide tuning bandwidth for applications with a small varactor tuning range is proposed. The method is applied to a 3.6 GHz DRO that would be employed in a phase-locked local oscillator with a specified tuning voltage of 0 to 10 V. Comparing this circular tuning stub to the straight line tuning stub used by Yom,^{10} the circular tuning stub seems to yield a wider tuning range and higher K_{V}, that is 0.47 percent and 1.89 MHz/V, respectively, as opposed to 0.003 percent and 0.04 MHz/V.

### Acknowledgment

The authors would like to thank B.W. Law, A.K.H. Mokhtar, K.E. Loh, J.L. Lai and W.S. Lam for their technical help and support in materials procurement, DRO design and fabrication and also Universiti Kebangsaan Malaysia.

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**Amir Effendy Muhammad-Afifi** *received his bachelor's degree in electronic engineering from the University of Southampton, UK, in 1997. He is working toward his master's degree in electrical and electronic engineering at the Universiti Sains Malaysia. He joined Motorola Malaysia in 1997 as a Design and Development Engineer for two-way radios. In 2000, he joined Ericsson Mobile Communication, Malaysia, where he was in charge of Ericsson GSM cellular phones production as a Verification Engineer. In August 2001, he joined Agilent Technologies Malaysia in Penang as a Microwave Products Engineer, where he managed Agilent test and measurements of microwave circuit modules. Since 2006, he has worked as a Design and Development Engineer. He is involved in the design of YIG oscillator, dielectric resonator oscillator and microwave amplifier. He is also involved in product improvement for Agilent microwave circuit modules.*

**Widad Ismail** *graduated from the University of Huddersfield, UK, in 1999 and earned First Class Honors in electronics and communications engineering. She received her doctorate in electronics engineering from the University of Birmingham, UK, in 2004. She is a Senior Lecturer at the School of Electrical and Electronics Engineering, USM in Nibong Tebal, Penang, Malaysia. She has contributed extensively in research in the areas of radio frequency identification (RFID), active integrated antennas (AIA), RF systems and wireless systems design.*

**Jit Singh Mandeep** *received his bachelor's degree in engineering (with honors) and doctorate in electrical and electronic engineering from the University of Northumbria, UK, and Universiti Sains Malaysia in 1998 and 2006, respectively. From 2006 to June 2009, he was attached to Universiti Sains Malaysia as a Lecturer. Currently, he is attached to the Universiti Kebangsaan Malaysia as a Senior Lecturer. His areas of specialization are radiowave propagation in satellite communication system, radar, antenna design, RF and microwave.*