Low-Phase-Noise Oscillator Using a High-Q_L Resonator with Split-Ring Structure and Open-Loaded T-Type Stub for a Tumor-Location-Tracking Sensor

Abstract

Sensors in the medical field to detect specific tissues, such as radars, must provide accurate signals from frequency generators. In order to supply an accurate frequency signal, the oscillator must have a low phase noise. Therefore, the resonator used in the oscillator must provide a high Q_L. Therefore, in this paper, we have proposed a low-phase-noise X-band oscillator that used a resonator with a high value of Q_L as a sensor for tissue-locating applications. The resonator had a split-ring structure and consisted of an open-loaded, T-type stub with a high-Q_L; such high-Q_L levels were enabled by controlling the length of the open-circuit in the T-type stub. This led to the generation of only low-phase noise in the proposed oscillator. Experimental results showed that, at an operating frequency of 10.08 GHz, the output power was 18.66 dBm, the second harmonic suppression was −34.40 dBc, and the phase noise was −138.13 dBc/Hz at an offset of 100 kHz. This proposed oscillator can be used as a sensor to detect the location of tissues during laparoscopic surgery.

1. Introduction

The development of medical technology has seen rapid growth in the use of radio frequency (RF) applications in medical services [1]. Medical device systems that use microwaves are extensively employed in treatment and diagnostics [2,3,4,5,6]. In the former, they are used to treat inflammation and tumors, while in the latter, they aid in the detection of tissue-based substances, such as tumor cells, DNA, cortisol, and glucose [2,3,4,5,6]. Markers are substances that help to track the location of a tissue (such as a tumor) [1,7,8]. Since sensors work by generating electrical signals of the required frequency, oscillators are employed in marker sensors. The oscillator used by the sensor to supply the correct frequency signal must have low phase noise. A method for designing a low-phase-noise oscillator can be a resonator having a high Q_L for the oscillator. Therefore, the design of a resonator with a high Q_L is very important.

Dielectric resonators (DRs) are promising elements because of their high-Q_L characteristics. However, their three-dimensional (3-D) structures not only limit their implementation to system-on-chip (SoC) and integrated circuit (IC) systems, but also render them unsuitable for mass production [9,10].

Resonators with planar structures (microstrip lines) are being extensively studied, with a specific focus on increasing their Q_L. The representative microstrip-line resonator is a hairpin structure, which has a physical length of λ_g/2. While hairpin structures are easy to fabricate [11], their Q_L is too low in performance to apply them to an oscillator. To overcome this disadvantage, spiral resonators have been considered as an alternative. However, although they are small and have higher Q_L values, they are still insufficient for application in oscillators [11].

To further increase the Q_L, a substrate-integrated waveguide (SIW) structure and an open-loop resonator with a T-stub inserted into it were studied in 2014. An analysis of their characteristics showed significantly improved values of Q_L. The SIW structure is patch-shaped and the structural characteristics of its feeding-line part make the Q_L adjustable [12,13,14,15]. The Q_L is increased by virtue of the dual structure used in the state where the T-stub is applied [16]; however, it also has the undesired effect of enlarging the resonator. This increase in area means that applying it to the oscillator would hinder system integration.

A triangle-folded resonator with a coupled line has a smaller size, with a physical length of λ_g/4 [17]. Since resonators do not use vias, this one has excellent performance because there is no energy loss to the via. However, although this device enabled the oscillator to achieve a low phase noise, its Q_L was relatively low.

In this paper, a low-phase-noise oscillator with a high-Q_L resonator, using a combination of a split-ring structure and an open-loaded T-type stub, is presented. The resonator is a combination of a split-ring structure and an open-loaded T-type stub, where a high-Q_L characteristic can be obtained by adjusting the length of the open-loaded T-type stub. The characteristic of the resonator is the band-stop type of resonance (S₂₁). Owing to the sharp band-rejection characteristic of the new resonator, very low phase noise can be obtained for the oscillator. This design strives to obtain excellent performance so that it can be applied to tissue- and tumor-tracking sensors.

2. Tumor-Tracking Oscillator and Sensor

During laparoscopic surgery, tumors located inside the colon and stomach are difficult to locate in the cavity due to the peritoneum. This brings with it the risk of making incisions in the wrong locations during tumor extraction, which could lead to medical accidents. The X-band tissue search radar is also used to determine the location of the tumor, as shown in Figure 1 [18,19].

Radars utilize oscillators to generate detection frequencies; such oscillators require high-Q_L resonators and low phase noise. Existing resonator-based sensors used in tissue detection have Q_L values of at least 50, as shown in

Table 1. Resonator Q_L for tissue marker applications.

Reference	Resonant Frequency (GHz)	QL	Detection Tissue
[4]	11.2	100	cortisol
[5]	12.3	50	DNA
[6]	7.54	130	glucose

. However, when these resonators are applied to oscillators, the phase noise of the signal generated during abnormality detection does not easily drop below even −100 dBc/Hz at a 100 kHz offset [20,21]. Therefore, resonators with higher Q_L values are needed to further reduce the phase noise of oscillators; this need is amplified when considering the possibility of the generation of severe jitter noises on the radar, which would hinder the detection of the marker.

3. Design of a Resonator and Experimental Results

The proposed resonator is composed of a dual spilt-ring structure and an open-loaded T-type stub, as shown in Figure 2. From the figure, Z_ex and Z_in are the characteristic impedances of the external and internal split-ring structures, while Z_T and Z_s are those of the series transmission line and open-loaded stub in the T-type structure.

Z_p1 and Z_p2 are the characteristic impedances of the gaps represented by gap sizes g_ex and g_in, while Z_op is that of an open-loaded T-type stub. In addition, l_TH, I_TV, l_ex1, and l_ex2 are the physical lengths of the external split-ring structure, and l_in,m,n (m = 1 to 3, n = 4 to 5) refers to the set of physical lengths of the internal split-ring structure. l_T and l_s are the physical lengths of the series transmission line and open-loaded stub in the T-type structure, respectively. The symbols w_ex, w_in, w_T, and w_s denote the widths of the external and internal split-ring structures, the series transmission line, and the open-loaded stub in the T-type structure, respectively, while g_ex and g_in indicate the coupling gaps between the split-ring structures and the open-loaded T-type stub, respectively. θ_TH, θ_TV, θ_ex1, and θ_ex2 are the electrical lengths of the external split-ring resonator and θ_in,m,n (m = 1–3, n = 4–5) is that of the internal split-ring structure, while θ_T and θ_s are those of the series transmission line and open-loaded stub in the T-type structure. In the equivalent circuit depicted in Figure 2, L_ex and L_in,m,n (m: 1–3, n: 4–5) are the inductances of the external and internal split-ring structures. Then, 1/L_in can be expressed as 1/L_in + 1/L_in = L_in (for in for in, m: 1 to 3, n: 4 + 5). L_T and L_s are the inductances of the series transmission line and open-loaded stub, respectively, while C_ex, C_in, C_T, and C_S are the capacitances of the external and internal split-ring structures, the series transmission line, and the open-loaded stub, respectively. C_op is the mutual capacitance between the transmission line and the ground plane, with C_p1 and C_p2 being those of the coupling gap between the split-ring structure and the open-loaded T-type stub, respectively. Lastly, port 1 and port 2 are the input and output ports, and the characteristic impedance of the ports is 50 Ω, which is called the feeding-line in the resonator structure of Figure 2. Then, the gm is the gap size between the resonator and feeding line. The physical structure of C_p2 (see equivalent circuit) is carried out the same as with g_m.

To design the resonator, the capacitance is given by Equations (1)–(6), where t is the thickness (0.018 μm) of the transmission line at the substrate and ε₀ and ε_r are, respectively, the free-space and relative permittivity (ε₀ = 8.854 × 10⁻¹² F/m) [22]. N is the number of turns (N = 3) in the split-ring structure, while C_m, the parasitic capacitance of the dielectric in the substrate, equaling 0.423 μF [22]. Finally, A is the metal dimension of the substrate, while d is the distance between the metal and the ground in the substrate [22].

$$C_{ex}=\left[\left(l_{TH}+l_{TV}\right)+2\left(t+g_{ex}\right)\right]C_{op}\left[\frac{{\epsilon }_0\left(1+{\epsilon }_r\right)}{2}\right]$$

(1)

$$C_{in,m,n}={\sum }_{n=1}^{N-1}\frac{C_{ex}}{4}=\frac{N-1}{2}\left[2l_{in,m,n}-\left(2N-1\right)\left(t+g_{in}\right)\right]C_m\left[\frac{{\epsilon }_0\left(1+{\epsilon }_r\right)}{2}\right]@C_m=\frac{{\epsilon }_{r}A}{d}$$

(2)

$$C_{p1}=\left(l_{TH}+l_{TV}\right)g_{ex}+g_{in}\left[\frac{{\epsilon }_0\left(1+{\epsilon }_r\right)}{2}\right]$$

(3)

$$C_{p2}=\left(l_{in,m,n}t\right)g_{ex}+g_{in}\left[\frac{{\epsilon }_0\left(1+{\epsilon }_r\right)}{2}\right]$$

(4)

$$C_s=3.937\times {10}^{-5}{l}_T\left({\epsilon }_r+1\right)\left[0.11\left(N-3\right)+0.252\right]$$

(5)

$$C_{op}=3.937\times {10}^{-5}{l}_s\left({\epsilon }_r+1\right)$$

(6)

The inductance used in designing the resonator is given by Equations (7)–(10), where λ_g, the guided wavelength, was 18.8 mm [22].

$$L_{ex}=\left[2\left(l_{TH}+l_{TV}\right)\right]-g_{ex}-2w_{ex}$$

(7)

$$L_{in,m,n}=2l_{in,n}-g_{in}-2w_{in,m,n}$$

(8)

$$L_T=2\times {10}^{-4}{l}_T\left[lo{g}_{10}\left(\frac{l_T}{w_T+t}\right)\right]+1.193+0.2235\left[\left(\frac{w_T+t}{l_T}\right){\lambda }_g\right]$$

(9)

$$L_s=2\times {10}^{-4}{l}_s\left[lo{g}_{10}\left(\frac{l_s}{w_s+t}\right)\right]+1.193+0.2235\left[\left(\frac{w_s+t}{l_s}\right){\lambda }_g\right]$$

(10)

In the resonator design, the characteristic impedance was given by Equations (11)–(17), where ω_r is the resonant frequency, β is the phase constant, and Z₀ is the characteristic impedance (Z₀ = 50 Ω) [22].

$$Z_{ex}=\frac{1-{\omega }_r^{2}2C_{ex}}{j{\omega }_r{C}_{ex}}$$

(11)

$$Z_{in,m,n}=\frac{1-{\omega }_r^{2}2C_{in,m,n}}{j{\omega }_r{C}_{in},m,n}$$

(12)

$$Z_{p1}=\frac{Z_{ex}}{jsin{\beta }_1+l_{ex}}$$

(13)

$$Z_{p2}=\frac{Z_{in,m,n}}{jsin{\beta }_2+l_{in,m,n}}$$

(14)

$$Z_{op}=\frac{j{\omega }_r{L}_s}{1-{\omega }_r^2{L}_s\left(2C_{op}\right)}$$

(15)

$${\beta }_1={\omega }_r\sqrt{C_{p1}\left(L_{ex}+L_{in,m,n}\right)}$$

(16)

$${\beta }_2={\omega }_r\sqrt{C_{p2}\left(L_{ex}+L_{in}\right)}$$

(17)

Split−ring resonators generally have high-Q_L values [23]. In addition, the open-loaded T-type stub (Z_T and Z_S) operates similar to a band-stop-type resonator with a high Q_L, as shown in Figure 3. From the figure, θ_T and θ_S are 30° and 45°, respectively, at the resonant frequency [24]. Then, Z_T and Z_S can be solved using Equations (18) and (19) for θ_T.

$$Z_T=Z_{0}cot{\theta }_T$$

(18)

$$Z_S=Z_0\frac{co{s}^2{\theta }_T}{1-2si{n}^2{\theta }_T}$$

(19)

where Z₀ is characteristic impedance (50 Ω). Then, θ_T must be greater than 0° and less than 45° (2θ_T < θ_T = 90°). If θ_T is greater than 45° (θ_T < 90°), Z_S reaches infinity, as shown in Figure 3. For the shunt stub, −jZ_S cot θ_S = ∞; thus, the open-loaded T-type stub behaves similar to an open stub. Z_T and Z_S are 86.6 Ω and 75 Ω, and θ_T and θ_S are 30° and 45°, respectively.

The calculated values of the characteristic impedance, electrical, length, and physical length of the proposed resonator are listed in

Table 2. Parameters of the proposed resonator.

Parameter		Value	Unit	Parameter		Value	Unit
Capacitance	Cex	1.86	pF	Characteristic impedance	Zex	127	Ω
	Cin,m,n	9.72	pF		Zin,m,n	200	Ω
	Cp1	8.81	pF		Zp1	41.7	Ω
	Cp2	9.36	pF		Zp2	81.2	Ω
	CS	6.43	μF		Zop	4.17	Ω
	Cop	1.20	mF		ZT	86.6	Ω
Inductance	Lex	2.208	H		ZS	75.0	Ω
	Lin,m,n	4.43	H	Electrical length	θTH	49.59°	deg
	LT	11.0	mH		θTV	27.27°	deg
	LS	5.02	H		θex1	16.6°	deg
Physical length	lTH	3.00	mm		θex2	8.59°	deg
	lTV	1.65	mm		θin1	32.8°	deg
	lex1	1.00	mm		θin2	11.2°	deg
	lex2	0.52	mm		θin3	6.72°	deg
	lin1	2.05	mm		θin4	2.08°	deg
	lin2	0.70	mm		θin5	4.64°	deg
	lin3	0.42	mm		θT	30.0°	deg
	lin4	0.13	mm		θS	45.0°	deg
	lin5	0.29	mm	Physical width	wex	0.19	mm
	lt	0.84	mm		win,m,n	0.19	mm
	ls	0.86	mm		>wT	0.14	mm
Gap size	gex	0.13	mm		wS	0.13	mm
	gin	0.13	mm	Phase constant	β1	2.42	rad/m
					β2	2.493	rad/m

.

When the open-loaded T-type stub is directly connected to the split-ring resonator, the Q_L of the resonator is greatly increased. Figure 4 shows the results of the simulation of the Q_L of the split-ring resonator (single), open-loaded T-type stub, and integrated split-ring resonator (single) with an open-loaded T-type stub. From the figure, the Q_L values of the split-ring resonator (single), open-loaded T-type stub, and integrated split-ring resonator (single) with the open-loaded T-type stub were 206 (S₂₁: 24.8 dB), 322 (S₂₁: 37.4 dB), and 323 (S₂₁: 56.6 dB), respectively.

In the open-loaded T-type stub of the proposed resonator, the Q_L started to change according to the tuning of the stub length. When the proposed resonator was designed by integrating the open-loaded T-type stub into the split-ring resonator, the Q_L was 333, as shown in Figure 5, and the length of the stub was 0.82 mm. However, if the stub length is tuned, Q_L varies. For example, the Q_L increases (from 83.0 to 583) in the stub length range of 0.78 mm to 0.86 mm, and it gradually decreases (from 500 to 98.7) thereafter.

The fabrication of the proposed resonator is shown in Figure 6. Specifically, the fabricated resonator employs a Teflon substrate with a low dielectric constant of 2.54, height of 0.54 mm, and thickness (t) of 0.018 μm, and the size of the resonator is 3.0 mm × 1.65 mm. The simulated value of Q_L is 683 at 10.0 GHz for this resonator, and the measured result is 632 at 10.008 GHz.

4. Oscillator Design and Measurement Results

In this study, a low-phase-noise X-band oscillator was designed using a new high-Q_L resonator, as shown in Figure 7. As shown in the figure, an oscillator was used for the series feedback structure and self-bias method, and the series feedback at the source was chosen as an oscillator, which provides the negative resistance (−R) to the gate of a GaAs-MESFET.

The oscillator is composed of a λ_g/4 transmission line (microstrip line) and a radial stub for a DC-bias circuit providing RF power to a wideband open-loaded circuit. The proposed high-Q_L resonator is connected to the gate (G) of the GaAs-MESFET. V_D, R_D, and Rg are the drain (D) bias voltage and drain (D) resistance; further, R_S and C_S are the source (S) resistance and source capacitance, respectively.

L_D and L_S are the RF-chock (RFC) in the drain (D) and source (S), respectively. Radial stubs are the RFC circuits in the drain (D) and source (S) loads. The gate (G) bias is self-biased, and a capacitor (C_{_by}) is used only for by-pass C for the bias. The fabricated oscillator was used as the Teflon substrate, and the dielectric constant (ε_r), height (h), and thickness (t) of the Teflon substrate were 2.55, 0.54 mm, and 0.018 mm. The fabrication was performed by wet etching, which is used for negative film development.

The measurement results of the new oscillator are shown in Figure 8, in which the oscillation frequency is 10 GHz. The phase noise of the oscillator is observed to be −138.13 dBc/Hz at an offset frequency of 100 kHz. Thus, the Q_L of the resonator has a considerable effect on the phase noise performance of the oscillator. Additionally, the output power and amount of second harmonic suppression for the X-band oscillator are 18.66 dBm and −34.40 dBc under bias conditions of V_DS = 3 V and I_D = 40 mA, respectively. The figure of merit (FOM) is given by Equation (20), which is −195.7 dBc/Hz at a 100 kHz offset, where the L{f_offset} is the phase noise in the dBc/Hz at the offset frequency, and f_offset is from the carrier (oscillation) frequency, f₀. P_DC is the DC power dissipation in mW [13].

$$\mathrm{FOM}=-20log\left(\frac{f_0}{f_{offset}}\right)+L\left\{f_{offset}\right\}+10log\left(\frac{P_{\mathrm{DC}}}{1\mathrm{mW}}\right)$$

(20)

An Agilent E4440A PSA series spectrum analyzer was used to measure the oscillations. The phase noise and output power of the fabricated oscillator were compared with those of oscillators developed in previous studies, as shown in

Table 3. Comparison between the parameters of the proposed oscillator and those of oscillators developed in previous studies.

Reference	Frequency (GHz)	Phase Noise (dBc/Hz) at 100 kHz	Output Power (dBm)	QL	FOM (dBc/Hz) at 100 kHz
This work	10.08	−138.13	18.66	632	−195.7
[10]	10.98	−121.6	1.800	−	−182.3
[11]	10.00	−95.40	10.16	190	−135.3
[12]	9.883	−97.60	3.020	260	−182.2
[13]	9.010	−104.3	1.800	104	−104.3
[14]	10.11	−108.7	4.600	520	−172.2
[15]	9.850	−124.8	3.600	243	−189.1
[16]	6.200	−104.62	14.68	430	−156.2
[17]	9.960	−128.30 (@ 1 MHz)	8.570	66.7	−193.2 (@ 1 MHz)
[20]	8.080	−109.94	2.140	−	−174.2
[21]	8.172	−112.0	4.000	−	−174.2

Offset frequency: 100 MHz [17].

.

5. Conclusions

In order to find the location of the marker, the existing method uses radiography-based fluoroscopic radiography to find the location through images [25]. However, the fluoroscopic radiography is large and heavy. In addition, fluoroscopic radiography has a high unit price. Therefore, the heavy size will induce difficulty in performing surgery. However, sensors to find markers are low in unit price and light in weight; the sensor is also small in size. Therefore, it is easy to handle during surgery. The most important thing in these sensors is the oscillator. Since the oscillator has a very low phase noise, it is considered to have excellent performance.

The designed oscillator consists of a plane shape. The resonator has an open structure, and this resonator has not applied a via design method. Therefore, the resonator has a high loaded quality factor (Q_L) because there is no loss of concentration of via energy [26,27]. When applying the proposed oscillator to a sensor, if the amplifier is connected, it can be used as a radar-based sensor with high performance, which would be very useful in finding markers installed on tumors. The reason is that markers are made of metal. When a signal generated from the oscillator is reflected through a metal marker, the sensor may detect a reflected signal to locate the tumor. Therefore, it will be important that the performance of the sensor to locate the tumor suppress the phase noise of the oscillator.

In this paper, a low-phase-noise-X-band oscillator with a high-Q_L resonator using an open-loaded T-type stub and split-ring structure is presented. The proposed oscillator has a high Q_L and low phase noise because it is a resonator in which an open-loaded T-type stub and a split-ring structure are combined. The proposed oscillator can increase the Q_L of a resonator by adjusting the length of an open-loaded T-type stub; thus, the phase noise of the oscillator can be sufficiently reduced. In addition, the resonator is very small. The oscillator has a high output power and can perform second harmonic suppression. The measurement results indicate that an output power of 18.66 dBm and second harmonic suppression of −34.40 dBc (at 13.26 GHz) can be realized. At an operating frequency of 10.084 GHz, the phase noise is −138.13 dBc/Hz at a 100 kHz offset. This low-phase-noise X-band oscillator can be fabricated with a monolithic microwave integrated circuit (MMIC) technique, owing to its entirely planar structure. It can be applied to sensors to detect the location of tissues during laparoscopic surgery.