Transmission line module for rotary traveling wave oscillator and design method thereof

Abstract

Provided are a transmission line module for a rotary traveling wave oscillator (RTWO) and a design method thereof. The transmission line module includes a substrate. The upper surface of the substrate is provided with a grounding metal layer, that is, a metal ground. The metal ground is provided with a rectangular groove. The rectangular groove penetrates front and rear sides of the metal ground along a length direction of the rectangular groove. The thickness of the rectangular groove is the same as the thickness of the metal ground. The rectangular groove is filled with a silicon dielectric plate that has the same shape and size as the rectangular groove. The upper surface of the silicon dielectric plate is provided with two parallel transmission lines along the length direction of the rectangular groove.

Claims

1. A design method of a transmission line module for a rotary traveling wave oscillator (RTWO), wherein the design method the following steps: S1: determining a length λ=u/f of one wavelength of a transmission line based on a frequency f required for the RTWO, wherein u is a wave propagation speed in the transmission line; and setting a total length of the transmission line to vary around the length λ of one wavelength; S2: assuming that the transmission line forms a Möbius strip, and dividing the total length of the transmission line by a phase number K required for the RTWO, to obtain transmission line modules each having a length l=λ/K; S3: assuming a width of each transmission line in any of the transmission line modules as W.sub.T, spacing between two transmission lines as S.sub.T, and spacing between two metal grounds obtained after cutting the rectangular groove as S.sub.M, wherein each transmission line module comprises two parallel transmission lines, and S.sub.M is a width of the rectangular groove provided on the metal ground; S4: initializing S.sub.M to zero, initializing the spacing S.sub.T between the transmission lines to S.sub.T0, and initializing the width W.sub.T of the transmission line to W.sub.T0, wherein S.sub.T0 and W.sub.T0 are preset initial parameters and respectively indicate a minimum value of the spacing between the transmission lines and a maximum value of the width of the transmission line; setting a step ΔS.sub.M, keeping the spacing S.sub.T between the transmission lines at S.sub.T0 and the width W.sub.T of the transmission line to W.sub.T0, increasing S.sub.M from 0 by the step ΔS.sub.M each time, performing electromagnetic field simulation on the transmission line module at different S.sub.M, to obtain resistance-inductance-conductance-capacitance (RLGC) parameters of the transmission line module, and calculating a quality factor Q.sub.lump of the transmission line at the different S.sub.M; and selecting a value of S.sub.M as final spacing between the metal grounds when S.sub.M increases without a significant increase in the quality factor Q.sub.lump of the transmission line, wherein the significant increase indicates that an increased value of Q.sub.lump is smaller than a preset threshold; S5: setting a step ΔS.sub.T, keeping the width W.sub.T of the transmission line at W.sub.T0, and keeping the spacing S.sub.M between the metal grounds at the value obtained in step S4; increasing S.sub.T from S.sub.T0 by the step ΔS.sub.T each time, performing the electromagnetic field simulation on the transmission line module at different S.sub.T, to obtain the RLGC parameters of the transmission line module, and calculating the quality factor Q.sub.lump of the transmission line at the different S.sub.T; and until Q.sub.lump deteriorates as S.sub.T increases, selecting a value of S.sub.T corresponding to the highest Q.sub.lump as the final spacing between the transmission lines, wherein Q.sub.lump deteriorating means that Q.sub.lump becomes smaller; and S6: setting a step ΔW.sub.T, keeping the spacing S.sub.M between the metal grounds at the value obtained in step S4, and keeping the spacing S.sub.T between the transmission lines at the value obtained in step S5; decreasing W.sub.T from W.sub.T0 by the step ΔW.sub.T each time, performing the electromagnetic field simulation on the transmission line module at different W.sub.T, to obtain the RLGC parameters of the transmission line module, and calculating the quality factor Q.sub.lump of the transmission line at the different W.sub.T; and until Q.sub.lump deteriorates as W.sub.T decreases, selecting W.sub.T corresponding to the highest Q.sub.lump as the final width of the transmission line, wherein Q.sub.lump deteriorating means that Q.sub.lump becomes smaller.

2. The design method according to claim 1, wherein the design method further comprises step S7: for each transmission line module in the Möbius strip, setting the width W.sub.T of the transmission line, the spacing S.sub.T between the transmission lines, and the spacing S.sub.M between the metal grounds according to data obtained in steps S4 to S6.

3. The design method according to claim 1, wherein the step of setting the total length of the transmission line to vary around the length of one wavelength comprises: keeping an absolute value of a difference between the total length of the transmission line and λ within a preset threshold.

4. The design method according to claim 1, wherein the phase number K is 8, 16, or 32.

5. The design method according to claim 1, wherein the quality factor Q.sub.lump of the transmission line is calculated as follows: calculating a propagation constant of the transmission line:
γ=α+jβ, wherein γ is the propagation constant of the transmission line, α is an attenuation constant of the transmission line, and β is a phase propagation constant of the transmission line; representing the propagation constant γ of the transmission line by using the following formula and the RLGC parameters:
γ=√{square root over ((R+jωL)(G+jωC))}, wherein R indicates a resistance per unit length, L indicates an inductance per unit length, G indicates a conductance per unit length, and C indicates a capacitance per unit length; determining an input impedance Z.sub.in of the transmission line module: $Z_{\mathrm{in}}=\sqrt{\frac{{\omega }^2\mathrm{LC}+j\omega \left(\mathrm{LG}-\mathrm{CR}\right)}{G^2+{\omega }^2{C}^2}}\frac{e^{4\alpha l}-1+2e^{2\alpha l}\sin \left(2\beta l\right)}{e^{4\alpha l}+2e^{2\alpha l}\cos \left(2\beta l\right)+1},$ wherein ω=2πf, f is an operating frequency, and l is the total length of the transmission line; and calculating the quality factor of the transmission line by the following formula: $Q_{\mathrm{lump}}=\frac{\mathrm{im}\left(Z_{\mathrm{in}}\right)}{\mathrm{re}\left(Z_{\mathrm{in}}\right)},$ simplified as: $Q_{\mathrm{lump}}\frac{\mathrm{im}\left(Z_{\mathrm{in}}\right)}{\mathrm{re}\left(Z_{in}\right)}=\frac{\beta }{\alpha }-\frac{\frac{\beta }{\alpha }+\frac{\alpha }{\beta }}{\frac{\alpha }{\beta }\sqrt{1+{\xi }^2}+\xi +1},$ wherein $\xi =\frac{\omega }{R/L-G/C}.$

6. A transmission line module for a rotary traveling wave oscillator (RTWO) using the design method according to claim 1, comprising a substrate, wherein an upper surface of the substrate is provided with a grounding metal layer, and the grounding metal layer is a metal ground; and the metal ground is provided with a rectangular groove, the rectangular groove penetrates front and rear sides of the metal ground along a length direction of the rectangular groove, a thickness of the rectangular groove is the same as a thickness of the metal ground, the rectangular groove is filled with a silicon dielectric plate, the silicon dielectric plate has a same shape and size as the rectangular groove, and an upper surface of the silicon dielectric plate is provided with two parallel transmission lines along the length direction of the rectangular groove.

7. The transmission line module according to claim 6, wherein the two parallel transmission lines are rectangular transmission lines.

8. The transmission line module according to claim 6, wherein a width of each of the two parallel transmission lines is shorter than one-half of a width of the rectangular groove.

9. The transmission line module according to claim 6, wherein the design method further comprises step S7: for each transmission line module in the Möbius strip, setting the width W.sub.T of the transmission line, the spacing S.sub.T between the transmission lines, and the spacing S.sub.M between the metal grounds according to data obtained in steps S4 to S6.

10. The transmission line module according to claim 6, wherein in the design method, the step of setting the total length of the transmission line to vary around the length of one wavelength comprises: keeping an absolute value of a difference between the total length of the transmission line and λ within a preset threshold.

11. The transmission line module according to claim 6, in the design method, wherein the phase number K is 8, 16, or 32.

12. The transmission line module according to claim 6, in the design method, wherein the quality factor Q.sub.lump of the transmission line is calculated as follows: calculating a propagation constant of the transmission line:
γ=α+jβ, wherein γ is the propagation constant of the transmission line, α is an attenuation constant of the transmission line, and β is a phase propagation constant of the transmission line; representing the propagation constant γ of the transmission line by using the following formula and the RLGC parameters:
γ=√{square root over ((R+jωL)(G+jωC))}, wherein R indicates a resistance per unit length, L indicates an inductance per unit length, G indicates a conductance per unit length, and C indicates a capacitance per unit length; determining an input impedance Z.sub.in of the transmission line module: $Z_{\mathrm{in}}=\sqrt{\frac{{\omega }^2\mathrm{LC}+j\omega \left(\mathrm{LG}-\mathrm{CR}\right)}{G^2+{\omega }^2{C}^2}}\frac{e^{4\alpha l}-1+2e^{2\alpha l}\sin \left(2\beta l\right)}{e^{4\alpha l}+2e^{2\alpha l}\cos \left(2\beta l\right)+1},$ wherein w=2πf, f is an operating frequency, and l is the total length of the transmission line; and calculating the quality factor of the transmission line by the following formula: $Q_{\mathrm{lump}}=\frac{\mathrm{im}\left(Z_{\mathrm{in}}\right)}{\mathrm{re}\left(Z_{\mathrm{in}}\right)},$ simplified as: $Q_{\mathrm{lump}}=\frac{\mathrm{im}\left(Z_{\mathrm{in}}\right)}{\mathrm{re}\left(Z_{\mathrm{in}}\right)}=\frac{\beta }{\alpha }-\frac{\frac{\beta }{\alpha }+\frac{\alpha }{\beta }}{\frac{\alpha }{\beta }\sqrt{1+{\xi }^2}+\xi +1},$ wherein $\xi =\frac{\omega }{R/L-G/C}.$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of a structure of the present disclosure.

(2) FIG. 2 is a schematic diagram of a structure of a conventional transmission line module.

(3) FIG. 3 is a simulation graph showing a relationship among parameters R, G, and S.sub.M according to an embodiment.

(4) FIG. 4 is a simulation graph showing a relationship among parameters L, C, and S.sub.M according to an embodiment.

(5) FIG. 5 is a simulation graph showing a relationship among parameters Q.sub.dis, Q.sub.lump, and S.sub.M under simulation according to an embodiment.

(6) FIG. 6 is a simulation graph showing a relationship between a frequency and normalized quality factors of a conventional transmission line and a 140 um differential transmission line according to an embodiment.

(7) FIGS. 7A-7D are four schematic diagrams showing connection modes of the transmission lines consisting of Möbius strips according to an embodiment.

(8) FIG. 8 is a circuit structural diagram of an RTWO designed according to the present application.

(9) Reference numerals: 1—substrate, 2—metal ground, 3—rectangular groove, and 4—transmission line.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(10) The technical solutions of the present disclosure are described in further detail below with reference to the accompanying drawings, but the protection scope of the present disclosure is not limited thereto.

(11) As shown in FIG. 1, a transmission line module for an RTWO includes the substrate 1, where an upper surface of the substrate 1 is provided with a grounding metal layer, that is, the metal ground 2.

(12) The metal ground 2 is provided with the rectangular groove 3, which penetrates front and rear sides of the metal ground 2 along the length direction of the rectangular groove 3. The thickness of the rectangular groove 3 is the same as the thickness of the metal ground 2. The rectangular groove 3 is filled with a silicon dielectric plate that has the same shape and size as the rectangular groove 3. An upper surface of the silicon dielectric plate is provided with the two parallel transmission lines 4 along the length direction of the rectangular groove 3.

(13) In this embodiment of the present application, the transmission lines 4 are rectangular transmission lines, and the width of either of the transmission lines 4 is smaller than one-half of the width of the rectangular groove 3.

(14) A design method of a transmission line module for an RTWO includes the following steps:

(15) S1: Determine the length λ=u/f of one wavelength of an entire transmission line based on a frequency f required for the RTWO, where u is the wave propagation speed in the transmission line, and set the total length of the transmission line to vary around the length λ of one wavelength.

(16) The setting of the total length of the transmission line to vary around the length of one wavelength means that an absolute value of the difference between the length of the transmission line and λ does not exceed a specified threshold.

(17) S2: Assume that the entire transmission line forms a Möbius strip and divide the total length of the transmission line by a phase number K required for the RTWO to obtain transmission line modules each having a length l=λ/K, where the phase number K is 8, 16, or 32.

(18) S3: Assume the width of each transmission line in any of the transmission line modules as W.sub.T, spacing between two transmission lines as S.sub.T, and the width of a rectangular groove provided on a metal ground, that is, spacing between two metal grounds obtained after cutting the rectangular groove, as S.sub.M.

(19) S4: Initialize S.sub.M to zero, initialize the spacing S.sub.T between the transmission lines to S.sub.T0, and initialize the width W.sub.T of the transmission line to W.sub.T0, where S.sub.T0 and W.sub.T0 are preset initial parameters and respectively indicate the minimum value of the spacing between the transmission lines and the maximum value of the width of the transmission line;

(20) set a step ΔS.sub.M, keep the spacing S.sub.T between the transmission lines at S.sub.T0 and the width W.sub.T of the transmission line at W.sub.T0, increase S.sub.M from 0 by the step ΔS.sub.M each time, perform electromagnetic field simulation on the transmission line module at different S.sub.M to obtain resistance-inductance-conductance-capacitance (RLGC) parameters of the transmission line module, and calculate a quality factor Q.sub.lump of the transmission line at different S.sub.M; and

(21) select a value of S.sub.M as the final spacing S.sub.M between the metal grounds when S.sub.M increases without a significant increase in the quality factor Q.sub.lump of the transmission line, where the significant increase means that an increased value of Q.sub.lump is smaller than a specified threshold.

(22) S5: Set a step ΔS.sub.T, keep the width W.sub.T of the transmission line at W.sub.T0, and keep the spacing S.sub.M between the metal grounds at the value obtained in step S4;

(23) increase S.sub.T from S.sub.T0 by the step ΔS.sub.T each time, perform electromagnetic field simulation on the transmission line module at different S.sub.T to obtain the RLGC parameters of the transmission line module, and calculate the quality factor Q.sub.lump of the transmission line at different S.sub.T; and

(24) until Q.sub.lump deteriorates as S.sub.T increases, select S.sub.T corresponding to the highest Q.sub.lump as the final spacing between the transmission lines, where Q.sub.lump deteriorates means that Q.sub.lump becomes smaller.

(25) S6: Set a step ΔW.sub.T, keep the spacing S.sub.M between the metal grounds at the value obtained in step S4, and keep the spacing S.sub.T between the transmission lines at the value obtained in step S5;

(26) decrease W.sub.T from W.sub.T0 by the step ΔW.sub.T each time, perform electromagnetic field simulation on the transmission line module at different W.sub.T to obtain the RLGC parameters of the transmission line module, and calculate the quality factor Q.sub.lump of the transmission line at different W.sub.T; and

(27) until Q.sub.lump deteriorates as W.sub.T decreases, select W.sub.T corresponding to the highest Q.sub.lump as the final width of the transmission line, where Q.sub.lump deteriorates means that Q.sub.lump becomes smaller.

(28) The design method further includes step S7:

(29) For each transmission line module in the Möbius strip, set the width W.sub.T of the transmission line, the spacing S.sub.T between the transmission lines, and the spacing S.sub.M between the metal grounds according to the data obtained in steps S4 to S6.

(30) The quality factor Q.sub.lump of the transmission line module is calculated as follows:

(31) calculating a propagation constant of the transmission line:
γ=α+jβ

(32) where γ is the propagation constant of the transmission line, α is the attenuation constant of the transmission line, and β is the phase propagation constant of the transmission line;

(33) representing the propagation constant γ of the transmission line by using the following formula and the RLGC parameters, where R indicates a resistance per unit length, L indicates an inductance per unit length, G indicates a conductance per unit length, and C indicates a capacitance per unit length:
γ=√{square root over ((R+jωL)(G+jωC))}

(34) determining an input impedance Z.sub.in of the transmission line module:

(35) $Z_{in}=\sqrt{\frac{{\omega }^{2}LC+j\omega \left(LG-CR\right)}{G^2+{\omega }^2{C}^2}}\frac{e^{4\alpha l}-1+j2e^{2\alpha l}\sin \left(2\beta l\right)}{e^{4\alpha l}+2e^{2\alpha l}\cos \left(2\beta l\right)+1}$

(36) where ω=2πf, f is an operating frequency, and l is the length of the transmission line; and

(37) calculating the quality factor of the transmission line module by

(38) $Q_{l\mathrm{ump}}=\frac{\mathrm{im}\left(Z_{in}\right)}{\mathrm{re}\left(Z_{in}\right)},$
which is simplified as:

(39) $Q_{\mathrm{lump}}=\frac{\mathrm{im}\left(Z_{in}\right)}{\mathrm{re}\left(Z_{in}\right)}=\frac{\beta }{\alpha }-\frac{\frac{\beta }{a}+\frac{a}{\beta }}{\frac{\alpha }{\beta }\sqrt{1+{\xi }^2}+\xi +1},\mathrm{where}\xi =\frac{\omega }{R/L-G/C}.$

(40) FIG. 2 is a schematic diagram of a principle of a conventional transmission line module. As can be seen, compared with the conventional transmission line module, the present application removes metal directly below and on two sides of the transmission line, such that the parasitic capacitance between the transmission line and the ground is smaller. With 8 um-wide transmission lines, RLGC parameters of the conventional transmission line module obtained through electromagnetic simulation are R=4650 Ω/m, L=270 nH/m, G=0.25 S/m, and C=150 pF/m, while RLGC parameters of the present application are R=5000 Ω/m, L=476 nH/m, G=0.75 S/m, and C=90 pF/m. It indicates that compared with the conventional structure, the transmission line used in this design significantly increases the values of L and G and decreases the value of C, such that a difference between R/L and G/C is smaller, thereby obtaining a transmission line module with a higher quality factor in the lumped model.

(41) In addition, in the present application, the RLGC parameters of the transmission line can be adjusted by changing the spacing S.sub.M between the two transmission lines. In an embodiment of the present application, the simulation results are shown in FIG. 3 to FIG. 6. FIG. 3 and FIG. 4 show that when the spacing S.sub.M between the differential transmission lines increases, G and L also increase and C decreases, thereby achieving a higher quality factor of the transmission line. For example, the differential transmission line is 140 um long and 8 um wide. FIG. 5 shows that when the spacing S.sub.M is changed, Q.sub.dis changes less, but the quality factor Q.sub.lump in the lumped model can be significantly optimized. As shown in FIG. 6, at 30 GHz, the optimized quality factor Q.sub.lump of the transmission line can reach 1.67 times of the conventional structure.

(42) As shown in FIGS. 7A-7D, in an embodiment of the present application, a Möbius strip can be formed with the transmission line by using any of the four structures (a) to (d), where the adjacent parallel differential transmission lines on each side of the Möbius strip should satisfy the values of W.sub.T, S.sub.T, and S.sub.M. The corners of the Möbius strip may alternatively be obtuse angles of 135 degrees, rather than right angles. The metal ground inside the Möbius strip may or may not be connected to the external metal ground, and the metal ground inside the Möbius strip may alternatively be removed after the design of the Möbius strip and the metal ground is completed.

(43) In an embodiment of the present application, inverters may be connected to the Möbius strip to form an RTWO. FIG. 8 is a structural diagram of the RTWO designed according to this embodiment. The oscillator uses a total of eight pairs of inverters and can output 16 different phases. The transmission line module of the present disclosure removes the metal under the transmission line to achieve a higher quality factor of the transmission line, thereby lowering the oscillator phase noise. The RTWO can operate between 24.34 GHz and 27.54 GHz with a tuning range of 12.3%. When the RTWO is tuned to 27.54 GHz, the measured phase noise is −124.54 dBc/Hz, corresponding to a FOM of 186.7 dBc/Hz. The chip has a power consumption of 4.6 mW and a supply voltage of 0.74 V, showing advantages in low-power applications. Tests show that the chip can still operate at a power consumption of 2.7 mW and maintain an optimal FoM of 184.6 dBc/Hz @10 MHz.

(44) Table 1 summarizes the performance parameters of recent RTWOs and multi-phase LC oscillators and shows by comparison that the RTWO formed by the transmission line in the present application consumes the least power while has a leading FoM among multi-phase oscillators in the millimeter wave band. When using the same CMOS 65 nm process, the design can improve the FoM by more than 3 dB compared with the conventional RTWO and has performance comparable to the design implemented by the more advanced 22 nm FDI-SOI process. Due to the optimized quality factor Q of the transmission line, the design achieves the highest FoM.sub.P of 198.7 dBc/Hz.

(45) TABLE-US-00001 The design of the present disclosure JSSC′18 JSSC′14 JSSC′18 JSSC′15 JSSC′11 JSSC′21 Topology RTWO RTWO RTWO Multi-phase Multi-phase Multi-phase RTWO VCO VCO VCO Process 65 nm 28 nm 65 nm 65 nm 40 nm LP 40 nm LP 22 nm FDI- SOI Frequency 24.3-27.5 16.1-19.8 51.9-56.5 74.8-79 21.4-25.1 48.6-52 21.4-25.1 (GHz) Tuning range 12.3% 20.6% 8.5% 5.5% 15.9% 6.8% 13.5% Supply voltage 0.74 1.3 1.2 1 1 0.8 0.8 (V) Power 4.6 75 36 13 23 35 21 consumption (mW) Phase noise −124.5 −132.8 −125 −116.5 −119 −127.8 −128.9 (dBc/Hz) @ 10 MHz FoM (dBc/Hz) 186.7 179.5 183.7 183 172 186.4 185.4 @ 10 MHz Phase number 16 16 4 8 8 8 16 FoM.sub.T 188.5 185.7 182.3 177.8 176 183 188.1 (dBc/Hz) FoM.sub.P 198.7 191.5 189.7 192 181 195.4 197.5 (dBc/Hz) Core area 0.12 0.38 0.1 0.3 0.063 0.09 0.24 (mm.sup.2)

(46) FoM=|phase noise|+20 log.sub.10(operating frequency/offset frequency)−10 log.sub.10(power consumption/1 mW), FoM.sub.T=FoM+20 log.sub.10(tuning range/10%), and FoM.sub.P=FoM+10 log.sub.10(phase number).

(47) The above explanation shows and describes several preferred embodiments of the present disclosure. But as mentioned above, it should be understood that the present disclosure is not limited to the form disclosed herein, and the explanation should not be regarded as an exclusion of other embodiments. Various combinations and modifications can be achieved through the above guides and technologies or knowledge in related fields within the scope of the concept of the present disclosure described herein. Modifications and changes made by those skilled in the art without departing from the spirit and scope of the present disclosure should fall within the protection scope of the appended claims of the present disclosure.