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Pei Qin, Quan Xue, Wenquan Che
The rapid development of wireless communications, software-defined radios, and ultrawideband (UWB) engenders an ever-increasing demand for clock generators that fully covers multiple frequency bands [1], [2], [3]. As the “heartbeat” that pumps clock generators, such as phase-locked loops (PLLs), microwave oscillators with wideband frequency tuning range (TR) are thus attracting a great deal of research interest.
LC oscillators are well known for their superior phase noise over ring oscillators and their other counterparts due to the sufficiently high quality factor (Q) of the LC tank. Therefore, LC oscillators are often selected as optimal architectures in applications such as base stations and cellular phones.
Conventional single-mode LC oscillators, which adjust their resonant frequencies merely by capacitive tuning through switched capacitors or varactors, often suffer from relatively small frequency-tuning capability as the increased variability in frequencies normally leads to deteriorated phase noise due to the degraded Q of the LC tanks. The TR of an LC oscillator with capacitive tuning can be represented as \[{TR} = {2}\frac{\sqrt{{\text{C}}_{p} + {C}_{\max}}{-}\sqrt{{\text{C}}_{p} + {C}_{\min}}}{\sqrt{{\text{C}}_{p} + {C}_{\max}} + \sqrt{{\text{C}}_{p} + {C}_{\min}}} \tag{1} \] where ${\text{C}}_{\text{p}}$ refers to the parasitic capacitance from the cross-coupled pairs, and ${C}_{\max}$ and ${C}_{\min}$ correspond to the maximum and minimum capacitances from the tuning capacitors.
Due to its limited on-off capacitance ratio $({C}_{\max}/{C}_{\min}),$ a single-mode LC oscillator normally covers a maximum frequency TR of around 40% in advanced CMOS nodes [4], [5], [6], [7], [8], [9], [10]. Considering the frequency fluctuations under process-voltage-temperature conditions and the frequency overlap margins when switching among different oscillators, the actual applicable frequency TR for a single-mode LC oscillator could be only around 20%. This TR is far from enough for those oscillators to cover the multiple bands in wireless communications, software-defined radios, or UWB. In wireless communication systems, to satisfy multiple communication standards, the one-octave band is normally required for oscillators. The one-octave band can easily synthesize all frequencies below those directly generated by the oscillators, thus covering all the required bands.
A conventional solution for realizing such a wideband TR is to employ multiple oscillators, as exemplified in Figure 1, where four oscillators are alternately switched on to realize the specific frequencies for different bands. Yet this clock configuration causes many adverse effects on the chip size, cost, power consumption, and design complexity of peripheral circuits, such as output buffers, clock distributions, control circuits, and power supplies. The optimal solution would achieve a wide-frequency TR using only one oscillator. However, it is extremely challenging to obtain wideband TR relying solely on conventional single-mode LC oscillators.
Figure 1. A conventional solution with four oscillators versus an optimal solution with one oscillator covering a one-octave band in all-digital PLLs. DIV: divider; MUX: multiplexer; FCW: frequency control word; OSC: oscillator; CKO: clock output; TDC: time to digital converter; DIG: digital; Fref: reference frequency; Ckin: clock in; CLKP/N: clock P/N.
Multimode switching techniques can greatly expand the frequency coverage for microwave LC oscillators by introducing more resonant modes; thus, they are good options for the realization of wideband oscillators. Therefore, this article aims to present multimode switching design techniques for microwave LC oscillators to extend their frequency TR and provide researchers interested in this domain with a comprehensive understanding of various aspects of these techniques.
There are several techniques that have been proposed in the literature to realize multimode switching for microwave LC oscillators [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56]. These techniques can be broadly classified into four methods: inductor switching (IS) [11], [12], [13], [14], [15]; transformer-loaded switching (TLS) [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]; multicore switching (MS) [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41]; and multimode resonance switching (MRS) [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56].
IS realizes a variable inductor by switching over its inductor segments, thus adjusting the resonant frequency of the oscillator. TLS makes use of the different loadings in the secondary coils of the transformer that help change the effective inductances for LC tanks, thus tuning the resonant frequencies. In MS, multiple oscillator cores are combined and alternately turned on and off to satisfy different frequency requirements, thus broadening the frequency TR. As for MRS, it takes advantage of the even and odd resonant modes of LC resonators to achieve more resonant modes for the LC resonators. These techniques are all useful methods for obtaining a wide-frequency TR in microwave LC oscillators; they all obtain different working principles and have different advantages and disadvantages. Thus, the following sections discuss the details of each of these techniques, including their basic concepts, design examples, merits, and drawbacks.
In general, an LC oscillator adopts an individual inductor $({L}_{d})$ as its inductive element, and its resonant frequency is adjusted by varying the switched capacitors or varactors $({C}_{d}),$ that is, the single-mode LC oscillator, as exemplified in Figure 2(a). However, as mentioned previously, switched capacitors or varactors normally are not sufficient to support the oscillator obtaining a frequency TR above 40%. In such cases, one approach to extend the frequency TR is to truncate the inductors into several segments by IS, thus increasing the effective inductances. Figure 2(b)–(d) displays several typical methods to realize the IS, such as shunt switches and bridge circuits.
Figure 2. (a) A conventional single-mode LC oscillator with an individual inductor (Ld), (b) the drain inductor, (c) the shunt switches, and (d) the bridge circuits. VDD: power supply; VSS: ground.
As we can see from Figure 2, the individual inductor $({L}_{d})$ can be directly truncated into segments by one or more shunt switches or transformed into a bridge circuit and then divided into segments by switches. As for the shunt switches in Figure 2(c), by turning on and off the switches or their combinations, different equivalent inductances can be achieved. Taking the switched inductor with one shunt switch as an example, assuming that the impedance of ${L}_{1}$ is ${Z}_{0}\times{(}{1}{-}{\alpha}{)/}{2}$ and ${L}_{2}$ is ${Z}_{0}\times{\alpha}{/}{2}{(}{0}\leq{\alpha}\leq{1},{Z}_{0} = {R}_{0} + {j}{\omega}{L}_{0}{),}$ the series impedance between A and B can be calculated as (2) [15]. \[{Z}_{{A}{-}{B}} = {Z}_{0}\times\left({{1}{-}{\alpha}}\right) + \frac{{Z}_{0}\times{\alpha}\times{R}_{\text{SW}}}{{Z}_{0}\times{\alpha} + {R}_{\text{SW}}}{.} \tag{2} \]
Neglecting the parasitic capacitance, when the switch is off, ${Z}_{{A} {-} {B}}$ equals (3). \[{Z}_{{A}{-}{B}} = {R}_{0} + {j}{\omega}{L}_{0}{.} \tag{3} \]
In addition, assuming ${R}_{0}\ll{\omega}{L}_{0}$ and ${R}_{\text{SW}}\ll{\omega}{L}_{0},$ when the switch is on, ${Z}_{{\text{A}} {-} {\text{B}}}$ is then simplified as (4). \[{Z}_{{A}{-}{B}}\approx{R}_{0}\left({{1}{-}\mathit{\alpha}}\right) + {R}_{\text{SW}} + {j}\mathit{\omega}{L}_{0}\left({{1}{-}\mathit{\alpha}}\right){.} \tag{4} \]
This indicates that there are two different effective inductances under the on and off states. Considering the equivalent inductances as coarse tuning and the variable capacitors as fine tuning, the frequency TR of the LC oscillator using switched inductors can be greatly increased compared to that of a single-mode configuration.
Obviously, when the switch is on, ${R}_{\text{SW}}$ is directly inserted as the effective series resistance into ${Z}_{{A} {-} {B}};$ thus, it will degrade the tank Q and deteriorate the phase noise. So, the switch needs to be well designed with a large transistor size to alleviate the degradation of Q. However, a switch with a large transistor reduces the self-resonant frequency of the inductor and also decreases the frequency TR due to its parasitic capacitance. Thus, the tradeoff of these design parameters has to be carefully considered in the oscillator design.
The number of shunt switches or inductor segments corresponds to the number of coarse tuning bands. A switched inductor with one shunt switch has been designed in several LC oscillators [11], [12]. Figure 3 displays a circuit schematic of the oscillator with one shunt switch; the realization of the switched inductor; the measured frequency; and the measured phase noise in [11]. By turning on and off the shunt switch, this oscillator obtains both high- and low-frequency bands with a measured overall frequency TR of 87.2% ranging from 3.3 to 8.4 GHz and a measured phase noise ranging from −122 to −117.2 dBc/Hz at a 1-MHz offset under a power consumption from 6.5 to 15.4 mW [11].
Figure 3. (a) The schematic of the IS LC oscillator with one shunt switch and the realization of the truncated inductor in [11], (b) the measured frequency TR, and (c) the measured phase noise. VSW: V_switch. (Source: Taken from [11].)
LC oscillators with multiple parallel switches have also been investigated as a means to broaden the frequency TR [13], [14]. Figure 4 shows a circuit schematic of the LC oscillator with three shunt switches and its inductor realization in [13]. The switched inductor is constructed by cascading four inductor loops with three shunt switches between the adjacent sections. This oscillator is incorporated in a millimeter-wave (mm-wave) signal generation circuit with a $\times{4}$ multiplier, where direct measurement results for the oscillator were not demonstrated. The measured frequency TR for the final signal generator ranges from 85 to 125 GHz with the phase noise varying from −108 to −102 dBc/Hz at a 10-MHz offset over the output frequency range [13].
Figure 4. The schematic of the IS LC oscillator with three shunt switches and its inductor realization in [13]. Diff.: differential. (Source: Taken from [13].)
A bridge circuit has been proposed as an effective method for alleviating the Q degradation from the IS. As shown in Figure 2(d), a bridge circuit is connected in parallel by one or more unbalanced switches. Taking a bridge circuit with one switch as an example, if we assume that the impedance of ${L}_{1,1}({L}_{2,2})$ is ${Z}_{0}\times{(}{1} + {\alpha}{)}$ and that of ${L}_{1,2}({L}_{2,1})$ is ${Z}_{0}\times{1}{-}{\alpha}{),}$ where ${\alpha} = \left({\Delta{L}{/}{L}}\right),\,{0}\leq{\alpha}\leq{1},$ and ${Z}_{0} = {R}_{0} + {j}{\omega}{L}_{0},$ the series impedance between A and B is calculated as (5) [15]. \[{Z}_{{\text{A}}{-}{\text{B}}} = {Z}_{0}\times\frac{{R}_{\text{SW}} + {Z}_{0}\left({{1}{-}{\alpha}^{2}}\right)}{{R}_{\text{SW}} + {Z}_{0}}{.} \tag{5} \]
Neglecting the parasitic capacitance, when the switch (SW) is off, ${Z}_{{A} {-} {B}}$ equals ${Z}_{0}{.}$
Assuming ${R}_{0}\ll{\omega}{L}_{0}$ and ${R}_{\text{SW}}\ll{\omega}{L}_{0}$ at high frequency, when the SW is on, ${Z}_{{A} {-} {B}}$ is given by (6). \[{Z}_{{\text{A}}{-}{\text{B}}}\approx{R}_{0}\left({{1}{-}{\alpha}^{2}}\right) + {R}_{\text{SW}}\times{\alpha}^{2} + {j}{\omega}{L}_{0}\left({{1}{-}{\alpha}^{2}}\right){.} \tag{6} \]
From (6), the effective series resistance of the SW is decreased by a factor of ${\alpha}^{2},$ which will somewhat alleviate the tank Q degradation. Figure 5 shows a circuit schematic of an LC oscillator using multiple unbalanced switches in the bridge circuit with the realization of the bridge inductor and the measured results. In Figure 5(b) and (c), the measured results show a wideband frequency TR covering from 9.9 to 20.3 GHz and a moderate phase noise ranging from −103 to −84 dBc/Hz with 5.2–7.1 mW of power consumption [15]. Although the bridge circuit theoretically could alleviate the Q degradation from the switches, the realization of the bridge inductor in this design does not reduce the phase noise because it employs multistacked metal layers.
Figure 5. (a) The schematic of an LC oscillator using multiple unbalanced switches in the bridge circuit and the realization of the bridge inductor in [15], (b) the measured frequency TR, and (c) the measured phase noise. VIA: Via; VCNT: V_control. (Source: Taken from [15].)
In summary, the IS technique provides an effective way to realize wideband LC oscillators. However, the phase noise of the oscillator is affected by the series switches in the inductive path. Although some methods have been proposed to alleviate this effect, they are still not highly effective; thus, further investigation to explore this technique is necessary.
Like IS, TLS applied in LC oscillators is also utilized to tune the effective inductance in the LC tank. However, compared to IS, TLS seems more appealing in mm-wave applications due to its higher flexibility in layout implementation. As shown in Figure 6, TLS can be categorized into three main types: namely, series loaded switching [16], [17], [18]; parallel loaded switching [19], [20], [21], [22], [23], [24]: and two-port loaded switching [25], [26], [27], [28]. In the following, these three methods will be discussed in detail.
Figure 6. TLS: (a) series loaded switching, (b) parallel loaded switching, and (c) two-port loaded switching. SWN: the Nth switch.
As shown in Figure 6(a), series loaded switching contains two coils, the primary coil and the secondary coil, where the secondary coil is divided into various series segments, and each is connected by switches. By turning on different switches or their combinations, the loading of the transformer changes, leading to variable equivalent inductances from the primary coil.
Assuming the transformer to be ideal with a coupling coefficient of k and the secondary coil to be simplified as ${N} = {1},$ the equivalent inductance $({L}_{eq})$ and resistance $({R}_{eq})$ can be calculated as (7) and (8), where R represents the equivalent resistance of the transistor SW, and C refers to its parasitic capacitance in parallel with R [17]. \begin{align*}{L}_{\text{eq}} & = \\ {L}_{1} & \times\frac{{R}^{2}{\left[{{1}{-}{\omega}^{2}{CL}_{2}\left({{1}{-}{k}^{2}}\right)}\right]}^{2} + {\omega}^{2}{L}_{2}^{2}{\left({{1}{-}{k}^{2}}\right)}^{2}}{{R}^{2}\left({{1}{-}{\omega}^{2}{CL}_{2}}\right)\left[{{1}{-}{\omega}^{2}{CL}_{2}\left({{1}{-}{k}^{2}}\right)}\right] + {\omega}^{2}{L}_{2}^{2}\left({{1}{-}{k}^{2}}\right)} \tag{7} \end{align*} \[{R}_{\text{eq}} = \frac{{R}^{2}{L}_{1}{\left[{{1}{-}{\omega}^{2}{CL}_{2}\left({{1}{-}{k}^{2}}\right)}\right]}^{2} + {\omega}^{2}{L}_{1}{L}_{2}^{2}{\left({{1}{-}{k}^{2}}\right)}^{2}}{{Rk}^{2}{L}_{2}}{.} \tag{8} \]
When the switch is turned on ${(}{R}\rightarrow{0}{),}\,{L}_{\text{eq}}$ is simplified as (9), reaching its minimum inductance ${(}{L}_{\text{e}\text{q}\_\text{m}\text{i}\text{n}}{)}{.}$ When the switch is turned off, it is acquired as (10), approaching the maximum inductance ${(}{L}_{\text{e}\text{q}\_\text{m}\text{a}\text{x}}{)}{.}$ \[{L}_{\text{e}\text{q}\_\text{m}\text{i}\text{n}} = {L}_{1}\left({{1}{-}{k}^{2}}\right) \tag{9} \] \[{L}_{\text{e}\text{q}\_\text{m}\text{a}\text{x}} = {L}_{1}\times\frac{{1}{-}{\omega}^{2}{CL}_{2}\left({{1}{-}{k}^{2}}\right)}{{1}{-}{\omega}^{2}{CL}_{2}}{.} \tag{10} \]
Several LC oscillators have been designed by employing this series loaded switching technique [16], [17], [18]. Figure 7(a) gives a circuit schematic of an LC oscillator using this technique. To realize multiple subbands, six switches are loaded symmetrically at different locations on the secondary coil. An oscillator designed with asymmetrical locations of the series switches is also reported in this work. The measured frequency TR is from 57 to 65.5 GHz, and the phase noise varies from −105.9 to −110.8 dBc/Hz at a 10-MHz offset under a power consumption of 6 mW [17].
Figure 7. (a) The schematic of the LC oscillator with series loaded TLS technique in [17], (b) the measured frequency TR, and (c) the measured phase noise. S1P: Switch_1_P; S2P: Switch_2_P; S3P: Switch_3_P; S1N: Switch_1_N; S2N: Switch_2_N; S3N: Switch_3_N. (Source: Taken from [17].)
Parallel loaded switching achieves multiband operation by replacing the secondary coil of the transformer with several parallel secondary coils, as shown in Figure 6(b). Regardless of whether these coils are loaded with switches, variable capacitors, or variable resistors, the equivalent inductances from the primary coil can be tuned. Multiple switches were employed to load the parallel coils in [20], [21], [22], and variable capacitors were applied in [19], [23].
Since the switch loaded transformer has been analyzed in (6)–(8), the variable resistor loaded design is analyzed here. As shown in Figure 6(b), assuming one ideal transformer with a single-turn secondary coil ${(}{N} = {1}{)}$ and a variable resistor $({R}_{v})$ loaded in the secondary coil with parasitic capacitance $({C}_{v}),$ the equivalent inductance $({L}_{\text{eq}})$ and resistance $({R}_{\text{eq}})$ can then be derived as (11) and (12), where both are functions of ${R}_{v}$ and ${C}_{v}$ [24]. \[{L}_{\text{eq}} = \frac{{R}_{v}^{2}{L}_{1}{\left[{{1}{-}{\omega}^{2}{C}_{v}{L}_{2}\left({{1}{-}{k}^{2}}\right)}\right]}^{2} + {\omega}^{2}{L}_{1}{L}_{2}^{2}{\left({{1}{-}{k}^{2}}\right)}^{2}}{{R}_{v}^{2}\left({{1}{-}{\omega}^{2}{C}_{v}{L}_{2}}\right)\left[{{1}{-}{\omega}^{2}{C}_{v}{L}_{2}\left({{1}{-}{k}^{2}}\right)}\right] + {\omega}^{2}{L}_{2}^{2}\left({{1}{-}{k}^{2}}\right)} \tag{11} \] \[{R}_{\text{eq}} = \frac{{R}_{v}^{2}{L}_{1}{\left[{{1}{-}{\omega}^{2}{C}_{v}{L}_{2}\left({{1}{-}{k}^{2}}\right)}\right]}^{2} + {\omega}^{2}{L}_{1}{L}_{2}^{2}{\left({{1}{-}{k}^{2}}\right)}^{2}}{{R}_{v}^{2}{k}^{2}{L}_{2}}{.} \tag{12} \]
As described in (11), if ${\omega}^{2}{C}_{v}{L}_{2}{<}{1},\,{L}_{\text{eq}}$ increases with the increment of ${R}_{v},$ and the maximum ${L}_{\text{eq}}$ is calculated as (13). \[{L}_{\text{e}\text{q}\_\text{m}\text{a}\text{x}} = {L}_{\text{eq}}\left({{R}_{v}\rightarrow\infty}\right) = {L}_{1}\left({{1} + \frac{{\omega}^{2}{L}_{2}{C}_{v}}{{1}{-}{\omega}^{2}{L}_{2}{C}_{v}}{k}^{2}}\right){.} \tag{13} \]
Conversely, the minimum ${L}_{\text{eq}}$ is simplified as (14). \[{L}_{\text{e}\text{q}\_\text{m}\text{i}\text{n}} = {L}_{\text{eq}}\left({{R}_{v}\rightarrow{0}}\right) = {L}_{1}\left({{1}{-}{k}^{2}}\right){.} \tag{14} \]
In practice, there is no clear boundary for series and parallel loaded switching when ${N} = {1}$ in the secondary coil. A wideband LC oscillator using switches and a variable resistor loaded transformer was designed in [24]. Its circuit schematic, the measured frequency TR, and the measured phase noise are shown in Figure 8(a)–(c), respectively. It achieves 64 frequency bands from 52.2 to 61.3 GHz with the loaded switch arrays providing coarse tuning through ${V}_{\text{b}1} {-} {V}_{\text{b}6}$ and the variable resistor providing fine tuning through ${V}_{fine}{.}$ The capacitive elements are all loaded in the secondary coil. Thus, the uniformity of this oscillator is improved, and the ${K}_{VCO}$ (720 MHz/V at band 8) is reduced by a factor of 10 compared to that of a conventional oscillator. The measured phase noise ranges from −94 to −118.75 dBc/Hz at a 10-MHz offset with an average power consumption of 8.7 mW for the voltage-controlled oscillator (VCO) core [24].
Figure 8. (a) The schematic of the LC oscillator with switch and variable resistor loaded TLS technique in [24], (b) the measured frequency TR, and (c) the measured phase noise (Source: Taken from [24].)
An LC oscillator with the classical parallel switch loaded TLS technique is shown in Figure 9. The transformer is composed of one primary coil and two secondary coils. By turning on different loaded switches in the secondary coils, this oscillator can work with three frequency bands with a frequency TR of 14%, as shown in Figure 9(b), ranging from 49.23 to 56.62 GHz. The measured phase noise varies from −87.5 to −93.7 dBc/Hz at a 1-MHz offset under an average power consumption of 7.2 mW [21].
Figure 9. (a) The schematic of the LC oscillator with parallel switch loaded TLS technique in [21] and its transformer realization, (b) the measured frequency TR, and (c) the measured phase noise. DCI: digital control inductor. (Source: Taken from [21].)
Two-port loaded switching is realized with the loading at the secondary coil of the transformer inversely connected back to the primary coil, thus generating the so-called two-port loading effect for the primary coil. As displayed in Figure 6(c), there are two main types of two-port loading methods that have been proposed in [25], [26], [27]. Using either ${M}_{1\text{P}/\text{N}}$ or ${M}_{2\text{P}/\text{N}},$ the loadings are both inversely connected back from the secondary coil to the primary coil. By incorporating these structures, the LC oscillator can operate at two bands, thus increasing its frequency TR.
Figure 10 shows the circuit schematic of the transformer-based two-port loading LC oscillator proposed in [27]. It oscillates in the high band when the switch is turned on, while it operates in the low band when the switch is turned off. A frequency TR of 22.3%, ranging from 62.1 to 78.3 GHz, was achieved in this design with the phase noise measured from −84.5 to −90.9 dBc/Hz at 1 MHz and from −105.8 to −112 dBc/Hz at 10 MHz, as shown in Figure 10(b) and (c). There are other methods to realize two-port loading, such as the oscillator in [26], which is operated by exploiting a one-port scheme in the low band while employing a two-port scheme in the high band.
Figure 10. (a) Schematic of the LC oscillator with two-port loaded switching TLS technique in [27], (b) the measured frequency TR, and (c) the measured phase noise. Op: output_P; ON: output_N. (Source: Taken from [27].)
In summary, these three methods for TLS can all extend the frequency TR of LC oscillators. Although the switches are not directly added in the main tank path, the series resistance from the switches still feeds back to the primary coil through the magnetic coupling, thus degrading the tank Q and the phase noise. In addition, multiple coil coupling introduces design complexity for the transformers, especially in low-frequency applications. Thus, TLS is more appealing in high-frequency applications, such as mm-wave.
A straightforward method to realize an LC oscillator with a wide-frequency TR is to employ multiple oscillators connected in parallel and commutate these oscillators by alternately switching them. This is somewhat like the architecture that was shown in Figure 1. There are indeed some designs that have combined several individual oscillators into a combined MS oscillator [29], [30]. Yet directly combining these oscillators occupies a large chip area, and MS oscillators with a compact chip size are much more favorable. By designing the inductive elements into compressed structures, such as overlapped eight-shaped inductors [31] and multicore transformers [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], the oscillators can be condensed into acceptably compact chip sizes while simultaneously realizing a wide-frequency TR through MS.
A dual-core switching LC oscillator with hybrid eight-shaped inductors was proposed in [31], and its schematic is displayed in Figure 11(a). Although eight-shaped inductors have moderate Qs, they are immune to stray magnetic fields, and can mutually cancel the self-generated magnetic fields that keep the Q of the inductor unaffected by the adjacent coils. While some coupling effect may survive that marginally impacts the coils, this effect is much less than that of coupled circular or rectangular inductors. As shown in Figure 11(a), the two eight-shaped inductors are overlapped with a smaller inductor inside a bigger inductor. By employing two different metal layers, the two inductors occupy no extra chip area other than that of the larger inductor. When the two active cores are switched on, this dual-core switching LC oscillator can achieve a very wide-frequency TR in excess of the one-octave band. Figure 11(b) and (c) shows the measured frequency TR of 75% ranging from 2.4 to 5.3 GHz and the measured phase noise ranging from −139 to −149 dBc/Hz at a 10-MHz offset under a power consumption from 4.4 to 6 mW [31].
Figure 11. (a) The schematic of the LC oscillator with dual-core switching in [31], (b) the measured frequency TR, and (c) the measured phase noise. (Source: Taken from [31].) FOM: figure of merit; HB: high band; LB: low band; PN: phase noise.
It is possible to further broaden the frequency TR of an LC oscillator by combining more cores. Figure 12(a) shows a circuit schematic of an LC oscillator using triple-core switching. Three inductors are coupled together as separate inductive elements for three LC oscillators. To obtain multiband operation, the coupling factors among the inductors must be kept small. Vertical coupling inductors are thus not good options here because triple inductors may require the use of several bottom metal layers, leading to a Q degradation of the inductor. In [32], planar coupling inductors are utilized with three inductors placed in a concentric configuration.
Figure 12. (a) The schematic of the LC oscillator with triple-core switching in [32], (b) the measured frequency TR, and (c) the measured phase noise. (Source: Taken from [32].)
Since this oscillator targets the sub-6G working band, the inductance of each inductor would be at least several hundred pH. Two-turn inductors are thus exploited, with the stacked metal layers in a small chip area. As shown in Figure 12(b) and (c), by commutating these oscillators with the cross-coupled pairs alternately turned on, this oscillator achieves three continuous frequency bands with a measured frequency TR of 128% ranging from 1.3 to 6 GHz and a phase noise ranging from −112 to –120 at a 1-MHz offset under a power consumption of 4.35–9.15 mW over all frequency bands, a very competitive TR performance.
When the operating frequency goes up to the mm-wave, the combination of MS and TLS would be a good method for the design of wideband LC oscillators [38], [39], [40], [41]. Figure 13(a) gives a circuit schematic of an LC oscillator using the combined dual-core switching and transformer parallel loaded switching techniques. As is clear from the figure, five single-turn inductors are planarly coupled together with two coils directly connected to the drain terminals of the cross-coupled transistors as the primary coils and the other three coils loaded with parallel switches as secondary coil loadings. Coarse tuning is obtained by either of two active cores; midrange tuning is realized through the loaded switches; and fine tuning is acquired by the variable capacitor array. The combination of MS and TLS techniques generates six frequency modes for the LC oscillator.
Figure 13. (a) The schematic of the LC oscillator with combined dual-core and TLS in [39], (b) the measured frequency TR, and (c)the measured phase noise. (Source: Taken from [39].)
Figure 13(b) and (c) shows the measured frequency TR ranging from 57.5 to 90.1 GHz with a frequency TR of 41.1% and a phase noise ranging from −112 to −104.5 dBc/Hz at a 10-MHz offset [39]. Because of inaccurate modeling of the coupled inductors, a small frequency discontinuity appears from 76.2 to 78.5 GHz between modes 4 and 5, which can be alleviated by adjusting the coupling factors to shift up the frequency of mode 4.
Therefore, the MS technique directly realizes the extension of the TR by switching the active cores. Unlike other techniques, no extra switches introduce other parasitics; thus, there is no extra TR loss introduced by this technique. From the referenced works, it appears that the MS technique could approach the ideal frequency TR by using multiple single-core LC oscillators.
MRS takes advantage of the switched inductance or capacitance between even and odd modes in the LC resonators, extending more resonant modes for LC oscillators. It is a very promising technique for designing wideband LC oscillators while simultaneously obtaining low phase noise. Unlike the aforementioned three techniques, which have no obvious beneficial effect on the phase noise, MRS could realize a wide-frequency TR while at the same time improving the phase noise performance through its multicore configuration. To realize even and odd modes in LC resonators, the LC oscillator normally has to work with at least two simultaneously active cores, which naturally decreases the phase noise of the oscillator by 3 dB.
To realize MRS, almost all LC oscillators employ inductor-based or transformer-based LC resonators [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56]. Figure 14(a) displays a schematic view of an LC resonator with symmetrical inductors and capacitors seen from ${Z}_{11}$ and ${Z}_{22},$ while Figure 14(b) depicts another transformer-based symmetrical LC resonator with one additional capacitor $({C}_{C})$ coupled between the two sides of the transformer.
Figure 14. Multimode resonance realized by (a) the inductor-based LC resonator and (b) the transformer-based LC resonator.
In even mode, the voltages across the two loops ${(}{A}\rightarrow{C}$ and ${B}\rightarrow{D}{)}$ are in phase (blue line in Figure 14); thus, ${V}_{AC} = {V}_{BD}{.}$ The centric inductor $({L}_{CM})$ sees a differential voltage at its two terminals, which makes its inductance count as part of the total inductance. Hence, the resonator can be simplified into two shunt LC tanks with ${L} = {2}{(}{L}{1} + {L}_{CM}{)}$ and ${C} = {C}_{1}{.}$ The resonant frequency is easily found as (15). \[{\omega}_{\text{even}} = \frac{1}{\sqrt{{2}\left({{L}_{1} + {L}_{M}}\right){C}_{1}}}{.} \tag{15} \]
In odd mode, the voltages in the two LC tanks are out of phase (red line in Figure 14), ${V}_{AC} = {-}{V}_{BD}{.}$ The two terminals of ${L}_{CM}$ are virtually grounded; they cannot be seen from ${Z}_{11}$ and ${Z}_{22}{.}$ The equivalent inductance and capacitance from ${Z}_{11}$ and ${Z}_{22}$ are thus equal to ${L} = {2}\,{L}_{1}$ and ${C} = {C}_{1},$ with the resonant frequency represented as (16). \[{\omega}_{\text{odd}} = \frac{1}{\sqrt{2{L}_{1}{C}_{1}}}{.} \tag{16} \]
Without considering ${C}_{C},$ the transformer-based resonator in Figure 14(b) could be made equivalent to Figure 14(a) by equating the transformer into a T-shaped circuit model. As a comparison, Figure 14(b) introduces an extra coupled ${C}_{C}$ that produces additional equivalent capacitances between the even and odd modes. The calculated resonant frequencies in even and odd modes are respectively given as (17) and (18) for Figure 14(b). \[{\omega}_{\text{even}} = \frac{1}{\sqrt{\left({{L}_{2} + {M}}\right){C}_{2}}} \tag{17} \] \[{\omega}_{\text{odd}} = \frac{1}{\sqrt{\left({{L}_{2}{-}{M}}\right){(}{C}_{2} + {C}_{C}{)}}}{.} \tag{18} \]
MRS can work based on either switched inductance or switched capacitance in even and odd modes of the LC resonators. Thus, many of the LC oscillators reported have incorporated these two elements into their designs to realize wideband frequency TR and low phase noise simultaneously.
Switched inductance- or capacitance-based MRS techniques have been widely used in a variety of LC oscillators to realize both wide TR and low phase noise [41], [42], [43], [44], [45]. Figure 15(a) shows a circuit schematic of a dual-mode LC oscillator simply using switched inductance. As shown in the layout sketch in Figure 15(a), the two inductor coils correspond to ${L}_{1}$ in Figure 14(a), while the long horizontal line refers to ${L}_{CM}{.}$ By adopting a switch array to control the phases of the signals at four ports, this oscillator can operate in two frequency bands covering from 14.8 to 18.7 GHz and from 20.8 to 26.6 GHz, as shown in Figure 15(b). There appears to be a frequency discontinuity between the two bands; this can be modified by adjusting the parameters or patterns of the inductors based on (14) and (15). The measured phase noise of this oscillator is shown in Figure 15(c), where it demonstrates that the oscillator obtains an optimum phase noise of −115.1 dBc/Hz at a 2-MHz offset while consuming only 4.8 mW of dc power, demonstrating simultaneous low phase noise and low power consumption [43]. There are also some other oscillators that merely exploit the switched capacitance, such as [42].
Figure 15. (a) The schematic of the dual-mode resonant LC oscillator with switched inductance-based MRS in [43] and the inductor realization, (b) the measured frequency TR, and (c) the measured phase noise. LDM: L in differential mode; PDC: power of DC. (Source: Taken from [43].)
As mentioned earlier, the inductance and capacitance can both be switched between the even and odd modes of the LC resonator, indicating that each corresponds to two resonant modes. By combining these modes, it is possible to realize quad-mode resonance for LC oscillators. In fact, an LC oscillator that subtly combines the switched inductance and the switched capacitance between the even and odd modes of the LC resonator has been proposed to achieve four reconfigurable resonant modes in [54]. As shown in Figure 16(a), the four reconfigurable resonant modes are realized with two symmetrical transformers forming the switched inductance through magnetic coupling and several cross-coupled capacitors producing the switched capacitance through electric coupling. A switch array at the center is employed to clamp the quad-core with specific phases corresponding to the required even and odd modes. The measured frequency TR and phase noise are shown in Figure 16(b) and (c), with a 73.2% frequency TR from 18.6 to 40.1 GHz and an optimum phase noise of −108.5 dBc/Hz at a 1-MHz offset, respectively [54]. The quad-mode and quad-core configuration of this oscillator achieves simultaneous wideband frequency coverage and low phase noise.
Figure 16. (a) The schematic of quad-mode resonant LC oscillator with switched inductance and capacitance combined MRS in [54] and the transformer realization, (b) the measured frequency TR, and (c) the measured phase noise. (Source: Taken from [54].)
The improvement in resonant modes for MRS LC oscillators is often limited by the parasitics of the mode selection or tuning circuits due to the increased complexity of the switch array and other tuning circuits. To address this challenge, one approach is to combine the MRS with other techniques, such as TLS, to alleviate the parasitic contribution from the mode selection circuits. An LC oscillator with combined MRS and TLS techniques was proposed in [55]. As shown in Figure 17(a), the oscillator introduces an additional tertiary magnetic coupling loop as the transformer-switching loading to extend more resonant modes. The transformer switching incurs negligible switch loss and Q degradation for the oscillator. Further, as shown in Figure 17(b), the inductor coils in the main LC tanks and the tertiary coil are all packed together as a multicoupling transformer structure, which saves a large amount of chip size. Based on the even and odd switching modes from MRS and the additionally introduced resonant mode from the TLS, this oscillator achieves three continuous frequency bands from 8 to 17 GHz with a frequency TR of 72%, as shown in Figure 17(c). The measured phase noise is shown in Figure 17(d), demonstrating a phase noise from −119.1 to −112.3 dBc/Hz at a 1-MHz offset [55].
Figure 17. (a) The schematic of the triple-mode LC oscillator with combined MRS and TLS techniques in [55], (b) the layout implementation, (c) the measured frequency TR, and (d) the measured phase noise. 100k, 100,000; 1 M, 1 million; 10 M: 10 million. (Source: Taken from [55].)
To sum up, the MRS technique outperforms other approaches for simultaneously achieving wide-frequency TR and low phase noise. However, it employs multiple active cores to realize the phase noise reduction, which accordingly consumes more dc power compared to other techniques. The oscillators using the MRS technique thus work with at least two cores. Figure 18 demonstrates the microphotographs of the quad-mode LC oscillator in [54] and the triple-mode LC oscillator in [55].
Figure 18. Microphotographs of (a) the quad-mode LC oscillator in [54] and (b) the triple-mode LC oscillator in [55]. (Source: Taken from [54] and [55].)
The primary techniques for realizing multimode switching in microwave LC oscillators have been described (i.e., IS, TLS, MS, and MRS). The discussion primarily focused on the realization of wide-frequency coverage, but there are several other characteristics of LC oscillators that are not discussed in detail due to space limitations.
Thus, a comparative analysis of the state-of-the-art is shown in Table 1. It can be seen from the table that the TLS technique tends to be appealing in mm-wave applications with a compact chip size and that the MRS technique obtains superior phase noise at a cost of consuming higher dc power through its multicore configuration. As presented, the oscillators using TLS techniques mainly focus on the applicable frequencies from 50 to 78 GHz, while the oscillators employing MRS techniques achieve the optimal phase noise of −119.1 dBc/Hz at 8 GHz at a 1-MHz offset [55]. In addition, all of these techniques utilize inductor or transformer-based structures to help introduce additional resonant modes. However, other structures may be able to realize the same frequency TR extension. Passive capacitive structures with discontinued capacitances and microwave multimode resonators all have the potential to realize multimode switching in microwave LC oscillators.
Table 1. The performance comparison of LC oscillators with multimode switching techniques.
A comprehensive review of multimode switching techniques for microwave LC oscillators was presented in this article. Four types of multimode switching techniques (i.e., IS, TLS, MS, and MRS) were discussed. For each technique, the basic concept; design equations; schematics; layout; measured performance; and advantages and disadvantages were elucidated in detail. Due to the specific realization of the passive elements, each technique may be suitable for applications in different frequency bands. Among the techniques discussed, IS and TLS may have adverse effects on the phase noise of LC oscillators due to the switch-on resistance or loading; MS has no obvious effect on the phase noise compared to its other counterparts, while MRS can optimize the phase noise via its multicore configuration but at the cost of higher dc power consumption. A comparative analysis of the presented designs is also shown to help readers better understand more characteristics of the microwave LC oscillators using the presented techniques.
This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant 2022ZYGXZR0076; in part by the Key-Area Research and Development Program of Guangdong Province under Grant 2018B010115001; in part by the National Key Research and Development Program of China under Grant 2018YFB1802000; and in part by the Guangdong Innovative and Entrepreneurial Research Team Program under Grant 2017ZT07X032. The corresponding author of this article is Wenquan Che.
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Digital Object Identifier 10.1109/MMM.2022.3233511