1 Introduction

In these last years the continuous growth in the communication systems market entailed demands for a wide range of radio frequency (RF) transceivers, leading to an increase in the research and development of such systems. In fact amongst the common demands, one finds the need for a local oscillator, which is usually part of a phase locked loop (PLL), capable of generating quadrature signals with the least possible phase error and phase noise. Low power consumption, low cost, highly integrated circuitry and wide tuning range are other crucial parameters that the RF design must consider.

Quadrature signals find application in many communication systems. For instance, in RF front-ends they are necessary in the implementation of image rejection and direct conversion transceivers, where they are used for modulation or demodulation requirements [1–5]. For high speed clock and data recovery systems, quadrature signals are required for half-rate phase detection, phase interpolation and frequency detection [6–8]. As a matter of fact various quadrature generation techniques have been reported in literature.

In those instances where square-wave signals are acceptable, a possible approach for generating quadrature signals is to use a master-slave flip-flop architecture in order to perform frequency division of a signal having twice the desired output frequency, resulting in inherently two quadrature signals [9–11]. The implementation is very area efficient since the inductor area is clearly much smaller for a voltage-controlled oscillator (VCO) operating at double the desired frequency whilst the divider occupies negligible area. Such topology alleviates VCO pushing and pulling effects especially in a fully integrated system. The main difficulty of such technique is the design of a VCO operating at twice the desired output frequency with low power consumption and low phase response, although the phase noise of the output signals is 6 dB less than that of the VCO due to the division function. Although the accuracy of the quadrature signals can very high, it can be affected by the duty cycle of the VCO signal and mismatch in the signal path through the digital components. The work in [11] proposes to use a divide-by-4 prescalar to eliminate the effect of the VCO signal duty cycle, but obviously this requires a VCO operating at four times the desired output frequency. A circuit that is the analogue version of the digital divider, called the regenerative frequency divider [12], gives a better phase noise response and consumes less power.

Quadrature signals can also be obtained by feeding the output(s) of a standard VCO to an RC polyphase filter [1, 13, 14]. The polyphase filter can also act as a wide-band linearisation operation on the oscillator signal as explained in [15]. The order of the polyphase filter must be high enough so as to ensure a sufficiently wide range over which quadrature shifting is achieved. This means that a large number of stages are required resulting in a larger resistive loss, thus requiring high power consumption and more stringent buffering [16]. In general the polyphase filtering approach has the difficulty of achieving good matching performance, meaning that both amplitude and phase tuning are important. Another well known method for quadrature generation is Haven’s Technique [17]. It is based on the principle that if two sinusoidal signals have equal amplitudes and a non-zero phase shift exists between them, the phase difference between the sum and the difference of these two signals is exactly equal to 90°.

The basic concept behind all the quadrature generation techniques mentioned above is to derive the quadrature signals by means of some transformation of a signal generated by a standard VCO. Another technique for obtaining quadrature signals is through the use of a VCO design capable of directly delivering these signals. An oscillator with multiple output phases can be realised in a ring oscillator architecture that connects several delays stages in a chain. Although very wide tuning can be achieved, as the operating frequency is increased, the power consumption and the phase noise make it practically useless [18]. In fact for high frequency quadrature signal generation, LC-VCOs are used since they have good phase noise performance due to their inherent bandpass filtering action that can suppress side-band noise, and outperform ring oscillators in terms of power consumption [19]. In this case to generate the quadrature signals two similar VCOs are coupled together in such a way as to force them to oscillate in quadrature. This architecture is commonly used because of the accuracy of the phase shift between the output signals, limited only by the device matching and mutual inductance between inductors [20]. However this technique doubles both the required area, and in some topologies, also the power consumption. It provides an undefined phase relationship for the quadrature outputs (see Sect. 2.1) and has limited tuning range since integrated variable capacitors have limited capacitance change with voltage. Nonetheless a quadrature cross-coupled LC-VCO is an ideal candidate for quadrature generation in high frequency applications due to its low-jitter performance and flexibility in bandwidth [21].

Some designs as the one presented in [18], take the merits from both the ring oscillator and the LC-oscillator to provide an architecture with defined multiphase characteristics and uses inductor loads to circumvent the issue of power consumption. Another architecture aims at utilising the extra power and chip area required for generating quadrature signals in order to improve the phase-noise as well [22]. The basic principle underlying this design is that a fourth-order band-pass filter can be composed of two weakly coupled tanks that may have a quality factor twice as high as that of a single tank. In addition, the transimpedance of such a higher order filter provides a 90° phase shift at resonance and enables the use of a ring-VCO architecture that inherently generates quadrature outputs and decreases phase noise in a significant way. The main disadvantage of such a topology is that since the coupling achieved through the capacitive network is weak, high attenuation results thus reducing the signal-to-noise ratio. One must compromise between doubling the quality factor and achieving a reasonable attenuation.

In this paper, we mainly review and compare reported quadrature cross-coupled voltage-controlled oscillators (QVCO) based on LC tank resonators. This review is divided into three main sections: Sect. 2 presents necessary preliminaries; then a comparison between the various topologies employed in the design of LC tank based quadrature cross-coupled oscillators is discussed in Sect. 3 with special reference to phase noise; finally, in Sect. 4 some concluding remarks are made.

2 Preliminaries

2.1 Cross-coupled quadrature voltage-controlled oscillators

The basic QVCO based on the cross coupling of two differential LC-tank VCOs, with the coupling transistors placed in parallel with the switching transistors was proposed in [23]. Figure 1(a) gives a schematic of the architecture, which is sometimes referred to as the parallel topology or just P-QVCO. The architecture consists of two matched coupled oscillators, which are based on the negative resistance differential topology, connected in such a way that they oscillate in quadrature at the frequency at which the Barkhausen Criterion is satisfied [24]. The coupled oscillators synchronize to exactly the same frequency, in spite of mismatches in their resonant circuits. Two identical oscillators are coupled by the coupling FETS (MCPL), such that there is a direct coupling in one direction and cross-coupling in the other. The negative resistance pair (MSW) overcomes the tank losses so as to achieve sustained oscillations.

Fig. 1
figure 1

(a) Circuit diagram of the P-QVCO and (b) Linear model of cross-coupled QVCOs

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A mathematical proof, presented in [25], shows that under fairly general conditions, a system consisting of four identical subsystems cross-coupled in a certain way will in fact generate four output signals that are exactly 90° apart in phase. The theory presented in [25] can be easily applied to LC coupled oscillators and closed form analysis can be made. Other linear models and comprehensive analysis of cross-coupled VCOs are presented in [26–29]. A similar model to those presented in these papers, is shown in Fig. 1(b). The two differential stages connected to each LC tank are modelled by transconductor cells g m and g mc . This equivalent system is composed of two identical blocks as the one inside the dashed box, plus an inversion stage modelling the cross connection. Let us define the phase delay introduced by these two blocks as: \(\phi _1 \) and \(\phi _2 \), which are nominally equal to the same phase \(\phi \). According to the Barkhausen criterion, the oscillation occurs if the phase-delay along the loop is a multiple of 360°. Therefore, the phase has two possible values: \( \phi \)  = ±90°—this means that in quadrature coupled VCOs the phase relationship is not intrinsically deterministic as in a ring oscillator [18].

When analysing such coupled oscillators a question that comes to mind is: how does the phase noise performance of coupled oscillators compare to that of single oscillators? Although the analysis presented in [20] showed that the overall phase noise in multiphase oscillators is n times lower than in the single phase case (n is the number of tanks in the oscillator), it did not take into consideration various effects that might not be negligible or even have a dominant effect on the actual phase noise performance in particular QVCO topologies.

The major problem is caused by the coupling between the VCO in a multiphase architecture. It is well known that when two differential LC tank oscillators are coupled to generate quadrature phases, the phase noise performance may be easily degraded by two mechanisms: the reduction of the effective Q when the current flowing in each tank is not in phase with the tank voltage (this leads the QVCO to oscillate off-resonance) and the additional noise generated by the coupling devices [26, 27, 30, 31]. This is especially noted in the P-QVCO: although it features low phase and amplitude errors, it also has a poor phase-noise behaviour [23], even though it was shown that a very good figure-of-merit can be obtained [32]. The parallel coupling transistor in the P-QVCO is responsible for a large contribution to phase noise [33, 34]. Some P-QVCO designs use PMOS transistors for coupling since they are known to contribute less noise than their NMOS counterpart both in the flicker and thermal noise regions [35, 36]. The designs presented in [33, 34] employ parasitic vertical bipolar transistors instead of CMOS transistors to mitigate the low-frequency noise introduced by the coupling devices. An important feature of the P-QVCO is that the phase noise and phase error are not independent of each other. In fact both phase noise and phase error are strong functions of α which is the ratio of the width of the coupling transistor to the width of the switching transistor, assuming both transistors have the same length. The phase accuracy of such a topology deteriorates quickly as the coupling between the two VCOs is weakened by decreasing α. On the other hand, phase noise greatly decreases with a decreasing α [27]. Considering this; it is straightforward to improve the phase-noise performance of the P-QVCO at the expense of its phase error performance [31]. This is the case for the already mentioned P-QVCO presented in [32], where a very high phase-noise FOM was obtained at the expense of a high phase error. Another concern with the P-QVCO is the current consumption since it demands 2(1 + α) times as much current as a single oscillator [27]. Due to the limitations of the P-QVCO topology, other cross-coupled quadrature VCO topologies were proposed for quadrature signal synthesis. These will be discussed and compared in Sect. 3.

2.2 Phase and amplitude error measurement

The overall phase and amplitude errors between the signals of a QVCO are very difficult to measure directly in a reliable way: these errors can be measured more accurately via a mixer circuit such as the single sideband (SSB) up-conversion circuit [23, 37] or the image rejection Weaver architecture [38]. Another technique uses a network analyser in tuned receiver mode, by which the phase shift between the two ports can be measured [38].

Figure 2 shows the block diagram representation of the SSB up-conversion circuit. By using the SSB up-conversion circuit the phase and amplitude errors are translated into the ratio of the wanted up-converted band (f QVCO − f LO) to the unwanted image band (f QVCO + f LO), where f QVCO is the oscillation frequency of the QVCO and f LO is the frequency of the low frequency quadrature source. This ratio is known as the Image Band Rejection ratio (IBR) or Image Rejection ratio (IMR) and is usually expressed in decibels. Assuming the low frequency quadrature source generates ideal quadrature signals it can be shown that:

$$ IBR = 10\log _{10} \left( {\frac{{P_ - }} {{P_ + }}} \right) = 10\log _{10} \left( {\frac{{1 + 2\left( {1 + \beta } \right)\cos \mu + (1 + \beta )^2 }} {{1 - 2\left( {1 + \beta } \right)\cos \mu + (1 + \beta )^2 }}} \right) $$
(1)

where P − is the power of the wanted sideband, P + is the power of the unwanted sideband, μ is the phase mismatch and β is the amplitude mismatch. Note that it is possible to measure the amplitude mismatch β by applying alternatively only the in-phase signal or the quadrature-phase signal to the SSB mixer circuit and measure the output signal [39]. This is important to verify if either the phase mismatch or the amplitude mismatch is limiting the IMR.

Fig. 2
figure 2

Block diagram of a SSB up-conversion circuit

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2.3 Figure of Merit

A Figure of Merit (FOM) can be defined for a QVCO taking into account the phase noise, power consumption and oscillation frequency [40]:

$$ FOM = 10\log _{10} \left( {\left( {\frac{{\omega _0 }} {{\Delta \omega }}} \right)^2 \frac{1} {{L_{SSB} (\Delta \omega )P}}} \right) $$
(2)

where ω 0 is the angular oscillation frequency, Δω is offset frequency, L SSB (Δω) is the phase noise with reference to carrier at Δω and P is the power consumption measured in milliwatts. The higher the value of the FOM the better the performance of the QVCO will be. FOM compares different oscillators by normalizing the phase noise, by the power consumption and oscillation frequency.

3 Comparison between various cross-coupled QVCO topologies

In this section, the main cross-coupled QVCO topologies reported in literature are compared with special reference to phase noise. Table 1 gives a brief summary of the experimental results of these quadrature oscillator topologies, including phase noise, oscillation frequency, tuning range, power consumption, FOM and technology used. Note that in Table 1, n/a stands for “not-available” and the designs in bold are ones which include a mixer circuit to determine the quadrature accuracy.

Table 1 Comparison between various cross-coupled QVCO topologies
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3.1 P-QVCO with phase shifter

The reason why the P-QVCO [23] is known to have poor phase-noise behaviour is because each resonator is not optimally driven at a zero-degree phase shift [32]. So since the resonating tank is not operated at the resonating frequency, the optimal quality factor of the tank is not achieved [53]. To improve their phase-noise response, phase shifters can be introduced between the cross-coupled oscillators [30, 34], such that the resonators are operated at the desired phase shift. The extra benefit of this approach is that since the current in the coupling transistors is made to be in phase with that of the negative resistance transistors, the coupling transistors will contribute to the negative resistance enabling a reduction of the transconductance of the switching transistors while still achieving sustained oscillations [30]. This is obviously done at the expense of increasing the number of components which can also lead to an increase in power consumption.

3.2 Series coupled QVCOs

The work presented in [26, 37, 41, 54] suggests that connecting the coupling transistor (MCPL) in series with the negative resistance transistor (MSW) in a cascode-like fashion, as shown in Fig. 3(a), greatly reduces the noise from the coupling device via degeneration [28]. This proposed design avoids the use of power consuming phase shifters [30] to improve the phase noise of the P-QVCO [32]. Since the coupling transistor does not require an additional biasing current, power consumption is reduced in such a topology [28]. The phase error is almost independent of α. In fact phase error acts like a design constant dependent of course on the actual amount of mismatch between ideally identical components. One of the methods of series coupling is referred as the Top-Series (TS) QVCO [26, 37, 54], shown in Fig. 3(a). When both P-QVCO and TS-QVCO are designed to have the same IBR [42], centre frequency and power consumption, it follows that the latter outperforms the former in terms of phase noise response. The major problem with this architecture is that the coupling transistors have to be about five times larger than the negative resistance transistors [37, 41, 54], thus loading the oscillator with large parasitic capacitances that reduce the tuning range, making this solution unsuitable for wide-band high frequency applications.

Fig. 3
figure 3

Series coupled QVCOs. (a) Top series QVCO, (b) Bottom series QVCO, (c) Middle series QVCO

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Alternative ways of achieving a series connection between the coupling and switching transistors have been reported. One of them is shown in Fig. 3(b) and is known as the Bottom Series (BS) QVCO [42]. In this configuration the coupling transistor is placed at the bottom of the switching transistor. As for the TS-QVCO, the phase error is almost independent of α. BS-QVCO has a higher FOM than the P-QVCO when both display the same phase-error and have same centre frequency and power consumption. This topology has a higher FOM but also a higher phase error than the TS-QVCO [42]. Another alternative way of series connection is the MS-QVCO [43], shown in Fig. 3(c), which stands for Middle Series QVCO and it is basically an improved TS-QVCO. It has a higher FOM than the other three topologies, but a phase error which is between that of the TS-QVCO and the BS-QVCO. It features very low phase noise especially at a low frequency offset.

3.3 Switched biasing QVCOs

According to the analysis in [55] the close-in phase noise of a CMOS VCO is largely determined by the flicker noise of the tail current source. Although many QVCO designs eliminate the tail current sources [32, 35, 41, 44] to improve phase noise, such an achievement comes at the expense of increased sensitivity to power supply fluctuations and noise. In [45] a P-QVCO with a switched bias technique is proposed: instead of employing a fixed tail current source, two tail transistors (MTAIL), which are controlled by the differential output voltage, are used for each VCO, as shown in Fig. 4(a). Since the tail transistors are turned off alternately by the differential output of the VCO during each oscillation period, their flicker noise is decreased by releasing the trapped electrons [56].

Fig. 4
figure 4

Switched biasing QVCOs. (a) Self-switched bias (b) Cross-switched bias scheme

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In [46], a similar topology is used with the difference that additional phase noise reduction is achieved by switching the tail current sources of the in-phase VCO core via the outputs of the quadrature-phase VCO core and vice-versa. The current sources of each VCO are also separated for the two differential pairs. As shown in Fig. 4(b), instead of switching the tail current sources of a VCO by its same outputs, as in [45], the 90° phase shift between the coupling input and the output of each VCO is used to optimally align the common-source node voltage Vs with the output voltage so that the minima of the common-source node voltage and that of the VCO output coincide such that a higher oscillation amplitude can be obtained with the same current level. By separating the tail current sources of the negative resistance and coupling transistors, the effective transconductance of the latter is decreased and thus their noise contribution is minimized [46].

3.4 Transformer-based resonator QVCOs

Some designs make use of a transformer-based LC resonator tank instead of a standard one to improve the performance of the QVCO [47]. For instance, the configuration proposed in [47] allows deep-turn-off state of the switching transistors and provides an enhanced resonator quality factor, achieving low phase noise characteristics. In such configuration the drain and gate dc-biases of the switching transistors can be separately controlled such that the QVCO can be made to operate at an optimum biasing level to reduce its phase noise. In [47] the coupling between the VCO cores is done via transistors as in traditional QVCO topologies: two tail-biased LC VCOs can also be cross-coupled by on-chip transformers to generate quadrature signals as shown in Fig. 5 [48]. The structure is similar to the transformer-feedback VCO presented in [47, 57], but the transformer is used to cross-couple the two LC VCOs. The primary coil of each of the transformers (Lp1a) resonates with the total capacitance at the transistor drain and at the same time is cross-coupled to the secondary coil (Ls1a) of the quadrature phase. Since in this topology the parasitic loading capacitance due to the coupling transistors is removed, a higher operating frequency results together with a larger tuning range, higher tank voltage and better phase noise. The transformers enable the signals at the sources of the transistors to swing below the negative supply, thus effectively reducing the voltage headroom requirements [48].

Fig. 5
figure 5

Transformer coupled QVCO

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As explained above, in many quadrature topologies the resonator tank is not operated at a zero degree phase shift and therefore the VCO oscillates off-resonance and the effective quality factor of the tank is reduced. The resonant phase shift of the bandpass LC network shown in Fig. 6 can be varied between 0° and 90° by varying the capacitive coupling coefficient K [22]. Two such networks can be coupled magnetically by using on-chip transformers instead of the inductors [49] to generate quadrature signals whilst using the maximum quality factor of the resonator by varying accordingly the resonant phase shift via the capacitive coupling coefficient K. Note that in such topologies the layout of the transformers determines a lot the performance of the quadrature signals especially as regards the amplitude and phase errors.

Fig. 6
figure 6

Capacitively coupled 4th order bandpass LC network

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3.5 Superharmonic coupled (SHC) QVCOs

It can be shown that if two VCOs are injected with anti-phase second harmonics, their fundamental outputs will be 90° shifted in phase, with the output frequency being half that injected [39, 58, 59]. In this technique, the quadrature coupling does not require the oscillation frequency to deviate from the tank resonance and consequently, the coupling does not reduce the phase stability of each individual oscillator and no increase in phase noise results [53].

3.5.1 Injection locked master-slave QVCOs

In [31, 60], the differential signals of an oscillator, running at twice the desired output frequency, are capacitively applied to the gates of the tail biasing transistors of two other slave VCOs designed to oscillate at the desired output frequency. This is done such that the high frequency VCO synchronizes the two slave VCOs, which act like narrow band injection locked frequency dividers (ILFDs), generating quadrature signals. As proposed in [38], the differential signals can also be injected via buffers into the common-mode nodes of the slave VCOs. As shown in [31] the synchronizing oscillator sets the output phase noise of the QVCOs, up to an offset frequency comparable to the locking range of the ILFDs, keeping in mind that the phase noise at the output will be 6 dB better than that of the high frequency VCO. Since the output phase noise response is controlled by that of the master VCO, the effect of mismatches on the accuracy of the quadrature signals can be reduced by utilizing coupling transistors [31] or using a frequency locked loop mismatch compensation scheme as proposed in [38].

3.5.2 QVCOs with common-mode superharmonic coupling

Two differential oscillators can also be made to oscillate in quadrature at a certain frequency by using a coupling network to enforce an anti-phase relationship between the second-order harmonics [39]. This eliminates the need of an extra VCO at twice the output frequency thus reducing the area and power overhead. As shown in Fig. 7(a) the quadrature coupling can be established by means of coupled inductors (L1–L2) which do not introduce any significant extra source of noise. The mutual coupling of the differential inductor at the common-mode nodes is such as to achieve injection of the second harmonic from one VCO to the other to lock the two VCOs together in quadrature [39, 50, 61]. The two VCO cores are in fact coupled through reciprocal injection locking [59]. In [50] the coupled inductor (L1–L2) is also used as a current source reducing supply headroom requirements.

Fig. 7
figure 7

QVCOs with common-mode superharmonic coupling. (a) Inductive coupled QVCO, (b) Capacitive coupled QVCO, (c) LC tank coupled QVCO

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Another LC-QVCO based on two injection locked oscillators with a second harmonic coupling is presented in [49, 62, 63]. The second harmonic coupling is achieved by means of connecting capacitively the gate of the tail bias transistor (MT1) in one oscillator to the drain of the tail bias transistor (MT2) in the other oscillator and vice-versa, as shown in Fig. 7(b). Similarly to the common-mode inductive coupling topology, this QVCO allows for a higher tuning range than other solutions that require coupling transistors at the output nodes and as proved in [64] this LC-QVCO achieves the same phase noise—current product as a single LC-VCO. This advantage is paid for with a poor quadrature accuracy.

In [6] two complementary differential VCOs are combined together at the NMOS and PMOS tail nodes by two separate LC tanks which are made to resonate at twice the output oscillation frequency f 0 (see Fig. 7(c)). Due to the large amount of energy circulating among the LC tanks, the coupling method is more effective than that proposed in [39, 50, 61]. When the noise from one VCO travels through the tail tanks to disturb the other VCO, most of it is translated to amplitude noise, and is removed by the built-in amplitude limiting mechanism of the oscillator [6]. The negative resistance transistors in each VCO inject little noise near f 0 and 2f 0 since the tail tanks present a high impedance at these frequencies leading to a greater impedance mismatch between the two VCO cores than in the transformer-based (inductor coupled) superharmonic coupled QVCO.

3.5.3 Source injected parallel-coupled QVCOs

A special case of SHC-QVCOs is the source injected parallel-coupled LC-QVCO (SIPC-QVCO) topology which makes use of transistors instead of a passive network to inject superharmonic signals from one VCO to another to achieve quadrature locking [65, 66]. At first sight, the SIPC-QVCO is a modified P-QVCO, since in this topology the drain nodes of the coupling transistors are connected directly to the supply voltage whilst in the P-QVCO, the drain nodes of coupling transistors are tied to the LC-tank. This seems a minor modification, but in reality the way in which the two topologies achieve the quadrature locking is completely different.

In fact the quadrature signals in a P-QVCO are generated by a combination of two differential VCOs and the cascade of two differential amplifiers (coupling transistors) with one of them in cross-connection [23] whilst in the SIPC-QVCO the differential VCOs operate as frequency dividers for signals injected at the common source nodes, with the coupling transistors operating as frequency doublers with large input voltage swing. The main advantages of this topology are that first of all the coupling transistors are separated from the LC-tuning circuits resulting in a wider tuning range as parasitic capacitances of the coupling transistors are separated [39]. Secondly a better phase noise response is achieved, because the flicker noise current generated by the coupling transistors does not interact with the tank and it is not up-converted to the frequency of oscillation by their switching action as in the P-QVCO topology [65]. As a matter of fact, a similar design is presented in [67] in which the QVCO is proposed for a multi-standard direct conversion receiver architecture.

3.6 QVCOs with deterministic output phase relationship

In certain applications such as clock and data recovery systems [6, 7] it is important to know the exact relationship of quadrature signals. In quadrature coupled VCOs the phase relationship is not intrinsically deterministic as in a ring oscillator [18] due to the bimodal oscillation effect, whereby the QVCO may exhibit two stable oscillation states at different operating frequencies [21, 27]. The work in [68] has shown that by coupling the VCOs via a phase lag circuit, the in-phase output always leads the quadrature-output by 90°, whilst when VCOs are coupled via a phase lead circuit, the in-phase output always lags the quadrature-output by 90°. A cascode-based coupling method for a P-QVCO is proposed in [21, 45] which effectively eliminates bimodal oscillation (see Fig. 8(a)). The cascode coupling stages create a phase delay which moves the QVCO operation away from the unstable boundary between the two modes of operation whilst providing considerable attenuation to the backward coupling, which can come into play at high frequency operation (>10 GHz) due to the transistor parasitics [21]. For other quadrature signal generation topologies which do not use coupling transistors, an alternative method to provide directivity to the quadrature phases consists of using the phase shift of four transistors connected in a ring structure as shown in Fig. 8(b), where I+/I− are the in-phase outputs and Q+/Q− are the quadrature-phase outputs of the QVCO.

Fig. 8
figure 8

(a) Cascoded coupling to eliminate phase ambiguity and bidirectional coupling in P-QVCO, (b) Transistor ring structure to eliminate phase ambiguity in QVCOs

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3.7 Other QVCO topologies

3.7.1 Varactorless QVCO

Conventionally, the VCOs output frequency is varied by tuning on-chip varactor diodes. For multi-GHz applications, varactor diodes should exhibit low parasitic capacitance and wide tuning range to cope with process variations. However, a wide-tuning range is difficult to achieve especially with a low supply voltage and there is a limit to the maximum variable capacitance available to varactors at high frequencies especially when on-chip inductors are used. So in the architecture presented in [19], the varactor diodes are removed and a switched-tuning technique [69] is used to set the VCOs output frequency. This QVCO comprises two mutually-coupled fixed frequency LC oscillators. Frequency tuning is achieved by varying the coupling coefficient between the two oscillators. Oscillation frequency is adjusted along with loop gain compensation. This mechanism ensures that current injected into LC tank remains constant regardless of frequency tuning, thus suppressing AM-to-PM conversion [36]. This VCO manifests wide tuning range to cope with process variations, while maintaining low phase noise performance. In addition, it inherently provides quadrature output phases.

3.7.2 QVCO with back gate coupling

Many designs have been reported to improve phase noise and power dissipation based on the conventional topology of the P-QVCO; however, the presence of the additional coupling transistors makes it inherently inferior to the topology presented in [51]. In fact in this architecture, the LC-QVCO topology enables quadrature coupling without requiring additional transistors. Coupling is achieved using the back-gate (or body terminal) of the negative resistance transistors. Note that here all transistors are assumed to be housed in separate wells, so that each transistor can be used as a full four-terminal device. This topology can be used if a triple-well process is available. A disadvantage of such a topology is that the large signals coupled through the bulk node may forward the p–n junction between the diffusions degrading the overall circuit performance [28].

3.7.3 QVCO with current-reuse technique

The work presented in [44] proposes a current-reuse technique [70] in a QVCO to lower its power consumption. The two coupled VCOs are cascaded in series to share the same biasing current as shown in Fig. 9. From an AC point of view, the circuit is equivalent to two identical VCOs.

Fig. 9
figure 9

QVCO with current-reuse technique

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Note that a large capacitor CGND is used to suppress the injection of the high-frequency noise by cancelling the large amplitude harmonics generated at the connecting node Va. In the proposed QVCO the current source is removed to avoid its contributed flicker noise and allow the utilisation of a low voltage supply. Due to the stacking of switching transistors the architecture cannot achieve low phase noise levels [44] and hence the back-gate coupling technique (see Sect. 3.7.2) is used to reduce phase noise.

3.7.4 QVCO with time-varying source degeneration coupling

In [52], a QVCO coupling technique based on the time-varying source degeneration of the oscillator switching transistors is presented. Such technique provides control of the quadrature signal accuracy with low phase noise and reduces headroom requirements. As shown in Fig. 10, differential triode-region coupling transistors (MCPL) are placed in series with the source decoupling capacitors Cs.

Fig. 10
figure 10

QVCO with time-varying source degeneration coupling

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These transistors, driven by the opposing oscillator core, degenerate the cross-coupled pair, effectively modulating their negative transconductance. Compared to conventional S-QVCOs, in which the coupling transistors also modulate the negative resistance to generate quadrature signals [47], this coupling mechanism consumes no voltage headroom enabling operation at low power supplies voltages, while the extra overdrive voltage of the coupling transistors provides an extra degree of freedom for controlling quadrature accuracy [52].

4 Concluding remarks

This review paper presented a comparative study of published integrated submicron CMOS cross-coupled quadrature voltage-controlled oscillator designs, based on LC resonator tanks operating at gigahertz frequencies. Although special reference to phase noise reduction is made, the comparison also concerned issues such as power consumption, tuning range and the phase accuracy of the quadrature signals. The effect of supply voltage reduction on the choice of the oscillator topology is also included in the discussion.

From this comparison it can be concluded that phase noise in QVCOs can be reduced by either:

  • making use of phase shifters so that cross-coupled oscillators such as the P-QVCO can be operated at the maximal quality factor provided by the LC tank [30, 33] or utilize a high-order bandpass LC network as the resonator whose resonant phase shift can be varied between 0° and 90° to accommodate the phase shift due to the coupling mechanism [49].

  • making use of a transformer-based LC resonator tank instead of a standard one to improve the performance of the QVCO due to its enhanced quality factor [47, 48].

  • couple the VCO cores by either the already available switching transistors [44, 51] or by the use of superharmonic injection [6, 39, 50, 62, 65] such that the noise contributed by coupling transistors is removed. Alternatively it is possible to couple them in a way to degenerate the noise of coupling transistors [26, 37, 42, 43, 54].

  • removing the tail bias current sources from the QVCOs [32, 35, 41, 44] or use a switched-bias technique so that their flicker noise is decreased by releasing the trapped electrons [45, 56].

Apart from the phase noise response, other issues are also important in the design of QVCOs. In quadrature coupled VCO, the phase relationship is not intrinsically deterministic as in a ring oscillator [18] due to the bimodal oscillation effect. The work in [21, 39, 45, 68] proposes techniques which force a QVCO to generate quadrature signals with a predetermined phase orientation. Some topologies also have the difficulty to ensure quadrature oscillation at the required frequencies due to multiple modes of oscillation [65, 67]. Some designs are incompatible with low supply voltages due to the stacking of transistors [26, 37, 42, 43, 54] and therefore topologies such as [52, 65] are suggested for lower supply designs. The complexity incurred by the topology is also another important issue: this must be seen in both the design/layout [30, 33, 47, 48] and the process requirements [44, 51]. When very low power consumption is important, topologies which make use of the current-reuse technique such as [44] can be utilized at an expense of reduced phase noise response. In the design of wide tuning range QVCOs, topologies such as [19] can be used, in which the tuning does not rely on the varactor performance. Also topologies in which the coupling mechanism does not present a large parasitic capacitance at the output nodes can be used in wide tuning range designs [39, 47, 51, 65].