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Design formula for band-switching capacitor array in wide tuning range low-phase-noise LC-VCO Hwann-Kaeo Chiou , Hsien-Jui Chen, Hsien-Yuan Liao, Shuw-Guann Lin, Yin-Cheng Chang Department of Electrical Engineering, National Central University, No. 300, Jhongda Road, Jhongli City, Taoyuan County 32001, Taiwan

a r t i c l e in fo

abstract

Article history: Received 30 November 2007 Received in revised form 9 May 2008 Accepted 19 May 2008 Available online 7 July 2008

A low phase noise with wide tuning range complementary LC cross-coupled voltage control oscillator (LC-VCO) using 0.18 mm CMOS technology is presented. This paper proposes a design formula for the choice of the value of varactor (DCvar) and band switch capacitor (Cs) for the binary-weighted bandswitching LC tank which is convenient to determine the proper tuning constant for wideband, lowphase-noise operations. This general formula considers the ratio of frequency overlap (ov) and all the parasitic effects from band-switching capacitor array and transistors. The designed VCO using a 4-bit band-switching capacitor array demonstrates the operating frequencies from 4.166 to 5.537 GHz with an equivalent tuning bandwidth of 28.26%. The measured tuning range of all sub-bands is well agreed with that of the post-layout simulation results. The measured phase noise is 123.1 dBc/Hz at 1 MHz offset in the 5.2 GHz band. The calculated ﬁgure-of-merit (FoM) of this VCO was as high as 187 dB. When considering the tuning bandwidth the designed VCO obtains a FoM-bandwidth product of 52.83, which is much better than previously published works. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Voltage control oscillator (VCO) Wideband Band switch LC tank Tuning range Low phase noise CMOS Wireless LAN

1. Introduction Voltage control oscillator (VCO) is an important building block in RF systems, and it is characterized by the performance of phase noise, frequency tuning range and DC power consumption. Many literature reports dealing with the low-phase-noise techniques in narrow-band VCO design have been published in [1–3]. Nowadays, communication system has already turned to multibands and multi-standards applications. Recently, several studies have been conducted regarding the method to provide a wide tuning range and maintain the low phase noise [4–6]. It becomes difﬁcult for VCO to meet the speciﬁcations with wideband tuning range, low phase noise and low power consumption simultaneously. The VCO with wide tuning range usually requires a larger tuning constant (KVCO) and a higher DC power consumption than the narrow-band VCO does. A large KVCO not only degrades the phase noise due to its large FM modulation but also consumes a large amount of DC power to start up the oscillation. Therefore, the speciﬁcations of power consumption, tuning range and phase noise are usually the trade-off among them in wideband LC-VCO design. The band-switching capacitor array is the most commonly used method in LC tank to solve this problem. Meanwhile, the

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E-mail address: [email protected] (H.-K. Chiou). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.05.007

switching capacitor array is also used to calibrate the frequency drifting under the process variation. Although this technique has been widely used in VCO design, the choice of the switching capacitor usually relies on the designers’ experience. Few guidelines or criteria for the switching capacitor design have been discussed in published literature. One major design parameter, the ratio of frequency overlap (ov), has seldom been taken into account in published works. In this paper, the authors proposed a general formula for the binary-weighted band-switching capacitor array in LC tank to obtain the proper tuning constant and achieve the performance of both low phase noise and wide frequency tuning range.

2. Formula for binary-weighted band-switching LC tank Fig. 1 shows the binary-weighted band-switching LC tank, which consists of an inductor and capacitor array. Fig. 2 illustrates the schematic diagram of the VCO, the device size of each transistor, inductance and capacitance of LC tank. The capacitance of the capacitor array comprises the varactor (Cvar) for the ﬁne tuning of the oscillation frequency, the band select switching capacitor (Cs) for the coarse tuning, the parasitic capacitor of the MOS switch (Csw) and the parasitic capacitor (Cp) from VCO core circuit (Mn1, Mn2 and Mp1, Mp2) and buffer ampliﬁer (Mn3, Mn4 and Mp3, Mp4). An example of 2-bit band-switching VCO is used for the

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f osc ðband_2Þ ¼ 2p

1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ LðC p þ ð2n 2ÞðC s kC sw Þ þ ð2n 3ÞC s þ DC var Þ

(2)

f osc ðband_3Þ ¼ 2p Fig. 1. The binary-weighted band-switching LC tank.

1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ LðC p þ ð2n 3ÞðC s kC sw Þ þ ð2n 2ÞC s þ DC var Þ

(3)

f osc ðband_4Þ ¼

1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ n 2p LðC p þ ð2 4ÞðC s kC sw Þ þ ð2n 1ÞC s þ DC var Þ

(4)

where DCvar ¼ CmaxCmin, Cmax is the maximum capacitance of the varactor, Cmin is the minimum capacitance of the varactor, CsJCsw is the parallel capacitor when the band switch turns off. If n is selected as 2, from Eq. (1), the equivalent switch capacitances are 3 (CsJCsw) and 0 Cs, respectively. The value of Cs is zero because no switch turns on at the ﬁrst band. The equivalent capacitance of the band switch equals the parallel capacitances of Cs and Csw (CsJCsw). The oscillation frequency of each sub-band is normalized by the ﬁrst band to derive the tuning ratio (Ki) and can be rewritten. Ki is deﬁned as the change of capacitance divided by total capacitance in the tank.

Fig. 2. The schematic representation of the VCO (WMn1/L ¼ WMn2/L ¼ 30 mm/0.18 mm, WMp1/L ¼ WMp2/L ¼ 90 mm/0.18 mm, WMn3/L ¼ WMn4/L ¼ 6 mm/0.18 mm, WMp3/L ¼ WMp4/L ¼ 27 mm/0.18 mm, L ¼ 0.312 nH, DCvar ¼ 0.403 pF, and Cs ¼ 0.201 pF).

Fig. 3. The tuning characteristic of 2-bits band switching (overlap ratio ¼ 12).

simplicity of the exposition and to derive the formula. Fig. 3 shows the frequency tuning characteristic using a 2-bit band-switching capacitor. In such a conﬁguration, the bit number (n) of the band switch is selected as 2, which can generate four sub-bands with a lower KVCO. The ov is denoted as the ratio of frequency overlap between the adjacent bands, which is usually chosen as 12. When the switch turns on, the additional capacitances will reduce the original tuning ratio of the varactor. As can be seen, KVCO of the second band is smaller than that in the ﬁrst band. The explicit expressions of the oscillation frequency (fosc) for the four subbands are given as f osc ðband_1Þ 1 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2p LðC p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var Þ

(1)

K 1 ðband_1Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 1 C p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var

(5)

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var K 2 ðband_2Þ ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 2ÞðC s kC sw Þ þ ð2n 3ÞC s þ DC var

(6)

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var K 3 ðband_3Þ ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 3ÞðC s kC sw Þ þ ð2n 2ÞC s þ DC var

(7)

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 1ÞðC s kC sw Þ þ ð2n 4ÞC s þ DC var K 4 ðband_4Þ ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ ð2n 4ÞðC s kC sw Þ þ ð2n 1ÞC s þ DC var

(8)

The tuning ratio of each sub-band Ki, as given in Eqs. (5)–(8), is normalized to the tuning ratio of K1. The overall tuning range (TR) is thus expressed as TR ¼ ð1 ovÞ ½f osc ðband_1Þ K 1 þ ½f osc ðband_1Þ K 2 ½f ðband_1Þ K 4 (9) þ½f osc ðband_1Þ K 3 þ osc ð1 ovÞ In order to provide more design insight, Cp and Csw are omitted from Eqs. (5)–(8) and can be rewritten as pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ DC var (10) K 1 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 1 0C s þ DC var pﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 DC var K 2 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:816 1C s þ DC var 0:5 þ 1

(11)

pﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 DC var K 3 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:707 2C s þ DC var 1þ1

(12)

pﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 DC var K 4 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:632 3C s þ DC var 1:5 þ 1

(13)

The resulting equations hold under the conditions of n ¼ 2 and ov ¼ 12. Because ov equals 12, the value of Cs is chosen as half of

ARTICLE IN PRESS H.-K. Chiou et al. / Microelectronics Journal 39 (2008) 1687–1692

DCvar. Finally, it can be arranged as an equation for the tuning range and a general formula as shown in Eq. (14) can be obtained: TR ¼ ð1 12Þ ½f osc ðband_1Þ 1 þ ½f osc ðband_1Þ 0:816 ) ½f ðband_1Þ 0:632 þ ½f osc ðband_1Þ 0:707 þ osc ð1 12Þ " 2 # nX 1 K n2 ¼ ð1 ovÞ½f osc ðband_1Þ Ki þ (14) ð1 ovÞ i¼1 From Eq. (14), TR, ov and n are obtained to derive the tuning range of band_1. The oscillation frequency (f0) is then used to choose DCvar and Cs. In an ideal case, the tuning characteristic of band_1 usually has a steep slope if Cp and Csw are omitted. However, it shows a gradual slope in practical implementation when parasitics exist. Nevertheless, Eq. (14) is still useful to estimate the preliminary values of DCvar and Cs in wide frequency tuning range VCO design.

3. VCO circuit design 3.1. Start-up condition Fig. 3 shows the circuit topology of VCO comprising complementary cross-coupled pairs and LC tank and output buffer. In order to achieve better performance of the phase noise, a 4-bit band switch is used to lower the KVCO of each sub-band. Eq. (15) illustrates the start-up condition of an oscillator: RTð2pf 0 Þ ¼ Q 2 r s ¼

ð2pf 0 LÞ2 1 rs ¼ ; gm X RT ð2pf 0 LÞ2 rs

(15)

where RT(2pf0) is the parallel equivalent resistance of the tank, Q is the quality factor of the tank, rs ispﬃﬃﬃﬃﬃ the ﬃ series equivalent resistance of the tank and f 0 ¼ 1=2p LC is the oscillation frequency. It indicates that the oscillation condition is limited in RT(2pf0) for a wide tuning range VCO design [4]. The RT(2pf0) usually changes in a wide frequency variation. As observed from Eq. (15), while all of the band switches turn on, the parasitic capacitor reaches the maximum value and the VCO operates at the lowest frequency band. Meanwhile, the associated RT(2pf0) has the smallest value. Although the VCO can stably oscillate at the highest band at a constant biased current, it may fail to oscillate in the lowest band. This is because of the RT(2pf0) at the lowest band (i.e., the tank has the maximum Cs), which is smaller than that at the highest band (i.e. the tank has the minimum Cs). That is to say, the low RT(2pf0) may cause gm RT(2pf0) to be smaller than 1 and fail to oscillate. This phenomenon restricts the low band oscillation of a wideband VCO and thus limits the tuning range.

quality factor (Q) of tank, the higher the output power, the lower the KVCO and the lower F can improve the phase noise. To reduce the tank parasitic resistance, a high Q inductor is recommended. Noise ﬁltering technique is adopted to reduce the current source noise from 2o0+Do0 and o0+Do0 down and up conversions [8]. The thermal and ﬂicker noise of the transistor are dependent on the MOS device size. The larger the device size, the lower the ﬂicker noise and the thermal noise. The band switches also contribute thermal noise, which is dependent on the MOS equivalent resistance (Ron). A large size ratio (W/L) of the band switch is chosen to lower the noise. As can be observed in Eq. (16), the phase noise can be improved by increasing the bias current (increasing power dissipation at ﬁxed Vdd) or inductance in the tank; namely, the VCO operates in current limit or inductor limit regime. However, when the output voltage swing is limited by Vdd and the waveform of VCO is rectiﬁed, the phase noise cannot be further improved even by increasing the bias current. At this point in time, VCO operates at the voltage-limited regime. The minimum phase noise occurs at the boundary of current- and voltage-limited regime [9]. This phenomenon has been checked by a simulator in this work. Fig. 4 shows the voltage swing at the tank of all sub-bands while switching the band switch in turn. At the highest band, the voltage swing has been adjusted to the maximum which is near the voltage difference between Vdd and tail current node. Under this circumstance, no more phase noise can be further improved even with increase in the bias current. It reaches the boundary of current- and voltage-limited regimes. This is the optimal biasing point of VCO design. While turning on the switch step-by-step to reach the lowest band, the voltage swing becomes gradually small. The phase noise degrades due to the smaller equivalent tank impedance. Under such circumstance, a convenient way to maintain good phase noise performance at the lowest band is by increasing the bias current to enlarge the swing at the tank. On the other hand, if the lowest band operates at optimal bias to achieve the lowest phase noise, an excessive voltage swing appears in higher bands due to the decrease of parasitics from band switch array. This too large voltage swing exceeds the optimal bias and consequently wastes power. Thus, the trade-off between phase noise and power consumption should be made in the wideband VCO design. The use of large device size for VCO core transistors allows the increasing bias current to reach maximal output swing up to near Vdd, that is to say, the VCO enters into voltage-limit operation. However, the larger size of the transistors inherently has larger parasitic capacitance, which results in a smaller inductor for a desired resonant frequency.

2.0

where Df is the offset frequency from the carrier frequency f0, F is an empirical parameter that describes the thermal noise and the ﬂicker noise of the transistor, kLC is a constant associated with the L and C values in the tank, Po is the RF power produced by the VCO and Vn is the noise voltage. As can be observed, the higher the

Highest Band

1.8

Lowest Band

1.6 1.4 Voltage (V)

3.2. Phase noise considerations Eq. (16) shows the modiﬁed Leeson’s formula [7], which offers a design guide to improve the phase noise of an oscillator: ( 2 f0 FKT f 1þ c LðDf ; K VCO Þ ¼ 10 log 2P o 2Q Df Df 2 ) K VCO V n þ (16) 2kLC Df

1689

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

100.0p

200.0p

300.0p

Time (Sec) Fig. 4. The voltage swing at the tank of all sub-bands.

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3.3. Derive the values of varactor (DCvar) and switch capacitor (Cs) In this complementary LC-VCO conﬁguration, the bias of the gate terminal of n-, p-MOS is set to near half of Vdd. According to Eq. (15), increase in both device size and inductor increases the bias current and RT(2pf0), which enhances the swing to meet the oscillation condition. The overall ﬁgure-of-merit (FoM) of VCO must be considered at the same time. At a ﬁxed operating frequency f0, with increase in the inductance in the tank, the capacitance will decrease. The associated RT(2pf0) and output swing increase as expressed in Eq. (15). Hence, the optimal value of inductor is chosen to let VCO swing at the boundary of currentand voltage-limited regimes. In this design, the inductance is chosen as 0.312 nH (half circuit) to meet this requirement. The corresponding Cp of the VCO core circuit is 0.223 pF and it should be taken care in practical implementation. Because the capacitance of tank is still unknown, the parasitic capacitance is omitted to obtain the initial tuning ratio as derived from Eqs. (10)–(13). Eq. (17) shows the overall tuning range when n is selected as 4: TR ¼ ð1 ovÞ ½f osc ðband_1Þ K 1 þ ½f osc ðband_1Þ K 2 ½f ðband_1Þ K 16 þ½f osc ðband_1Þ K 3 þ þ osc ð1 ovÞ 1 ¼ 1 ½f osc ðband_1Þ 1 þ ½f osc ðband_1Þ 0:816 2 ) ½f ðband_1Þ 0:342 (17) þ½f osc ðband_1Þ 0:707 þ þ osc ð1 12Þ Assume the value of ov is 12. For an overall tuning range from 4 to 5.6 GHz, the calculated high and low frequencies in band_1 according to Eq. (17) are 5.6 and 5.2092 GHz, respectively. Fig. 5 is used to derive the values of DCvar and Cs. In this case, given the values of frequencies of band_1 (5.6 and 5.2092 GHz) and inductor (0.312 nH), the required total capacitances for these two frequencies are 2.588 and 2.991 pF, respectively. Hence, the tuning varactor must provide this capacitance difference, i.e., (DCvar) ¼ 2.991–2.588 pF ¼ 0.403 pF, and Cs is chosen as half of this value (0.201 pF) to obtain ov equal to 12. The required DCvar is implemented with a constant capacitor (Ccon) plus Cvar. The simulated oscillation frequency is below the initial guess oscilla-

Frequency, f0 (Hz)

5.6 G

2.588 pF

Band_1

Cs = (1-ov)(ΔCvar)

ΔCvar = 0.403 pF

390.7 M

2.991 pF 5.209 G f0 = L = 0.312 nH

tion frequency due to the existence of parasitic capacitance from the cross-coupled transistors, buffer ampliﬁer and band-switching MOS. Thus, lesser capacitance than the original Ccon should be used to compensate for the redundant parasitic capacitor. Fig. 6 shows the pre-layout simulated tuning range of a 4-bit band-switching VCO. The overall tuning range is 1.893 GHz and is larger than the original value of 1.6 GHz. This can be attributed the absence of Cp and results in a steep slope of Ki between two sub-bands. An extra term for Cp should be added to modify Eqs. (10)–(13). The modiﬁed equations for Ki of 16 sub-bands are shown in Eqs. (18)–(21). For simplicity, they only shows the modiﬁed Km1, Km2, Km3 and Km16 as pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ DC var K m1 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 1 C p þ 0C s þ DC var

(18)

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ DC var K m2 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:869 C p þ 1C s þ DC var

(19)

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ DC var K m3 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:779 C p þ 2C s þ DC var

(20)

6.0G

5.5G Frequency (Hz)

The smaller inductor possesses the higher quality factor and small equivalent tank resistance that lead to a lower output swing. Therefore, the lower the inductance the better the phase noise. However, it must spend more power consumption in LC-VCO. The optimized phase noise design should be compromised among device size, inductance and power consumption. To satisfy the oscillation condition of all sub-bands, the swing of the tank must be large enough to ensure the lowest band oscillation.

5.0G

4.5G

4.0G

3.5G 0.0

0.6

0.8 1.0 Vtune (V)

1.2

1.4

1.6

1.8

5.4 5.2 5.0 4.8 4.6 4.4

2√LC

4.2

Fig. 5. The schematic diagram of VCO tuning characteristic to derive the value of varactor Cvar and switch capacitor Cs (L ¼ 0.312 nH, fosc(band_1) ¼ 390 MHz).

0.4

5.6

1

Vtune

0.2

Fig. 6. Pre-layout simulation result of the tuning range (DCvar ¼ 0.403 pF, Cs ¼ 0.201 pF, L ¼ 0.312 nH, and Cp ¼ 0.223 pF).

Frequency (GHz)

1690

0.0

0.2

0.4

0.6

0.8 1.0 Vtune (V)

1.2

1.4

Fig. 7. Post-layout simulation result of the tuning range.

1.6

1.8

ARTICLE IN PRESS H.-K. Chiou et al. / Microelectronics Journal 39 (2008) 1687–1692

(21)

It can be seen from Eqs. (18)–(21) that the slope of Ki changed more gradually than that in Eqs. (10)–(13) due to the presence of Cp. By substituting Kmi into Eq. (17), the overall tuning range equals 1.811 GHz, which is close to the pre-simulated value of tuning range (1.893 GHz). After the pre-layout simulation, EM-simulation is required to extract the parasitic inductors and capacitors produced by those metal lines. The post-layout simulation of tuning range is shown in Fig. 7.

4. Experimental results The VCO was fabricated in TSMC 0.18 mm CMOS technology. The optimal device size of this VCO is illustrated in Fig. 3, and the chip photo is shown in Fig. 8. This chip consists of a VCO and

1:100 kHz -98.2151 dBc/Hz 2:1 MHz -123.1022 dBc/Hz

-40 Phase Noise (dBc/Hz)

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C p þ DC var K m16 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:414 C p þ 15C s þ DC var

1691

-60 -80 1 -100 2

-120 Measurement Simulation

-140 1k

10k

100k 1M Frequency Offset (Hz)

10M

Fig. 10. The simulation and measured phase noise of the VCO.

5.6G

Frequency (Hz)

5.4G 5.2G 5.0G 4.8G 4.6G 4.4G 4.2G Fig. 8. Die photograph of the fabricated VCO.

0.0

0.4

0.6

0.8 1.0 Vtune (V)

1.2

1.4

1.6

Fig. 11. The measured tuning range of the fabricated VCO.

10 0

0.2

>1: 5.40924182 GHz

-7.5906 dBm

Output Power (dBM)

-10 -20 -30 -40 -50 -60 -70 -80 -90 5.030

5.032

5.034 5.036 Frequency (GHz)

5.038

Fig. 9. The measured output spectrum of the VCO.

5.040

Fig. 12. Phase noise is inversely proportional to output power.

1.8

ARTICLE IN PRESS 1692

H.-K. Chiou et al. / Microelectronics Journal 39 (2008) 1687–1692

Table 1 Performance comparisons of the recently published VCO design Ref.

Tech. (mm)

fosc (GHz) and BW

Phase noise (dBc/Hz)

foffset (MHz)/f0 (GHz)

Power (mW)

FOM (dB)

FOM BW (dB)

[1] [2] [3] [5] [10] [11] This work

0.18 0.18 0.18 0.18 0.25 0.25 0.18

4.61–5 (8.3%) 5.13–5.33 (3.8%) 5.33 5.00–5.42 (8.06%) 5.02–5.35 (6.47%) 4.32–5.3 (20.37%) 4.166–5.537 (28.25%)

120.9 126 147.3 125 117 114.6 123.1

1/5.0 1/5.33 10/5.33 1/5.25 1/5.35 1/4.95 1/5.16

3 17.2 14 4.2 6.9 4.3 10.8

189.6 188.2 190.4 195.2 183.1 182.1 187

15.74 7.15 NA 15.7 11.85 37.1 52.83

a divider (the divider is not presented in this paper). The die size of this circuit is 1 1.15 mm2. The circuits are measured via onwafer probing with four external bond-wires to control the band switch bits. The measurements were performed with AgilentTM signal source analyzer (SSA) E5052A. Fig. 9 shows the output spectrum and output power of the fabricated VCO. The output power is 7.59 dBm. Fig. 10 shows the simulat and the measured phase noises are 123.6 and 123.1 dBc/Hz, respectively, at 1 MHz offset over the 5.2 GHz band. The measured results present a predictive accuracy approximately equivalent to the calculated data. Fig. 11 depicts the tuning characteristics by switching a 4-bit switch capacitor array. The VCO operates from 4.166 to 5.537 GHz with 28.25% tuning range. As compared in Fig. 7, the measured tuning range of all sub-bands is well agreed with the post-layout simulation result. The dc power dissipation of VCO core and buffer ampliﬁer consumes currents of 6 and 2 mA from a 1.8 V supply. The FoM of this VCO is calculated as high as 187 dB. In favor of a properly piecewise KVCO design, the better performance of VCO may be attributed to the optimized bias condition for power-saving which keeps VCO operation near the boundary of voltage and current limit regimes at the highest band, and other bands to be close to this regime. In addition, this VCO shows phase noise of 121.3 dBc/Hz at 1 MHz offset of the 5.4 GHz, 122.6 dBc/Hz at 1 MHz offset of the 5.27 GHz, 120.2 dBc/Hz at 1 MHz offset of the 4.87 GHz, and 119.4 dBc/Hz at 1 MHz offset of the 4.76 GHz. The variation of phase noise from low to high depends on the swept frequency from high to low. This is because the equivalent tank resistance becomes smaller at the lowest band than that at the highest band under a constant current bias. Leeson’s formula states that the phase noise is partially dependent on the output power of the VCO; Fig. 12 reveals this tendency. It indicates that the phase noise is inversely proportional to output power. Only if the output power exceeds the boundary of currentand voltage-limited regimes [9], it shows the degradation of phase noise when frequency is tuned up to 5.2 GHz. Table 1 summarizes

the overall performance of recent VCO designs. Note that the product of FoM and tuning bandwidth reveals a performance index of VCO if considering the trade-off of tuning bandwidth and phase noise. As can be seen, this design presents a FoMbandwidth product of 52.83, which is much better than those in previously published works.

Acknowledgments This paper is partially supported by the National Science Council of the Republic of China under Contract No. NSC 96-2628E-008-001-MY3. The National Chip Implementation Center (CIC) and TSMC for chip fabrication are also acknowledged. References [1] M.-D. Tsai, Y.-H. Cho, H. Wang, A 5-GHz low phase noise differential colpitts CMOS VCO, IEEE Microwave Wireless Components Lett. (2005) 327–329. [2] T.Y. Kim, A. Adams, N. Weste, High performance SOI and bulk CMOS 5 GHz VCOs, IEEE Radio Freq. Integrated Circuits Symp. Dig. (2003) 93–96. [3] R. Aparicio, A. Hajimiri, Circular-geometry oscillators, IEEE Int. Solid-State Circuits Conf. Dig. Tech. Papers (2004) 378–379. [4] A.D. Berny, A.M. Niknejad, R.G. Meyer, A 1.8-GHz LC VCO with 1.3-GHz tuning range and digital amplitude calibration, IEEE J. Solid-State Circuits (2005) 909–917. [5] Z. Li, K.O. Kenneth, IEEE J. Solid-State Circuits (2005) 1296–1302. [6] A. Fard, T. Johnson, D. Aberg, A low power wide band CMOS VCO for multistandard radios, Proc. IEEE Radio Wireless Conf. (2004) 79–82. [7] N.H.W. Fong, J.-O. Plouchart, N. Zamdmer, D. Liu, L.F. Wagner, C. Plett, N.G. Tarr, Design of wide-band CMOS VCO for multiband wireless LAN applications, IEEE J. Solid-State Circuits (2003) 1333–1342. [8] A. Hajimiri, T.H. Lee, Design issues in CMOS differential LC oscillators, IEEE J. Solid-State Circuits (1999) 717–724. [9] J.J. Rael, A.A. Abidi, Physical processes of phase noise in differential LC oscillators, Proc. IEEE Custom Integrated Circuits Conf. (2000) 562–569. [10] C.M. Hung, B. Floyd, K.O. Kenneth, Fully integrated 5.35-GHz CMOS VCOs and prescalers, IEEE Trans. Microwave Theory Tech. (2001) 17–22. [11] B. Min, H. Jeong, 5-GHz CMOS LC VCOs with wide tuning ranges, IEEE Microwave Wireless Components Lett. (2005) 336–338.