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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 i n f o

Article history:

Received 30 November 2007

Received in revised form

9 May 2008

Accepted 19 May 2008Available online 7 July 2008

Keywords:

Voltage control oscillator (VCO)

Wideband

Band switch

LC tank

Tuning range

Low phase noise

CMOS

Wireless LAN

a b s t r a c t

A low phase noise with wide tuning range complementary LC cross-coupled voltage control oscillator

(LC-VCO) using 0.18mm 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 band-

switching LC tank which is convenient to determine the proper tuning constant for wideband, low-

phase-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 is123.1 dBc/Hz at 1 MHzoffset in the 5.2 GHz band. The calculated figure-of-merit (FoM) of this VCO was as high as187 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.

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 [13].

Nowadays, communication system has already turned to multi-

bands 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[46]. It becomes

difficult for VCO to meet the specifications with wideband tuning

range, low phase noise and low power consumption simulta-

neously. 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

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 guide-

lines 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 capaci-

tor 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. 2illustrates

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,Mn2and Mp1,Mp2) and buffer amplifier (Mn3,Mn4and

Mp3,Mp4). An example of 2-bit band-switching VCO is used for the

ARTICLE IN PRESS

Contents lists available atScienceDirect

journal homepage: ww w.elsevier.com/locate/mejo

Microelectronics Journal

0026-2692/$- see front matter& 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.mejo.2008.05.007

Corresponding author. Tel.: +8863 4269021; fax: +8863 4255830.

E-mail address: [email protected] (H.-K. Chiou).

Microelectronics Journal 39 (20 08) 1687 1692
http://www.sciencedirect.com/science/journal/mejhttp://www.elsevier.com/locate/mejohttp://localhost/var/www/apps/conversion/tmp/scratch_9/dx.doi.org/10.1016/j.mejo.2008.05.007mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_9/dx.doi.org/10.1016/j.mejo.2008.05.007http://www.elsevier.com/locate/mejohttp://www.sciencedirect.com/science/journal/mej

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simplicity of the exposition and to derive the formula.Fig. 3shows

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, KVCOof the

second band is smaller than that in the first band. The explicit

expressions of the oscillation frequency (fosc) for the four sub-

bands are given as

foscband_1

1

2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffi

LCp 2n 1CskCsw 2n 4CsDCvarq

(1)

foscband_2

12p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiLCp 2n 2CskCsw 2n 3CsDCvar

q (2)

foscband_3

1

2pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi

LCp 2n 3CskCsw 2n 2CsDCvarq (3)

foscband_4

12p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiLCp 2n 4CskCsw 2n 1CsDCvar

q (4)where DCvarCmaxCmin, Cmax is the maximum capacitance ofthe 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 ofCs is zero because no switch turns on at the first band. The

equivalent capacitance of the band switch equals the parallel

capacitances ofCsand Csw (CsJCsw).

The oscillation frequency of each sub-band is normalized bythe 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.

K1band_1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCp 2n 1CskCsw 2n 4CsDCvar

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Cp 2n 1CskCsw 2n 4CsDCvarq 1 (5)

K2band_2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiCp 2n 1CskCsw 2n 4CsDCvar

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffi

Cp 2n 2CskCsw 2n 3CsDCvarq (6)

K3band_3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffi

Cp 2n 1CskCsw 2n 4CsDCvarqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiCp 2n 3CskCsw 2n 2CsDCvar

q (7)

K4band_4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiCp 2n 1CskCsw 2n 4CsDCvar

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffi

Cp 2n 4CskCsw 2n 1CsDCvarq (8)

The tuning ratio of each sub-band Ki, as given in Eqs. (5)(8), is

normalized to the tuning ratio ofK1. The overall tuning range (TR)

is thus expressed as

TR 1 ov foscband_1 K1 foscband_1 K2

foscband_1 K3 foscband_1 K4

1 ov

(9)

In order to provide more design insight, Cpand Csware omittedfrom Eqs. (5)(8) and can be rewritten as

K1ffiffiffiffiffiffiffiffiffiffiffiffiDCvar

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0CsDCvar

p 1 (10)



p ffiffiffi

1p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:5 1p 0:816 (11)



p ffiffiffi

1p

ffiffiffiffiffiffiffiffiffiffiffiffi1 1

p 0:707 (12)


p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3CsDCvarp

ffiffiffi1

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:5 1p 0:632 (13)

The resulting equations hold under the conditions ofn2 andov12. Because ov equals 12, the value of Cs is chosen as half of

ARTICLE IN PRESS

Fig. 1. The binary-weighted band-switching LC tank.

Fig. 2. The schematic representation of the VCO (WMn1/LWMn2/L30mm/0.18mm,WMp1/LWMp2/L90mm/0.18mm, WMn3/LWMn4/L6mm/0.18mm, WMp3/LWMp4/L27mm/0.18mm,L0.312 nH,DCvar0.403pF, andCs 0.201 pF).

Fig. 3. The tuning characteristic of 2-bits band switching (overlap ratio12).

H.-K. Chiou et al. / Microelectronics Journal 39 (2008) 168716921688

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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 1 12 foscband_1 1 foscband_1 0:816

foscband_1 0:707 foscband_1 0:632

1 12

)

1 ovfoscband_1 Xn21

i1Ki

Kn

2

1 ov" #

(14)

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

chooseDCvarand 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 ofDCvarand Csin wide frequency

tuning range VCO design.

3. VCO circuit design

3.1. Start-up condition

Fig. 3 shows the circuit topology of VCO comprising comple-

mentary 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 KVCOof each sub-band. Eq. (15)

illustrates the start-up condition of an oscillator:

RT2pf0 Q2rs2pf0L2

rs; gmX

1

RT rs

2pf0L2 (15)

where RT(2pf0) is the parallel equivalent resistance of the tank, Q

is the quality factor of the tank, rs is the series equivalent

resistance of the tank and f0 1=2pffiffiffiffiffiffi

LCp

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 1and fail to oscillate. This phenomenon restricts the low band

oscillation of a wideband VCO and thus limits the tuning range.

3.2. Phase noise considerations

Eq. (16) shows the modified Leesons formula[7], which offers

a design guide to improve the phase noise of an oscillator:

LDf; KVCO 10 log f0

2QDf

2FKT

2Po1 fc

Df

(

KVCOVn2kLCDf

2) (16)

whereDfis the offset frequency from the carrier frequencyf0,Fis

an empirical parameter that describes the thermal noise and the

flicker noise of the transistor,kLCis a constant associated with the

LandCvalues in the tank,Pois the RF power produced by the VCOand Vn is the noise voltage. As can be observed, the higher the

quality factor (Q) of tank, the higher the output power, the lower

theKVCOand the lower Fcan improve the phase noise. To reduce

the tank parasitic resistance, a high Qinductor 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 alsocontribute 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 Vddand 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. 4shows the voltage swing at the

tank of all sub-bands while switching the band switch in turn. Atthe 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.

ARTICLE IN PRESS

0.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.6

1.4

1.8

2.0

Lowest

Band

Voltage

(V)

Time (Sec)

Highest

Band

300.0p200.0p100.0p

Fig. 4. The voltage swing at the tank of all sub-bands.

H.-K. Chiou et al. / Microelectronics Journal 39 (2008) 16871692 1689

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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.

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 ofVdd. 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 current-

and voltage-limited regimes. In this design, the inductance ischosen as 0.312 nH (half circuit) to meet this requirement. The

correspondingCpof the VCO core circuit is 0.223 pF and it should

be taken care in practical implementation. Because the capaci-

tance 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 1 ov foscband_1 K1 foscband_1 K2

foscband_1 K3 foscband_1 K16

1 ov

1 12

foscband_1 1 foscband_1 0:816

foscband_1 0:707 fosc

band_1

0:342

1 12)

(17)

Assume the value of ov is 12. For an overall tuning range from 4 to

5.6GHz, the calculated high and low frequencies in band_1

according to Eq. (17) are 5.6 and 5.2092 GHz, respectively.

Fig. 5is used to derive the values ofDCvarand Cs. In this case,

given the values of frequencies of band_1 (5.6 and 5.2092GHz)

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)2.9912.588 pF 0.403 pF, and Cs is chosen as half ofthis value (0.201 pF) to obtain ov equal to 12. The required DCvaris

implemented with a constant capacitor (Ccon) plus Cvar. The

simulated oscillation frequency is below the initial guess oscilla-

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. 6shows 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 twosub-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

modifiedKm1, Km2, Km3and Km16as

Km1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

CpDCvarpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Cp 0CsDCvarp 1 (18)


CpDCvarp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCp 1CsDCvar

p 0:869 (19)


CpDCvarpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCp 2CsDCvar

p 0:779 (20)

ARTICLE IN PRESS

5.6 G

390.7 M

5.209 G

Vtune

Frequency,

f0(Hz)

2.588pF

Cvar= 0.403pF

Cs= (1-ov)(Cvar)

2.991pF

L = 0.312nH

f0=1

2LC

Band_1

Fig. 5. The schematic diagram of VCO tuning characteristic to derive the value ofvaractor Cvarand switch capacitor Cs (L0.312 nH,fosc(band_1)390 MHz).

0.0

3.5G

4.0G

4.5G

5.0G

5.5G

6.0G

Frequency(Hz)

Vtune (V)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Fig. 6. Pre-layout simulation result of the tuning range (DCvar0.403pF,Cs0.201pF, L0.312 nH, andCp0.223pF).

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

Frequency(GHz)

0.0

Vtune (V)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

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


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CpDCvarpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Cp 15CsDCvarp 0:414 (21)

It can be seen from Eqs. (18)(21) that the slope ofKi 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

inFig. 7.

4. Experimental results

The VCO was fabricated in TSMC 0.18mm CMOS technology.

The optimal device size of this VCO is illustrated inFig. 3, and the

chip photo is shown in Fig. 8. This chip consists of a VCO and

ARTICLE IN PRESS

Fig. 8. Die photograph of the fabricated VCO.

10

-10

-20

-30

-40

-50

-60

-70

-80

-90

5.030 5.032 5.034 5.036 5.038 5.040

0

Frequency (GHz)

OutputPower(dBM)

>1: 5.40924182 GHz -7.5906 dBm

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

1k 10M

-140

-120

-100

-80

-60

-40

MeasurementSimulation

PhaseNoise(dBc/Hz)

Frequency Offset (Hz)

2

1

1:100 kHz -98.2151 dBc/Hz2:1 MHz -123.1022 dBc/Hz

10k 100k 1M

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

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

0.0

4.2G

4.4G

4.6G

4.8G

5.0G

5.2G

5.4G

5.6G

Frequency(Hz)

Vtune (V)

1.80.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

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

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a divider (the divider is not presented in this paper). The die size

of this circuit is 1 1.15mm2. The circuits are measured via on-wafer 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 phasenoises are123.6 and123.1 dBc/Hz, respectively, at 1 MHz offsetover 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 inFig. 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 as187 dB. Infavor of a properly piecewiseKVCOdesign, 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 of121.3 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 at1 MHz offset of the 4.87GHz, and119.4dBc/Hz at 1 MHz offset ofthe 4.76GHz. 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.

Leesons formula states that the phase noise is partially dependent

on the output power of the VCO; Fig. 12reveals this tendency. It

indicates that the phase noise is inversely proportional to output

power. Only if the output power exceeds the boundary of current-

and voltage-limited regimes[9], it shows the degradation of phase

noise when frequency is tuned up to 5.2 GHz.Table 1summarizes

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 FoM-

bandwidth 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 96-2628-

E-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 colpittsCMOS VCO, IEEE Microwave Wireless Components Lett. (2005) 327329.

[2] T.Y. Kim, A. Adams, N. Weste, High performance SOI and bulk CMOS 5 GHzVCOs, IEEE Radio Freq. Integrated Circuits Symp. Dig. (2003) 9396.

[3] R. Aparicio, A. Hajimiri, Circular-geometry oscillators, IEEE Int. Solid-State

Circuits Conf. Dig. Tech. Papers (2004) 378379.[4] A.D. Berny, A.M. Niknejad, R.G. Meyer, A 1.8-GHz LC VCO with 1.3-GHz tuningrange and digital amplitude calibration, IEEE J. Solid-State Circuits (2005)909917.

[5] Z. Li, K.O. Kenneth, IEEE J. Solid-State Circuits (2005) 12961302.[6] A. Fard, T. Johnson, D. Aberg, A low power wide band CMOS VCO for multi-

standard radios, Proc. IEEE Radio Wireless Conf. (2004) 7982.[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 applica-tions, IEEE J. Solid-State Circuits (2003) 13331342.

[8] A. Hajimiri, T.H. Lee, Design issues in CMOS differential LC oscillators, IEEEJ. Solid-State Circuits (1999) 717724.

[9] J.J. Rael, A.A. Abidi, Physical processes of phase noise in differential LCoscillators, Proc. IEEE Custom Integrated Circuits Conf. (2000) 562569.

[10] C.M. Hung, B. Floyd, K.O. Kenneth, Fully integrated 5.35-GHz CMOS VCOs andprescalers, IEEE Trans. Microwave Theory Tech. (2001) 1722.

[11] B. Min, H. Jeong, 5-GHz CMOS LC VCOs with wide tuning ranges, IEEEMicrowave Wireless Components Lett. (2005) 336338.

ARTICLE IN PRESS

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] 0.18 4.615 (8.3%) 120.9 1/5.0 3 189.6 15.74[2] 0.18 5.135.33 (3.8%) 126 1/5.33 17.2 188.2 7.15[3] 0.18 5.33 147.3 10/5.33 14 190.4 NA[5] 0.18 5.005.42 (8.06%)

125 1/5.25 4.2 195.2 15.7

[10] 0.25 5.025.35 (6.47%) 117 1/5.35 6.9 183.1 11.85[11] 0.25 4.325.3 (20.37%) 114.6 1/4.95 4.3 182.1 37.1This work 0.18 4.1665.537 (28.25%) 123.1 1/5.16 10.8 187 52.83


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