Wideband Two-Integrator Oscillator-Mixer

Lui's Bica Oliveira('), Jorge R. Fernandes(l), L. M Filanovsky(2) and C. J. M Verhoeven 3o

(1) I.S.Tecnico/INESC-ID Lisboa, R. Alves Redol 9 - 1000 Lisboa, Portugal(2) University of Alberta, Edmonton, Alberta, Canada, T6G 2E1(3) Technical University of Delft, Mekelweg 4, 2628 CD Delft, The Netherlands

{luis.b.oliveira;jorge.femandes} ginesc-id.pt;igorWee.ualberta.ca;c.j.m.verhoeven(its.tudelft.nl

Abstract - Oscillators with quadrature output signals arerequired in modern RF front-ends. In this paper we present atwo-integrator wide tuning range oscillator that can performalso the mixing function. After a high level (Matlab) study theoscillator was designed for AMS 0.35 gm CMOS technology.The circuit level simulations show that the oscillator is tunablein the range of 900 MHz to 5.8 GHz by changing a tuningcurrent, and mixing may be performed throughout this range.

Index terms - Sinusoidal oscillators, quadrature oscillators,mixers, combiners.

I. INTRODUCTION

Presently, a significant research effort is devoted to thedevelopment of integrated wireless systems capable of operatingwith different telecommunications standards. Here we propose aquadrature oscillator that is able to operate in a wide range offrequencies, from 900 MHz to 5.8 GHz, and which can alsoperform the mixing function.

In a first order RC oscillator, the current through a capacitor isreversed when the capacitor voltage reaches a reference level [1]; aSchmitt trigger is used for level detection. To reduce the phasenoise one should increase the triangular signal amplitude with thedemand of extra supply power. Coupling of two first order RCoscillators provides quadrature outputs, and also reduces the effectof mismatches. They add second order effects only [2][3]. LC(second order) oscillators have lower phase noise than RCoscillators, but, when they are coupled (to produce quadratureoutputs), the phase noise is degraded [4][5]. Both RC and LCoscillators have usually a tuning range below one decade.

In the circuit described in this paper two integrators are used(i.e. the Schmitt trigger is substituted by a second integrator). Thisresults in a higher oscillation frequency, and the design goal toobtain a wideband (about a decade frequency range) quadratureoscillator is realized.

We investigate this two-integrator oscillator and its keyparameters: tuning range, oscillation frequency, phase noise, andalso the possibility of performing the mixing function withoutchanging the quadrature relation between the oscillator outputs.Integration of the mixing function in a quadrature oscillator has theadvantages of reducing the area and power consumption.

We present a theoretical study of the circuit phase noise andderive the equations for a shunt noise current and for a series noisevoltage to calculate the phase noise. These noise sources are relatedwith the circuit switching action [6].

This work was supported by POSI and the PortugueseFoundation for Science and Technology through project POCTI/38533/ESE/2001 and scholarship BD 10539/2002.

In Section II a high level study for this two-integratoroscillator-mixer is presented. In Section III a circuitimplementation is shown, and also the equations for the phasenoise are derived. In Section IV we present simulation results forthe tuning range, phase noise, oscillation amplitude, and mixingperformance. Finally, in Section V we draw some conclusions.

II. HIGH LEVEL STUDY

A. Two-integrator oscillator

The basic oscillator is composed of two integrators and twohard-limiters implementing the sign function (Fig. 1). The blocksare connected in a negative feedback loop providing quadratureoutputs. Each integrator output determines the input polarity of theother integrator [1]. The oscillation frequency is proportional to theintegrators' constant, and depends also on the integrator outputinitial values. The integrator output waveforms are triangular (Fig.2). The hard-limiter outputs are rectangular waveforms.

Fig 1 - Two-integrator oscillator with hard-limiters

G,-o

10Time (s)

Fig. 2 - Two-integrator oscillator (Fig. 1) triangular outputs

0-7803-9210-8/05/$20.00 ©2005 IEEE

385

Assume that in the circuit of Fig. 1 the integrator constants areequal and, for t = 0, the integrator 1 has the value of IV for theoutput and integrator 2 has the value of 3V. Fig. 3 (a) shows thatthe sum of the integrator outputs defines the oscillation amplitudeVout.

The oscillation frequency is (with sign function hard-limiters):

- Kifo - 4Vout

(1)

where Ki is the integration constant.

Fig. 3 (b) shows that, with two different integration constantsthe oscillator will react by changing the amplitude. In this case theamplitude is different in both integrator outputs, but they have thesame frequency and are accurately in quadrature.

S~~ ~ ~~ $\4 2 . *^ . ii. ... #,,'

.2 AWz V;'' t ~4 1__.__0 5 10 15 2D 25 30 s 10 Is 20 25a 0

TIM (si Tim IS)

a)Fig. 3 - a) Equal integrator constants;

b) Different integrator constants.

b)

Tio IS)Fig. 5 - Two-integrator oscillator (Fig. 4) sinusoidal outputs.

B. Two-integrator oscillator-mixer

In order to preserve the quadrature relationship it is crucial notto change the zero crossings at the integrator outputs. Therefore,the only way of injecting the RF signal without changing theoscillator performance is by modulating the level of the integratorwaveforms at the comparator inputs (Fig. 6). Then the oscillatorsignals remain in quadrature after the injection of a RF signal (Fig.7) and we realize the mixing function. The injected signal must bealways positive; it is a sinusoidal with a DC component. If a soft-limiter is considered (oscillator with sinusoidal amplitudes) asimilar behavior occurs.

The amplitudes of the outputs depend on the initial conditions ofboth integrators and their integration constants:

Vouti = Vint I + - Vint 2 and Vout2 = Vint 2 + 2 VintIKi2 Kil

where Vint] and Vint2 are the initial conditions on the integrators.

The oscillation frequency is obtained by substituting (2) in (1):

(3)4

f =fl =f2 --4Vint I Vint 2Kil Ki2)

The hard-limiters are critical blocks because it is difficult todesign them for high frequencies. At very high frequencies thelimiter works as a linear amplifier with soft limiting (Fig. 4). Theoutput waveforms are now approximately sinusoidal (Fig. 5). Yet,the quadrature relationship is preserved.

(2)

Fig. 6 - Two-integrator oscillator-mixer block diagram

I I.

Fig.7-Osillato-m10 Is 20

Fig. 7 -Oscillator-mixer modulated outputs

Fig. 4 - Two-integrator oscillator with soft-limiters.

III. CIRCUIT IMPLEMENTATION

The two-integrator oscillator circuit is presented in Fig. 8. Eachintegrator is realized by the differential pair (transistors M) and acapacitor (C). There is an additional differential pair (transistorsML), with the output cross-coupled to the inputs, which performstwo related functions:

- compensation of the losses to make the oscillationpossible (negative resistance in parallel with C);

- amplitude stabilization, due to the non-linearity.Current sources with current II,el, control the amplitude, and

the oscillator frequency is controlled by current sources Itune

386

It should be noted that the correspondence between the circuitof Fig. 8 and the block diagrams in the previous section (Figs. 1and 3) is conceptual and not topological: the integrators withlimited output shown in Fig. 8 are modelled by the ideal integratorsin cascade with limiters (Figs. 1 and 3).

The circuit of Fig. 8 can work in two different modes. In thelower frequency range, the performance has some resemblance tothat of the block diagram shown in Fig. 1. The waveforms areapproximately triangular. In the upper frequency range the circuitof Fig. 8 is modelled by that of Fig. 3. The outputs areapproximately sinusoidal.

The simulation results below show that results derived fromthe block diagrams. They are also useful to describe theperformance of the circuit shown in Fig. 8.

in =2 4i and vn (fm )= JFJ4KTRUUsing (1) the oscillation frequency is:

fo0 = therefore -f- I4CV AI 4CV

and f _- foav V

where V = VH - VL = 2RI,eve, is the output voltage defined by theamplitude stabilization circuit.

Replacing (6) and (5) in (4) the phase noise due to the current andvoltage noise source is, respectively:

L(fm)2kFT (1fo2Ri tune

m

and L(fmV)= R )

Fig. 8 - Two-integrator oscillator with amplitude stabilization

The circuit is designed for the 0.35gm CMOS technologyfrom AMS. The circuit parameters are: R = 200 Q, for Mtransistors (W/L)=160 gm / 0.35 gim, and for ML transistors(W/L) =80pm / 0.35 gim, C= 200 fF, ILet= 2 mA. The circuitsupply voltage is 3V.

The phase noise is associated with the current source switchingand the input voltage noise of the comparators. The sources ofphase noise can be represented by noise sources in series andparallel with the capacitor C: a shunt noise current in(fm) and a seriesnoise voltage v,(f), for small-signal low-frequency noise sourcesof frequencyfm [6]:

The phase noise is [6]:

L(fm) rAf) (4)

and the peak frequency shift for the current and voltage noisesource is, respectively [6]:

Afpk =9a> in (fm) and,ai

Afpk =- vn(fim)av

The amplitude voltage and current noise sources are,

respectively[6]:

As follows from (8), to reduce the phase noise it is necessaryto increase: the amplitude (V), the capacitance (C), or current(Vtune, with a penalty in power consumption and area.

IV. SIMULATION RESULTS

A. Two-integrator oscillator

We obtain an extended tuning range: 900MHz to 5.8GHz bychanging the tuning current, 'tune between 418gA and 4.13mA(this range might be further extended). In the range between900MHz and 2.4 GHz the frequency changes linearly with the It'm(Fig. 9) and this corresponds to the first case of the high levelstudy in section II (oscillator with triangular waveforms). Forfrequencies higher than about 2.4 GHz, the circuit outputs are moreclose to sinusoidal (corresponding to the second case of the highlevel study). The frequency will be proportional to the gain of theMOS differential pair, which, in turn, is proportional to the squareroot of the current. This explains the shape of the curve offrequency versus tuning current (Fig. 9) for higher frequencies.

77

6

5

I

a4 -

c= 3 -C22

- Linear

L-Simulated'!

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5haure [mA]

Fig. 9 - Frequency versus tuning current

Fig. 10 shows that if we change the integrator constants by20%, the oscillator amplitudes change, but the oscillator outputsremain accurately in quadrature. This simulation is done for thelinear tuning region where the outputs are approximatelytriangular. For very high frequencies, the tuning becomesnonlinear, and the output voltages are close to sinusoidal, yet theyare in quadrature.

387

(6)

(7)

(8)

1-o

19 21

Time (ns)

Fig. 10 - Effect of changing the integrator constants by 20%.

We simulatefrequencies (Tablenoise is lower than -

the phase noise for different oscillationI). We can observe that the oscillator phase-117.5 dBc/Hz over the tuning range.

Table I - Phase noise

Current Control Frequency Phase Noise(@lOMHz)418 ,A 900 MHz -1 18.98 dBc/Hz829 pA 1.8 GHz -121.62 dBc/Hz935 pA 2.0 GHz -121.53 dBc/Hz1.14 mA 2.4 GHz -121.07 dBc/Hz4.13 mA 5.8 GHz -1 17.50 dBc/Hz

B. Two-integrator oscillator-mixer

By adding the RF signal to the level current control ('level = IDC+ IRF) we perform mixing. Fig. 11 shows that the oscillator outputsare modulated by the injected signal, yet the oscillator outputsremain in quadrature. Thus, a wideband two-integratoroscillator-mixer with accurate quadrature outputs is obtained. InFig. 11 it is shown the simulation in the upper frequency range (at5 GHz) but outputs remain accurately in quadrature in all thetuning range.

2.4

fLo

fLo-fi fLo+fl

1 2 3 4 5 6 7 8 9 10Frequency (GHZJ

Fig. 12 - Oscillator-mixer modulation (spectrum)

V. CONCLUSIONSWe outlined a high-level study of a two-integrator oscillator in

which the key aspects are analyzed: quadrature relationship,amplitude and oscillation frequency. We studied the two-integratoroscillator working with hard limiting (triangular outputs) and withsoft-limiting (sinusoidal outputs). In both cases in the presence ofmismatches the circuit changes the amplitude and oscillationfrequency, but the outputs remain in quadrature.

We presented a new wideband two-integrator oscillator circuitthat performs the mixing function throughout the tuning range,while preserving the quadrature relationship.

A circuit implementation was given, and the expressions havebeen derived for the phase noise of current and voltage noisesources. The circuit has a large tuning range from 900 MHz to5.8 GHz, and is suitable for use in modem RF applications. Thecircuit can work in two different modes: at lower frequencies it isclose to a relaxation oscillator, with triangular and square outputs;at higher frequencies it is closer to a second order oscillator withsinusoidal outputs. The frequency is proportional to the tuningcurrent between 900 MHz and about 2.4 GHz (triangular outputs).For higher frequencies (sinusoidal outputs) the frequency isproportional to the square root of the tuning current.

REFERENCES

; 2.2 00 / 0 ,,; \ t ,0 ,, t \ [1] C. Verhoeven, First-Order Oscillators, PhD Thesis, TU Delft,1989.

[2] J. Femandes, M. Kouwenhoven, and C. van den Bos, "TheEffect of Mismatch and Disturbances on the Quadrature

E 2 ./--' ---;'-- Relation of a Cross-Coupled Relaxation Oscillator",ISCAS'OJ, vol. I, pp.476-479, May 2001.

[3] L. B. Oliveira, J. Femandes, M. Kouwenhoven, C. van denBos and C. J. M. Verhoeven, "A Quadrature Relaxation

1.818 18.1 18.2 18.3 18.4 18.5 Oscillator-mixer in CMOS", ISCAS'03, vol. I, pp. 689-692,

Time (ns) May 2003.

Fig. 11 - Modulated signals (time domain) [4] D. Leenaerts, J. van der Tang and C. Vaucher, Circuit Designfor RF Transceivers, Kluwer, 2001.

We have applied a signal of frequency fi to the current source [5] L. B. Oliveira, J. Fernandes, I. M. Filanovsky and C. J. M.IIev. By performing an FFT we have obtained the spectrum shown Verhoeven, "A 2.4 GHz CMOS Quadrature LCin Fig. 12 (for the I output). Oscillator-mixer", ISCAS'04, vol. I, pp. 165-168, May 2004.

[6] B. Moore, "Noise in CMOS Voltage Controlled RelaxationOscillators", Analog Integrated Circuits and SignalProcessing, vol. 23, pp. 7-16, 2000.

388