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    IV. C O N C L U S I O N

    This report show s that we are able to increase the output pow er

    of the 87Rbmaser by about 5 dBm by us ing opt ical pumping at both

    ends and to m ake the shor t- term frequency s tabil i ty improvement

    of about a factor of 1.4. The short-term frequency stability might

    be improved fu r ther by us ing tw o diode lasers with higher intens i ty

    and by optimizing the ce ll temperature. Our measurements are con-

    sistent with the density matrix treatment.

    A C K N O W L E D G M E N T

    The authors thank Tan Yongfang fo r technical support .


    [l ] P. Davidovits and R. Novick, The optically pumped rubidium

    maser, Proc . IEEE vol. P-54, pp. 155-170, 1966.





    Brousseau and


    Vanier, A compact 87Rbmaser, IEEE

    Trans. Ins t rum. Me a s . , vol. IM-24, pp. 291-295, 1975.

    [3] M. Tetu, G . Busca and J. Vanier, Short-term frequency stability of

    the 87Rbmaser, IEEE Trans. Ins t rum. Meas. , vol. IM-22, pp. 250-

    257, 1973.

    [4] M. Tessier and J Vanier, Theorie du maser au rubidium 87, Can.

    [5] J . Vanier, R elaxation in rubidium-87 and the rubidium maser, Phys.

    [6] G. Busca, M. Tetu and J. Vanie r, Light shift and light broadening in

    J . Phys . ,

    vol. 49, pp. 2680-2689, 1 971.

    Rev . ,

    vol. 168, pp. 129-149, 1968.

    the 87Rbmaser, Can. J Phys . , vol.


    pp. 1379-1387, 1973.

    A Simple Wide-Band Sine Wave Quadrature


    Ralph Holzel

    Abstract-A simple sine wave oscillator delivering two signals in

    quadrature has been developed, covering the frequency range from



    Hz to 100 MHz and being voltage-controllable over each fre-

    quency decade. The circuit consists of two


    phase shift stages using

    active allpass filters and an inverter,


    arranged in a feedback loop.

    Although general application is envisaged, the design is particularly

    suitable in particle electrorotation studies.



    Quadrature generators , i . e . , generators producing tw o s ignals of

    ident ical f requency and a mpli tude but of dif ferent phase angle, are

    used in a var iety of a ppl icat ions , as for exam ple in telecommuni-

    cations f I quadrature mixers and s ingle-s ideband generators [11


    for measurement purposes in vector generators


    selective volt-

    meters [2]. They have foun d furthe r utility in the physical charac-

    terization of microscopic particles and biological cells using the

    phenomenon of electrorotation, whereby rotational torques are in-

    duced through application of rotating electric fields of variable fre-

    quency [3]-[SI. The availability of wide bandwidth qu adrature


    cillators of simple design is important for such studies, and it is

    Manuscript received August 21, 1992; revised October 20, 1992.

    The autho r is with the Institute of M olecular and Biomolecular Electron-

    IEEE Log Number 9207680.

    ics, University of Wales, Bangor LL57 IUT, United Kingdom.







    42, NO. 3 J UNE 1993

    0018-9456/93 03.00 1993 IEEE

    this consideration that has led to the circuit development described


    Rectangular quadrature signals (i.e. , of 90 phase shift) are

    readily available up to some tens of MHz using ring oscillators


    by dividing the f requency of a square wave by tw o and combining

    this with the original signa l via logic gate s [SI. Sinusoidal voltages

    can be generated using special commercially available ICs (e.g. ,

    Burr Brown 4423 up to


    kH z) . Higher f requencies can be

    achieved by programming the differential equation of a sinusoidal

    oscillation with the help of operational amplifiers [6]. For that two

    integrator s tages are connected in ser ies with an inver ter , of which

    the output is fed back to the input of the f i rs t s tage. How ever , the

    upper f requency l imit of such an osci l lator


    still limited by the

    relatively low bandwidth of the integrators.

    Here we describe a circuit that utilizes two allpass filters as 90

    phase shif ters in ser ies with an inver ter operat ing up to 100 MHz.

    11 D ESIG NC O N S I D E R A T I O N S

    Ideal first-order allpass filters (Fig. 1) are characterized by a fre-

    quency-dep endent phase shift varying from 80 at low frequen-

    cies to 0 at high frequencies, given by



    -2 arccot (27rfRC), (1)

    while the am plificat ion equa ls uni ty for R I


    R t all frequencies

    [7]. Cascading two allpasses and an inverter and feeding back the

    output to the first stage (Fig. 2) lead to an oscillation [8] at the

    frequency where


    = -90 i . e . , a t

    f = 2 7 m - I .

    Equat ions (1) and (2) only hold for moderately low frequencies ,

    since real operational amplifiers exhibit an additional phase shift

    increasing with f requency du e to paras it ic capaci tances . G eneral ly,

    oscillation can only occur if


    + 02 +


    = - 3 6 0 .


    long as the inver ter s tage does not add any addi t ional phase

    error , i . e . , pi = 18 0, the sum of the al lpasses phase shifts must

    amount to


    + 02 = 3 6 0


    = 180 for osci l lat ion. For iden-

    tical allpass stages (oI and 02are ident ical , even i f they d o not work

    ideal ly, e.g. , at higher f requencies . W ith





    180 and


    = 02 follows


    = 02 = 90. That means the output s ignals are

    always in quadrature provided 1) the inverters phase error is zero

    and 2) the al lpass s tages are ident ical. Therefore, the bandwidth of

    the inver ter is more important fo r the circui t s f requency range than

    the bandwidth o f the al lpasses .

    In selecting suitable operational amplifiers account should be

    taken of the fact that all stages work at amplifications of unity.

    Therefore, many high-speed operational amplifiers, that are usually

    not uni ty gain s table, cannot be used or only so with some restric-

    tions. To cancel variations in amplification and to maintain low

    dis tor t ions , the inver ters gain should also be controllable. How -

    ever , inver ter gains deviat ing f rom unity wil l correspond to de-

    viating allpass gains and thus lead to an inequality of the output


    In order to control the osci l lat ion f requency via a dc vol tage,

    field effect transistors (FET), light dependent resistors (LDR)


    capaci tance diode s can be used. Th e lat ter are less useful for f re-

    quencies below 1 kHz because of their maxim um capaci tance val-

    ues of about


    nF and the typical input res is tance of the order 1


    f fast operational amplifiers. FETs are available as matched

  • 7/26/2019 A Simple Wide-band Wave Quadrature Oscillator




    VOL 42,

    NO. 3, JUNE 1993




    First-order allpass filter.



    q s i n




    U,sn (cot+ )





    = -90 cp =-90 cp .





    Block-diagram o f the quadrature oscillator.

    pairs and thus have the adv antage over LDR's in achieving equal i ty

    of both phase shift stages. Furthermore, the approximately recip-

    rocal dependence of the drain-source-resistance o n the gate-source-



    can be exploited to achieve a l inear relationship be-

    tween controlling voltage and oscillator frequency.






    To prevent instability caused by stray effects mainly of the two-

    pole switch SI Fig. 3) only moderately fast operational amplifiers

    (Analog Devices AD 847, ful l power bandwidth 10MH z) are used

    in the allpass stages. The


    network at the inverter 's input per-

    mits a s table function of the fas t op a mp , which otherwise would

    need a gain of 4 or more. The osci l lation a mpli tude is l imited by

    the nonlinearity of germanium diodes AA


    and can b e adjus ted

    by V, via FET B F 256, which works as a voltage-controlled resis-

    tor. At f requencies below a few MHz the FET c an be replaced by

    a fixed resistor, since the amplitude rem ains nearly constant. H ow-

    ever, fo r minimizing signal distortion it is advisable to contro l the

    gain automatically via


    and a PI-regulator, that measures the ac-

    tual oscillation amplitude.

    The f requency can be tuned by Vfiwhich co ntrols the drain-

    source-res is tances of the F ET pair




    Good linearity be-

    tween controlling voltage and oscillation frequency was achieved

    over a whole f requency decade as shown in Fig.

    4 .

    By switching

    the frequency-determining capacitors a frequency range of more

    than 7 decades f rom below 1 Hz up to 10 MHz could be covered.

    On examining the use of different types of operational amplifiers

    in the allpass stages it was found that, as a good measure of the

    accessible frequency range, the full power bandwidth cited in the

    semiconductor's datasheet can be used rather than the unity gain

    or 3

    dB bandwidth.

    The s ignal 's harmonic content at


    kH z am ount s to -24 d B

    for the third and less than


    dB for al l other harmonics , i f the

    gain control voltage V, is kept constant at a value that allows fre-

    quency variations over several decades. If V , is opt imized and con-

    trolled automatically by a PI-regulator the third harmonic is re-

    duced to



    Even higher frequencies can be achived using faster amplifiers

    and through a reduction of stray capacitances.


    this purpose a


    Fig. 3 . Circuit diagram of the voltage-controlled sine quadrature oscillator

    operating up to



    controlling voltage

    V, PI



    Dependence o f the output frequency of the sine quadrature VCO

    Fig. 3) on the controlling dc voltage.

    Fig. 5 . Circuit diagram of the quadrature VCO for frequencies up to 100


    1 2 3

    controlling voltage V [V



    Dependence o f the output frequency of the quadrature VCO Fig .

    5) on the controlling dc vo ltage.

    second circuit was built employing surface mount compone nts (Fig.

    5 ) , with the very fas t op amp O PA 621 (Burr Brown, ful l power

    bandwidth 80MH z) being em ployed in the al lpass f i l ter stages and

  • 7/26/2019 A Simple Wide-band Wave Quadrature Oscillator






    NO. 3

    J UNE


    with the relatively large FET p air being replaced by tw o capaci-

    tance diodes. A dual-gate M OSFE T, fol lowed by a bipolar col lec-

    tor s tage, operates as a vol tage-control led inver ter , and the L C net-

    work at the MO SFETs d rain suppresses parasi t ic osci l lat ions at

    230 M Hz caused by the o p amp ( that is usual ly only s table at gains

    of at least 2). By these means the f requency range was extended to

    100 MHz, al though somewhat higher operat ing f requencies are

    possible, provided unequal amplitudes of the quadrature outputs

    can be tolerated. The correlation between tuning voltage and fre-

    quency is l inear over nearly a f requency de cade (Fig. 6) , w ith de-

    creas ing s lop e above 80 MH z.

    This quadrature osci l lator design has been successful ly em-

    ployed to generate rotating electrical fields in studies of the ac

    electrokinetics of biological cells [3], [4].


    A simple vol tage-controlled s ine wave osci l lator with quadrature

    output has been developed, which is useful at f requencies f rom

    below 1 Hz to about 100 MH z for appl ications such a s the s tudy

    of particle electrorotation phenom ena. If a lower frequency limit is

    required, this should be achieved by rapid switching of the fre-

    quency-determining capacitors with analogue switches [lo], rather

    than by using large electrolytic capacitors. A furth er expansion o f

    the bandwidth to higher frequencies might be possible using even

    faster hybrid operational amplifiers or discrete components, but this

    would be at the expense of the circuits simplicity.

    A C K N O W L E D G M E N T

    Valuable advice and discuss ions with Prof . R. Pethig, Dr . K.

    Winkler (Free University Berlin), and Dr. J. Burt are acknowl-

    edged with grat i tude, as is the award by the Commiss ion of the

    European Community.

    R E F E R E N C E S

    P. Horowitz and W. H ill,

    The Art ofElec tronics.


    U.K. :

    Cambridge University Press, 1991, ch. 5.16, p. 291.

    U . Tietze and


    Schenk, Electronic Circu ifs: Design and Applic a-

    tions. Berlin, Germany: Springer, 1991, ch. 25.3.4, pp. 795-796.

    R. Holzel and 1. Lamprecht, Dielectric properties of yeast cells as

    determined by electrorotation, Biochim. Biophys. Ac fa, vol. 1104,

    Y Huang, R. Holzel, R. Pethig, and X.-B. Wang, Differences in

    the AC electrodynamics of viable and non-viable yeast cells deter-

    mined through combined dielectrophoresis and electrorotation stud-

    ies, Phys. Med. Biol. , vol. 37, pp. 1499-1517, 1992.

    J . Gimsa, R. Glaser, and

    G .

    Fuhr, Th eory and app licaton of the

    rotation of biological cells in rotating electric fields (electrorota-

    tion), in Physical Characterization of Biological Cells, W. Schutt,

    H. Klinkman,

    I .

    Lamprecht and T. Wilson, Eds. Berlin, Germany :

    Verlag Gesundheit, 1991, pp. 295-323.

    U. Tietze and C . Schenk, Electronic Circuits: Design and Applica-


    Electronic Circuits: Design and Applications. Berlin, Ger-

    many: Springer, 199 1, ch. 14.10.2, pp. 394-395.

    H. Schmidt, Hochwertiger durchstimmbarer Nf-Sinusoszillator,

    Elektronik, vol29, H 19, pp. 113-1 14, 1980.

    U. Tietze and C. Schenk, Electronic Circuits: Design and Applica-


    H. Lemme, CMOS-Bausteine ersetzen Vielfach-Potentiometer


    vol. 29, H 19 , p. 114, 1980.

    pp. 195-200, 1992.

    Berlin, Germany: Springer, 1991, ch. 15.4, pp. 425-428.

    Berlin: Springer, 1991, ch. 5.7, pp. 89-91.

    An Algorithm for Solving Roberts-von Hippel

    Equation: Separation


    Close Solutions

    T. P. Ig les ias , A. S eoane, and J . Rivas

    Abstract-The proximity


    the solutions


    the transcendental equa-

    tion tanh Z / Z =


    on the com plex plane arising in the determination of

    the comple x dielectric permittivity with the short-circuited line method

    is studied. A numerical procedure is described which is capable of oh-

    taining the required number of solutions, even those lying very close

    to each other, from one single initial point. The method is applied to

    measurements of various organic liquids.

    I . IN TR O D U C TIO N

    The shor t-circui ted l ine method for the determinat ion of the

    complex dielectric permittivity [11 requires solving a transcen den-

    tal equation of the form (tanh

    z ) / z

    = on the complex plane,

    where is obtained experimen tally. Although this equation pos-

    sesses infinite solutions, only one of them is physical. In order to

    el iminate this ambigui ty i t is necessary ei ther to know in advanc e

    an approximate value of the permittivity, to carry out two experi-

    ments with samples of different thickness,


    to perform m easure-

    ments at two nearby frequencies [2], [3]. Before deciding which of

    the solut ions is the physical one i t is necessary to be able to ident ify

    and distinguish from each oth er all solutions which ca n be relevant.

    In practice it is enough to c onsid er only a few of the infinite solu-

    tions, with small values of the real part, given the range of dielec-

    tric permittivities of usual substances. It is important to identify

    and dis t inguish close roots w hen s tud ying, for ins tance , the effect

    that the thickness of the sample has on the uncer tainty of the per-

    mittivity [4]. It is also necessary when measuring dielectric per-

    mit t ivi t ies with network analyzers , where the impedance of the

    sample is measured for a cont inuous range of f requencies and a

    fixed sample thickness [5]. An analogous situation arises in the

    time-domain dielectric characterization technique which uses a

    short-circuited sample.

    Several methods for the resolut ion of the equat ion above hav e

    been developed. One of them is Dakin-Works approximation [6] ,

    which is not applicable for samples with loss tangent tan




    due to the large errors that can ar ise, as i t is shown by S 0 Nelson

    et al. [7] . There are also graphical methods such as Rober t-von

    Hippels [l ] or Delbos-Demaus [8] . The lat ter is used when the

    sample has constant thickness. Com puters have al lowed the use of

    i terat ive numerical me thods , of which the m ore commonly used is

    Newton-Raphsons [ 4 ] , [9] . This method converges f rom a good

    ini tial approximate value to o ne s ingle roo t ,


    that if there were

    two roots close to each other one of them might be ignored. G el inas

    et al. [lo] also use Netwons method for the case Re c) 0 s ince

    there are no close roots corresponding to this region of the com plex


    Manuscript received January 16, 1992; revised July 7, 1992.



    glesias is with the De partamento de Fisica Aplicada, Facultad de

    Ciencias, Universidad de Vigo, 36200 Vigo, Spain.

    A. Seoane is with the Departamento de Teoria de la Seiial, E.T.S.I.T.,

    Universidad de Vigo, 36200 Vigo, Spain.

    J Rivas is with the D epartamento de Fkic a Aplicada, Facultad de Fis-

    ica, Universidad de Santiago de Compostela, Santiago de Compostela,


    IEEE Log Number 9207671.

    0018-9456/93 03.00 993 IEEE