DIGITALLY CONTROLLED QUADRATURE OSCILLATOR EMPLOYING TWO ZC-CG-CDBAs

Transcription

1 DIGITALLY ONTOLLED QUADATUE OSILLATO EMPLOYING TWO Z-G-DBAs Josef Bajer, Dalibor Biolek UD/BUT, Det. of EE/Microelectronics Kounicova 65/Udolni 53, Brno, zech eublic ABSTAT: A simle quadrature oscillator is roosed, based on the ell-knon tointegrator toology. Each integrator is emloyed by Z-G-DBA (Z-oy ontrolled Gain urrent Differencing Buffered Amlifier). The current gain is controlled digitally on the rincile of -2 current divider. The designed structure enables an indeendent control of the oscillation frequency and the oscillation condition. The designed circuit is manufactured ith the utilization of commercial integrated circuits and its roer oeration is demonstrated. Keyords: Quadrature oscillator, digital control, Z-G-DBA 1 INTODUTION Quadrature oscillators (QOs) find their alications in analog signal rocessing, communications, measurements, and controlling systems of oer electronics [1]. ecently, several tyes of active elements ere used for QO synthesis such as OTA [2], II [3], DV [4], FA [5], A [6], FTFN [7], voltage and current buffers [8], [9], DTA [10], [11], and DBA [12]. The latter QO emloys to DBAs, each of them simulating integrator, and roer negative and ositive feedback aths accomlish the oscillation condition (O) hich can be set indeendently of the oscillation frequency (OF). Also, the OF can be set via external resistors or caacitors ithout disturbing the O. In this aer, e sho that the oscillator from [12] can be imroved by relacing the conventional DBA by Z-G-DBA element (Z oy ontrolled Gain DBA), nely introduced in [13]. Digital control of the current gain enables digital control of the oscillation frequency, hich ill be directly roortional to the digital ord. The theory of oeration is verified via exerimental chi and commercial integrated circuits. 2 Z-G-DBA Z oy ontrolled Gain DBA in Fig. 1 consists of lo-imedance DU (urrent Differencing Unit) [13], F (ontrolled urrent Folloer), and unity-gain voltage buffer [14]. The difference of currents I and I n flos to the F, being available also at zc (z-coy) terminal. F oerates as a current attenuator, multilying its inut current by the transfer, 0 < 1, and roviding its outut current to the z terminal.

2 V V n I I n Z-G-DBA n zc z Izc Iz I V 0V I n 0V I n DU I -I n I -I n Z-G-DBA F 1 (I -I n ) V zc V z (a) zc z (b) Fig. 1: Z-G-DBA, (a) schematic symbol, (b) behavioral model. Z-G-DBA oeration is defined by the folloing set of circuit equations: I z V z I zc V zc V = I V I V n I n (1) The coefficient can be set either manually or electronically. The electronic control can be rovided by analog or digital method. The latter is advantageous from the oint of vie of digital control of oscillator arameters. Since the Z-G-DBA chi is not currently available, it as built according to the diagram in Fig. 2. Z-G-DBA..digital control exerimental chi OPA860 I ΔI ΔI x- ΔI -2 1 DTA x+ I n x+ AD5445 n z x- ΔI = I I n set zc zc z I z Fig. 2: Imlementation of Z DBA ith digital gain control. As shon in Fig. 2, the DU as imlemented by an exerimental chi ith multileoutut DTA [15], fabricated in MOS 0.7 μm technology. Four-outut OTA, hich is a art of the DTA, rovides to coies of difference current to zc terminals, and it also drives the -2 netork hich is imlemented by commercial 12-bit multilying digital-to-analog converter AD5445 [16]. Diamond transistor, hich is a art of OPA860 [17], rovides loimedance outut for roer oeration of AD5445 and it also guarantees the high-imedance character of the z terminal. The resistor set together ith the inut resistance in of the AD5445 (ca 10 kohms) is a art of current divider hich can recisely change the loer limit of digitally controlled gain from its default value 0 to in /( set + in ). For examle, hen selecting set = in = 10 kohms, then the current gain can be controlled ithin the range from 0.5 to 1 ith full 12-bit resolution. As shon belo, via setting the loer limit of, e set loer limit of the oscillation frequency of the QO.

3 3 POPOSED DIGITALLY ONTOLLED QUADATUE OSILLATO The roosed QO ith digital control, starting from the circuit idea ublished in [12], is shon in Fig V o1 V o2 n z 1 zc 3 n z 2 zc 1 I o 1 2 I o 2 4 Fig. 3: Quadrature oscillator ith digital control of the frequency. Analysis of the characteristic equation of this circuit yields formulae of the oscillation frequency and oscillation condition: OF: 1 2 ω osc =, (2) O: 2 = 4. (3) Note from (2) and (3) that OF can be adjusted by 1, 2, 1, 3, 1, 2 ithout disturbing the O, and that the O can be set by 2 or 4 ithout affecting the OF. Since 2 sets the ositive and 4 negative feedback, 2 must be chosen smaller than 4 for roer starting-u the oscillations. As shon in Section 4, the O automatic control can be easily accomlished e.g. by otocouler ith hotoresistor. It is evident that circuit in Fig. 3 can rovide harmonic signals ith the frequency given by Eq. (2) if the condition (3) is fulfilled. An additional analysis determines the ratios of comlex magnitudes of generated voltages V o2 /V o1 and currents I o2 /I o1 : V V o2 o =, j I I o2 o = j. (4) As results from (4), the voltage and also current signals are formed by orthogonal airs. When accomlish the design conditions 1 = 2 =, 1 = 2 =, 1 = 3 =, (5) then the above ratios of magnitudes remain 1 indeendently of OF tuning, and Eq. (2) is reduced to the form

4 OF: ω 0 =. (6) Thus, the oscillation frequency is directly roortional to the digitally controlled gain. 4 EXPEIMENTAL VEIFIATION In order to verify the above rincile of digitally controlled QO, the circuit from Fig. 3 as designed ith Z-G-DBAs imlemented according to Fig. 2. Diamond transistor OPA860 as biased via adj =330 Ohms, see [17]. The range of control as defined from 0.5 to 1 by set = 10 kohms. The assive elements of the oscillator ere designed as follos: 1 = 2 = 3 = 4.7 kohms, 1 = 2 = 56 F. According to (6), the corresonding theoretical oscillation frequency is khz for = 1 and khz for = 0.5. For automatic amlitude stabilization, resistor 4 as relaced by a hotoresistor hich is a art of otocouler 3WK16341, and the internal LED of the otocouler as sulied by rectified voltage V o1. Then each increase of V o1 causes loering 4 and thus boosting the negative feedback hich decreases the amlitude back. Fig. 4 shos measured aveforms V o1 and V o2 for = 1. The data measured has been exorted from digital oscilloscoe to Orad PSice 16 in order to erform FFT steady state analysis. The THD as ca 0.9%. 0.5V 0V -0.5V 0s 2us 4us 6us 8us 10us time Vo1 Vo2 Fig. 4: Measured aveforms for = 1, exorted to POBE. The measured relationshi beteen the oscillation frequency and the 16-bit digital ord for controlling is given in Fig. 5. The linearity of this frequency control is excellent. Hoever, the measured frequency range is from khz to khz, hich is aroximately 20 er cent belo the above mentioned theoretical values. The analysis of real influences reveals to sources of this error: 1) Parasitic caacitance of z- terminal hich is formed by the caacitance of the collector terminal of diamond transistor in arallel to the inut caacitance of voltage buffer (see Fig. 2), together more than 4 F [17]. This caacity is added to the orking caacity of 56 F, causing OF decrease by ca 7 er cent. 2) Parasitic resistance of z- terminal, hich is determined dominantly by the collector resistance of the

5 diamond transistor. According to [17], its value is rather lo, ca 54 kohms, and thus it influences the OF significantly. frequency [khz] digital ord (decadic) Fig. 5: Frequency versus digital ord for control. 5 ONLUSIONS The oscillator roosed here rovides voltage and also current signals in a quadrature. It offers more degrees of freedom for mutually indeendent control of the oscillation frequency and oscillation condition. Digital control of the current gain of the Z-DBA, active devices used for QO imlementation, enables an easy digital control of the frequency ithout disturbing the oscillation condition. The exeriments described in Section 4 confirmed this imortant feature, also calling attention to real influences hich can decrease the oscillation frequency belo its theoretical value. The key arasitic factor seems to be the internal resistance of the z-terminal of DBA. To eliminate the OF decrease, the active elements should be designed ith such a resistance as high as ossible. 6 AKNOWLEDGMENT This ork as suorted in art by the Grant Agency of the zech eublic under grant No. 102/08/0784, and by the research rogrammes MSM , MSM , and MO FVT The research has also received funding from the Euroean ommunity s Seventh Frameork Programme under grant agreement No , and by the ENIA Euroean Programme E3A.

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