Research Article All-Pass Filter Based Linear Voltage Controlled Quadrature Oscillator

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1 Hindawi Active and Passive Electronic Components Volume 27, Article ID , 8 pages Research Article All-Pass Filter Based Linear Voltage Controlled Quadrature Oscillator Koushick Mathur, Palaniandavar Venkateswaran, 2 and Rabindranath Nandi 2 Department of Electronics & Communication Engineering, UIT, Burdwan University, West Bengal 734, India 2 Department of Electronics & Telecommunication Engineering, Jadavpur University, Kolkata 732, India Correspondence should be addressed to Rabindranath Nandi; robjutel@yahoo.co.in Received 4 June 27; Accepted 27 July 27; Published 29 August 27 Academic Editor: Jiun-Wei Horng Copyright 27 Koushick Mathur et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A linear voltage controlled quadrature oscillator implemented from a first-order electronically tunable all-pass filter (ETAF) is presented. The active element is commercially available current feedback amplifier (AD844) in conjunction with the relatively new Multiplication Mode Current Conveyor (MMCC) device. Electronic tunability is obtained by the control node voltage (V) of the MMCC. Effects of the device nonidealities, namely, the parasitic capacitors and the roll-off poles of the port-transfer ratios of the device, are shown to be negligible, even though the usable high-frequency ranges are constrained by these imperfections. Subsequently the filter is looped with an electronically tunable integrator (ETI) to implement the quadrature oscillator (QO). Experimental responses on the voltage tunable phase of the filter and the linear-tuning law of the quadrature oscillator up to 9.9 MHz at low THD are verified by simulation and hardware tests.. Introduction Realization of first-order all-pass filters had been reported earlier using various types of active building blocks (ABBs), namely, VOA [], Current Conveyor and its variants [2 5], DDA[6],DDCC[7],DVCC[8,9],VDIBA[],andOTA, with differential amplifier [] as listed in Table ; some of these building blocks are implemented with a basic device (OTA, CC, or DVCC) combined with some signal (current or voltage) differential unit. Recent literature suggests that electronic function circuits fabricated by commercially available IC modules are capable of providing desired results [2 6]. A varied genre of ABBs emerged during the recent past for realizing diverse functions towards signal processing/ wave forming/filtering applications. Fabrication of internal design of such ABBs in CMOS technology leads to easy verification. However, recent studies address the issues of such approach concerning involvement of fabrication cost and complexity in their nodal relations with such wide variety of ABBs [2, 4, 6]. Use of readily available off-the-shelf devices thus may be an alternate approach to obtaining satisfactory results. Some recent composite blocks yield quite useful results on signal processing applications wherein two types of basic commercially available chips are conjoined (e.g., DDCC, DVCC, and VDIBA). It has been suggested that composite blocks may provide better results in comparison to the constituent elements [7]. So for such ABBs requiring more than one commercially available IC, it is still economical and more convenient compared to chip fabrication [2, 6, 7]. The relatively new MMCC element [8] used in this work is thus configured using readily available CFA (AD844) and multiplier (AD835) [9] elements. The useful feature of the MMCC is that it has an in-built control voltage terminal (V) which is conveniently utilized for electronic tuning of a circuit parameter. Hence the conventional method of transconductance (g m )tobiascurrent(i b ) conversion is avoided; such conversion needs additional hardware complexity and involvement of thermal voltage (V T ) [3,, 6]. We now present here an electronically tunable all-pass filter (ETAF) using the composite CFA-MMCC block. Next a linear voltage controlled quadrature oscillator (LVCQO) is implemented with the ETAF being looped in feedback with an electronically tunable integrator (ETI).

2 2 Active and Passive Electronic Components Table : Comprehensive summary of recent APFs. Ref. ABB ABB implementation f p reported (Hz) Tunability [] VOA HA 2544C opamp 25 K RC [2] CCII LF 356N opamp with current mirror.6 K RC [3] DO-CCCII Dual-output current controlled conveyors.63 M I b [4] CCC II with OA Current controlled conveyor 2.5 K I b [5] DO-CCII CC II with additional z-copy node 3.89 M RC [6] DDA Differential amplifier (DA) 6 K RC [7] DDCC Current conveyor with DA 38 K RC [8] DVCC VDU followed by OTA 4 K I b [9] DVCC VDU followed by CC.59 M RC [] VDIBA OTA with differential input buffer 9.4 M I b [] OTA OTA with DA 375 K I b Proposed CFA-MMCC CFA844 and multiplier AD M V Notes. (a) Designs in [, 2, ], based on commercially available IC modules; (b) comprehensive listing of recent APFs using various ABBs presented in [5]. Detailed analysis is carried out taking into account the device imperfections, namely, parasitic shunt-r z C z components and the roll-off poles of the port-transfer ratios. Effects of these nonidealities are negligible but the higher range of usable frequencies is constrained. The oscillation frequency (ω o )is active-insensitive relative to port-mismatch error (ε). Experimental results on ETAF and quadrature oscillator responses are verified by PSPICE simulation and hardware test. 2. Analysis TheproposedETAFisshowninFigure(a)wherethenodal relations are as follows: CFA: I z =αi x, V x =βv y,andv o =δv z MMCC: I z =ai x, V x = b(kv y V y2 ),andv w =γv z. The port tracking ratios are ideally unity but may be postulated by error coefficients ( ε ) asα=( ε i )=a, β= ( ε V )=b,andδ=( ε z )=γ,wherek (./volt) is the multiplication constant [2]. Analysis of Figure (a) yields the transfer function G V o /V i as G= {δ δ 2 m+(δ δ 2 )α 2 β 2 }snτ {α α 2 δ δ 2 abγ} () [snτ + α δ abγ] parasitic elements, yielding a modified transfer where m = r 3 /r 4, n=r 2 /r,andτ = RC/kV. In ideal devices port tracking ratios are all unity; assuming the realizability conditions as m==n(r,2,3,4 =r)for simplicity, we get (sτ ) G= (2) (sτ + ) which is the nonminimum phase all-pass function, where transmission gain G = and phase (θ)istunableinarange 8 θ,beingvariablebycontrolvoltage(v)as θ=π 2arctan ( ωrc ). (3) kv 3. Effects of Nonidealities 3.. Parasitic Components. The parasitic components appear as shunt-r z C z arms at current source nodes of the device; as per data-book [2], the typical values are 2 r z (MΩ) 5 and 3 C z (pf) 5.5; ratio of circuit resistors (KΩ) relative to r z is assumed to be negligible. Reanalysis now with finite parasitic elements yields modified transfer elements in Figure (a) exhibiting a single-pole roll-off model [22], given by where G = (n 2 s 2 +n s+n o ) (d 3 s 3 +d 2 s 2 +d s+d o +), (4) n 2 =ττ z (+σ) n =τ(+σ) ( + μ )+(μ 3 τ z ) n o =μ 3 ( + μ ) d 3 =ττ z τ z2 (+σ) d 2 ={ττ z (+σ) ( + μ 2 )} +ττ z2 {(+σ) ( + μ )} + (μ 3 τ z τ z2 ) d =τ{(+σ) ( + μ )+(μ 3 τ z )} ( + μ 2 ) d o =μ 2 +{τ z2 μ 3 ( + μ )} σ= C z3 C, μ,2 = r, r z,2

3 Active and Passive Electronic Components 3 E o w z MMCC + k y y 2 x V r z3 C z3 C o r 2 x CFA y z R E r r 3 r 4 x z CFA 2 y r z2 V o C z2 y y 2 X AD835 k + AD844 w r z C z V i (a) (b) Z Figure : (a) First-order ETAF. (b) Implementation of MMCC with commercially available ICs. μ 3 = R kvr z3 τ z,2 =rc z,2, τ z,2 τ. Then (4) simplifies to G = (5) [s 2 ττ z +sτ ] [s 3 ττ z τ z2 +s 2 (τ z +τ z2 )+sτ+]. (6) The frequency-domain behavior may be estimated by writing s=jωin (6), given by where ζ = ζ 2 = G (ω) = ω2 ω p ω z ; ω 2 ω z2 ω z [jωτ ( + ζ )] [j {ωτ ( ζ 2 )} + ( ζ 3 )], (7) ω p (filter-pole frequency) = τ, ω z = τ z ; ζ 3 =ω 2 τ(τ z +τ z2 ) τz=τz2=τz 2ω2 ττ z 2ω2 ω p ω z. With C z 3.3 pf (measured) and r=kω,weestimated value of the parasitic pole frequency f z 54MHz. Hence for usable ranges of < f z, effects of parasitic capacitors are negligible and G =G; therefore the nominal APF function is preserved with the limit f f z. (8) 3.2. Roll-Off Pole of Device-Port Transfer Ratios. At relatively high-frequency ranges, the port-transfer ratios α, β, δ and a, b, γ of the active components are as follows: α o,2 α,2 = (sp,2 +) δ,2 = β 2 = a= b= γ= δ o,2 (sp 3,4 +) β o2 (sp 5 +) a o (sp i +) b o (sp V +) γ o (sp z +). The dc values of all the products of port coefficients in () may be taken as unity; for example, α o,2 { (ε i +ε i2 )} since ε i,2. The modified APF function (G )isnowwrittenas where (9) G = [Δ +Δ 2 (Δ ) sτ Δ 3 M], () [sτ + Δ 4 M (s)] Δ =δ δ 2 Δ 2 =α 2 β 2 Δ 3 =α α 2 Δ 4 =α δ {s 2 p 3 p 4 +s(p 3 +p 4 )+} {s 2 p p 5 +s(p +p 5 )+} {s 2 p p 2 +s(p +p 2 )+} () (2) (3) {s 2 p p 3 +s(p +p 3 )+}. (4)

4 4 Active and Passive Electronic Components Table 2: Comparative description of recent QO designs. Ref. Device used Electronic tunability Linear tuning law f o reported (Hz) Tuning by THD (%) [5] DO-CCII No No 2.33 M RC [] VDIBA Yes No 8.5 M I b 2.25 [2] CFA No No 99 K RC [4] CFA No No 398 K RC.42 [23] OTA Yes Yes 64 K I b [24] VOA No No 6 K RC [25] CFOA No No 59 K RC 3.6 [26] CDTA Yes No.73 M I b 3. [27] CCCDBA Yes No 49 K I b 2.2 [28] CCCCTA Yes No. M g m 2.9 [29] OTA Yes No.59 M g m 2.2 Proposed CFA-MMCC Yes Yes.2 M V The function M(s) relates to the MMCC block; it is decomposed as M(s) = M o (s) M e (s),wherem o = /sτ o and M e (s) = [(sp i +)(sp V +)(sp z +)]. (5) It has been observed that the 3 db corner frequencies for all the port-transfer ratios appear at close proximity, and hence these may be assumed equal without loss of generality [22]. Therefore calculations for examining the effects of the roll-off poles become simpler if we write p 5 /ω p.writing u=(ω/ω p ) and solving for () we get Δ (jω) = { u 2 +2ju} (6) which implies Δ = (+4u 2 ) and NΔ = arctan(2u). Similar results are checked for (2) to (4). For the effects of the MMCC roll-off, we put ψ=(ω/ω m ),wherep i,v,z /ω m ;solving(5),weget M e (jω) = [( 3ψ 2 ) + j3ψ { (ψ 2 (7) /3)}] which reduces to M e =and NM e = arctan(3ψ). This analysis indicates that effects of roll-off poles of the active building blocks are quite negligible in the range of operating frequencies (f <f p,m ). 4. LVCQO Implementation Quadrature oscillators find diverse application in measurement systems [3 33] and in communication circuits, quadrature mixers, SSB-modulator, vector generator, and data conversion. A comprehensive summary of recent QO designs is listed in Table 2. It may be seen that even though a number of such oscillators were reported, very few are linearly tunable. We now present the linear VCO as implemented by forming a regenerative feedback loop formed with the ETAF in Figure (a) and the ETI in Figure 2; transfer of ETI is H (s) = {sτ o (+ξ) +(R o /r z )}, (8) V i y MMCC V y 2 + R o x k w z Figure 2: Electronically tunable integrator (ETI). where τ o = R o C o /kv, ξ = C o /C z,andr o /r z ; henceh(s) = /sτ o. Grounding of the capacitor (C) facilitates absorbing C z in C-values at predesign level. Device imperfection relative to port-transfer roll-off pole frequencies (ω a,b,γ ) is estimated by writing H (s) = (abγ) sτ o where ε T =(ε i +ε V +ε z ). The deviation due to roll-off is V o C o C z r z ( ε T) {(sτ o ) }, (9) ={( s ω a )+}{( s ω b ) + } {( s ω γ )+}. (2) As in previous section if we assume ω a,b,γ ω m and put ψ= (ω/ω m ),then reduces similar to (7) as =, N = arctan (3ψ). (2)

5 Active and Passive Electronic Components (db) k M Frequency (Hz) (B) M (A) 6 2M e f p (-(T) (A) 3. ;N f p =9. (B).2 ;N f p =6. (A) (9 V=9vIFNs) (B) (6 V=6vIFNs) (a) THD (%).25 Amplitude (volt) Mhz 9 MHz V ip (volt) (b) 7.5 M 25n Time (sec) (c) 5n Frequency (Hz) 5M (d) 4 7 V (dc volt) Simulation Hardware (C = 8 J&, R=4Ω) Hardware (C =4J&, R=4Ω) (e) Figure 3: Continued.

6 6 Active and Passive Electronic Components (A) (B) (C) (A) (-T) (B) (4 MHz) u=(f/f o ) (C) (8 MHz) Gain-crossover point (f) Gain (db) f o (-(T) Quadrature phase error THD% (Δ ) Figure 3: Measured response of ETAF and QO. (a) AP phase response: (A) = 9 V.d.c.; (B) = 6 V.d.c. (b) AP-THD (%) to 7th harmonic. (c) QO wave response tuned at MHz quadrature signals at V o and E o nodes. (d) QO spectral response of MHz for phase-noise evaluation. (e) QO linear-tuning response. (f) Measured tuning error of VCO. Nowimplementationofoscillatorisderivedbyequating{ GH(s)} which gives the characteristic equation (CE): CE: Realizability condition: s 2 τ o τ+s(τ o τ)+= τ o =τ R=R o, C=C o (22) Oscillation frequency: ω o = kv RC. So tuned frequency (f o in Hz) is linearly and directly variable by control voltage (V) V f o = (2πRC). (23) The proposed method provides direct electronic tunability of oscillation frequency by the control voltage (V). No additional current processing circuitry for g m to bias current (I b ) conversion is needed, as seen in the previous designs shownintable,andthermalvoltage(v T )isnotinvolved. It may be seen that ω o is practically active-insensitive, S ωo ε.5ε. 5. Experimental Results The response of V-tunability of the proposed ETAF and LVCQO had been verified by PSPICE simulation [34] and hardware tests; these are shown in Figure 3. ETAF responses, along with its phase error (θ e ) and THD (measured to 7th harmonic), are shown in Figures 3(a) and 3(b) which are relatively low compared to [, 24, 25]. Some small phase error (θ e ) on the experimentally generated sinusoid quadrature signals deviated around 9 wasmeasuredasshownin Figure 3(c). The oscillator spectral response in Figure 3(d) shows the LVCQO spectral response wherein phase noise measured is 7 dbc/hz at an offset of KHz from the tuned frequency of MHz; this response is measured by Tektronix spectrum analyzer (RSA36B) [35]. This result is better as compared to that in [4]. A new method of examining the VCO tuning error (β%) is adoptedbymeasuringtheshift(δf)inf o at phase cross-over frequency. The tested value of β% in the overall tuning range of MHz MHz was observed to be less than 4.5%. 6. Conclusion A new design of ETAF function and its subsequent application to the implementation of a VCQO with linear-tuning law arepresented.theactiveblocksarecommerciallyavailable CFA (AD844) and four-quadrant multiplier (AD835) which are readily available IC modules. Responses of the function circuits are verified experimentally with PSPICE simulation and hardware tests. The quadrature oscillator had been tuned by control voltage (V) in a linear range (band-spread) of.5 f o (MHZ) 9.9 at low THD. The design does not need any additional current processing circuitry; hence there is no extra quiescent dissipation. Power dissipation of the proposed oscillator circuit is about 33 mw. The circuit is practically active-insensitive relative to device-port trackerror (ε). Analysis on the effects of device parasitic components indicates insignificant effect on design equations, even though parasitic capacitors tend to limit the usable high-frequency range. In this work, a relatively new building block, namely, the MMCC, had been utilized for the voltage (V) controlled linearly tunable quadrature oscilator design with 7 dbc/hz phase noise at KHz offset as shown in Figure 3(d). Thus a comparatively better quality result had been obtained as is shown in Table 2.

7 Active and Passive Electronic Components 7 It may be seen in Tables and 2 that in the cited designs active devices used are certain primary blocks with auxiliary voltage/current differencing unit (VDU/CDU) or differential amplifiers with their associated parasitics which tend to limit the desired range of frequency (f p or f o )[6].Also,tuning by g m or I b needs additional current processing circuits with parasitic capacitors. The authors believe that, owing to such topological distinction, the frequency tuning ranges are somewhat lower. However in the case of design by VDIBA [], the range improves owing to the fact that the active component OPA-86 has itself a bandwidth (BW) of 47 MHz. In the proposed design, no such VDU/CDU and g m -to-i b conversion circuitry are used; this circuit is structured with commercially available AD844 (BW = 6 MHz) and AD835 (25 MHz) IC modules to achieve relatively higher frequency, wherein effects of port-mismatch roll-off poles and parasitics hadbeenincludedinsupport. Conflicts of Interest The authors declare that they have no conflicts of interest. References [] S. J. G. Gift, Application of all-pass filters in the design of multiphase sinusoidal systems, Microelectronics Journal,vol.3, no.,pp.9 3,2. [2] M. Higashimura and Y. Fukui, Realization of current mode allpass networks using a current conveyor, IEEE Transactions on Circuits and Systems,vol.37,no.5,pp.66-66,99. [3] S. Öztayfun, S. Kilinç, A. Çelebi, and U. Çam, A new electronically tunable phase shifter employing current-controlled current conveyors, International Electronics and Communications,vol.62,no.3,pp ,28. [4] S. Minaei and O. 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