# Electronically Controllable Explicit Current Output Sinusoidal Oscillator Employing Single VDTA

Authors: Dinesh Prasad; D. R. Bhaskar
Journal: ISRN Electronics
 (2012)

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## Abstract

A new current-mode sinusoidal oscillator employing a single voltage differencing transconductance amplifier (VDTA), two grounded capacitors, and one grounded resistor has been proposed. The proposed sinusoidal oscillator offers the following advantageous features: (i) use of grounded capacitors which are attractive from the view point of IC implementation as well as eliminating/accommodating parasitic capacitances, (ii) independent control of frequency of oscillation and condition of oscillation, (iii) ready availability of explicit current-mode output, (iv) low active and passive sensitivities, and (v) a very good frequency stability. The workability of the proposed configuration has been established by PSPICE simulations.


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## Body

## 1. Introduction

In the synthesis of signal processing/signal generation circuits, current-mode (CM) operation has received much attention over the conventional voltage-mode (VM) operation due to its wider bandwidth and high linearity [1]. There is a growing interest in the realization of sinusoidal oscillators with explicit CM output because these oscillators may be employed as test signal generators for the testing of CM filters, CM precision rectifier, and so forth, which would otherwise require additional voltage to current converter when tested by using conventional VM oscillators [2]. Sinusoidal oscillators find numerous applications in communication, control systems, signal processing, instrumentation, and measurement systems; see [3–5] and the references cited therein. Explicit current-mode sinusoidal oscillators (ECMSOs) based upon different active single building blocks are available in the literature; see [6–13] and the references cited therein.In [14], many active building blocks have been introduced, VDTA is one of them. Although a CMOS realization of VDTA and its RF filter application has been introduced in [15], to the best knowledge and belief of the authors no other application has been reported in the open literature so far. Therefore, the purpose of this paper is to propose a new ECMSO using a single VDTA along with three passive components (two grounded capacitors and one grounded resistor), which offers (i) use of grounded capacitors which are attractive from the viewpoint of IC implementation as well as eliminating/accommodating parasitic capacitances, (ii) independent control of frequency of oscillation and condition of oscillation (iii) ready availability of explicit current-mode output, (iv) low active and passive sensitivities, and (v) a very good frequency stability. Apart from realizing the intended type of ECMSO, the proposed topology has other modes of operation also. The workability of   the new circuit has been verified by PSPICE simulations.


## 2. The New Oscillator Configuration

The symbolic notation of the VDTA is shown in Figure1, where VP and VN are input terminals and Z, X+, and X- are the output terminals. All terminals of VDTA exhibit high impedance values [15]. The VDTA can be described by the following set of equations:
(1)[IZIX+IX-]=[gm1-gm1000gm200-gm2][VVPVVNVZ].
A routine circuit analysis yields the following characteristic equation:
(2)s2+s1C1(1R1-gm1)+gm1gm2C1C2=0.
Thus, the condition of oscillation (CO) and frequency of oscillation (FO) are given by
(3)(1R1-gm1)≤0,ω0=gm1gm2C1C2.
Therefore, it is seen that CO can independently be controlled by resistor R1 while FO is electronically controllable by transconductance gm2.Figure 1
The symbolic notation of VDTA.With the feedback link broken at node “P” and considering the VP terminal of VDTA as the input, the two open loop transfer functions realized by the proposed circuit are given by
(4)V0aVin=gm1gm2/C1C2s2+s(1/R1C1)+gm1gm2/C1C2,V0bVin=s(gm1/C1)s2+s(1/R1C1)+gm1gm2/C1C2.
Thus, in this mode, the same configuration can be used to realize low-pass and band-pass filters simultaneously. From (4), the natural frequency (ω0) and bandwidth (BW) are given by
(5)ω0=gm1gm2C1C2,BW=1R1C1.
Thus, it is seen that ω0 and BW are independently tunable.In the third mode of operation, the current transfer functions obtained from Figure2 are given by
(6)I0(s)I01(s)=-gm2sC1,I02(s)I01(s)=gm2sC1,I03(s)I01(s)=1sC1R1.
For sinusoidal steady state, (6) becomes
(7)I0(jω)I01(jω)=gm2ωC1ej90°,I02(jω)I01(jω)=gm2ωC1e-j90°,I03(jω)I01(jω)=1ωC1R1e-j90°.
Thus, the phase difference ϕ between (I0 and I01) is 90° and between (I02 and I01), and (I03 and I01) is -90°.Figure 2
The proposed configuration.Hence, the currents (I0 and I01), (I02 and I01) and (I03 and I01) are in the quadrature form. To extract the currents I01, I02 and I03 explicitly another device with their inputs virtually grounded  will be required due to which although the capacitors C1, C2 and resistor R1 will not be physically connected to ground but they will still be virtually grounded [16].


## 3. Nonideal Analysis

It is useful to count the effect of various VDTA nonideal parameters on the CO and FO of the proposed oscillator. Taking into account the finiteP-terminal parasitic impedance consisting of a resistance RP in parallel with capacitance CP, the finite N-terminal parasitic impedance consisting of a resistance RN in parallel with capacitance CN, the finite X-terminal parasitic impedance consisting of a resistance RX in parallel with capacitance CX and the parasitic impedance at the Z-terminal consisting of a resistance RZ in parallel with capacitance CZ, then the non-ideal expression of CO and FO can be given by
(8)(1/RX+1/RN)(C2+CX+CN)+(1/R1+1/RZ+1/RP-gm1)(C1+CZ+CP)≤0,ω0=gm1gm2+(1/RX+1/RN)ℛ(C1+CZ+CP)(C2+CX+CN),where ℛ denotes (1/R1+1/RZ+1/RP-gm1), then, the active and passive sensitivities of ω0 can be found as(9)SC1ω0=-C12(C1+CZ+CP),SCZω0=-CZ2(C1+CZ+CP),SC1ω0=-CP2(C1+CZ+CP),SC2ω0=-C22(C2+CX+CN),SCXω0=-CX2(C2+CX+CN),SCXω0=-CN2(C2+CX+CN),SR1ω0=-(1/RX+1/RN)2R1{gm1gm2+(1/RX+1/RN)ℛ},SRZω0=-(1/RX+1/RN)2RZ{gm1gm2+(1/RX+1/RN)ℛ},SRPω0=-(1/RX+1/RN)2RP{gm1gm2+(1/RX+1/RN)ℛ},SRXω0=-(1/R1+1/RZ+1/RP-gm1)2RX{gm1gm2+(1/RX+1/RN)ℛ},SRNω0=-(1/R1+1/RZ+1/RP-gm1)2RN{gm1gm2+(1/RX+1/RN)ℛ},Sgm1ω0=gm1{gm2-(1/RX+1/RN)}2{gm1gm2+(1/RX+1/RN)ℛ},Sgm2ω0=gm1gm22{gm1gm2+(1/RX+1/RN)ℛ}.
From the above mentioned sensitivity values, it is easy to figure out that all the active and passive sensitivities are no more than half in magnitude.


## 4. Frequency Stability

Using the definition of the frequency stability factorSF as given in [5], SF=(dϕ(u)/du)∣u=1 (where u=ω/ω0  is the normalized frequency and ϕ(u) represents the phase of the open-loop transfer function of the oscillator circuit), with C1=C2=C, gm1=1/R1=gm, and gm2=ngm; the SFof the proposed oscillator is found to be 2n. Therefore, very good frequency stability is obtainable by selecting larger value of n.


## 5. Simulation Results

To confirm theoretical analysis, the proposed ECMSO was simulated using CMOS VDTA from [15]. Power supply voltages were taken as VDD=-VSS=0.9 V and IB1=IB2=IB3=IB4=150 μA biasing currents are used. The transistor aspect ratios are taken from [15]. The passive elements of the configuration were selected as C1=C2=0.01 nF and R1=1.7 kΩ. The transconductances of VDTA were controlled by bias currents. PSPICE generated output waveforms indicating transient and steady-state responses are shown in Figures 3(a) and 3(b), respectively. These results, thus, confirm the validity of the proposed configuration. The total harmonic distortion (THD) of the proposed oscillator is found to be 2.66% (Figure 4). A comparison with other previously known ECMSOs using single active building block has been given in Table 1. Figure 5 shows the frequency responses of the BP and LP filters obtained from the proposed configuration. From Figures 6, 7, and 8, it is clear that the two currents are in quadrature.Table 1
Active component
Grounded capacitors
Floating capacitors
Resistors
Availability of explict current-mode output
Electronic tunability
Reference
1
3
0
5
Yes
No
1
2
1
4
Yes
No
[8]
1
1
2
4
Yes
No
1
1
1
5
Yes
No
1
2
0
3
Yes
No
[9]
1
2
0
3
Yes
No
[10]
1
0
3
3
Yes
No
[11]
1
1
2
3
Yes
No
1
2
0
3
Yes
No
[12]
1
0
2
5
Yes
No
[13]
1
2
0
1
Yes
Yes
Proposed(a) Transient output waveform. (b) Steady-state response of the output.
(a)
(b)Figure 4
Simulation result of the output spectrum.Figure 5
Frequency response of LP and BP filters.Figure 6
Steady-state response of the quadrature outputs ofI0 and I01.Figure 7
Steady-state response of the quadrature outputs ofI01 and I02.Figure 8
Steady-state response of the quadrature outputs ofI03 and I01.As a sample example, Figure8 shows that the two currents are in quadrature and the measured value of phase shift between two waveforms is =89.047°.


## 6. Concluding Remarks

A new application of VDTA has been introduced in the realization of a novel ECMSO. In oscillator mode, the circuit offers (i) independent control of frequency of oscillation and condition of oscillation, (ii) use of grounded capacitors which are attractive from the viewpoint of IC implementation as well as eliminating/accommodating parasitic capacitances, (iii) ready availability of explicit current-mode output, (iv) low active and passive sensitivities, and (v) a very good frequency stability.  In filter mode, the structure realizes LP and BP filter responses simultaneously with independent control ofω0 and BW. In third mode of operation, the circuit offers quadrature current-mode outputs. The validity of the proposed configuration in various modes of operation has been established by the PSPICE simulations.



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*Source: 382560-2012-09-18.xml*