# Electronically Controllable Sinusoidal Oscillator Employing CMOS VD-DIBAs

Authors: Dinesh Prasad; D. R. Bhaskar; K. L. Pushkar
Journal: ISRN Electronics
 (2013)

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## Abstract

A new electronically controllable sinusoidal oscillator employing two voltage differencing-differential input buffered amplifiers (VD-DIBAs), two grounded capacitors, and one grounded resistor is presented. The proposed configuration offers (i) independent control of condition of oscillation (CO) and frequency of oscillation (FO) formerly by resistance and later through transconductance, (ii) low active and passive sensitivities, and (iii) a good frequency stability. The workability of the proposed configuration has been demonstrated by SPICE simulation.


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## Body

## 1. Introduction

Sinusoidal oscillators find numerous applications in communication, control systems, signal processing, instrumentation, and measurement systems. In the recent past, a large number of single resistance controlled oscillators (SRCOs) have been proposed, see [1–11]; however, in all these SRCOs, the frequency of oscillation can be controlled by varying the values of resistances involved. Obviously, by replacing one of the grounded resistors by JFETs/MOSFETs, electronic tunability can be established, see [2, 4] and the references cited therein. Electronically controllable sinusoidal oscillators (ECSOs) based on different active building blocks are available in the literature, see [12–17] and the references cited therein. The advantages, applications, and usefulness of recently introduced new active building block named voltage differencing-differential input buffered amplifier (VD-DIBA) are now being recognized in the literature [18–20]. Recently, electronically controllable grounded and floating simulated inductance circuits using VD-DIBAs have been introduced in [20]. However, to the best knowledge and belief of the authors, no ECSO using VD-DIBAs has yet been presented in the open literature so far. The purpose of this paper is, therefore, to propose a new ECSO using VD-DIBAs along with a minimum possible number of grounded  passive components,  which offers (i) independent control  of oscillation  frequency and condition of oscillation, (ii) low active and passive sensitivities, and (iii) a good frequency stability factor.


## 2. The Proposed Configuration

The schematic symbol and behavioral model of the VD-DIBA are shown in Figures1(a) and 1(b), respectively [18]. The model includes two controlled sources: the current source controlled by differential voltage (V+-V-), with the transconductance gm, and the voltage source controlled by differential voltage (Vz-Vv), with the unity voltage gain. The VD-DIBA can be described by the following set of equations:
(1)(I+I-IzIvVw)=(0000000000gm-gm00000000001-10)(V+V-VzVvIw).(a) Schematic symbol, (b) behavioral model of VD-DIBA.
(a)
(b)The proposed new ECSO configuration is shown in Figure2.Figure 2
The proposed configuration.A routine circuit analysis of Figure2 yields the following characteristic equation:
(2)s2+s1C1(1R1-gm1)+gm1gm24C1C2=0.Thus, the condition of oscillation (CO) and frequency of oscillation (FO) are given by(3)(1R1-gm1)≤0,ω0=gm1gm24C1C2.Therefore, it is seen that FO is independently controllable by transconductancegm2 of the VD-DIBA2 (which is current controllable by bias current, IB2), whereas CO is independently established through the resistor R1. The above routine circuit analysis can also be obtained using the analysis performance as given in [21, 22].The CMOS implementation of VD-DIBA is shown in Figure3. For this purpose, the TSMC CMOS 0.18 μm process parameters are used for all MOSFETs in the circuit of Figure 3.Figure 3
CMOS Implementation of VD-DIBA,VDD=-VSS=1V,IB1=IB2=IB3=IB4=IB5=IB6=150μA and IB7=30μA [20].Transistor aspect ratios are indicated in Table1.Table 1
Transistor
W/L (μm)
M1, M2, M5, M6, M9, M10, M13–M18
3.6/0.36
M3, M4, M7, M8, M11, M12, M19–M24
16.6/0.36The TSMC CMOS 0.18μm process parameters are given in Table 2.Table 2
MODELn nmos
MODELp pmos
LEVEL   = 7, VERSION = 3.1            TNOM    = 27             TOX     =4.1E-9 XJ      = 1E-7           NCH     = 2.3549E17      VTH0    = 0.3696986 K1      = 0.6064385      K2      = 1.63871E-3     K3      = 1E-3, K3B     = 2.763267       W0      = 1E-7           NLX     = 1.71872E-7 DVT0W   = 0              DVT1W   = 0              DVT2W   = 0, DVT0    = 1.3330881      DVT1    = 0.3683763      DVT2    = 0.0540199 U0      = 258.9066683    UA      = -1.504141E-9   UB      = 2.428646E-18 UC      = 5.105195E-11   VSAT    = 9.896282E4     A0      = 1.8904342 AGS     = 0.4044483      B0      = -4.706134E-8   B1      = 1.294942E-6 KETA    = -2.730673E-3   A1      = 5.916677E-4    A2      = 0.9069159 RDSW    = 105            PRWG    = 0.5            PRWB    = −0.2 WR      = 1              WINT    = 0              LINT    = 1.69494E-8, XL      = 0              XW      = -1E-8 DWG     = -3.773529E-9 DWB     = 5.239518E-9    VOFF    = −0.0883818     NFACTOR = 2.1821266 CIT     = 0              CDSC    = 2.4E-4         CDSCD   = 0, CDSCB   = 0              ETA0    = 2.470369E-3    ETAB    = 1.047744E-5 DSUB    = 0.0167866      PCLM    = 0.7326932      PDIBLC1 = 0.1823102, PDIBLC2 = 3.38377E-3     PDIBLCB = −0.1           DROUT   = 0.7469045 PSCBE1  = 8E10           PSCBE2  = 1.254966E-9    PVAG    = 0, DELTA   = 0.01           RSH     = 6.5            MOBMOD  = 1 PRT     = 0              UTE     = −1.5           KT1     = −0.11 KT1L    = 0              KT2     = 0.022          UA1     = 4.31E-9 UB1     = -7.61E-18      UC1     = -5.6E-11       AT      = 3.3E4 WL      = 0              WLN     = 1              WW      = 0 WWN     = 1              WWL     = 0              LL      = 0 LLN     = 1              LW      = 0              LWN     = 1 LWL     = 0              CAPMOD  = 2              XPART   = 0.5 CGDO    = 7.9E-10        CGSO    = 7.9E-10        CGBO    = 1E-12  CJ      = 9.539798E-4    PB      = 0.8            MJ      = 0.380768 CJSW    = 2.53972E-10    PBSW    = 0.8            MJSW    = 0.1061193 CJSWG   = 3.3E-10        PBSWG   = 0.8            MJSWG   = 0.1061193 CF      = 0              PVTH0   = 7.505753E-4    PRDSW   = −2.7650517 PK2     = -4.42044E-4 WKETA   = 3.100384E-3    LKETA   = −0.0104103 PU0     = 10.8203648     PUA     = 2.896652E-11   PUB     = 1.684125E-23 PVSAT   = 1.388017E3     PETA0   = 8.758549E-5    PKETA   = 1.549791E-3
LEVEL   = 7 VERSION = 3.1            TNOM    = 27             TOX     =4.1E-9 XJ      = 1E-7           NCH     = 4.1589E17      VTH0    = −0.3835898 K1      = 0.59111        K2      = 0.0258663      K3      = 0 K3B     = 7.9143108      W0      = 1E-6           NLX     = 1.20187E-7 DVT0W   = 0              DVT1W   = 0              DVT2W   = 0 DVT0    = 0.6117215      DVT1    = 0.2286816      DVT2    = 0.1 U0      = 106.5280265    UA      = 1.125454E-9    UB      = 1E-21 UC      = -1E-10         VSAT    = 1.593712E5     A0      = 1.6904754 AGS     = 0.3667554      B0      = 5.263128E-7    B1      = 1.496707E-6 KETA    = 0.0237092      A1      = 0.2276342      A2      = 0.6915706 RDSW    = 304.9893888    PRWG    = 0.5            PRWB    = 0.2553725 WR      = 1              WINT    = 0              LINT    = 3.217673E-8 XL      = 0              XW      = -1E-8          DWG     = -2.44019E-8 DWB     = -9.06003E-10   VOFF    = −0.0878287     NFACTOR = 1.8560303 CIT     = 0              CDSC    = 2.4E-4         CDSCD   = 0 CDSCB   = 0              ETA0    = 0.1672562      ETAB    = −0.1249603 DSUB    = 1.0998181      PCLM    = 2.2249148      PDIBLC1 = 8.275696E-4 PDIBLC2 = 0.0420477      PDIBLCB = -1E-3          DROUT   = 0 PSCBE1  = 1.073111E10    PSCBE2  = 3.099395E-9    PVAG    = 15 DELTA   = 0.01           RSH     = 7.4            MOBMOD  = 1 PRT     = 0              UTE     = −1.5           KT1     = −0.11 KT1L    = 0              KT2     = 0.022          UA1     = 4.31E-9  +UB1     = -7.61E-18      UC1     = -5.6E-11       AT      = 3.3E4 WL      = 0              WLN     = 1              WW      = 0 WWN     = 1              WWL     = 0              LL      = 0 LLN     = 1              LW      = 0              LWN     = 1 LWL     = 0              CAPMOD  = 2              XPART   = 0.5 CGDO    = 6.41E-10       CGSO    = 6.41E-10       CGBO    = 1E-12 CJ      = 1.200422E-3    PB      = 0.8478616      MJ      = 0.4105254 CJSW    = 2.001802E-10   PBSW    = 0.8483594      MJSW    = 0.3400571 CJSWG   = 4.22E-10       PBSWG   = 0.8483594      MJSWG   = 0.3400571 CF      = 0              PVTH0   = 2.098588E-3    PRDSW   = 4.4771801 PK2     = 1.799383E-3    WKETA   = 0.0295614      LKETA   = -1.935751E-3 PU0     = −1.3399122     PUA     = -5.27759E-11   PUB     = 1E-21 PVSAT   = −50            PETA0   = 1.003159E-4    PKETA   = -3.434535E-3


## 3. Nonideal Analysis

LetRz and Cz denote the parasitic resistance and parasitic capacitance of the Z terminal. Taking into account the nonidealities of the VD-DIBA, namely Vw=(β+Vz-β-Vv), where β+=1-ε1(ε1≪1) and β-=1-ε2(ε2≪1) are voltage tracking errors of the VD-DIBA then the expressions for CO and FO are found to be
(4){(C2+CZ)(1R1-gm1)+1RZ(C1+C2+2CZ)}≤0,ω0={(1/R1+1/RZ-gm1)RZ+β2+(1+β1--β1+)gm1gm2(1+β2-)(1+β1-)}C1C2.TakingC1=C2=C≫Cz, and Rz≫R1, then (4) reduces to
(5)(1R1-gm1)≤0,ω0=(1+β1--β1+)β2+gm1gm2(1+β1-)(1+β2-)C2.This nonideal analysis can also be determined using the analysis performance as given in [23].The active and passive sensitivities are calculated as(6)SCω0=-1,Sβ1+ω0=-β1+2(1+β1--β1+),Sβ1-ω0=β1+β1-2(1+β1--β1+)(1+β1-),Sβ2+ω0=12,Sβ2-ω0=-β2-2(1+β2-),Sgm1ω0=12,Sgm2ω0=12,
which are all low.


## 4. Frequency Stability

Using the definition of the frequency stability factorSF as given in [2–4] 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, where n is a frequency-controlling transconductor ratio, the SF of the proposed oscillator is found to be n. Therefore, a good frequency stability is obtainable by selecting larger value of n.


## 5. Simulation Results

To verify the theoretical analysis, the proposed circuit has been simulated using the CMOS-based VD-DIBA (Figure3). The component values used were C1=C2=0.05nF, and R1=1.65KΩ, the CMOS VD-DIBA was biased with ±1 V D.C. power supplies with IB1=IB2=IB3=IB4=IB5=IB6=150μA and IB7=30μA. The transconductances of VD-DIBA are controlled by bias currents. SPICE generated output waveforms indicating transient and steady state responses are shown in Figures 4(a) and 4(b), respectively. These results, thus, confirm the validity of the proposed configuration. Figure 5 shows the output spectrum, where the total harmonic distortion (THD) is found to be 1.26%. The oscillator circuit of Figure 2 has been checked for robustness using Monte-Carlo simulations, the sample result has been shown in Figure 6, which confirms that for ±10% variations in the value of R1, the value of oscillation frequency remain close to its normal value of 1.005 MHz and hence almost unaffected by change in R1. A comparison with other previously known ECSOs has been given in Table 3.Table 3
Reference number
No. of active elements
No. of passive elements
No. of grounded capacitors
Independent electronic tunability
[12]
2
3 to 7
2
Yes
[13]
3
2
2
Yes
[14]
3
3
3
Yes
[15]
3
2
2
Yes
[16]
4
2
1
No
Proposed
2
3
2
Yes(a) Transient output waveform, (b) steady-state response of the output.
(a)
(b)Figure 5
Simulation result of the output spectrum.Figure 6
Result of Monte-Carlo Simulation of oscillator circuit of Figure2.


## 6. Concluding Remarks

A new circuit configuration employing two VD-DIBAs along with a minimum possible number of grounded passive elements (i.e., only one resistor and two capacitors) has been proposed. In oscillator mode, the circuit offers (i) independent control of condition of oscillation and frequency of oscillation former by resistance and later through transconductance, (ii) low active and passive sensitivities, and (iii) a good frequency stability for larger values ofn. The validity of the proposed circuit has been established by SPICE simulations.



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