Generation of Four Phase Oscillators Using Op Amps or Current Conveyors

J. of Active and Passive Electronic Devices, Vol. 0, pp. 207 22 Reprints available directly from the publisher Photocopying permitted by license only 205 Old City Publishing, Inc. Published by license under the OCP Science imprint, a member of the Old City Publishing Group Generation of Four Phase Oscillators Using Op Amps or Current Conveyors Ahmed M Soliman,* and Chun Ming Chang 2 Electronics and Communication Engineering Department, Cairo University, Egypt 2 Department of Electrical Engineering, Chung Yuan Christian University, Chung-Li, 32023, Taiwan A novel four phase oscillator circuit using two balanced output Op Amps is given. The circuit considered is generated from a two integrator loop oscillator circuit which uses three single input Op Amps and employs the minimum number of capacitors namely two. An equivalent current conveyor circuit which employs grounded resistors and capacitors is obtained from the three Op Amp circuit by equivalent block replacement. Another equivalent unity gain cells four phase oscillator realizing the same characteristic equation and using two grounded capacitors is also given. Nodal Admittance Matrix (NAM) expansion is used to generate the family of current conveyor four phase oscillators. Spice Simulation results are given. Keywords: Four-phase oscillators, Balanced output Op Amp, unity gain cells, current conveyor.. INTRODUCTION Sinusoidal oscillators are basic building blocks in active circuits and have several applications in electronics and communication circuits [-4].This paper is partially a review paper and starts by summarizing the two integrator loop oscillators realized using three single input Op Amps which is used as the basic circuit in realizing a novel four phase oscillator circuit using two balanced output Op Amps. *Corresponding author: E-mail: asoliman@ieee.or 207 207-22 pp JAPED 205-0.indd 207 7/28/205 :4:6 PM

208 Ahmed M Soliman and Chun Ming Chang Recently there has been an interest in the realization of four phase oscillators [5-6]. The four phase oscillators generate four sinusoidal signals with a phase shift of 90 degrees between each two successive signals. Their applications are in signal processing and measurements [5]. The four phase oscillator can also be used as a floating output quadrature oscillator [5]. The circuit introduced in [5] is based on using two differential output current inverter buffered amplifiers (DO-CIBA) as basic building blocks. The circuit uses two grounded capacitors and four floating resistors. The circuit introduced in [6] is based on using four differential voltage current conveyors (DVCC) [7] as well as two grounded capacitors and four resistors, three of them are floating. In this paper a family of six circuits using grounded capacitors as well as grounded resistors and using current conveyors (CCII) [8] and inverting current conveyors (ICCII) [9] are generated using NAM expansion. 2. OP AMP BASED OSCILLATORS 2.. Three single input Op Amp oscillators Three alternative circuits are given in Fig. and will be summarized in this section. FIGURE (A) The three single input Op Amps oscillator [] 207-22 pp JAPED 205-0.indd 208 7/28/205 :4:6 PM

generation of Four Phase Oscillators Using Op Amps 209 The first circuit given in this paper is the three Op Amp two integrator loop circuit shown in Fig. a. It employs three single input Op Amps, two floating capacitors and four floating resistors []. Assuming ideal Op Amps the Nodal admittance Matrix (NAM) equation of the circuit is given by: Y= sc G G 2 sc () 2 The radian frequency of oscillation is given by: GG 2 ω o = CC 2 (2) This circuit has the disadvantage of having no independent control on the oscillation condition. A modification to the circuit of Fig. a to provide control on the oscillation condition was given in references [2] and is shown in Fig. (b). Its NAM equation is given by: FIGURE (B) The modified single input Op Amps oscillator 207-22 pp JAPED 205-0.indd 209 7/28/205 :4:6 PM

20 Ahmed M Soliman and Chun Ming Chang FIGURE (C) The modified single input Op Amps oscillator sc Y = GG 4 G G G 2 sc2 + G3 (3) The condition of oscillation can be controlled by G 4 and is given by: C C 2 4 = GG GG 3 (4) Although the circuit has now a control on the oscillation condition, the quadrature output property however is lost due to the connection of G 4. The circuit Fig. c represents a modified version to the circuit of Fig. (b) by changing position of G 4. This represents an alternative form to the recently reported three Op Amp oscillator circuit with independent control on both the condition of oscillation and on the frequency of oscillation [3-4]. The NAM equation for this circuit is given by: 207-22 pp JAPED 205-0.indd 20 7/28/205 :4:7 PM

generation of Four Phase Oscillators Using Op Amps 2 FIGURE 2 The modified single input Op Amps oscillator Y= sc G G 2 sc2+ G3 G (5) 4 The characteristic equation in this case is given by: 2 s CC + s C (G G ) + GG = 0 (6) 2 3 4 2 The condition of oscillation is given by: G 3 = G 4 (7) The condition of oscillation is controlled by G 3 or G 4 without affecting the radian frequency of oscillation which is given by Eq. (2) and is independently controlled by G or G 2 without affecting the condition of oscillation. 2.2 New two balanced output two Op Amp oscillator circuit A new four phase oscillator circuit using two balanced output Op Amps is shown in Fig. 2. The circuit is generated from Fig. (c) by removing the inverting stage and utilizing the inverting output of the second op Amp and connecting it to the inverting input through G 4. The circuit has the same NAM equation as given by (5). This is a very attractive four phase oscillator circuit. 207-22 pp JAPED 205-0.indd 2 7/28/205 :4:7 PM

22 Ahmed M Soliman and Chun Ming Chang FIGURE 3(A) Four phase unity gain cells grounded capacitor oscillator [4] 3. UNITY GAIN CELLS BASED OSCILLATORS It is important here to review a recently reported grounded capacitor four phase oscillator using unity gain cells [4]. The circuit is shown in Fig. 3(a) and has the same characteristic equation given by (6). Its NAM equation however is different from that given in (5) and is given by: Y= sc G G 2 sc2 + G3 G (8) 4 The three types of unity gain cells used are defined as follows: The Voltage Inverter (VI) is defined by: I 0 0 V V2 = 0 (9) I2 The Current Follower (CF) is defined by: V 0 0 I I2 = 0 V (0) 2 207-22 pp JAPED 205-0.indd 22 7/28/205 :4:7 PM

generation of Four Phase Oscillators Using Op Amps 23 The Current Inverter (CI) is defined by: V 0 0 I = I2 0 V () 2 Next grounded resistor and grounded capacitor four phase oscillators are considered. 4. CURRENT CONVEYOR BASED OSCILLATORS For completeness the definitions of CCII and ICCII are given next. The CCII is defined by [8]: IY VX IZ = 0 0 0 0 0 0 ± 0 VY IX VZ (2) The positive sign in the third row applies to CCII+ whereas the negative sign is for CCII-. The ICCII is defined by [9]: IY VX IZ 0 0 0 = 0 0 0 ± 0 VY IX VZ (3) The positive sign in the third row applies to ICCII+ whereas the negative sign is for ICCII-. A new grounded resistors and grounded capacitors four phase oscillator is obtained from Fig. (c) by realizing each of the three building blocks using CCII or ICCII as shown in Fig. 3(b). The parasitic resistances R X and R X2 can be absorbed in R and R 2 respectively. The parasitic capacitances C Z and C Z2 + C Z3 can be absorbed in C and C 2 respectively. This circuit however is affected by the parasitic resistances R X3. In this section a family of four phase oscillators is generated from Eq. (5) using the conventional systematic synthesis framework using NAM expansion presented in [0-2]. 207-22 pp JAPED 205-0.indd 23 7/28/205 :4:8 PM

24 Ahmed M Soliman and Chun Ming Chang FIGURE 3(B) Equivalent circuit to Fig. (c) using CCII-, ICCII+ and ICCII- Starting from Eq. (5) and add a third blank row and column and then connect a voltage mirror (VM) between nodes 2 and 3 and a norator between nodes and 3 in order to move G from the, 2 position to the diagonal position 3, 3 to become G as follows: Y= sc G sc + G G 2 2 3 4 0 0 0 0 0 G (4) Adding a fourth blank row and column to the above equation and then connect a VM between nodes and 4 and a CM between rows 2 and 4 in order to move G 2 from the 2, position to the diagonal position 4, 4,the following NAM is obtained: Y= sc 0 0 sc + G G 0 0 2 3 4 0 0 0 0 G 0 0 0 0 G 2 (5) 207-22 pp JAPED 205-0.indd 24 7/28/205 :4:8 PM

generation of Four Phase Oscillators Using Op Amps 25 FIGURE 4(A) Four phase grounded passive element oscillator circuit. Adding a fifth blank row and column to the above equation and then connect a nullator between nodes 2 and 5 and a CM between nodes 2 and 5 in order to move G 4 from the 2, 2 position to the diagonal position 5, 5 to become G 4 the following NAM is obtained: Y = sc 0 0 0 0 0 sc + G 0 0 0 2 3 0 0 G 0 0 0 0 0 G 0 0 0 0 0 2 G 4 (6) The above equation is realized as a five node circuit using one nullator, one norator, two VM and two CM. Noting that the nullator and CM with a common terminal realize a CCII+ acting as a negative impedance converter (NIC) and the circuit shown in Fig. 4a using one ICCII and one ICCII+ and a CCII+ is obtained. An alternative realization is obtained from the following NAM equation: 207-22 pp JAPED 205-0.indd 25 7/28/205 :4:8 PM

26 Ahmed M Soliman and Chun Ming Chang Y= sc 0 0 0 0 0 sc2 + G3 0 0 0 0 0 G 0 0 0 0 0 G2 0 0 0 0 0 G 4 (7) The above equation is realized as a five node circuit using two norators, three VM and one CM. Noting that the VM and norator with a common terminal realizes an ICCII acting as an NIC and the circuit is shown in Fig. 4b using two ICCII and one ICCII+. In order to generate the complete family of four-phase oscillators, Fig. 5 is generated from Fig. 4(a) or (b) by replacing CCII or ICCII by generalized conveyor (GC) which is defined by: IY VX IZ = 0 0 0 a 0 0 0 K 0 VY IX VZ (8) The characteristic equation for the circuit of Fig. 5 is given by: FIGURE 4(B) Four phase grounded passive element oscillator circuit 2. 207-22 pp JAPED 205-0.indd 26 7/28/205 :4:9 PM

generation of Four Phase Oscillators Using Op Amps 27 FIGURE 5 Generalized conveyor grounded passive element oscillator 2 scc + s C [G - a K G ] - ak akgg = 0 (9) 2 3 3 3 4 2 2 2 The necessary conditions of oscillation are given by: a K a 2 K 2 = - (20) G 3 =G 4 (2) There are 6 oscillator circuits that satisfy Eq. (20) and are included in Table. From these oscillators only six circuits realize four-phase oscillator circuits as shown in the right column of Table. 5. SIMULATION RESULTS The active building block used in all simulations included in this paper is the differential voltage current conveyor (DVCC) [7]. The DVCC is defined as a five port building block with a describing matrix of the form: V I I I I X Y Y2 Z+ Z- 0-0 0 I 0 0 0 0 0 V = 0 0 0 0 0 V 0 0 0 0 V - 0 0 0 0 V X Y Y2 Z+ Z- (22) 207-22 pp JAPED 205-0.indd 27 7/28/205 :4:9 PM

28 Ahmed M Soliman and Chun Ming Chang TABLE Sixteen alternative realizations obtained from the circuit of Fig.5 Circuit a K a 2 K 2 a 3 K 3 GC GC 2 GC 3 Four Phase - + + + + + ICCII+ CCII+ CCII+ No 2 + - + + + + CCII- CCII+ CCII+ No 3 + + - + + + CCII+ ICCII+ CCII+ No 4 + + + - + + CCII+ CCII- CCII+ No 5 + - - - + + CCII- ICCII- CCII+ No 6 - + - - + + ICCII+ ICCII- CCII+ Yes 7 - - + - + + ICCII- CCII- CCII+ No 8 - - - + + + ICCII- ICCII+ CCII+ Yes 9 - + + + - - ICCII+ CCII+ ICCII- No 0 + - + + - - CCII- CCII+ ICCII- No + + - + - - CCII+ ICCII+ ICCII- Yes 2 + + + - - - CCII+ CCII- ICCII- No 3 + - - - - - CCII- ICCII- ICCII- Yes 4 - + - - - - ICCII+ ICCII- ICCII- Yes 5 - - + - - - ICCII- CCII- ICCII- No 6 - - - + - - ICCII- ICCII+ ICCII- Yes The DVCC is a very powerful building block as it realizes each of CCII+, CCII-, ICCII+ and ICCII- as special cases. Fig. 6 represents the CMOS- DVCC circuit [7], the transistor aspect ratios are given in Table 2 based on the 0.5mm CMOS model from MOSIS. The supply FIGURE 6 CMOS circuit of the CCII or ICCII [7] 207-22 pp JAPED 205-0.indd 28 7/28/205 :4:9 PM

generation of Four Phase Oscillators Using Op Amps 29 TABLE 2 Dimensions of the MOS Transistors of Figure 6 MOS Transistors W(μm) / L(μm) M, M 2, M 3, and M 4 2.5/ M 5 and M 6 8/ M 2, M 3, M 4, M 5, and M 6 20/2.5 M 7 and M 8 0/ M 9, M 0, M, M 7, and M 8 40/2 voltages used are ±.5 V and V B = - 0.52V and V B2 = 0.33V.The Spice simulation results for two of the four phase oscillator circuits are shown in Fig.7 Fig. 7(a) represents the output voltage waveform of the oscillator of Fig. 4(a) designed for oscillation radian frequency equal to 0 M rad/s by taking C = C 2 = 0 pf, R = R 2 =0 kohm, R 3 =R 4 = 20 kohm. Total power dissipation equal to 2.9446 m-w. FIGURE 7(A) CMOS circuit of the CCII or ICCII [7] 207-22 pp JAPED 205-0.indd 29 7/28/205 :4:20 PM

220 Ahmed M Soliman and Chun Ming Chang FIGURE 7(B) The output waveforms of circuit 2 in Fig. 4(b) Fig. 7(b) represents the output voltage waveform of the oscillator of Fig. 4(b) designed for same frequency as before. Total power dissipation equal to 2.9442 m-w. 6. CONCLUSIONS A novel four phase oscillator circuit using two balanced output Op Amps. Six new four phase oscillators are generated using NAM expansion. Simulation results are included for two of the six phase oscillator circuits. REFERENCES [] M.E. Van Valkenburg. Analog Filter Design, Holt, Rinehart and Winston; 982:549-569. [2] B.D.O. Anderson. Oscillator design problem. IEEE J Solid-State Circuits, 6 (97) 89-9. 207-22 pp JAPED 205-0.indd 220 7/28/205 :4:2 PM

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