Condition of phase angle for a new VDGA-based multiphase variable phase shift oscillator from 0 To 90

Received Jul 20, 2019 Revised Dec 19, 2019 Accepted Feb 1, 2020 A novel interesting type of variable phase angle voltage mode oscillator using modern building block has been presented in this paper. The new proposed oscillator configuration which uses four voltage differencing gain amplifier (VDGA) and two grounded capacitors can generate two sinusoidal signals that change out of phase by 0 to 90 degree. It has four floating and explicit voltage mode outputs where every two outputs have the same phase. The circuit is characterized by (i) the condition of phase angle of the oscillation (PO) (this concept is introduced for the first time in this paper) can be tuned electronically (ii) the gain of the floating outputs can be controlled independently (iii) it provides electronic control of condition of oscillation (CO) and independent control of frequency of oscillation (FO). The Total Harmonic Distortion (THD) of the output waveforms was obtained and the results were reasonability values (less than 4.5%). The non-ideal analysis and simulation results are investigated and confirmed the theoretical analysis based upon VDGAs implementable in 0.35μm CMOS technology. Simulation results include time response and frequency response outputs generated by using the PSPICE program.


INTRODUCTION
One of the most applications in analog signal processing is the sinusoidal oscillators, which have a linear circuit characteristic. Multiphase sinusoidal oscillators are common circuits in analog circuit design. Multiphase sinusoidal oscillators find applications in signal processing, instrumentation, measurement, communication and control systems [1][2][3][4][5][6][7]. Depending on the phase shift between the phases, the multiphase oscillator circuits are available in different angles [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. All these generators are specified with fixed phase shift angles like the phase shifter. There are many circuits achieve variable phase shift by varying passive components or varactor diode, etc. But the variable phase shift angle sinusoidal oscillators by using modern building blocks is not finding in the open literature yet.
In the synthesis of analog signal processing configurations, there are many important electronic active elements (modern building blocks) which they are reviewed in [24,25]. Modern building blocks found many applications in filtering, oscillating and immitance function circuits, such as Operational Transconductance Amplifiers (OTA) [26], operational amplifier [27], feed-back operational amplifiers (CFOAs) [28], Voltage differencing gain amplifier (VDGA) [29], Current Conveyors (CC) [30][31][32][33], etc. that have been frequently witnessed in literature. Recently, one of the significant electronically tunable active devices named voltage differencing gain amplifier (VDGA) is successfully used in analog signal processing circuits and analog wave generation [34]. It is the modified version of the VDTA and VDBA devices. VDGA is an attractive device due to its capability of adjusting the output voltage gain. There are various applications of variable phase shift sinusoidal oscillators such as quadrature amplitude modulators (QAM), phase modulators (PM), phase shift keying (PSK) etc., hunce the challenge of designing such circuit is an important characteristic to reduce the coplexty of the design by introducing one circuit with variable phase shift agenest multiple circuits produces multiple phase shift, therefore the main aim of this paper is to introduce a novel circuit that achieves a variable phase angle oscillator by using electronic active elements.
The proposed sinusoidal oscillator circuit introduced in this paper can generate two sinusoidal signals which change out of phase by 0 to 90 degree. The circuit uses four VDGAs and two grounded capacitors which preferred in monolithic fabrication. It has four floating outputs where every two outputs have the same phase angle that specified with explicit voltage mode. The circuit is characterized by (i) the condition of the phase shift angle of oscillation between the phases can be tuned electronically (ii) the gain of the floating outputs can be controlled independently (iii) it provides electronic control of the condition of oscillation (CO) and independent control of the frequency of oscillation (FO).

PROPOSED CIRCUITS
The active element voltage differencing gain amplifier (VDGA) was introduced in [35]. It is a fourterminal analog building block shown symbolically in Figure 1, where includes three high impedance terminals (p, n and z) and one low impedance terminal (w), in which its voltage at the terminal z is transferred to a voltage at the terminal w amplified by adjustable transfer gain (β).
where gm is the transconductance, Vp and Vn are the input voltages at non-inverting and inverting input terminals, respectively, and β is the voltage gain. As defined in the literature, the CMOS realization VDGA as depicted of in Figure 2 [34,35] can be usually provides electronic tunability through its three separate transfer gain cells M1A-M9A, M1B-M9B, and M1C-M9C and their transconductances are gmA=gm, gmB and gmC , respectively. The proposed circuit of realization variable phase shift sinusoidal oscillator is shown in Figure 3. It enjoys with four floating outputs Vo1, Vo2, Vo3 and Vo4 where Vo1 and Vo3 have the same phase while the other two Vo2 and Vo4 have another same phase, the shift between their phases can be changed from 0 o -90 o . The amplitude gain of the output circuit can be controlled separately by varying the transeconductances of the B and C celles as written in (2): where i = 1, 2, 3 and 4 for the i th VDGA. Hence Vw can be adjusted by means of IBB and IBC that showed in Figure 2. Analysing the proposed circuit of Figure 3 reveals the following characteristic equation: The frequency of oscillation (FO), the condition of oscillation (CO) and the condition of phase shift angle can be obtained as: The condition of the phase shift angle (PO) between V1 and V2: 1 From the equations above, the phase shift can be controlled by changing the ratio of (gm4 / gm2) then the desired angle can be obtained. The oscillation condition (CO) can be adjusted by gm3 and the frequency condition (FO) controlled independently by gm1.

NON IDEAL ANALYSIS
In this section, the effect of non-idealities of the VDGA on the characteristic equation of the proposed oscillators has been stated; the VDGA can be specified by the following set of equations: where α= 1 -ε, and |ε| << 1 denotes the transconductance error of the VDGA. Similarly, deriving the non-ideal characteristic equation of the proposed variable phase angle oscillator circuit of Figure 3 by taking the VDGA non-idealities yields: The new equations (8-10) with respect to non-ideal VDGA of the proposed circuit show that as a result of tracking error of the VDGA, the quantities of the CO, FO and PO are slightly changed, which can be compensated by gmi , where i= 1, 2, 3 and 4, of the VDGAs.

INFLUENCE OF VDGA PARASITIC IMPEDANCE
The influence of the parasitic elements of the VDGA on the characteristic equation of the proposed oscillators has been re-analyzed. The simplified non-ideal macro model of VDGA used for analysis is shown in Figure 4. Figure 4 shows the equivalent parasitic impedances existing at the terminals p, n, z, and w of the nonideal VDGA as represented terminal conductance Gp, Gn, Gz, Gw and capacitance Cp, Cn, Cz. Including these parasitic impedances, the complete structure of the nonideal circuit of the proposed oscillator is represented in Figure 5.

SIMULATION RESULT
One of the advantages of the proposed design, the variable phase shift oscillator angle can be changed from 0 o to 90 o . To verify the performance of the oscillator phase shift angle change between V1 and V2 of Figure 5 Table 1 shows the biased currents and their trransconductance of the circuit VDGAs, also the transconductance values achieved in the simulations along with the practical and theoretical output frequencies and total harmonic distortions (THD) for the new generator circuit are presented. SPICE frequency simulations of the generated voltage waveforms have been found a very good matching between simulation and theoretical values, and PSPICE THD simulations of the generated voltage waveforms were 2.29-3.32 %, thus, the results were reasonability values (less than 4.5%).  Figure 8 (a-d) show frequency spectrum waveforms also with same with phase shift angle of these waveforms. The proposed generator design enjoys independently tuned voltage gain which any one of the floating outputs (Vo1, Vo2, Vo3 and Vo4) can be controlled electronically by the transconductance of B or C cell showed in Figure 2, hence, the circuit has explicit voltage mode and a wide range of the controlled output gain. Figure 9 shows the equi-amplitude output voltage waveforms with different phase shift angles (30 o

COMPARISON WITH OTHER WORKS
There are many oscillator circuits which include; out of phase by 90 o called quadrature oscillator [8][9][10][11][12][13][14][15], out of phase by 45 o [16][17][18][19], out of phase by 120 o [20 (circuit of Figure 2 therein) -22] or hybrid phase angles [20 (circuit of Figure 4 therein)] or generate n number of signals equally spaced in phase which require n units of active and passive devices [22,23]. All these generators are specified with fixed phase shift angles like the phase shifter. While the proposed circuit has the characteristics of variable phase angle, variable output amplitude and reasonable values of THD, as well as has the simplicity. By simple modification, it can also generate variable phase shift by 90 o t0 180 o by connecting another VAGA at point 2 in Figure 3 (ground terminal n and connect terminals p and z to point 2).

CONCLUSION
There is not finding variable phase shift sinusoidal oscillator in the open literature. This paper introduces a novel interesting type of variable phase shift oscillator. Also introduces a new concept the condition of the phase angle of the oscillation (PO) which presents the phase shift condition of the desired angle. The new proposed oscillator configuration, that uses four voltage differencing gain amplifier (VDGA) and two grounded capacitors, can generate two sinusoidal signals. It has four floating outputs where every two outputs have the same phase with explicit voltage mode output. The proposed circuit offers (i) phase shift change out of phase by 0 to 90 degree (ii) the gain of the floating outputs can be controlled independently for a wide rang (iii) its PO can be tuned electronically (iv) electronic controllability of CO and independent control of FO. SPICE frequency simulations of the generated voltage waveforms have been found a very good matching between simulation and theoretical values, and PSPICE THD simulations of the generated voltage waveforms were 2.29-3.32 %, thus, the results were reasonability values. The non-ideal analysis of the proposed circuit produces the error to be around 2% which represent acceptable value and simulation results and confirmed the theoretical analysis. The performance based VDGAs of the proposed configuration has been simulated using PSPICE program with CMOS 0.35 µm parameters.