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Realisation of some current-mode fractional-order VCOs/SRCOs using multiplication mode current conveyors

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Abstract

In this paper for the first time a catalogue of linear voltage-controlled fractional-order oscillators employing multiplication-mode current conveyor (MMCC) have been systematically derived using state variable approach. The work also includes detailed relevant analysis of the derived oscillators. Furthermore, three special cases are considered for each of the derived oscillators. Non-ideal analysis has been done for all the oscillators to show the impact of port non-idealities on the frequency. Port parasitics are also examined to justify the deviation between the theoretical and the simulated frequency values against the controlling voltage. Fourier analysis has been carried out to find out the total harmonic distortion figures. Functionality of all the oscillators have been verified on PSPICE utilizing the library files of AD844 and AD835 to realize MMCC. Simulation results are also provided for each special case including the integer-order case. Relevant MATLAB plots are provided for one of the oscillators to facilitate comparison between factional-order and oscillation parameters of the oscillator.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Ambedkar Institute of Advanced Communication Technologies and Research (GGSIP University), New Delhi, Delhi, India

    K S. Subhadhra & Ravindra K. Sharma

  2. Department of Industrial Policy and Promotion, Ministry of Industries, Government of India, New Delhi, India

    S. S. Gupta

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Appendix: Derivation of state matrix coefficients for FO-VCO 2.3 of Table 2

Appendix: Derivation of state matrix coefficients for FO-VCO 2.3 of Table 2

figure d

By utilizing MMCC’s terminal relationship as given in Eq. (1) and voltage across C1 as x1 and across C2 as x2, we can write KCL at the nodes of C1 and C2 as

$$ C_{1} \frac{{dx_{1} }}{dt} = \frac{{kV_{c} x_{2} - kV_{c} x_{1} }}{{R_{1} }} + \frac{{kV_{c} x_{2} }}{{R_{2} }} $$
(18)
$$ C_{1} \dot{x}_{1} = - \frac{{kV_{c} x_{1} }}{{R_{1} }} + \frac{{kV_{c} x_{2} }}{{R_{1} }} + \frac{{kV_{c} x_{2} }}{{R_{2} }} $$
(19)

which can be rearranged as

$$ \dot{x}_{1} = \left( { - \frac{{kV_{c} }}{{R_{1} C_{1} }}} \right)x_{1} + \frac{{kV_{c} }}{{C_{1} }}\left( {\frac{1}{{R_{1} }} + \frac{1}{{R_{2} }}} \right)x_{2} $$
(20)
$$ C_{2} \frac{{dx_{2} }}{dt} = \frac{{kV_{c} x_{2} - kV_{c} x_{1} }}{{R_{3} }} $$
(21)
$$ C_{2} \dot{x}_{2} = - \frac{{kV_{c} x_{1} }}{{R_{3} }} + \frac{{kV_{c} x_{2} }}{{R_{3} }} $$
(22)

Similarly, Eq. 22 can be rearranged as

$$ \dot{x}_{2} = \left( { - \frac{{kV_{c} }}{{R_{3} C_{2} }}} \right)x_{1} + \left( {\frac{{kV_{c} }}{{R_{3} C_{2} }}} \right)x_{2} $$
(23)

Comparing Eqs. (20) and (23) with Eq. (3) the coefficients of the state matrix can be obtained as follows

$$ a_{11} = - \frac{{kV_{c} }}{{R_{1} C_{1} }}; \;a_{12} = \frac{{kV_{c} }}{{C_{1} }}\left( {\frac{1}{{R_{1} }} + \frac{1}{{R_{2} }}} \right); \;a_{21} = - \frac{{kV_{c} }}{{R_{3} C_{2} }};\; a_{22} = \frac{{kV_{c} }}{{R_{3} C_{2} }} $$

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Subhadhra, K.S., Sharma, R.K. & Gupta, S.S. Realisation of some current-mode fractional-order VCOs/SRCOs using multiplication mode current conveyors. Analog Integr Circ Sig Process 103, 31–55 (2020). https://doi.org/10.1007/s10470-020-01590-4

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