Free running VCO based on an unstable transistor circuit system stability optimization under delayed electromagnetic interferences and parasitic effects and engineering applications


  • Ofer Aluf Netanya, Israel



Free running VCO, PLL, WBFM, Delay Differential Equations (DDEs), Bifurcation, Stability, Integrated circuit, CMOS, Bi-CMOS, Clock generation, ASIC, FPGA


IN this article, Very Crucial subject discussed in free running VCO based on an unstable transistor circuit system stability optimization under delayed electromagnetic interferences and parasitic effects. Additionally we discuss Free running VCO integrated circuit applications (PLLs, DLL, clock generation, etc.). There are many techniques to generate a Wideband Frequency Modulation (WBFM) signal: analog based, digitally based and hybrid based techniques. The VCO is a very low cost method of generating WBFM signals, such as chirp signals. The VCO has some important properties that are common to all frequency sources. These properties are frequency range, settling time, post-tuning drift, sensitivity and Maximum Sensitivity Ratio (MSR), frequency total accuracy, frequency modulation span, and modulation frequency bandwidth. The VCO frequency of oscillation depends on the resonance frequency set by its equivalent capacitance and inductance. By applying variable bias voltage to a Varactor diode, the capacitance is changed and the oscillation frequency is changed accordingly. The first delay line in our circuit (1) represents the electromagnetic interference in the Varactor diode (D1). We neglect the voltage on the first delay line (V1→ε) and the delay is on the current which flows through Varactor diode. The second and third delay lines (2 and 3) represent the circuit microstrip line's parasitic effects before and after the matching circuit. We neglect the voltages on the second and third delay lines (Vk→ε ; k=2, 3) and the delays are only on the current which flow through the microstrip lines. The free running VCO circuit can represent as delayed differential equations which, depending on variable parameters and delays. There is a practical guideline which combines graphical information with analytical work to effectively study the local stability of models involving delay dependent parameters. The stability of a given steady state is determined by the graphs of some function of τ1, τ2, τ3.


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How to Cite

Aluf, O. (2019). Free running VCO based on an unstable transistor circuit system stability optimization under delayed electromagnetic interferences and parasitic effects and engineering applications. Discoveries in Agriculture and Food Sciences, 7(3), 35–75.