In this paper, the method of determining the stability of the voltage-to-current converter (VCC) with complex load, which is built on the DC amplifier with a deep negative feedback (NFB) by current. The feedback signal is formed on precise resistor, which is connected in series with an inductive load. The deep feedback and complex load can cause a violation of the stability of the VCC across the whole dynamic range of operation.
Additional complexity to ensure stability of the VCC is provided by complex nature of the load. Outside the range of middle frequencies (over 30 kHz) the transfer coefficient is determined by the inductance of load and by the resistor, which forms feedback signal. The feedback factor stops to be a real value and becomes a complex. The phase of NFB signal voltage begins to change and the NFB effect on providing the specified accuracy and on the speed of the current setting in the inductive load is reduced. Upon reaching the large phase shifts in circuit of the VCC amplifier and inductive load at certain frequencies NFB becomes positive, leading to a significant distortion of the output signal and the deterioration of the basic parameters of the VCC, in the worst case, to the self-excitation.
It is shown that the stability of VCC is affected by the gain of the amplifier without accounting the NFB influence, depth of feedback and the inductive load time constant Н. Since the gain of the amplifier without accounting the NFB influence and transfer coefficient of the circuit, – inductive load - NFB signal formation resistor, depends on the frequency, the VCC with a load is analyzed as at least the second-order operating system. This system has a tendency to self- excitation and can only be conditionally stable.
The analysis of methods for determining the stability of VCC with deep feedback was carried out. The determination of stability criterions of Mikhailov, Routh–Hurwitz and Nyquist was considered on the real Bode diagrams. It was determined that in order to find the stability margin, the most advisable in practice to apply the Nyquist stability criterion in its graph-analytical implementation.
The stability of the VCC, which is built using operational amplifiers which are presented by one equivalent RC-circuit, was analyzed. The design method for constructing the total amplitude-frequency characteristic, accounting the parameters of the VCC and inductive load, is given. Two examples of VCC implementation: with low inductance load and with large inductance load, are considered. The analytical expressions for determination of the equivalent frequency poles of the system are presented. There is showed how to choose the shunting resistor to ensure the stability. The dependencies of the amplitude-frequency and phase-frequency characteristics on the shunt resistor of inductive load are illustrated, showing its effect on the stability of the VCC operation, as well as the margin of stability of the phase.