HTS High Q Resonant Controller

High Tc superconductor (HTS) technology has been used to develop an advanced high Q resonant circuit and its devices. With a HTS, a very high Q circuit can be achieved; consequently special aspects such as high voltage generation and high current control can be theoretically and practically realized. Theoretical study has been carried out, as well as a practical approach has been made for the concept verification. This paper describes the theory of this high Q resonant circuit and the operational principle of its high voltage generation and current control. Introduction A resistor R capacitor C inductor L series resonant circuit has been explored with regard to its voltage aspects of using a high Tc superconductor (HTS) [1,2]. The relation between the circuit quality factor Q and its voltage aspects has been studied, and formed a method of high voltage generation. Then a method of generating high voltage from a low voltage source has been explored. This high voltage generator using the resonant circuit mainly consists of an inductor, a capacitor, a DC battery source, and an electronic switch. As a fundamental principle, the resonant circuit generates the voltage which is proportional to the circuit Q value. As a basic principle of operational approach, a low voltage DC power source can be used and its polarity is reversed at a certain frequency, and this control is achieved with an electronic switch. Resistance in the circuit will limit the Q value and therefore voltages that can be achieved in practice; however HTS technology can dramatically reduce the resistance and present a very high Q value. Both theoretical analysis and practical device operation principle will be presented in this paper with the advantages of using a high Q circuit made by HTS Bi-2223/Ag multifilament wires. Operation Theory Q Value and Voltage Feature of a Resonant Circuit. The build-up voltage in a resistive R-C-L series resonant circuit, as shown in Fig. 1, is related to the circuit quality factor Q. The quality factor of a resonant circuit is Q = ωoL/R, sometimes called the magnification factor, and ωo = [(1/LC)-(R/4L)] is the resonant frequency in rad s. The potential difference across the capacitor at resonance is Q times as large as the applied emf Vp (rms). For a sinusoidal power supply, the voltage across the capacitor VCmax at resonance is given by VCmax = Q Vp (1) For using a DC power supply with an electronic switch to reverse the polarity, the maximum voltage VCmax can be expressed as VCmax = Q VB’ (2) where VB’ is the effective voltage of the low voltage power source. If the used switching controller has rectangular wave form with low voltage source polarity switching frequency f, the build-up voltage wave form F(t) can be expressed by Fourier series as F(t) = (4VB/π)[sinωt + (1/3)sin3ωt + (1/5)sin5ωt + ...] (3) The generator only resonates on the first harmonic with amplitude of 4VB/π. Therefore VB’ = 4 VB/π (4) and the maximum build-up voltage is related to the R-C-L resonant circuit Q value by VCmax = Q (4VB/π) (5) Reducing the R-C-L resonant circuit resistance is achieved by introducing the superconducting inductor; the circuit Q value will be then dramatically increased, which leads to a very high voltage across the capacitor. Fig.1. A R-C-L series resonant circuit with a DC source. Resistance-Less Circuit. In a R-C-L resonant circuit as shown in Fig. 1, when switch S is closed in this circuit, the instantaneous current i(t) and capacitor voltage VC(t) solutions respectively are ( ) ( ) i t e V V sin t L Rt 2L CO B = +         − ω ω (6) ( ) ( ) V t V V 1 e cos t R 2L sin t V C CO B Rt 2L CO = + − +           − − ω ω ω (7) where R < 2(L/C), VCO is the initial capacitor voltage. Both equations describe decaying sinusoids with VC(t) approaching a steady state value of VB, and i(t) approaching a steady state value of zero. For the circuit using a superconducting inductor and no separate resistor, then R will become very small. If R = 0 Ω, then Eq. 6 and Eq. 7 can be simplified to ( ) ( ) i t V V sin t L CO B = + ω ω (8) ( ) ( ) V t V V cos t V C CO B B = − + + ω (9) where ω = (LC) rad s. These two equations describe constant magnitude sinusoids with the average values of i(t) and VC(t) being zero and VB respectively. When switch S in Fig. 1 is closed, VC(t) = VC(0) = -VCO. One half a resonant cycle later, this voltage will have increased to VC(t) = VC(π/ω) = -(VCO + VB)(-1) + VB = VCO + 2VB (10) If the battery is disconnected at this point of time, and then reconnected in the opposite polarity for the next half cycle, then the initial capacitor voltage VCO is changed to VCO-new, and it is given by VCO-new = -VC(t) = -(VCO + 2VB) (11) Half a cycle later, VC(t) = VC(2π/ω) becomes VC(t) = -[-(VCO + 2VB) + (-VB)](-1) + (-VB) = -(VCO + 4VB) (12) If the battery is reversed every half cycle thereafter, then the VC(t) is VC(t) = (VCO + 6VB); -(VCO + 8VB); (VCO + 10VB); ...etc (13) This is the build-up voltage for an ideal non-resistive circuit. Consequently the positive and negative peak voltages can be described by the following equation, i.e. in a resistance-less circuit, the voltage across the capacitor C after n cycles will be VC (n) = (-1) (VCO + 2nVB) (14) where n is the iteration number, and VCO is the initial capacitor voltage. Practical Resistive Circuit. From Eq. 6, when t = π/ω, i = 0, if the electronic bridge in the Fig. 1 changes DC source polarity, the capacitor voltage is given by VC1 = (VCO+VB)(1+eπω)-VCO (15) After the polarity is changed n times, the capacitor voltage becomes VCn = (VCn-1+VB)(1+eπω)-VCn-1 (16) If VCO = 0, then VC1=VB(1+eπω) VC2=(VC1+VB)(1+eπω)-VC1 =VB(1+2eπω+eπω) ... VCn=(VCn-1+VB)(1+eπω)-VCn-1 =VB(1+2eπω+2eπω...+2eπω+eπω) =VB(1+e)+2VB ∑ −