Carrier wave amplitude control in power source for stabilizing DC voltage by utilizing frequency dependence of resonance

摘要

In the power supply composed of a driver circuit generating the carrier, a resonance circuit driven by the carrier and a rectification circuit generating the dc voltage by rectifying the amplitude-modulated carrier supplied by the resonance circuit and stabilizing the output voltage by the feeding back the voltage error between the output voltage and a reference voltage externally supplied to set up the output voltage, to the frequency and the amplitude of the carrier, the frequency response of the dc power supply is improved both by providing the pole located at the origin with a transfer function where the dc voltage, generated by rectifying and smoothing the output of the resonance circuit, is fed back to the frequency of the carrier and by not providing the pole at the origin with a transfer function where the dc voltage is fed back to the amplitude of the carrier.

主权项

1. In a system of differential equations describing operation of
such a power supply including
1. a driver circuit,2. a resonance circuit,3. a rectification and smoothing circuit,4. an error amplifier,5. a voltage controlled oscilator herafter abbreviated to VCO, and6. a reference voltage; wherein
1. the driver circuit generates a carrier which is supplied to the resonance circuit, the carrier being modulated in frequency and fixed in amplitude,2. the resonance circuit converts the frequency-modulated carrier at the input to an amplitude-modulated carrier at the output,3. the rectification and smoothing circuit rectifies the amplitude-modulated carrier supplied by the resonance circuit to a direct-current output voltage of the power supply,4. the error amplifier outputs the voltage difference between the output voltage and the reference voltage to the VCO,5. the VCO generates the frequency in which the carrier is modulated, the frequency being shifted according to the voltage difference, and6. the reference voltage is externally supplied to set up the output voltage of the power supply;consisting of
1. equationsⅆⅆt⁢p=q⁢⁢ϕ-p⁢⁢δ+rr⁢w[1]ⅆⅆt⁢q=-p⁢⁢ϕ-q⁢⁢δ+ri⁢w[2] derived from a second order differential equation for forced oscillation of the resonance circuit by introducing variables p and q transforming the second order differential equation to a couple of first order differential equations:(a) δ being a half band width of the forced oscillation,(b) φ being frequency of the carrier in terms of angular velocity.(c) ω being a fixed amplitude of the carrier, and(d) rr and ri being coefficients of the amplitude of the carrier; 2. equationμ⁢ⅆⅆt⁢z+z=v⁢p2+q2[3] approximating the output voltage supplied by the rectification and smoothing circuit:(a) z being the output voltage,(b) μ being a time constant for smoothing, and(c) the carrier outputted by the resonance circuit being rectified to a direct-current voltage ν√{square root over (p2+q2)} where ν is a multiplier at rectification; 3. equationⅆⅆt⁢ϕ=kd⁡(E⁡(z-λ)+A⁢ⅆⅆt⁢z+B⁢ⅆ2ⅆt2⁢z)[4] feeding back the voltage difference and its derivatives to the frequency of the carrier:(a) the output voltage being divided by d so as to fit an input range of the error amplifier,(b) the voltage difference supplied to the VCO being d z−n where n is a fixed voltage supplied externally,(c) k being a conversion coefficient of the VCO,(d) k(d z−n) being transformed to kd (z−λ) where λ is the reference voltage, and(e) A, B and E being constants; and 4. the characteristic polynomial mF(h) for the system of differential equations having equations 1, 2, 3, and 4 defined around an equilibrium point being given bymF⁡(h)=h⁡(δ2+2⁢⁢h⁢⁢δ+ϕe2+h2)⁢(h⁢⁢μ+1)μ+kw⁢⁢ϕe⁡(hA+h2⁢B+E)⁢vrdϕe2+δ2⁢μ[5] where(a) r being defined by √{square root over (rr2+ri2)}, and(b) φe being φ at the equilibrium point;extension comprising
1. the amplitude of the carrier being varied with the voltage difference fed back asw-G⁡(z-λ)-H⁢ⅆzⅆt:[6] (a) ω being the amplitude of the carrier without the feedback, and(b) G and H being constant; 2. equationⅆⅆt⁢p=q⁢⁢ϕ-p⁢⁢δ+rr⁡(w-G⁡(z-λ)-H⁢ⅆzⅆt)[7] derived by replacing ω in expression 1 with expression 6; 3. equationⅆⅆt⁢q=-p⁢⁢ϕ-q⁢⁢δ+ri⁡(w-G⁡(z-λ)-H⁢ⅆzⅆt)[8] derived by replacing ω in expression 2 with expression 6; and 4. the characteristic polynomial mV(h) for the system having equations 7, 8, 3, and 4 being given bymV⁡(h)=h⁡(δ2+2⁢⁢h⁢⁢δ+h2+ϕe2)⁢(h⁢⁢μ+1)μ+ϕe⁢wk⁡(E+hA+h2⁢B)⁢vrdϕe2+δ2⁢μ+hvr⁡(δ2+h⁢⁢δ+ϕe2)⁢(G+hH)ϕe2+δ2⁢μ.[9]