Abstract
The present disclosure provides a control method, in which charge control is combined with input voltage feedforward control and output current feedforward control. It can be shown that the combination of the charge control with the feedforward control performs better than the combination of the direct frequency control (DFC) with the feedforward control. In particular, the combination of the charge control with the feedforward control has much better load transient response with respect to the load transient response of the combined direct frequency control and feedforward control.
Claims
1. An isolated DC-DC converter comprising: a full-bridge switching stage having at least four active switches; a resonant network having a plurality of inductors and plurality of capacitors; a transformer connected to the resonant network; an output stage connected to the transformer and configured to generate an output voltage or current; an isolated charge sensor connected to the resonant network to generate a resonant inductor current charge signal; and a switch controller to generate and provide control signals to the at least four active switches based on at least the resonant inductor current charge signal and the output voltage or current.
2. The converter of claim 1, further comprising a voltage feedforward controller configured to sense a voltage input to the full-bridge switching stage, wherein, the switch controller is further configured to provide the control signals based on the voltage input sensed by the voltage feedforward controller.
3. The converter of claim 1, further comprising a current feedforward controller configured to sense an output current from the output stage, wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller.
4. The converter of claim 1, further comprising: a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage; a current feedforward controller configured to sense an output current from the output stage; wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller and the input voltage sensed by the voltage feedforward controller.
5. The converter of claim 1, wherein the isolated charge sensor comprises an additional sensing winding of a resonant inductor of the plurality of inductors with the sensing winding connected to a double integrator circuit input terminals to produce the resonant inductor current charge signal as a voltage at its output terminals.
6. The converter of claim 5, wherein the double integrator circuit comprises passive electrical elements.
7. The converter of claim 5, wherein the double integrator circuit comprises passive and active electrical elements.
8. The converter of claim 5, further comprising a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage, wherein, the switch controller is further configured to provide the control signals based on the voltage input sensed by the voltage feedforward controller.
9. The converter of claim 5, further comprising a current feedforward controller configured to sense an output current from the output stage, wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller.
10. The converter of claim 5, further comprising: a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage; a current feedforward controller configured to sense an output current from the output stage; wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller and the input voltage sensed by the voltage feedforward controller.
11. The converter of claim 1, wherein the isolated charge sensor is electrically equivalent to a second transformer with first and second terminal pairs, the first terminal pair connected in series with the at least one of the plurality of inductors, and the second terminal pair connected to an integrator circuit to produce the resonant inductor current charge signal as a voltage.
12. The converter of claim 11, wherein the integrator circuit comprises a capacitor.
13. The converter of claim 11, further comprising a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage, wherein, the switch controller is further configured to provide the control signals based on the input voltage sensed by the voltage feedforward controller.
14. The converter of claim 11, further comprising a current feedforward controller configured to sense an output current from the output stage, wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller.
15. The converter of claim 11, further comprising: a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage; a current feedforward controller configured to sense an output current from the output stage; wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller and the input voltage sensed by the voltage feedforward controller.
16. The converter of claim 1, wherein the plurality of capacitors comprises a first capacitor and a second capacitor, and the isolated charge sensor is electrically equivalent to a second transformer with first and second terminal pairs, the first terminal pair connected in parallel with the first capacitor and the second terminal pair connected to a resistor to produce the resonant inductor current charge signal as a voltage.
17. The converter of claim 16, further comprising a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage, wherein, the switch controller is further configured to provide the control signals based on the input voltage sensed by the voltage feedforward controller.
18. The converter of claim 16, further comprising a current feedforward controller configured to sense an output current from the output stage, wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller.
19. The converter of claim 16, further comprising: a voltage feedforward controller configured to sense an input voltage to the full-bridge switching stage; a current feedforward controller configured to sense an output current from the output stage; wherein, the switch controller is further configured to provide the control signals based on the output current sensed by the current feedforward controller and the input voltage sensed by the voltage feedforward controller.
20. The converter of claim 1, wherein the plurality of inductors of the resonant network includes at least one of a magnetizing inductance and a leakage inductance of the transformer.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0076] FIG. 1 is a block diagram of a resonant isolated DC-DC converter.
[0077] FIG. 2 is a circuit diagram of a conventional LLC resonant DC-DC converter. The converter in FIG. 2 has a full-bridge switching stage on the primary side, a full-bridge rectifier on the secondary side, and a CLC output filter.
[0078] FIG. 3 is a block diagram of a full-bridge LLC resonant DC-DC converter with direct frequency control.
[0079] FIG. 4 is a block diagram of a half-bridge LLC resonant DC-DC converter with direct frequency control and input voltage feedforward control.
[0080] FIG. 5 is a small-signal block diagram of an LLC resonant converter with direct frequency control and input voltage feedforward control.
[0081] FIG. 6 shows Bode plots of control-to-output transfer function G.sub.VC, open-loop audio-susceptibility transfer function G.sub.VV, and transfer function G.sub.FV.sup.FC of the ideal input voltage feedforward control for the LLC converter with direct frequency control.
[0082] FIG. 7 is a block diagram of a resonant zero-voltage-switching DC-DC converter with two-loop control.
[0083] FIG. 8 is a block diagram of a conventional half-bridge LLC resonant DC/DC converter with the average-current-mode control.
[0084] FIG. 9 is a block diagram of a conventional half-bridge LLC resonant DC/DC converter with the CC1 implementation.
[0085] FIG. 10 shows key control waveforms of a conventional half-bridge LLC resonant DC/DC converter with the CC1 implementation.
[0086] FIG. 11 is a block diagram of a conventional half-bridge LLC resonant DC/DC converter with the CC2 implementation.
[0087] FIG. 12 shows key control waveforms of a conventional half-bridge LLC resonant DC/DC converter with the CC2 implementation.
[0088] FIG. 13 shows a combined block diagram of a full-bridge LLC resonant converter with charge control in accordance with an embodiment of the present disclosure
[0089] FIG. 14A shows a circuit diagram of a charge sensor based on the sensing winding of resonant inductor in accordance with an embodiment of the present disclosure.
[0090] FIG. 14B shows a charge sensor based on the sensing winding of resonant inductor in accordance with a passive embodiment of the present disclosure.
[0091] FIG. 14C shows a charge sensor based on the sensing winding of resonant inductor in accordance with an active embodiment of the present disclosure.
[0092] FIG. 15A shows a circuit diagram of a charge sensor based on sensing resonant inductor current I.sub.LR, in accordance with an embodiment of the present disclosure.
[0093] FIG. 15B shows a charge sensor based on sensing resonant inductor current I.sub.LR, in accordance with a passive embodiment of the present disclosure.
[0094] FIG. 16 shows a circuit diagram of a charge sensor based on sensing resonant capacitor voltage V.sub.CR with a voltage transformer in accordance with an embodiment of the present disclosure.
[0095] FIG. 17 shows a combined circuit diagram of a conventional LLC converter resonant tank and an equivalent circuit diagram of the voltage-transformer-based charge sensor in accordance with an embodiment of the present disclosure.
[0096] FIG. 18 shows a combined circuit diagram of an LLC converter resonant tank and an equivalent circuit diagram of the voltage-transformer-based charge sensor in accordance with an embodiment of the present disclosure.
[0097] FIG. 19 shows an exemplary plot of LLC converter voltage gain M versus frequency with and without the voltage-transformer-based charge sensor in accordance with an embodiment of the present disclosure.
[0098] FIG. 20 shows a block diagram of the charge control combined with the output current feedforward control and the input voltage feedforward control in accordance with an embodiment of the present disclosure.
[0099] FIG. 21 shows a small-signal block diagram of the resonant converter with the charge control combined with the output current feedforward control in accordance with an embodiment of the present disclosure.
[0100] FIG. 22 shows exemplary Bode plots of transfer functions Z.sub.TH, G.sub.VC.sup.CC, and G.sub.FI of a full-bridge LLC converter with the charge control and the output current feedforward control in accordance with an embodiment of the present disclosure.
[0101] FIG. 23 shows a block diagram of the direct frequency control combined with the output current feedforward control in accordance with an embodiment of the present disclosure.
[0102] FIG. 24 shows a small-signal block diagram of a resonant converter with the direct frequency control combined with the output current feedforward control in accordance with an embodiment of the present disclosure.
[0103] FIG. 25 shows exemplary Bode plots of transfer functions Z.sub.O.sup.OL, G.sub.VC, and G.sub.FI.sup.FC of a full-bridge LLC converter with the direct frequency control and the output current feedforward control in accordance with an embodiment of the present disclosure.
[0104] FIG. 26 shows Bode plots of OCF control transfer functions G.sub.FI and G.sub.FI.sup.FC for the charge control and the direct frequency control, respectively, in accordance with an embodiment of the present disclosure.
[0105] FIG. 27 shows the output voltage response to the output current pulse for an LLC converter with the charge control and for the LLC converter with the DFC, with and without the OCF control, in accordance with an embodiment of the present disclosure.
[0106] FIG. 28 shows a block diagram of the charge control combined with the input voltage feedforward control in accordance with an embodiment of the present disclosure.
[0107] FIG. 29 shows a small-signal block diagram of a resonant converter with the charge control combined with the input voltage feedforward control in accordance with an embodiment of the present disclosure.
[0108] FIG. 30 shows exemplary Bode plots of transfer functions G.sub.VV.sup.CC, G.sub.VC.sup.CC, and G.sub.FV of a full-bridge LLC converter with the charge control and the input voltage feedforward control.
[0109] FIG. 31 shows magnitude plots of the closed-loop audio-susceptibility G.sub.VV.sup.CL for the LLC converter charge control, with and without the input voltage feedforward control, in accordance with an embodiment of the present disclosure.
[0110] FIG. 32 shows the output voltage response to the input voltage 100-Hz ripple for an LLC converter with the charge control, with and without the IVF control in accordance with an embodiment of the present disclosure.
[0111] FIG. 33 shows exemplary Bode plots of transfer functions G.sub.VV, G.sub.VC, and G.sub.FV.sup.FC of a full-bridge LLC converter with the DFC and the input voltage feedforward control in accordance with an embodiment of the present disclosure.
[0112] FIG. 34 shows magnitude plots of closed-loop audio-susceptibility G.sub.VV.sup.CL for DFC, with and without the input voltage feedforward control in accordance with an embodiment of the present disclosure.
[0113] FIG. 35 shows the output voltage response to the input voltage 100-Hz ripple for an LLC converter with the DFC, with and without the IVF control in accordance with an embodiment of the present disclosure.
DETAILED DESCRIPTION
[0114] In this disclosure, a new control method to improve transient response to both load (I.sub.OUT) and input (V.sub.IN) disturbances and to reduce a low-frequency output voltage ripple of a resonant converter is provided. Previous publications mostly considered the application of charge control to half-bridge LLC. Ref. [18] considered charge-control for a full-bridge LLC converter. The inventors recognized and appreciated the need for a cost-effective implementation of charge control in full-bridge LLC converters.
[0115] One aspect of the present disclosure is the implementation of charge control in a full-bridge LLC converter as shown in FIG. 13. When implementation of the charge control in the full-bridge LLC converter is selected, there are several important practical considerations: [0116] 1. The full-bridge LLC topology is typically used for DC-DC converters whose output power is in the multi-kW range. [0117] 2. These high-power DC-DC converters typically employ digital control and are required to have multiple communication channels with the centralized power system controller. This communication is much simpler and cost-effective when the digital signal processor (DSP) is located on the transformer secondary side. In this case, communication signals have the same ground as the system controller and no isolation devices for communication channels are necessary. [0118] 3. With the DSP located on the secondary side, there is no need to transfer output voltage or current feedback signals over the isolation boundary. Today's analog signal isolation devices have either poor speed at low cost or adequate speed, but at high cost.
[0119] Taking these practical considerations into account, it is highly desirable to use an isolated charge sensor which can deliver the sensed signal directly to the secondary-side controller. There are several approaches which could potentially meet this requirement at low cost. In one embodiment (the first approach) the signal is sensed at the terminals of an additional sensing winding of the resonant inductor. In another embodiment (the second approach) the resonant inductor current is sensed with a current transformer. In yet another embodiment (the third approach) the resonant capacitor voltage is sensed with a voltage transformer. These three approaches are described below in detail.
[0120] An implementation of the first approach is shown in FIG. 14A. The simplified equivalent circuit of the resonant inductor with sensing winding is shown inside rectangle 1410 in FIG. 14A and includes inductance LR and ideal transformer TX. The resonant inductor power winding is located on the left side of the drawing, whereas the sensing winding is located on the right side of the drawing. Ideal transformer TX with turns ratio N.sub.LR:1, where N.sub.LR is the number of power winding turns. The sensing winding typically has one turn, but generally can have any number of turns.
[0121] Since voltage V.sub.LR across the resonant inductor power winding is related to current I.sub.LR as V.sub.LR=L.sub.R dI.sub.LR/dt, voltage V.sub.S across the sensing winding is proportional to the second derivative of charge Q. To obtain sensor output voltage V.sub.SENSE, proportional to charge Q, a double integrator circuit 1420, shown in FIG. 14A, is required.
[0122] Double integrator 1420 can be implemented with a passive or an active circuit. One embodiment of a passive double integrator implementation is shown in FIG. 14B. The sensing winding in FIG. 14B is terminated with inductor L.sub.S. Due to the symmetry of the power and sensing sides of the resonant inductor, sensing winding current I.sub.S is proportional to current I.sub.LR. This current is sensed with a current transformer CT, whose equivalent circuit in FIG. 14B is represented by ideal transformer TX1 and magnetizing inductance L.sub.MS. The CT secondary current, which is proportional to current I.sub.S, flows through integrating capacitor C.sub.S. Therefore, sensor output voltage V.sub.SENSE is proportional to charge Q.
[0123] One exemplary embodiment of an active double integrator implementation is shown in FIG. 14C. The first integration stage is implemented by passive circuit R.sub.1, C.sub.1, whereas the second integration stage is implemented by the active circuit including operational amplifier U1, resistors R.sub.2, R.sub.3, and capacitor C.sub.2.
[0124] The second implementation of the isolated charge sensor with the current transformer is shown in FIG. 15A. The current transformer (CT) can be used for sensing resonant current I.sub.LR, because the resonant capacitor blocks the DC current flowing through the resonant inductor. CT senses resonant inductor current I.sub.LR and its equivalent circuit in FIG. 15A includes ideal transformer TX2 with turns ratio 1:N.sub.CT and secondary-side magnetizing inductance L.sub.MS. The CT secondary winding provides the input signal for the integrator circuit in FIG. 15A.
[0125] In one embodiment of the second approach, the CT secondary winding is terminated with capacitor C.sub.S, as shown in FIG. 15B. Current I.sub.LR, reflected to the secondary side, splits between magnetizing inductance L.sub.MS and output capacitor C.sub.S. The distribution of reflected current I.sub.LR/N.sub.CT between magnetizing inductance L.sub.MS and capacitor Cs depends on the switching frequency. Input/output relationship of the charge sensor in FIG. 15B is described by transfer function
V.sub.SENSE/I.sub.LR=1/N.sub.CT.Math.s.Math.L.sub.MS/(1+s.sup.2.Math.L.sub.MS.Math.C.sub.S). (3)
[0126] Equation (3) reveals that the sensor transfer function has a zero at zero frequency and double resonant poles at frequency f.sub.RES=1/(2π.Math.√{square root over (L.sub.MS.Math.C.sub.S)}). When converter switching frequency is much higher than resonant frequency f.sub.RES, transfer function (3) is simplified to
V.sub.SENSE/I.sub.LR=1/N.sub.CT.Math.1/(s.Math.C.sub.S). (4)
[0127] Equation (4) demonstrates that at high frequencies the sensor integrates current I.sub.LR and, therefore, sensor output voltage V.sub.SENSE is proportional to charge Q. Component values L.sub.MS and C.sub.S are selected to keep resonant frequency f.sub.RES well below converter minimum operating frequency.
[0128] The third approach for the charge control of the full-bridge LLC converter is based on sensing of the resonant capacitor voltage with the voltage transformer (VT). The simplified equivalent circuit of the voltage transformer sensor is shown in FIG. 16, where TX3 is an ideal transformer with turns ratio N.sub.VT=N.sub.VTP/N.sub.VTS, L.sub.MP and L.sub.LEAK are the primary-side magnetizing and leakage inductances, and R.sub.S is the output resistor of the sensor. As can be seen in FIG. 16, voltage VCR is divided between leakage inductance L.sub.LEAK and parallel combination of magnetizing inductance L.sub.MP and reflected resistance R.sub.S.Math.N.sub.VT.sup.2. Input/output relationship of the voltage sensor in FIG. 16 is described by transfer function
V.sub.S/V.sub.CR=1/N.sub.VT.Math.1/[1+L.sub.LEAK/L.sub.M+sL.sub.LEAK/(R.sub.S.Math.N.sub.VT.sup.2)]. (5)
[0129] Equation (5) reveals that VT sensor transfer function has a single pole at frequency f.sub.PV=2π/(L.sub.LEAK/(R.sub.S.Math.N.sub.VT.sup.2)) and no zeroes. For typical transformer, L.sub.LEAK<<L.sub.MP and transfer function (5) is simplified to
V.sub.SENSE/V.sub.CR≅1/N.sub.VT.Math.1/[1+s.Math.L.sub.LEAK/(R.sub.S.Math.N.sub.VT.sup.2)]. (6)
[0130] When voltage V.sub.CR is sensed with the voltage transformer, it is important to minimize the VT effect on the resonant tank operation. FIG. 17 shows combined circuit diagram of the LLC resonant tank and equivalent circuit diagram of the VT sensor with resistor R.sub.S reflected to the primary side and inductance L.sub.LEAK neglected. There are two ways of the VT detrimental interaction with the resonant tank. First, VT primary winding creates the DC current path which bypasses capacitor C.sub.R and, therefore, can lead to saturation of transformer T1 and VT itself. To eliminate the DC current path, resonant capacitor C.sub.R is split into two series-connected capacitors C.sub.R1 and C.sub.R2, as shown in FIG. 18. The capacitance value of resonant capacitor C.sub.R and the capacitance value of series-connected capacitors C.sub.R1 and C.sub.R2 should be the same. Second, VT magnetizing inductance L.sub.MP becomes an extra resonant component of the resonant tank which affects converter voltage gain M=N.Math.V.sub.O/V.sub.IN. This effect can be observed in FIG. 19, which shows calculated gain M with and without inductance L.sub.MP. Inductance L.sub.MP introduces extra pole at frequency f.sub.P≈1/(2π.Math.√{square root over (2.Math.L.sub.MP.Math.C.sub.R1)}) and zero at frequency f.sub.Z≈1/(2π.Math.√{square root over (L.sub.MP.Math.C.sub.R1)}). To minimize the effect of these pole and zero, their frequencies should be well below the converter operating range. It is sufficient to select inductance L.sub.MP high enough to make frequencies of extra pole and zero significantly lower than resonant frequency f.sub.RM=1/(2π.Math.√{square root over ((L.sub.M+L.sub.R).Math.C.sub.R)}), where C.sub.R=C.sub.R1.Math.C.sub.R2/(C.sub.R1+C.sub.R2). This condition is met in FIG. 19, where f.sub.P=3.5 kHz, f.sub.Z=5.0 kHz and f.sub.RM=34 kHz. FIG. 19 also shows that, at frequencies above 15-20 kHz, magnetizing inductance L.sub.MP practically has no effect on the converter voltage gain M.
[0131] With the disclosed sensing approaches, both CC1 and CC2 implementations in the full-bridge LLC converter are possible. For CC2 implementation in the full-bridge converter, sensing of the input voltage is not required.
[0132] Another aspect of the present disclosure is the improvement of the LLC converter response to disturbances of the output current and input voltage. The improvement is achieved by combining the charge control with the feedforward output current control and the feedforward input voltage control. The corresponding control block diagram is shown in FIG. 20. To implement output current feedforward (OCF) control, output current I.sub.O in FIG. 20 is sensed and processed by OCF controller, whose output signal is summed with error amplifier output signal V.sub.EA. To implement input voltage feedforward (IVF) control, input voltage V.sub.IN is sensed and processed by IVF controller, whose output signal is subtracted from signal V.sub.1, as shown in FIG. 20.
[0133] Note that proposed feedforward control can have only input voltage feedforward control or only output current feedforward control or both of them. Usually, the charge control has much better input disturbance rejection than the direct frequency control (Refs. [19]-[20]), and, depending on converter specifications, the input voltage feedforward control may not be required. However, as was mentioned before, the charge control cannot significantly improve the load disturbance rejection with respect to DFC, and the output current feedforward control is highly desirable.
[0134] To determine ideal transfer function of the output current feedforward control, the small-signal block diagram of the disclosed control, shown in FIG. 21, is employed. For the converter with the charge control, its output port is represented in FIG. 21 with the Thevenin equivalent circuit, which includes Thevenin dependent voltage source G.sub.VC.sup.CC.Math.V.sub.CONT and Thevenin impedance Z.sub.TH, where G.sub.VC.sup.CC=V.sub.O/V.sub.CONT is the control-to-output transfer function of the charge control and Z.sub.TH is the converter output impedance with charge control loop closed, voltage feedback loop opened, and output current feedforward control loop opened.
[0135] In addition to the Thevenin equivalent circuit, the block diagram in FIG. 21 also includes: [0136] 1. Transfer function K.sub.D of the output voltage sensor; [0137] 2. Transfer function G.sub.EA of the error amplifier; [0138] 3. Combined transfer function G.sub.FI of output current sensor and OCF controller.
[0139] When output voltage feedback path and output current feedforward path are closed, converter small-signal closed-loop output impedance Z.sub.O.sup.CL is derived from the block diagram in FIG. 21 as
[00003]
where T.sub.V=K.sub.D.Math.G.sub.EA.Math.G.sub.VC is the voltage feedback loop gain.
[0140] Equation (7) indicates that complete cancellation of the small-signal output current disturbance is possible when
G.sub.FI=Z.sub.TH/G.sub.VC.sup.CC. (8)
It should be noted that ideal small-signal feedforward control transfer function G.sub.FI, defined by equation (8), cannot completely cancel the real-life input disturbance for two major reasons: [0141] 1. Both power stage and feedback frequency control are nonlinear blocks and their large-signal behavior cannot be adequately represented by small-signal transfer functions Z.sub.TH and G.sub.VC.sup.CC which depend on converter operating point, namely, on the input voltage and the output current; [0142] 2. Since both Z.sub.TH and G.sub.VC.sup.CC are frequency-dependent transfer functions, ideal transfer function G.sub.FI is also frequency dependent. The accurate implementation of its all poles and zeroes could be too complex for practical feedforward control.
[0143] As an example, the Bode plots of transfer functions Z.sub.TH, G.sub.VC.sup.CC, and G.sub.FI of the full-bridge LLC converter with the charge control are shown in FIG. 22.
[0144] The output current feedforward control can be applied also to resonant converters with the direct frequency control. The exemplary implementation of the OCF control in the full-bridge LLC converter with the DFC is shown in FIG. 23, whereas its corresponding control block diagram is shown in FIG. 24. As for the charge control, the converter output port is represented in FIG. 24 with the Thevenin equivalent circuit, which includes Thevenin dependent voltage source G.sub.VC.Math.V.sub.CONT and Thevenin impedance Z.sub.O.sup.OL, where G.sub.VC is the DFC control-to-output transfer function and Z.sub.O.sup.OL is the converter output impedance with voltage feedback path opened and output current feedforward control path opened.
[0145] In addition to the Thevenin equivalent circuit, the block diagram in FIG. 24 also includes: [0146] 1. current source I.sub.O which represents the small-signal load current perturbation; [0147] 2. transfer function K.sub.D of the output voltage sensor; [0148] 3. transfer function G.sub.EA of error amplifier; [0149] 4. Combined transfer function G.sub.FI of the output current sensor and OCF controller.
[0150] When output voltage feedback path and output current feedforward path are closed, converter closed-loop output impedance Z.sub.O.sup.CL is derived from the block diagram in FIG. 24 as
[00004]
[0151] Equation (9) indicates that complete cancellation of the small-signal output current disturbance is possible when
G.sub.FI.sup.FC=Z.sub.O.sup.OL/G.sub.VC. (10)
[0152] For the DFC, ideal small-signal feedforward control transfer function G.sub.FI.sup.FC, defined by equation (10), cannot completely cancel the real-life load disturbance for the same reasons mentioned above for transfer function G.sub.FI, corresponding to the charge control.
[0153] As an example, the Bode plots of transfer functions Z.sub.O.sup.OL, G.sub.VC, and G.sub.FI.sup.FC of the full-bridge LLC converter with the DFC are shown in FIG. 25. For comparison, OCF control transfer functions G.sub.FI and G.sub.FI.sup.FC for the charge control and the direct frequency control, respectively, are plotted in FIG. 26. For practical OCF control implementation, approximation of its control function by the constant gain is highly desirable. FIG. 26 reveals that transfer function G.sub.FI can be approximated by the constant gain to much higher frequency than transfer function G.sub.FI.sup.FC. For example, the magnitude of transfer function G.sub.FI deviates by 3 dB from its dc value at 30.2-kHz frequency, whereas the magnitude of transfer function G.sub.FI.sup.FC deviates by 3 dB from its dc value at 1.2-kHz frequency. Also the phase of transfer function G.sub.FI deviates by 45° from zero value at 20.4-kHz frequency, whereas the phase of transfer function G.sub.FI.sup.FC deviates by 45° from zero value at 1.1-kHz frequency.
[0154] This is very significant advantage of the combined charge control and OCF control with respect to the combined DFC and OCF control. This advantage is demonstrated in FIG. 27, which shows the LLC converter response to the load disturbance. The upper plot in FIG. 27 shows the output current which steps up from 17 A to 83 A at time t=0.2 ms and steps back to 17 A at t=1.3 ms. The middle plot in FIG. 27 shows the transient waveforms of output voltage V.sub.O for the charge control with and without the OCF control. This plot demonstrates that, with the OCF control added to the charge control, transient output voltage undershoot is reduced by 81% from −323 mV to −60 mV, whereas transient output voltage overshoot is reduced by 65% from 321 mV to 113 mV. The lower plot in FIG. 27 shows the transient waveforms of output voltage V.sub.O for the DFC with and without the OCF control. This plot demonstrates that, with the OCF control added to the DFC, transient output voltage undershoot is reduced by 18% from −477 mV to −391 mV, whereas transient output voltage overshoot is reduced by 20% from 483 mV to 387 mV. The waveforms in FIG. 27 confirm that combination of the charge control with the OCF control is much more beneficial than combination of the DFC with the OCF control.
[0155] The disclosed implementation of the charge control with the input voltage feedforward (IVF) control is presented next. The block diagram of the disclosed control is shown in FIG. 28. To determine the ideal transfer function of the IVF control, the small-signal block diagram of the proposed control, shown in FIG. 29, is employed. The block diagram in FIG. 29 includes: [0156] 1. transfer function G.sub.VV.sup.CC from input voltage V.sub.IN to output voltage V.sub.O with the charge control loop closed and with the voltage feedback and feedforward control paths opened; [0157] 2. control-to-output transfer function G.sub.VC.sup.CC of the charge control; [0158] 3. transfer function K.sub.D of output voltage sensor; [0159] 4. transfer function G.sub.EA of error amplifier; [0160] 5. Combined transfer function G.sub.FV of the input voltage sensor and feedforward controller.
[0161] Transfer function G.sub.VV.sup.CL from input voltage V.sub.IN to output voltage V.sub.O with the feedback and feedforward paths closed is derived from the block diagram in FIG. 29 as
[00005]
where T.sub.V=K.sub.D.Math.G.sub.EA.Math.G.sub.VC is the voltage feedback loop gain.
[0162] Equation (11) indicates that complete cancellation of the small-signal input voltage disturbance is possible when
G.sub.FV=G.sub.VV.sup.CC/G.sub.VC.sup.CC. (12)
[0163] It should be noted that ideal small-signal IVF control transfer function G.sub.FV, defined by equation (12), cannot completely cancel the input disturbance for the reasons, explained earlier.
[0164] As an example, the Bode plots of transfer functions G.sub.VV.sup.CC, G.sub.VC.sup.CC, and G.sub.FV of the full-bridge LLC converter with the charge control are shown in FIG. 30. At low frequencies, transfer function G.sub.FV can be approximated with its dc gain. For example, the G.sub.FV magnitude deviates from its dc value by 3 dB at 58.9-kHz frequency, whereas the G.sub.FV phase deviates from zero by 45° at 23.4-kHz frequency. For the charge control and transfer function G.sub.FV approximated by its dc gain, the Bode plots of input-to-output transfer function G.sub.VV.sup.CL, called closed-loop audio-susceptibility, of the full-bridge LLC converter with and without the IVF control were calculated from (11) and are shown in FIG. 31. In the off-line power supplies, the DC-DC stage is supplied from the front-end stage output which has considerable ripple of the doubled line frequency. The doubled line frequency is typically in the 100-120 Hz range. As the DC-DC stage output voltage has stringent ripple requirements, the low audio-susceptibility at the doubled line frequency is highly important. In FIG. 31, addition of the IVF control to the charge control reduces the audio-susceptibility by 42 dB from −68 dB to −110 dB at 100-Hz frequency.
[0165] Simulated input and output voltage waveforms for the charge control with and without the IVF control are shown in FIG. 32. The upper waveform in FIG. 32 is the converter input voltage ac component which has 30-V.sub.PP magnitude. The lower waveforms show the converter output voltage and its lower-frequency component. To obtain the lower-frequency component, the converter output voltage signal was processed by the low-pass filter with 2.5-kHz bandwidth. Without the IVF control, the output voltage waveform and its low frequency component in FIG. 32 have 38-mV.sub.PP and 13-mV.sub.PP ripple, respectively. With the IVF control added, the output voltage waveform and its low frequency component have their ripple reduced to 30-mV.sub.PP and 0.64-mV.sub.PP, respectively. Therefore, the addition of the IVF control reduces the magnitude of the output voltage low frequency component 20.3 times.
[0166] When the IVF control is applied together with the direct frequency control, its ideal transfer function G.sub.FV.sup.FC is calculated using equation (2). The Bode plots of transfer functions G.sub.VC, G.sub.VV, and G.sub.FV.sup.FC of the full-bridge LLC converter with the DFC are shown in FIG. 33. At low frequencies, transfer function G.sub.FV.sup.FC can be successfully approximated with its dc gain. For example, the G.sub.FV.sup.FC magnitude deviates from its dc value by 3 dB at 77.5-kHz frequency, whereas the G.sub.FV.sup.FC phase deviates from zero by 45° at 26.4-kHz frequency.
[0167] For the DFC and transfer function G.sub.FV.sup.FC approximated by its dc gain, the Bode plots of closed-loop audio-susceptibility G.sub.VV.sup.CL of the full-bridge LLC converter with and without the IVF control were calculated from (1) and are shown in FIG. 34. According to FIG. 34, addition of the IVF control to the DFC reduces the audio-susceptibility by 23 dB from −47 dB to −70 dB at 100-Hz frequency. Simulated input and output voltage waveforms for the DFC with and without the IVF control are shown in FIG. 35. The upper waveform in FIG. 35 is the converter input voltage ac component which has 30-V.sub.PP magnitude. The lower waveforms show the converter output voltage and its lower-frequency component. Without the IVF control, the output voltage waveform and its low frequency component in FIG. 35 have 161-m V.sub.PP and 49-mV.sub.PP ripple, respectively. With the IVF control added, the output voltage waveform and its low frequency component have their ripple reduced to 49.4-mVPP and 24-mVPP, respectively. Therefore, the addition of the IVF control reduces the magnitude of the output voltage low frequency component 5.8 times. Hence, the presented data confirms that addition of the IVF control to the charge control has more performance benefits than addition of the IVF control to the direct frequency control.
[0168] Therefore, the combined charge and feedforward controls disclosed herein have significantly better performance with respect to the combined direct frequency and feedforward controls.
[0169] For the purposes of describing and defining the present disclosure, it is noted that terms of degree (e.g., “substantially,” “slightly,” “about,” “comparable,” etc.) may be utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison, value, measurement, or other representation. Such terms of degree may also be utilized herein to represent the degree by which a quantitative representation may vary from a stated reference (e.g., about 10% or less) without resulting in a change in the basic function of the subject matter at issue. Unless otherwise stated herein, any numerical value appearing in the present disclosure are deemed modified by a term of degree (e.g., “about”), thereby reflecting its intrinsic uncertainty.
[0170] Although various embodiments of the present disclosure have been described in detail herein, one of ordinary skill in the art would readily appreciate modifications and other embodiments without departing from the spirit and scope of the present disclosure as stated in the appended claims.
