Doctoral school of energy- and geo-technology January 15–20, 2007. Kuressaare, Estonia
Output Filter for the High-Voltage DC/DC Converter Margus Müür, Dmitri Vinnikov Tallinn University of Technology [email protected]
Abstract This paper presents the output filter analysis and design for the high-voltage isolated DC/DC converter. The topology of the filter is the second order low-pass LC but in row with the relative simplicity it demonstrates excellent performance. Filter steady state analysis as well as simulation results are discussed.
Keywords Second order LC-filter, simulation, voltage ripple
Introduction All DC/DC converter topologies have an output filter to supply the load with an almost constant voltage waveform. The output filter has a strong influence on the performance of the converter and an important impact in its size. One of the most common output filter configuration is the LC network. The values of the inductor and capacitor are determined by the output voltage requirements and by the topology of the converter. Nowadays the Department of Electrical Drives and Power Electronics of Tallinn University of Technology is developing a prototype of a brandnew isolated 3 kV DC/DC converter for the supplying internal 350 V DC-bus of a commuter train. The implementation of new 6.5 kV IGBTs enable further simplification of power circuits (Fig. 1) with no changes in the blocking voltage capability of the inverter leg. The DC/DC converter parameters are submitted in Table 1.
Parameters Input voltage range (V) Output voltage (V) Peak output current (A), (during 1 min) Switching frequency (Hz)
Values 2200...4000 350 ± 2.5% 143 1000
In the discussed half-bridge topology the maximum duty cycle D (D=ton/T) of each switch is 80% from the half-period at rated load. In practice it means that isolation transformer must be specified to provide maximal current just with the minimal input voltage (i.e., 2200 V). The respective voltage before the output filter (U3) and the output filter inductor current (IL) are shown in Fig. 2. Apparently, the most demanding operation conditions to the output filter are at the maximum input voltage (i.e., 4000 V) and rated load, when the duty cycle D becomes 44% of the half-period (Fig. 3).  I, U
Table 1. High-voltage DC/DC converter parameters
stable. The desired output voltage regulation overshoot is only 2.5 % (i.e. 8.75 V), which makes the design of control system and output filter very challenging.
Fig. 2. Diode rectifier output voltage U3 and inductor current IL during the minimum input voltage conditions (maximal switch duty cycle) I, U U3
D6 IL Inout
Fig. 1. High-voltage DC/DC converter circuit The converter output is connected to an intermediate DC-bus of a train. The function of the intermediate DC-bus is to interconnect secondary converters (output modules). Despite the very wide primary voltage fluctuations the output voltage must remain 118
Fig. 3. Diode rectifier output voltage U3 and inductor current IL during the maximum input voltage conditions (minimal switch duty cycle)
1 Output filter design relations The output LC-filter is used primarily in power supplies where voltage regulation is important and where the output current is relatively high and subject to varying load conditions. This filter is mainly used in the high power applications. Low-pass LC-filter consists of an input inductor (L0) and an output filter capacitor (C0) (for the details see Fig. 1). Inductor L0 is placed at the input of the filter and is in series with the output of the rectifier circuit. Since the action of an inductor is to oppose any change in current flow, the inductor tends to keep a constant current flowing to the load throughout the complete cycle of the applied voltage. As a result, the output voltage never reaches the peak value of the outgoing transformer voltage. The reactance of the inductor (XLo) reduces the amplitude of ripple voltage without reducing the DC output voltage by an appreciable amount (the DC resistance of the inductor is just a few ohms).  The shunt capacitor (C0) charges and discharges at the ripple frequency rate, but the amplitude of the ripple voltage is relatively small because the inductor (L0) tends to keep a constant current flowing from the rectifier circuit to the load. In addition, the reactance of the shunt capacitor (XCo) presents low impedance to the ripple component existing at the output of the filter, and thus shunts the ripple component around the load. The capacitor attempts to hold the output voltage relatively constant at the average value of the voltage. The value of the filter capacitor (C0) must be relatively large to present a low opposition (XCo) to the pulsating current and to store a substantial charge. The rate of the charge for the capacitor is limited by the low impedance of the AC source (the transformer), by the small resistance of the diode, and by the counter electromotive force (CEMF) developed by the coil. Therefore, the RC-charge time constant is short compared to its discharge time. Consequently, when the pulsating voltage is first applied to the LC-filter, the inductor (L0) produces a CEMF which opposes the constantly increasing input voltage. The net result is to effectively prevent the rapid charging of the filter capacitor (C0). Thus, instead of reaching the peak value of the input voltage, C0 only charges to the average value of the input voltage. After the input voltage reaches its peak and decreases sufficiently, the capacitor (C0) attempts to discharge through the load resistance (RLoad), what is connected to filter output. C0 will only partially discharge because of its relatively long discharge time constant. The larger is the value of the filter capacitor, the better the filtering action. However, because of physical size, there is a practical limitation to the maximum value of the capacitor. The first step is to choose an output filter inductor. In the filter inductance calculation is assumed that the inductor current is not discontinuous. It is
discontinuous only when the front end of the inductor current ramp has dropped to zero and that this occurs when the output DC current (minimum) has fallen to half of the filter inductor ripple current amplitude dI. Then: 
dI = 2 ⋅ I outm = U L ⋅
ton t = (U 3 − U out ) ⋅ on , L0 L0
where Ioutm – minimal output current (half the ramp amplitude dI), UL – voltage drop on filter inductor, U3 –rectifier output voltage, Uout – converter output voltage (filtered), ton –switch on-state time, L0 –filter inductance to be calculated. Output voltage defining equation 
U out = U 3 ⋅
2 ⋅ ton , T
thus, the ton calculation equation is 
U out ⋅ T . 2 ⋅U3
As it was stated before, for the values of the output filter components L0 and C0, the worst operating point is at the maximum input voltage level and at the rated load conditions (i.e., minimum duty cycle operation). At this point, the operating duty cycle of the inverter switches becomes 44% from the halfperiod. Thus, ton is
U out ⋅ T 0.44 ⋅ T = . 2 ⋅U 3 2
The voltage U3 can be derived from Eq. 4
U out ⋅ T = 2.27 ⋅ U out . 0.44 ⋅ T
If Eqs. 4 and 5 are placed in Eq. 1, then
dI = (2.27 ⋅ U out − U out ) ⋅
(0.44 ⋅ T / 2) = 2 ⋅ I L0
The filter inductance equation derived from Eq. 6 is
0.14 ⋅ U out ⋅ T . I outm
Then if the minimum current Ioutm is specified as 5% (7.15 A) of the nominal output current Inout the inductance equation is
2.8 ⋅ U out ⋅ T . I nout
Based on equation 8, the chosen filter inductor inductance has to be at least 6.86 mH. The next step is to choose output filter capacitor. It is assumed that the output capacitor size will be determined by the ripple current and ripple voltage 119
specifications only. Assume that the ripple voltage at the terminals of C0 can be 17.5 V (5% of the output voltage). The current change in L0 during the “on” period will mainly flow into C0, and hence the capacitance value required to give a voltage change of 17.5 V can be calculated as follows (the following equation assumes a perfect capacitor with zero ESR) 
dI ⋅ ton . Ur
Thus, the output filter capacitor capacitance minimum value is 180 µF, if the peak-to-peak ripple voltage is 5% of the output voltage and the allowed filter inductor current ramp amplitude is 10% of the nominal output current. With the minor modifications the same equations (1-9) can be applied to the maximum duty cycle operation (minimal amplitude value of U3). Table 2 shows the duty cycle variation when input voltage changes. Furthermore, it is shown the values of L0 and C0 to obtain required inductor current ripple (10%) and output voltage ripple (5%).
2.1 Simulation with the minimal input voltage The output voltage pulse amplitude of an isolation transformer is minimal and the pulse width is longest (on-state time of each IGBT transistor is 0.4 T). Fig. 5 demonstrates simulated inductor current (IL) and output current (Iout) waveforms. The peak-topeak inductor current ripple is not exceeding 5%, which is in the good agreement with the requirements. Output current ripple is less than 1%. 150A
Table 2. Calculated filter parameters for the different operation points Amplitude value of U3 440 V 795 V Switch duty cycle D 0.8(T/2) 0.44(T/2) Value of L0 2.45 mH 6.86 mH Value of C0 327 µF 180 µF
Fig. 5. Inductor current (IL) and output current (Iout) waveforms with the maximum switch duty cycle Fig. 6 demonstrates rectifier output voltage (U3) and converter output voltage (Uout) waveforms. The peak-to-peak output voltage ripple is less than 1%.
2 Output filter simulations
PSpice simulation circuit of the output LC-filter for a high voltage DC/DC converter is shown in Fig. 4.
Fig. 4. PSpice simulation circuit of the output LC-filter All used components are ideal, what means that the voltage drops were not considered in simulations. To simplify the circuit only the resistive load was used. Two pulse voltage sources were used to simulate the transformer output voltage. For finding transformer output voltage amplitude Eq. 2 was used. The output filter was proven in two different conditions: with maximum switch duty cycle (minimal converter input voltage Uin) and with minimum switch duty cycle (maximal converter input voltage Uin). Both simulations were made with maximum load that is most demanding for the output filter design. Values of filter elements to be tested are L0=7 mH and C0=180 µF. 120
-100V 0s V(D3:2)
Fig. 6. Rectifier output voltage (U3) and converter output voltage (Uout) with the maximum switch duty cycle 2.2 Simulation with the maximal input voltage The output voltage pulse amplitude of an isolation transformer is reaching its maximum and the pulse width is shortest (on-state time of each IGBT transistor is 0.22 T). Fig. 7 demonstrates simulated inductor current (IL) and output current (Iout) waveforms. The peak-topeak inductor current ripple is not exceeding 10%, which is in the good agreement with the requirements. Output current ripple is about 1.5%.
Output Current, Iout 54 36 1001 1501 Output Current
IOUT, A 140 120A 12.0ms I(L2)
Fig. 7. Inductor current (IL) and output current (Iout) waveforms with the minimum switch duty cycle Fig. 8 demonstrates rectifier output voltage (U3) and converter output voltage (Uout) waveforms. The peak-to-peak output voltage ripple is about 1.5%.
Output Voltage, Uout 36 1001
Fig. 9. Simulated waveforms of the isolated halfbridge DC/DC converter with proposed LC-filter
-100V 0s V(RLoad:2)
Fig. 8. Rectifier output voltage (U3) and converter output voltage (Uout) with the minimum switch duty cycle
3 Converter dynamic response Above-presented simulations are demonstrating that filter components were selected properly. Corresponding voltage and current ripple values are minimal. Thus, for the prototype it was decided to implement the laminated iron-core inductor with inductance value of 5 mH. Two electrolytic capacitors (EPCOS B437 560 µF, 450 V) will be connected in series with the total capacitance value of 280 µF. To test the converter dynamic response with the selected output filter components the generalized mathematical model of the converter was developed by help of Simplorer simulation software. The converter model was tested with the maximal input voltage conditions (4000 V) and during the random load step change (see Fig. 9), when the output current of the converter is changing instantly from some intermediate value (70 A) to a maximal value (143 A).
The maximum inductor current ripple is about 10%, while the output current ripple is less than 2%. The voltage ripple of unregulated output is about 1.5%. The voltage overshoot during load step change is 14%, which can be fully compensated by the appropriated control system algorithm.
Conclusion Output filters play a very important role in DC/DC converters. Important aspects of converters such as dynamic response, size and cost are closely related to the components of the filter. Small values for the filter components improve the performance of the converters and increase the power density, whereas minimum values should be provided to guarantee the filtering objective.
References  D. Vinnikov, „Research, Design and Implementation of Auxiliary Power Supplies for the Light Rail Vehicles”, PhD Thesis, Tallinn, 2005.  Pressman, A.I., “Switching Power Supply Design”, Second Edition, McGraw-Hill, 1998.  Billings, K.H., “Switchmode Power Supply Handbook”, McGraw-Hill, 1989.