Design of input filter for DC/DC module of satellite power supply

As the "heart" of the satellite, the reliability of the power supply is very high. The DC/DC module in the satellite power supply system is mainly responsible for converting the output 42V DC voltage into other levels of DC voltage to meet the power requirements of different devices. The DC/DC module input filter has two main functions: one is to prevent the electromagnetic interference generated by the DC/DC module from being transmitted along the power line to affect other devices; the other is to prevent the high-frequency voltage on the power line from being transmitted to the output end of the DC/DC module. The LC passive filter has the above two functions. The design goal is to achieve a balance between the size and cost of the filter.

Undamped LC filter

Figure 1 shows an undamped LC passive filter. Ideally, a second-order filter attenuates by 12 dB per octave after the resonant frequency f0. It has no gain before f0, and the gain reaches a peak at the resonant frequency f0.

(1)

Figure 1 Undamped LC filter

A key factor in the design of a second-order filter is the attenuation characteristics at frequency f0. The gain at the resonant frequency is very large, which also amplifies the noise at this frequency. The nature of the problem can be better understood by analyzing the transfer function of the filter. Its transfer function is

(2)

The transfer function can also be expressed in radians:

(3)

where , is the resonant frequency in radians; is the damping factor.

The transfer function has two negative poles and , and the damping factor ζ represents the gain at this angular frequency. When ζ<1, the two poles are complex numbers, and the imaginary part makes the gain peak at the resonant frequency.

Figure 2 Transfer function of LC filter with different damping factors

The smaller the damping factor, the greater the gain at the resonant frequency, and the gain is infinite when the ideal zero damping is reached. However, the internal resistance of the component limits the gain from reaching its maximum value. Here, the damping factor acts like a virtual component, preventing the gain from reaching its peak value.

In input filter design, the damping factor has a great relationship with system performance. The damping factor affects the transfer function of the feedback control loop and also causes oscillation at the output of the switching power supply.

Middlebrook's law of additional elements states that an input filter cannot significantly change the closed-loop gain of the converter if the output impedance curve of the input filter is much lower than the input impedance curve of the converter. In other words, it is very important to keep the peak output impedance of the filter lower than the input impedance of the converter to avoid oscillation (see Figure 3).

Figure 3 Filter output impedance and switching power supply input impedance

From a design point of view, the best filter performance-to-volume ratio is obtained based on 1/√2 times the minimum damping factor (at this time, the gain attenuation at the resonant frequency is 3dB), so that the control system achieves good stability.

Parallel Damping Filter

In most cases, the undamped second-order filter in Figure 1 is not easy to meet the attenuation requirements, so consider choosing a damped filter.

The damping filter shown in Figure 4 is composed of a resistor Rd and a capacitor Cd connected in series and then in parallel with the filter capacitor C. The function of the resistor Rd is to reduce the output impedance peak of the filter at the resonant frequency; the capacitor Cd suppresses the DC component of the input voltage to prevent Rd from consuming power.

Figure 4 Parallel damping filter

In order not to affect the resonant frequency of the LC main filter, the impedance of capacitor Cd at the resonant frequency should be smaller than Rd and larger than the capacitance value of the filter.

The output impedance of the filter can be calculated from the three parallel block impedances:

(4)

The transfer function is

(5)

Here, Zeq2.3 is the parallel value of Z2 and Z3. There is one zero and three poles on the transfer function. The zero and the first pole are very close to the frequency ω≈1/RdCd, and the other two main poles fall at the resonant frequency . In the approximate calculation, the zero and the first pole can be ignored, so this formula approximately expresses a second-order filter (when the frequency is greater than ω≈1/RdCd, (1+RdCds)≈RdCds)).

(6)

The approximate calculation formula of the parallel damped filter is the same as the transfer function of the undamped filter. The only difference is that the resistor Rd must be added to the calculation of the damping factor ζ.

Figure 5 and Figure 6 are the output impedance and transfer function of the parallel damped filter, respectively.

Figure 5 Parallel damping filter output impedance

Figure 6 Parallel damping filter transfer function

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Series Damped Filter

Another form of damping filter is that the resistor Rd and the inductor Ld are connected in series and then in parallel with the filter inductor L (see Figure 7). At the resonant frequency, the resistor Rd has a higher impedance than Ld.

Figure 7 Series damping filter

Like the parallel filter, the output impedance and transfer function of the series filter can be calculated using equations (7) and (8).

(7)

(8)

Here, Ld=nL.

The transfer function of the series damped filter can be approximately calculated as:

(9)

When the damping factor , the peak value is minimized. The optimal damping resistance value is:

Here, n=2/15.

The disadvantage of the series damped filter is that the high-frequency attenuation capability is weakened (see Figure 10).

Multi-stage filter

Multistage filters provide high attenuation at high frequencies and are compact and low cost because they allow the use of lower value inductors and capacitors as the number of components increases (see Figure 8).

Figure 8 Multi-stage input filter

Based on the impedance of each frame, the output impedance and transfer function can be calculated.

Figures 9 and 10 are comparisons of the output impedance and transfer function of a second-order damped filter, a series damped filter, and an undamped filter.

Figure 9 Output impedance of series damped filter and second-order damped filter

Figure 10 Transfer function of series damped filter and second-order damped filter

The second-order filter is optimized as follows: the output impedance peak of the filter is attenuated by 80dB, and the output impedance peak is less than 2Ω.

The switching power supply suppresses noise with a frequency lower than the feedback control loop intersection frequency, and the input filter should be able to suppress high-frequency signals. The input filter resonant frequency must be less than one-tenth of the feedback control loop bandwidth to better perform forward filtering.

Capacitor and Inductor Selection

Correct selection of capacitors and inductors is an important aspect affecting filter performance. Selecting high-frequency attenuation capacitors with low ESL and low ESR will result in low output ripple. Most common capacitors are aluminum electrolytic capacitors.

The output capacitor should be divided into many different small capacitors and connected in parallel, and the total value of the capacitor remains unchanged, so that it has low ESL and low ESR characteristics. The selected inductor should be able to minimize the parasitic capacitance of the filter, and the input and output leads should be as far apart as possible. It is best to use a single-layer and stacked coil method to make the inductor.