Design of active power filter for narrow-band power line communications

In power line communication (PLC), couplers such as coupling transformers and band-pass matching coupling circuits are usually required for coupling, band-pass filtering, and impedance matching. However, the cost and size of transformers prevent them from being an economic and compact solution for PLC couplers. In addition, passive band-pass matching coupling circuits need accurate impedance matching and possibly incur power losses. In this paper, a 6th order multiple feedback (MFB) active power filter with the minimum number of components was designed for narrow-band PLC, which has high input impedance and low output impedance, allowing outstanding performance in main voltage isolation, suppressing the current-harmonics and compensating the reactive power simultaneously. Finally, simulations were conducted in the range of 95 kHz-125 kHz (CENELEC “B-band”), which confirmed that the new filter met the CENELEC requirements for transmission and disturbance levels.

economic and compact solution for PLC couplers. In addition, band-pass matching coupling circuits [7][8][9] are often fabricated by passive components, which need accurate impedance matching and possibly incur power losses.
In this paper, for overcoming these problems an active power filter was designed for suppressing the current-harmonics and compensating the reactive power simultaneously. The active power filter is a Butterworth filter using a multiple feedback topology which has a fairly flat pass-band characteristic and a relatively sharp attenuation outside the pass-band. It should be noted that although the new active filter design focuses on the CENELEC B band (95 kHz-125 kHz) as an example, the same principles will hold for any of the CENELEC bands.

CENELEC band allocation
The European PLC standard was approved by CENELEC, which divides frequency (3 kHz-148.5 kHz) into four different sub-bands, and provides maximum transmission and disturbance levels for different bands when transmitting data over power line. Table 1 lists the PLC frequency bands and their maximum transmission and disturbance levels [10]. CENELEC-A band is exclusively for utility providers and the other three (CENELEC-B, C, D) bands are open for end user applications. In this paper, an active power filter was designed based on the CENELEC B band (95 kHz-125 kHz).

Multiple-Feedback filter topology
Multiple-Feedback (MFB) topology is one of the simplest circuits with the minimum number of components, which is often implemented with 2 th order response for single operational amplifier. Figure 1 is a 2 th order MFB band-pass filter. The standard form for transfer function [11] of all 2 th order band-pass filters is where Q is quality factor, 0  and 0 H are the resonant frequency and resonant gain, respectively.
As shown in figure 1, node equations can be expressed as Eq. (2 ) and Eq. (3).
According to Eq. (2) and Eq. (3), the transfer function of this MFB band-pass filter is illustrated in Eq. (4) (1), the proper filter characters can be obtained when designing a MFB band-pass filter.
In order to simplify the calculation, equation is usually assumed established. The Eq. (5) can be expressed as Eq. (6).

Cascade design of MFB filter
Each MFB filter stage with one operational amplifier will be 1 st or 2 nd order, which should be cascaded to achieve higher order MFB filter. In order to design a 6 th order MFB bandpass filter, three 2 nd order MFB filter stages are cascaded. According to Eq. (8), the design of each 2 nd order stage needs the parameters of quality factor Q , resonant frequency 0  and resonant gain 0 H , which can be obtained from cumbersome polynomial equations. Thankfully there are some resources can be used to look up when designing a MFB band-pass filter rather than dealing with cumbersome polynomial equations. Each type of filter (such as Butterworth, Chebychev, Bessel) has its own coefficient table based on the desired filter order number. The coefficients table serve as a quick design reference of designing a proper filter instead of complex mathematical calculations.

The design of the 6 th order MFB Band-pass Filter
The designed MFB band-pass filter is focused on the CENELEC "B band" (95 kHz-125 kHz), whose resonant frequency Step 1 The calculation of Quality factor According to the resonant frequency and bandwidth of the designed active band-pass filter, the equation of the quality factor is:

Simulation results and analysis
The simulation was conducted in PSPICE. Figure 3 illustrates the 6 th order MFB filter topology, which includes three 2 nd order MFB filter stages. The calculation process of each stage (see section 3) is complex even with the simplified coefficient table, previously given.   As shown in figure 5, the attenuation of the 6 th order MFB filter at 50 Hz is approximately -230 dB. If a 50 Hz, 340V peak voltage is resident at the input side of the MFB filter, the disturbance level is about 1 peak nV , which is much lower than the CENELEC maximum disturbance levels (see table. 1) and exhibits outstanding performance in main voltage isolation.

Conclusion
In this paper, a 6 th order active MFB filter was designed for narrow-band PLC to achieve the CENELEC specifications. Although the new active filter design focuses on the CENELEC B band (95 kHz-125 kHz) using a MFB topology as an example, the same principles is adequate for any of the CENELEC bands. The active filter was analyzed with a series of simulations, which exhibits an excellent flat pass-band and meets the CENELEC requirements for transmission and disturbance levels.