The different options will each have a different Q-factor, allowing the designer to choose a resonance behavior that best suits the circuit they are designing in a trade-off with efficiency.įor a standard Pi filter, the typical size and weight of the components will require the allocation of a significant board area. In contrast, the Pi filter will have multiple combinations of component values that all produce the impedance necessary for the given frequency. A simple L-C filter will only have single component values where the filter produces the required impedance for a given frequency. Impedance MatchingĪ benefit of Pi filters over simple L-C filters is the greater flexibility they offer the circuit designer for impedance matching. In this configuration, the Pi filter is also known as a Power Line filter. In the other direction, it prevents high-frequency noise generated by the switch-mode power converter circuit from being conducted back through the power supply and onto the mains line. In one direction, it reduces noise present on the AC input that will appear at the rectifier output. An added benefit is the transformer will also provide two-way common-mode noise filtering. Replacing the inductor in the low-pass Pi filter with a transformer will deliver the same ripple filtering function but with the benefit of providing isolation between the rectifier output and the switch-mode power converter. They act to minimize the ripple on the rectified power line at the input to the converter stage of the power supply circuit. Their AC-powered power supplies application is typically immediately after the bridge rectifier circuit and before the switch-mode control circuit. A constantly changing output load or high current drift will result in poor voltage regulation. The Pi filter requires a stable output voltage to be effective. In addition, such components will be bulky and expensive, impacting board design. This limitation also has to be weighed up with the high input capacitance requirements and high voltage rating. This current will also flow through the inductor, meaning that an inductor with a high power-rating will be required in applications with a high output voltage. However, any current flow through the filter when a load is applied to the output will result in a voltage drop, and so the Pi filter cannot provide voltage regulation. Its other main advantage over different filter types is good ripple reduction. The Pi filter will produce a high output voltage with minimal current drain, producing only a very small voltage drop at the output. Finally, the output capacitor filters any AC component that has passed through the inductor. Next, the inductor performs the next filtering stage, effectively removing any ripple. The input capacitor performs the first and foremost stage of filtering out the AC component. The three components that form the Pi filter each act to block alternating current flow and pass direct current flow. This article will only be looking at the low-pass filter arrangement. The high-pass filter equivalent is formed by using a capacitor in series between the input and output with two inductors, one across the input and the other across the output. The main application of Pi filters in power supplies is to smooth a rectifier’s output by acting as a low pass filter. The low-pass filter used for power supply filtering is formed from an inductor in series between the input and output with two capacitors, one across the input and the other across the output. Pi filters can be designed as either low pass or high pass filters, depending on the components used. It is typical for filter design to be an iterative “guess and check” process until the exact desired weights or frequency response is obtained.Pi Filters are a type of passive filter that gets its name from the arrangement of the three constituent components in the shape of the Greek letter Pi (π). The filter lengths are not exact but are reasonably close to the length L=21 the filter was designed with. Similarly from Figure 7, the second filter with and gives a filter length approximation ofĪnd the second filter with and gives a filter length approximation of Using the parameters from Figure 7, =39 and, the filter length for a transition bandwidth of is approximated to be However the cut-off frequency has no impact which reinforces the earlier filters from Figures 4 – 8. The approximation in ( 2) shows that changes to the transition bandwidth will directly impact the sidelobe attenuation when the filter length is held constant. The frequencies and can be in any units as long as they are consistent. Where is the transition bandwidth, is the sampling frequency and is the sidelobe attenuation in dB. Fred harris’ filter length approximation is
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