= Idc Xc1 Xc2 √2/Idc X L = Idc Xc1 Xc2√2/Idc RLX L The ripple factor formula of the pi filter is Now V’ ac rms = V ac rms Xc2/X L = I dc Xc1√2 * Xc2/X L The ripple voltage can be attained by multiplying Xc2/XL The above equation is the i/p capacitor’s reactance at 2nd harmonic distortion. Substitute the value of ‘Vr’ in the above expression When C =C1 in the pi filter, then the RMS value of o/p voltage can be expressed as component maintains its journey toward the choke ‘L’ So, capacitor C1 avoids a considerable amount of a.c. component of rectifier o/p output as it gives unlimited reactance toward the d.c. The first filter capacitor (C1) provides small reactance toward a.c. The filtering act of these three components in the filter circuit is discussed below. The rectifier’s output is applied across the input terminals of the filter like 1 & 2. Simply one section of the filter is shown however numerous equal sections are frequently utilized to progress the smoothing act. Here C1 is connected across the o/p of the rectifier ‘L’ is connected in series & ‘C2’ is connected across the load. This is the reason that the circuit is named as a pi filter. These three components are arranged in the form of greek letter pi. This circuit is designed with two filter capacitors namely C1 and C2 and a choke mentioned with ‘L’. Figure 5 is for the readers to believe that simulations do match measurements.The pi filter circuit design is shown below. The main essence is about Monte Carlo Analysis and the tolerance effects. The below figure 5 is obtained after doing proper gating analysis and sufficient information about the capacitors and inductors have been taken care. You may ask me, how can I trust simulations, you may see the heading and reporting again to make sure that simulations do match measurements if proper care is taken into consideration. It is a 10 min analysis, which can help you to save money and irritation. So it is always good to do worst case analysis on the important components. Customer was 3 db about the limit line and he had to shelve again 8000 dollars to get the product certified. Unfortunately a ll he/she had to do was to change the inductor to a better tolerance value and use a semi shielded inductor. It can be seen that maximum limit and the minimum limit had 4 dB difference in the values. Tolerances considered for the inductors is 20% and the tolerances considered for the capacitors is 10%.įigure 5: Inset View at the Fundamental Harmonic Frequency. Nevertheless we stick to 200 KHz and the analysis has been done according to the data sheet. However when measured on the board, the fundamental harmonic was at 210 KHz. Switching frequency of the IC is close to 200 KHz. LISN schematic is added based on the CISPR standard. Input voltage is 48 volts and the output voltage is 15 volts with an efficiency of 95%. The below circuit is a typical buck converter. Now coming to Monte Carlo, Monte Carlo is an analysis method used by design engineer to increase the robustness and reliability of their products. Just to let you know LTSpice is a free tool. To do the conducted emission analysis along with Monte Carlo analysis, I have taken LT spice where Monte Carlo analysis is an internal function in the LTspice. In the end of this document, you will find the functions that can be used apart from the uniform distribution. You may also try Gaussian or other distributions in the Monte Carlo analysis. After discussing with capacitor and inductor vendors, we understood that most of them follow uniform distribution for the tolerance values. I came to this conclusion after working on more than 25 -28 circuits.įor now, let us see how Monte Carlo analysis can help you out to adjust and understand the capacitors and inductor values and see the variations in the conducted emissions. To be honest and also it is my only and only perception that without appropriate Ferrite beads or X caps or Y caps (common mode emission) and proper PCB layout it is near to impossible to achieve those above limits in conducted emissions. On top of that, most of the customers in order to reduce the bill of material cost use caps and inductors without understanding the tolerances and their limitations.Īs an example, customers are using a simple PI filter topology (excel sheet provided by the IC Company) in DC DC converters or in AC DC converters and expecting the results to be either in Class 3 or Class 4 limits (CISPR 25-Automotive). The idea behind this topic came when I recently understood how much a tolerance on a inductor and capacitor can hamper a product certification.
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