Designers then only have to find the greater of the two resistances between the load and the source to finish calculating the parallel resistance of the network. Unlike the constituent L networks, the pi network provides designers with enough components to cover the necessary degrees of freedom (greater of the source or load resistance, natural angular frequency, and transformation ratio) – selecting three components ensures all the variables are solvable. Rather, it indicates the reactance relationship for the parallel/series components: parallel inductors and series capacitors or parallel capacitors and series inductors are valid assignments, provided the relationship stays constant throughout the network.įrom a desired Q-factor, it’s a straightforward proposition to determine the rest of the pi network’s values. For calculations, the pi network may denote the parallel components as positive and the series components as negative – this is not the reactance of the components. Connecting these two L networks creates a parallel “virtual” (no corresponding component) resistance between the two L networks. The three-component network is simply an iterated form of the two-component network the pi network features two L networks back-to-back, with the parallel components on the outside of the filter and the series component in the middle. Unlike two-component networks, three-component networks can achieve higher Q-values as a rule of thumb, the maximum Q-value obtained by a two-component network is the minimum value a three-component network can attain. (The Q-factor bandwidth definition, where fc is the center frequency and BW is the bandwidth.) Pi network impedance matching is one implementation designers can use that affords considerable flexibility over the more rudimentary L networks.Ĭomparing 3-Component Impedance Matching Networks In purely resistive networks, circuit designers can accomplish this with only resistors, but more sophisticated applications require reactive elements (i.e., capacitors and inductors) to achieve this setting. Filter networks also have a secondary but equally valuable role in aiding power delivery: impedance matching the source to maximize power transferability. Pi network impedance matching uses series and parallel inductors and capacitors to load match the source impedance.īuilding filter networks is necessary for signal conditioning that separates desired signal bandwidths from noise that can harm signal quality or damage components at high enough frequencies. Pi networks use two outer parallel components and a middle series component.įor comparison purposes, a pi filter is effectively two L filters back-to-back but simplifies the two series components in the middle to a single entity.Īfter finding the constraints of the pi network, designers need to calculate the equivalent impedance to match the source.
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