![]() ![]() Fortunately, equivalent circuit techniques are just as viable on reactive and resistive elements. ![]() Symbolically, if the source were to have an impedance of R + jX (where j is the imaginary number), then the matched impedance at the load would be R - jX.įiguring the impedance at the load can be challenging if the pi network has many components. Matching the source impedance requires the complex conjugate at the load (in this example, our pi network), which is an impedance of the same resistance and opposite impedance. The impedance is a value comprised of a real component (the resistance) and an imaginary component (the reactance). ![]() With the filter values sorted, designers must impedance match the filter to the source. Depending on the sign of the reactance and the relationship between the parallel and series components in the pi network, engineers then have the component type (either a capacitive or inductive element). (Where R> is the greater source and load resistance value.)įrom here, designers can solve for the component values of the individual L networks separately before combining the “series” components of each by adding the reactance. 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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