Limitations of Impedance matching Networks and the Bode-Fano Criterion

When designing an impedance matching network for an RF application, it is important to know the limitations of the design. For example, the maximum reflection coefficient is ideally quite small, but the bandwidth should be large. The Bode-Fano Criterion can specify the limitations of various load configurations to specify how exactly this tradeoff can occur. In addition, complexity of the circuit must be taken into account. The equations differ depending on the configuration of the load impedance.

bodefano

The lossless matching networks are passive and lossless. These equations lead to the conclusion that increasing the bandwidth of the matching network can be achieved by increasing the maximum reflection efficient in the passband. In addition, a reflection of zero cannot possibly be achieved unless the bandwidth is zero. This means that a perfect match can only be achieved at a finite number of discrete frequencies (you can’t have a straight line of zero reflection within the passband, only at specific points in the passband). It also shows that as R and C increase, match quality decreases. Circuits with higher Quality factors (store energy longer) are harder to match than low Q circuits.

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