Optimal Source Impedance to Trade-Off Power and Noise and to Achieve a Desired S11

In the design of a low noise amplifier,LNA, or mixer driver stage there exists an optimal source source impedance to provide the maximum power transfer into the transistor and thus the maximum gain. There also exists an optimal source impedance, Znopt, to provide the minimum noise figure for the circuit. At the maximum power source impedance, Zpopt, the input is matched to the source impedance and no reflections occur. This is desirable, because the filters attached to designed for the LNA or mixer, are designed for a matched load impedance, but can tolerate a certain amount of deviation from it's desired impedance. The amount of acceptable deviation is usually specified by the maximum return loss, or S11, the filter can handle. The routine below finds the source impedance to the LNA or mixer, which will provide the lowest noise figure and mximum gain, while maintaining a desired S11 specification. The calculation is performed by drawing a straight line between the optimal noise and power source impedances and finding where it intersects the desired S11 contour. This line intersects the contour at two points, so the point must be chosen, which is closet to the optimal noise source impedance. Sometimes, the desired S11 specification is acheived at the optimal noise source impedance. In this case the optimal noise source impedance is chosen over the intersecting point. This calculation is not optimal in the truest sense, because the noise and power gain circles are not coencentric, but it serves as an excellent estimate to meet design criteria. A few important notes: 1. The optimal source impedance for minimum noise figure should be calculated with estimates of ALL back-end noise components (mixers, PGA's, filters, A/Ds). Doing so will push the noise match much closer to the power match. 2. Simultaneous input-output match of a device (i.e optimum power match) may be unstable, which will push the desired source impedance closer to the noise match.