![]() ![]() Grey areas on the figures represent regions of instability. Circle C 2 doesn't surround the Smith Chart origin. Input Stability circle |S 22| > 1 and |ΔS| > |S 11|įigure 8-2d. Output Stability circle |S 11| > 1 and |ΔS| 1 and |ΔS| 1 and |ΔS| > |S 22| Circle C 2 surrounds the Smith Chart origin. Two-Port Network Stability in the General Case (S 12 Different from Zero)Ī two-port network is unconditionally stable if the reflection coefficients Γ in and Γ out (seen from input and output) have magnitudes R 2, the circle does not surround the origin (Figure 8-1). It merely indicates that oscillations may occur if you fail to exercise extreme care in choosing the source and load impedances. The conditions |S 22| > 1 or |S 11| > 1 do not indicate, however, that the network cannot be used as an amplifier. When |S 22| 1 or |S 11| > 1, the two-port network is potentially unstable, and will oscillate for certain values of source and load impedance Γ S = 1/S 11 or Γ L = 1/S 22. G 1 and G 2 are called the mismatch gain. In this case we write a simplified version of the transducer gain equation (Eq. This case is interesting, because it supports a simple example that helps to highlight certain rules without the need for heavy mathematics. The magnitudes |Γ S| and |Γ L| of the source and load reflection coefficients Γ S and Γ L are less than or equal to 1, which means that the corresponding impedances have positive real parts.įirst, we study a one-sided two-port network for which S 12 = 0. Consider the following network (an LNA), connected to its source and load impedances. One characteristic of two-port networks is that |S 21| ≠ |S 12|, and that most of the time |S 21| > |S 12|. S-parameters also allow the calculation of optimum source and load impedances, either for simultaneous conjugate matching or simply to help choose the source and load impedances for a specified transducer gain. Scattering parameters allow the calculation of potential instabilities (trend toward oscillation), maximum available gain, input and output impedances, and transducer gain. Two-port networks can be completely characterized by their scattering (S) parameters. A bit of planning and some basic, a priori knowledge of the LNA to be used can go a long way toward preventing oscillation in an amplifier design. Experience shows this to be true, but it need not be the case. Some say the easiest way to build an oscillator is to design an amplifier. The third exercise stresses the importance of matching a potentially unstable LNA in its stable area. ![]() The second deals with an LNA matched in the constant desired gain condition. The first shows how to match an LNA in the maximum available gain condition. Part 3 completes the series by presenting application examples. In this part, we jump into the RF aspect of low noise amplifiers by examining stability (tendency for oscillation), impedance matching, and general amplifier design, using scattering parameters (S-parameters) as design tools. In Part 1, we started our discussion with a brief background on transmission lines and a reminder about RF power gain definitions. Emphasis is on S-parameters as design tools. Stability, impedance matching and general amplifier design are covered. This part covers the RF aspects of low-noise amplifiers. ![]()
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