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RF Electronics Chapter 8: Amplifiers: Stability, Noise and Gain Page 280 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Figure 8.5. Amplifier block diagram. In general: source in source S G 1 1 2 Eqn. 8.9 2 21 0 S G Eqn. 8.10 load out load L G 1 1 2 Eqn. 8.11 The gain of the whole amplifier is: L s T G G G G 0 Eqn. 8.12 Under ideally matched conditions G S = 1 and G L =1 so that the gain is thus: 2 21 S G T , as was obtained before in equation 8.8 Stability Oscillations will occur if G S or G L For oscillations due to the input, G S so that from equation 8.9, in * source = 1 result in oscillations. in and source are both complex variables. Oscillators often are designed by deliberately making in * source = 1. Equation 8.4 shows how in depends on other parameters, including load , which together with source can be manipulated to ensure that in * source = 1 is only satisfied at one frequency, thus ensuring stable oscillations. The amplifier is stable if in < 1 for all values of load , since for a passive source | source | < 1, so that in * source is always <1. Similarly, for oscillations due to the output, G L so that from equation 8.11, out * load = 1. For oscillator design, equation 8.5 shows how out depends on other parameters, including source , which together with * load can be manipulated to ensure that out * load = 1 is only satisfied at one frequency, thus ensuring stable oscillations. The amplifier is stable if out < 1 for all values of source , since for a passive load | load | < 1, so that out * load is always <1. For unilateral amplifiers S 12 = 0, so that in = S 11 and out = S 22. This makes it relatively easy to ensure that the amplifier is stable. However many amplifiers are not unilateral, making it more difficult to determine the load and source conditions where the amplifier is stable. RF Electronics: Design and Simulation 280 www.cadence.com/go/awr