Analog Circuit Design: Structured Mixed-Mode Design, by Michiel Steyaert (Editor), Arthur H.M. van Roermund

By Michiel Steyaert (Editor), Arthur H.M. van Roermund (Editor), Johan H. Huijsing (Editor)

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The source and load impedance have to be chosen such as to maximize the power transfer. Then the Kirchhof equations have to be written for the RLC prototype with admittances in the series branches and impedances in the shunt branches: A scaling factor R=1/gm is introduced to obtain appropriate values for Z and Y. These equations are rewritten into a state-space form. The filter is directly realized from these state-space equations as a combination of integrators. X contains the state-space variables which 27 in the case of gm-C filters correspond to voltages over the integrating capacitors.

Hence, to include phase information and to exploit the real transfer function, a Volterra series model is applied [7]. The disadvantage is that the model is somewhat more complex but is still manageable with programs like Maple® that can handle symbolic expressions. 5 (Figure 8). However, for the sake of brevity, only a third-order harmonic distortion is calculated here and not an intermodulation distortion product. With respect to the model complexity, the only difference is that fewer terms are involved in the calculations.

Due to the (over)simplified modeling of the transistor (A = 0, C = 0), only the noise-current source at the output will contribute to the total equivalent noise of the amplifier. This noise will be transformed to the input into two equivalent sources: where and Note that we cannot define a noise figure for the block behind the amplifier in a situation like this since the amplifier has an infinite output impedance. Assuming that we can ignore the contributions of this block with respect to the noise production of the transistor itself, we find (with a Norton-Thevenin transformation) for the total equivalent 60 input noise: This noise can be minimized by making the two contributions of the transistor equal, which leads to With amounts to in the present example, the optimum value of This requires a collector bias current of 5mA.

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