Amplifier

An ideal amplifier increases signal strength from input to output and blocks all signals flowing into the output. The ideal amplifier is an isolator with voltage gain $G$ and is determined by the following Z or Y parameters (valid for DC and AC simulation).

$$Z_{11} = Z_1 \qquad Z_{12} = 0$$ (9.80)

$$Z_{21} = 2\cdot\sqrt{Z_1\cdot Z_2}\cdot G \qquad Z_{22} = Z_2$$ (9.81)

$$Y_{11} = \frac{1}{Z_1} \qquad Y_{12} = 0$$ (9.82)

$$Y_{21} = -\frac{2\cdot G}{\sqrt{Z_1\cdot Z_2}} \qquad Y_{22} = \frac{1}{Z_2}$$ (9.83)

With the reference impedance of the input $Z_1$ and the one of the output $Z_2$ and the voltage amplification $G$, the scattering parameters of an ideal amplifier write as follows.

$$S_{11} = \frac{Z_1-Z_0}{Z_1+Z_0}$$ (9.84)

$$S_{12} = 0$$ (9.85)

$$S_{22} = \frac{Z_2-Z_0}{Z_2+Z_0}$$ (9.86)

$$S_{21} = \frac{4\cdot Z_0\cdot\sqrt{Z_1\cdot Z_2}\cdot G}{(Z_1+Z_0)\cdot(Z_2+Z_0)}$$ (9.87)