Voltage and current sources

For an AC analysis, DC sources are short circuit (voltage source) or open circuit (current source), respectively. Accordingly, for a DC analysis, AC sources are short circuit (voltage source) or open circuit (current source), respectively. As these sources have no internal resistance, they are noisefree.

The MNA matrix of a current source is (with short circuit current $I_0$ flowing into node 1 and out of node 2):

$$\begin{bmatrix}.&.\\ .&.\\ \end{bmatrix} \cdot \begin{bmatrix}V_{1}\\ V_{2}\\ \end{bmatrix} = \begin{bmatrix}I_0\\ -I_0\\ \end{bmatrix}$$ (9.141)

The MNA matrix of a voltage source is (with open circuit voltage $U_0$ across node 1 to node 2):

$$\begin{bmatrix}.& .& 1\\ .& .&-1\\ 1&-1& 0\\ \end{bmatrix} \cdot ... ...}\\ V_{2}\\ I_{in}\\ \end{bmatrix} = \begin{bmatrix}0\\ 0\\ U_0\\ \end{bmatrix}$$ (9.142)

The MNA matrix of a power source is (with internal resistance $R$ and available power $P$):

$$\begin{bmatrix}\dfrac{1}{R} & -\dfrac{1}{R} \\ -\dfrac{1}{R} & \d... ...matrix}\sqrt{\dfrac{8\cdot P}{R}}\\ -\sqrt{\dfrac{8\cdot P}{R}}\\ \end{bmatrix}$$ (9.143)

The factor "8" is because of:

• transforming peak current value into effective value (factor two)
• at power matching the internal resistance dissipates the same power as the load (gives factor four).

The noise current correlation matrix of a power source equals the one of a resistor with resistance $R$.

All voltage sources (AC and DC) are short circuits and therefore their S-parameter matrix equals the one of the DC block. All current sources are open circuits and therefore their S-parameter matrix equals the one of the DC feed.