# Signal parameters of a Darlington

I have the next circuit

simulate this circuit – Schematic created using CircuitLab

$V_{BB}$ and $V_i$ represent the output voltage of a previous stage of a circuit. Assuming that $\beta = 200,r_x = 0, V_A = \infty$, what would be the input resistance of the circuit (i.e. the resistance seen from the base of Q1), the output resistance of the circuit (i.e. the resistance seen from the node $V_o$) and voltage amplification $A_v = \frac{v_i}{v_o}$=?

I'm having trouble dealing with R2. I thought of expressing these parameters as follows:

$R_i = r_{\pi 1}+\beta \cdot (1000\Omega //r_{\pi 2})+\beta \cdot 50\Omega$

$R_o = 50\Omega //(\frac{r_{\pi 1}}{\beta}+1000\Omega//\frac{r_{\pi 2}}{\beta})$

Is this ok? And regarding the amplification, I have no idea of how to calculate it. I hope you can give me a hand.

• For Ri you are not accounting for the current through R2 from Q1. – jippie Feb 20 '16 at 19:36
• @jippie What is missing in the expresion of $R_i$ I wrote above? – Tendero Feb 20 '16 at 19:38