Output Resistance R_o

The output resistance of an EF amp is low which is usually desirable for voltage amplifiers. To find an analytical expression for the output resistance, we drive the output with a test voltage and determine the current that is drawn, while the input is shorted. The ratio of the test voltage to drawn current is the output resistance.

To find R_o consider the circuit in Fig. 2.13, which is our EF amp driven by a voltage source V_s with source resistance R_S.

  

Figure 2.13: Circuit for theoretically determining R_o of EF amp.

Let's set v_s=0, and drive the output with voltage v_x. The resistance v_x sees is R_o = R_E||R_TE, where R_TE is the resistance seen looking into the emitter. Recall, that the emitter is the n-side of a forward biased pn junction, and thus offers little resistance. Performing the emitter-base loop analysis gives

$$v_x=\Delta V_e= -\Delta V_{be}-\Delta I_b (R_B\vert\vert R_S)$$ (54)

$$i_x=-\Delta I_e=-\beta \Delta I_b$$ (55)

Where i_x is the small signal current going into the emitter of the BJT. Dividing v_x by i_x gives

$$R_{TE}=\frac{v_x}{i_x}=\frac{r_{\pi} + R_S\vert\vert R_B}{\beta}$$ (56)

Thus, the output resistance is usually fairly small since it contains a division by $\beta$.