Open Loop Analysis

Before hooking up the feedback connections, let's perform an open loop analysis of the circuit, which is shown without feedback in Fig. 5.6, starting with the DC bias conditions.

  

Figure 5.6: Open Loop Configuration of Op-Amp-Like Circuit

The DC analysis is almost the same as before, except now we have to determine the current going through transistor Q4, which gets its bias from V_CC through R_C2 and V_C2. Recall from Section 2, that we have established the DC voltages at the collectors of Q1 and Q2, by determining the current provided by the current source Q3, and the determining the drops across R_C1 and R_C2, where

 

V_C2 = V_CC-I_C2R_C2 (119)

Now that we have added Q4, it would appear as though the DC voltage at V_C2 would have to be changed to accommodate the current I_B4. This would give

 

V_C2 = V_B4=V_CC-(I_C2+I_B4)R_C2 (120)

However, since $\beta$ is usually greater than 100, the effective resistance to ground seen by I_B4 at V_C2 is $\beta R_{E4}$. Since in most cases $\beta R_{E4}$ is more than 20 times greater than R_C2, I_B4 is negligible compared with I_C2, so we can say that even with Q4, V_C2 is still given by

$$V_{C2}= V_{B4} \approx V_{CC}-I_{C2}R_{C2}$$ (121)

Now I_E4 is readily determined by

$$I_{E4}=\frac{V_{B4}-0.7}{R_{E4}}$$ (122)

Now that we have I_E4, we can approximate $I_{E4} \approx I_{C4}$,and determine $g_{m4}=\frac{I_{C4}}{V_t}$. Using g_m4 will help determine the small signal output resistance of the circuit.