Exercise 8.5 A simple opamp schematic

In the circuit below, the NPN transistors $T_1$ and $T_2$ are identical; for these NPNs $\mathit{\beta fe}=500$. Also the PNP transistors $T_3$ and $T_4$ are identical; for these PNPs, $\mathit{\beta fe}=100$. For all four transistors the small-signal output resistance $r_{\mathit{ce}}$ can be neglected.

For the circuit, $V_{\mathit{CC}}=15V$, $R_1=R_2=10k\mathrm{\Omega }$, and $I_{\mathit{TAIL}}=1\mathit{mA}$.

a)

Give an estimate for the current $i_{\mathit{OUT}}$ as defined in the circuit, for $v_1=v_2=0V$.

b)

Let’s assume that we apply $v_2=0V$ and $v_1=+10\mathit{mV}$. Estimate or calculate the resulting $i_{\mathit{OUT}}$.

c)

Let’s again assume that we apply $v_2=0V$ and $v_1=+10\mathit{mV}$. Estimate or calculate the resulting $v_{\mathit{OUT}}$.

d)

Derive or approximate the value of $v_{\mathit{OUT}}$ for $v_1=+100\mathit{mV}$.

e)

Derive or approximate the value of $v_{\mathit{OUT}}$ for $v_1=-100\mathit{mV}$.

f)

To increase the circuit’s input voltage range, emitter resistors $R_E$ are inserted in series with the emitters of $T_1$ and $T_2$.

Estimate the increase in input voltage range for $R_E=500\mathrm{\Omega }$. For this, you may assume that the range is limited by the values for which $95\%$ of $I_{\mathit{TAIL}}$ is flowing through either $T_1$ or $T_2$.