Design an NPN voltage-divider CE bias network supplied from V_(CC)=15.0 V

Design an NPN voltage-divider CE bias network supplied from \(V_{CC}=15.0\,\mathrm{V}\). The emitter resistor \(R_E\) goes to ground, the collector resistor \(R_C\) goes to \(V_{CC}\), and the divider is \(R_1\) from \(V_{CC}\) to base and \(R_2\) from base to ground. Use the forward-active model \(V_{BE}=0.700\,\mathrm{V}\), \(I_C=\beta_F I_B\), \(I_E=(\beta_F+1)I_B\), and ignore Early effect and leakage. Nominal targets at \(\beta_F=100\) are \(I_C=2.00\,\mathrm{mA}\), \(V_{CE}=7.00\,\mathrm{V}\), and \(V_E=2.50\,\mathrm{V}\). Additional constraints, all at this same \(\beta_F=100\): - the Thevenin resistance of the divider must satisfy \(R_{TH}=R_1\parallel R_2\le 0.100\,(\beta_F+1)R_E\); - the unloaded divider current \(I_{\mathrm{div}}=V_{CC}/(R_1+R_2)\) must be at least \(10.0\,I_B\); - every resistance must be positive. (a) Compute the unique \(R_E\) and \(R_C\) that meet the nominal \(I_C\), \(V_{CE}\), and \(V_E\). Compute \(I_B\), \(I_E\), \(V_B\), and \(V_C\). (b) Among all divider pairs meeting both the \(R_{TH}\) inequality and the \(I_{\mathrm{div}}\) inequality with equality in whichever bound is the more restrictive, compute \(R_1\), \(R_2\), \(R_{TH}\), \(V_{TH}\), and \(I_{\mathrm{div}}\). (If both inequalities can be met simultaneously with equality in one and slack in the other, enforce the tighter bound and verify the other.) (c) Holding the four resistances of (a)–(b) fixed, recompute the Q-point at \(\beta_F=60.0\) and at \(\beta_F=180\). Report both collector currents, both \(V_{CE}\) values, and confirm forward-active operation (\(V_C>V_B\) and \(V_{CE}>0.200\,\mathrm{V}\)) at both extremes.

\(R_E\) and \(R_C\) are fixed by the three nominal voltages/current independently of the divider.