An NPN common-base amplifier is biased in forward active with the base at DC bias and…

An NPN common-base amplifier is biased in forward active with the base at DC bias and AC ground. The emitter is the input: \(v_{\mathrm{sig}}\) with \(R_{\mathrm{sig}}=50.0\,\Omega\) drives the emitter through an ideal coupling capacitor. Collector resistor \(R_C=1.50\,\mathrm{k}\Omega\) joins \(V_{CC}=6.00\,\mathrm{V}\) to the collector, and \(R_L=1.50\,\mathrm{k}\Omega\) is coupled from the collector to ground. Established current \(I_C=2.00\,\mathrm{mA}\), \(\beta=100\), \(V_T=26.0\,\mathrm{mV}\), \(V_A=\infty\), \(V_{BE}=0.700\,\mathrm{V}\). Use \(g_m=I_C/V_T\), \(r_\pi=\beta/g_m\), \(\alpha=\beta/(\beta+1)\), and \(r_e=r_\pi/(\beta+1)=1/g_m\). The small-signal emitter current \(i_e\) enters the emitter terminal; the collector current increment \(i_c\) leaves the collector. Midband capacitors are shorts. (a) Determine \(g_m\), \(r_e\), \(r_\pi\), and \(\alpha\). Determine \(R_{\mathrm{in}}\) looking into the emitter with the base at AC ground. (b) Determine \(v_e/v_{\mathrm{sig}}\), \(v_o/v_e\), and \(v_o/v_{\mathrm{sig}}\) at midband, with \(v_o\) the collector-to-ground voltage. State the sign of \(v_o/v_e\). (c) Determine the current gain \(i_c/i_e\) into the parallel combination \(R_C\parallel R_L\). Compare it with \(\alpha\). (d) Compute the numerical ratio \(\lvert v_o/v_{\mathrm{sig}}\rvert\) that would be obtained if a student replaced \(R_{\mathrm{in}}\) by \(r_\pi\) (common-emitter input resistance) while keeping the same output network. Report the factor by which that mistake misestimates \(\lvert v_o/v_{\mathrm{sig}}\rvert\).

Common-base input resistance is the emitter resistance \(r_e=1/g_m\), not \(r_\pi\).