Exercise 11.4 An RF amplifier

The circuit schematic in the figure below is a more of less regular common emitter amplifier. The circuit contains two inductors; $L_C$ is an explicit inductor while $L_{\mathit{wire}}$ is the inductor that models the wire between emitter and ground. This is the only wired modelled in this question.

a)

Assuming that $L_{\mathit{wire}}=0$, derive the voltage gain of this circuit, including load $R_L$. For now,

• the capacitors can be assumed to be low ohmic at signal frequencies
• the impedance of $L_C$ can be assumed to be much larger than $R_L$

b)

Including $L_{\mathit{wire}}$, derive the voltage gain of this circuit, including load $R_L$. For now,

• the capacitors can be assumed to be low ohmic at signal frequencies
• the impedance of $L_C$ can be assumed to be much larger than $R_L$

c)

Now for $V_{\mathit{CC}}=5V$, $\mathit{\beta fe}=100$ and $R_B=88k\mathrm{\Omega }$, $T=300K$, derive the (bias) $I_C$ and the $g_m$ of the transistor.

d)

Using the values in the previous question, calculate the numerical value of the decrease in voltage gain due to 1 cm wire (making up $L_{\mathit{wire}}$ at 100 MHz. You may use the rule-of-thumb wire inductance of 1nH/mm.

e)

As explained before, any junction can be associated with a (voltage dependent) capacitance. Taking into account only the capacitance associated with the base-emitter junction, $C_{\mathit{be}}$, and assuming for now $L_{\mathit{wire}}=0$, derive an expression for voltage gain.