Final answer:
The voltage gain of a common-emitter amplifier is calculated using the formula Av = -gm(RC || ro || R2), which requires knowledge of transconductance and the circuit's DC biasing conditions to find the necessary parameters such as the collector current.
Step-by-step explanation:
To determine the voltage gain of a transistor amplifier circuit with given resistor values, we can apply the small-signal model for a BJT amplifier. The voltage gain (Av) is defined as the ratio of the output voltage to the input voltage. The formula to calculate the voltage gain in a common-emitter amplifier with bypass capacitor across RE is Av = -gm(RC || ro || R2), where gm is the transconductance, RC is the collector resistor, ro is the output resistance of the transistor, and R2 is the load resistor.
We start by calculating the transconductance gm, which is gm = Ic/Vt, where Ic is the collector current and Vt is the thermal voltage (approximately 25 mV at room temperature). We must first find the collector current (Ic) using the provided VCC, beta (β), and resistor values. However, to accurately calculate Ic we need more information such as the base-emitter voltage (Vbe) which is typically around 0.7 V. If we assume Vbe, we can estimate Ic from the circuit's DC biasing conditions.
Once we have Ic, we calculate gm, and then the voltage gain using the aforementioned formula. This process involves a series of steps and general circuit analysis principles to reach the final answer.