As shown in Figure 12.20, an amplifier has a voltage gain of...

As shown in Figure 12.20, an amplifier has a voltage gain of 10 , and is driven by an input voltage source with an internal resistance of $20 \mathrm{k} \Omega$. Calculate the voltage gain of the entire circuit if the input resistance to the amplifier is (a) $50 \mathrm{k} \Omega$, (b) $100 \mathrm{k} \Omega$, (c) $1 \mathrm{M} \Omega$. Figure P12.20 can't copy

As shown in Figure 12.20, an amplifier has a voltage gain of 10 , and is driven by an input voltage source with an internal resistance of $20 \mathrm{k} \Omega$. Calculate the voltage gain of the entire circuit if the input resistance to the amplifier is
(a) $50 \mathrm{k} \Omega$,
(b) $100 \mathrm{k} \Omega$, (c) $1 \mathrm{M} \Omega$.
Figure P12.20 can't copy

Key Concepts

Voltage Divider Principle

This principle describes how an input voltage is divided among series-connected resistive elements. When a source with internal resistance is connected to a load (such as an amplifier input impedance), the voltage at the load is a fraction of the source voltage determined by the values of the source resistance and the load resistance. This concept is fundamental for understanding how voltage levels are affected by impedance in a circuit.

Amplifier Voltage Gain

Amplifier voltage gain is the ratio of the output voltage to the input voltage of the amplifier stage. It amplifies the voltage that appears at its input, but this input voltage is often affected by preceding stages, such as voltage dividers. Understanding the intrinsic gain of an amplifier is crucial for predicting how the overall circuit amplifies signals.

Input Impedance and Loading Effect

Input impedance is the resistance seen by the source when it is connected to a circuit. The loading effect occurs when this input impedance interacts with the source's internal resistance, forming a voltage divider. This results in a reduced voltage being delivered to the subsequent circuit stage, which in turn affects the overall gain of the system.

Cascaded Circuit Analysis

In cascaded circuits, the overall voltage gain is the product of the voltage division factor from the source to the first stage and the gain of the subsequent stage. This analysis method is essential for designing and understanding multi-stage circuits where each stage influences the signal level received by the next stage.

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