For the cascaded system of Fig. 177 with two identical...

For the cascaded system of Fig. 177 with two identical stages, determine: a. The loaded voltage gain of each stage. b. The total gain of the system, $A_{v}$ and $A_{v_{s}}$. c. The loaded current gain of each stage. d. The total current gain of the system $A_{i_{L}}=I_{o} / I_{i}$. e. How $Z_{i}$ is affected by the second stage and $R_{L}$. f. How $Z_{o}$ is affected by the first stage and $R_{s}$. g. The phase relationship between $V_{o}$ and $V_{i}$.

For the cascaded system of Fig. 177 with two identical stages, determine:
a. The loaded voltage gain of each stage.
b. The total gain of the system, $A_{v}$ and $A_{v_{s}}$.
c. The loaded current gain of each stage.
d. The total current gain of the system $A_{i_{L}}=I_{o} / I_{i}$.
e. How $Z_{i}$ is affected by the second stage and $R_{L}$.
f. How $Z_{o}$ is affected by the first stage and $R_{s}$.
g. The phase relationship between $V_{o}$ and $V_{i}$.

Key Concepts

Phase Relationship

The phase relationship between an amplifier's input and output is critical in understanding the operational characteristics of the circuit, particularly whether the signal is inverted or remains in phase. In cascaded systems, the overall phase shift is cumulative and needs careful consideration to ensure proper signal integrity, especially in feedback or frequency-dependent applications.

Interstage Impedance Loading Effects

The connection between amplifier stages introduces loading effects where the output impedance of one stage interacts with the input impedance of the next. These interactions can alter the effective gain and bandwidth of the system. Additionally, external source and load resistances, such as Rs and RL, play a significant role in modifying both input and output impedance values, thereby influencing the overall transfer function of the cascaded system.

Overall System Gain

Overall system gain in a cascaded system is the cumulative gain achieved by multiplying the individual gains of each stage. This concept emphasizes how the interconnection of multiple amplifier stages impacts the final output, whether the focus is on voltage, current, or power gain. It also involves consideration of loading effects between stages.

Loaded Voltage Gain

Loaded voltage gain is the voltage amplification factor of an amplifier stage when the loading effects of the connected circuit elements (such as the input impedance of the following stage and the external load resistors) are taken into account. It is different from the open-circuit or intrinsic gain because real-world connections modify the voltage divider relationships.

Cascaded Amplifier Stages

This concept refers to connecting two or more amplifier circuits in series, where the output of one amplifier becomes the input to the next. Cascading can multiply the overall gain and affect other parameters such as input and output impedances, making the study of interstage interactions essential for accurate performance prediction.

Loaded Current Gain

Loaded current gain refers to the ratio of the output current to the input current of an amplifier stage when the effects of connected loads are included. This measure is crucial for understanding how effectively a stage can drive the subsequent circuits, particularly when the load presents a non-negligible impedance.

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