For the network of Fig. 172: a. Determine AvLL, Zi, and Zo. b. Sketch the two-port model of Fig.

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For the network of Fig. 172: a. Determine AvLL, Zi, and Zo....

For the network of Fig. 172: a. Determine $A_{v_{\mathrm{LL}}}, Z_{i}$, and $Z_{o}$. b. Sketch the two-port model of Fig. 63 with the parameters determined in part (a) in place. c. Determine $A_{v_{L}}$ and $A_{v_{s}}$. d. Calculate $A_{i_{2}}$ e. Change $R_{L}$ to $5.6 \mathrm{k} \Omega$ and calculate $A_{v_{j}} .$ What is the effect of increasing levels of $R_{L}$ on the gain? f. Change $R_{s}$ to $0.5 \mathrm{k} \Omega$ (with $R_{L}$ at $2.7 \mathrm{k} \Omega$ ) and comment on the effect of reducing $R_{s}$ on $A_{v_{v}}$ g. Change $R_{L}$ to $5.6 \mathrm{k} \Omega$ and $R_{s}$ to $0.5 \mathrm{k} \Omega$ and determine the new levels of $Z_{i}$ and $Z_{o}$. How are the impedance parameters affected by changing levels of $R_{L}$ and $R_{s} ?$

For the network of Fig. 172:
a. Determine $A_{v_{\mathrm{LL}}}, Z_{i}$, and $Z_{o}$.
b. Sketch the two-port model of Fig. 63 with the parameters determined in part (a) in place.
c. Determine $A_{v_{L}}$ and $A_{v_{s}}$.
d. Calculate $A_{i_{2}}$
e. Change $R_{L}$ to $5.6 \mathrm{k} \Omega$ and calculate $A_{v_{j}} .$ What is the effect of increasing levels of $R_{L}$ on the gain?
f. Change $R_{s}$ to $0.5 \mathrm{k} \Omega$ (with $R_{L}$ at $2.7 \mathrm{k} \Omega$ ) and comment on the effect of reducing $R_{s}$ on $A_{v_{v}}$
g. Change $R_{L}$ to $5.6 \mathrm{k} \Omega$ and $R_{s}$ to $0.5 \mathrm{k} \Omega$ and determine the new levels of $Z_{i}$ and $Z_{o}$. How are the impedance parameters affected by changing levels of $R_{L}$ and $R_{s} ?$

Key Concepts

Parameter Extraction and Sensitivity Analysis

Parameter extraction involves determining the numerical values of a circuit’s defining characteristics, such as gain and impedances, from its schematic or measured data. Sensitivity analysis studies how variations in component values, like changes in source and load resistances, affect overall performance metrics of the amplifier. This process is critical for optimizing circuit design and ensuring adequate performance under different operating conditions.

Two-Port Network Modeling

Two-port network modeling is a fundamental method used to represent complex circuits as simplified black-box models with input and output ports. This approach characterizes a circuit by parameters such as voltage gain, input impedance, and output impedance, which allow engineers to predict circuit behavior, analyze the signal flow, and study the effects of loading without dealing with the entire circuit complexity.

Voltage Gain

Voltage gain is a measure of the amplification provided by a circuit and is defined as the ratio of the output voltage to the input voltage. It is an essential parameter in amplifier design and analysis as it determines how effectively an input signal is amplified. In two-port network models, different definitions of voltage gain may be used based on the specific loading conditions, highlighting the importance of distinguishing between the unloaded gain and the gain when source or load impedances are considered.

Input and Output Impedance

Input and output impedance are critical parameters that quantify how a circuit interacts with the source and the load. The input impedance determines how much of the source signal is absorbed by the network, affecting signal strength and bandwidth, while the output impedance influences how effectively the amplified signal is delivered to the load. Correct impedance matching can maximize power transfer and minimize reflections, which is particularly important in high-frequency or precision applications.

Loading Effects

Loading effects refer to the influence that the source and load impedances have on the performance of the network, particularly on the gain. Changes in the source impedance can affect the voltage division at the network’s input, while variations in the load impedance can alter the output voltage through further voltage division. Understanding these effects is key to designing circuits that maintain desired performance even when external conditions, such as connected instruments or varying loads, change.

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