hybrid model theoritical pyq

Here is your strictly PYQ-focused, exam-standard study note covering all theory questions asked regarding the Hybrid Model and $h$-parameters, excluding the derivations and numericals.

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1. Definition of Hybrid Model & $h$-parameters

• Exact PYQs:
  • “What is meant by hybrid parameter in ac analysis of BJT?” (Asked in: 2024)
  • “Define hybrid model and hybrid parameters.” (Asked in: 2018)
  • “Define h-parameters.” (Asked in: 2020, 2016, 2015)

Definition: The hybrid equivalent model is a mathematical two-port model used for small-signal BJT AC analysis. It relates the four variables of a two-port network (input voltage $V_i$, input current $I_i$, output voltage $V_o$, output current $I_o$) using a set of parameters.

These parameters are called $h$-parameters (hybrid parameters) because the mixture of variables (Voltage and Current) in the defining equations results in a “hybrid” set of measurement units:

• $h_{11}$ ($h_i$): Input impedance (measured in ohms).
• $h_{12}$ ($h_r$): Reverse transfer voltage ratio (unitless).
• $h_{21}$ ($h_f$): Forward transfer current ratio (unitless).
• $h_{22}$ ($h_o$): Open-circuit output admittance (measured in siemens).

Unlike the $r_e$ model where parameters are defined by actual circuit operating conditions, hybrid parameters are defined in general terms for any operating condition.

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2. Advantages of the Hybrid Model

• Exact PYQs:
  • “What are the advantages of hybrid model?” (Asked in: 2021, 2019, 2016)

The hybrid model was historically the most widely used model because of the following advantages:

1. Real Numbers: The $h$-parameters are real numbers at audio/low frequencies.
2. Easy to Measure: They are relatively easy to measure experimentally.
3. Graphical Determination: They can be obtained directly from the transistor’s static characteristic curves.
4. Manufacturer Provided: A set of $h$-parameters is conveniently specified and provided by manufacturers on transistor data sheets, allowing for immediate comparison between different devices.
5. Convenience: They are particularly convenient to use in linear circuit analysis and design.

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3. Determining $h$-parameters from Characteristic Curves

• Exact PYQs:
  • “How can you determine h-parameters from transistor characteristic curves?” (Asked in: 2020, 2016, 2015)

Because the characteristic curves of a transistor are not perfectly straight lines, $h$-parameters depend heavily on the chosen Quiescent ($Q$) point. They are determined graphically by taking partial derivatives (finding the slope or spacing between curves) around a specific $Q$-point:

• $h_{ie}$ (Input Impedance): Determined from the input/base characteristics. It is the ratio of a small change in base voltage to the change in base current ($\Delta V_{BE}/\Delta I_B$), keeping the collector voltage ($V_{CE}$) constant.
• $h_{re}$ (Reverse Voltage Ratio): Determined from the input/base characteristics. It is the ratio of a small change in base voltage to the change in collector voltage ($\Delta V_{BE}/\Delta V_{CE}$), keeping the base current ($I_B$) constant.
• $h_{fe}$ (Forward Current Gain): Determined from the output/collector characteristics. It is the ratio of a small change in collector current to the change in base current ($\Delta I_C/\Delta I_B$), keeping the collector voltage ($V_{CE}$) constant.
• $h_{oe}$ (Output Admittance): Determined from the output/collector characteristics. It is the ratio of a small change in collector current to the change in collector voltage ($\Delta I_C/\Delta V_{CE}$), keeping the base current ($I_B$) constant.

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4. Drawing the Hybrid Equivalent Models

• Exact PYQs:
  • “Draw the exact and appropriate hybrid model of three common configurations.” (Asked in: 2021, 2019, 2016)
  • “Draw the hybrid models of three different configurations of transistor.” (Asked in: 2018)

(Note for the exam: You must draw the general two-port structure first, then apply the specific subscripts).

• The General Structure: The input circuit consists of a resistor ($h_i$) in series with a voltage-controlled voltage source ($h_r{V}_o$). The output circuit consists of a current-controlled current source ($h_f{I}_i$) in parallel with an output resistor/conductance ($1/h_o$).
• Common-Emitter (CE): Add the subscript ‘e’. The input terminals are Base and Emitter. The parameters are $h_{ie},h_{re},h_{fe},h_{oe}$. Input current is $I_b$, output current is $I_c$.
• Common-Base (CB): Add the subscript ‘b’. The input terminals are Emitter and Base. The parameters are $h_{ib},h_{rb},h_{fb},h_{ob}$. Input current is $I_e$, output current is $I_c$.
• Common-Collector (CC): Add the subscript ‘c’. The input terminals are Base and Collector. The parameters are $h_{ic},h_{rc},h_{fc},h_{oc}$. Input current is $I_b$, output current is $I_e$.

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5. Justification: “Input Impedance is a Function of Load Impedance”

• Exact PYQs:
  • “The input impedance is a function of load impedance – Justify the statement using the hybrid modeling concept.” (Asked in: 2022, 2021, 2017)

Justification: To prove this, we examine the fundamental equations of the exact hybrid model.

1. From the input loop of the hybrid circuit, the input voltage is: $V_1=h_i{I}_1+h_r{V}_2$.
2. The input impedance ($Z_i$) is the ratio of input voltage to input current ($V_1/I_1$). Dividing the first equation by $I_1$ yields: $Z_i=\frac{V_1}{I_1}=h_i+h_r\frac{V_2}{I_1}$.
3. We know that the output voltage ($V_2$) is the product of the output current ($-I_2$) and the load impedance ($Z_L$). Furthermore, output current $I_2$ is related to input current $I_1$ by the current gain ($A_I$). Therefore: $V_2=-I_2{Z}_L=A_I{I}_1{Z}_L$.
4. Substituting this expression for $V_2$ back into our $Z_i$ equation gives the final relationship: $Z_i=h_i+h_r{A}_I{Z}_L$.

Conclusion: Because the load impedance ($Z_L$) directly appears in the mathematical expression for the input impedance ($Z_i$), any change in the external load will physically feed back through the reverse voltage ratio ($h_r$) and alter the input impedance. Therefore, the input impedance is strictly a function of the load impedance.