Hybrid Model (Calculation of h-Parameters)

Summary

This lecture introduces the hybrid model, a method used in small signal transistor analysis. The hybrid model, also called the H-parameters model, predates the re model and is useful for different operating conditions. The lecture explains how to calculate H-parameters, which represent a mix of dimensions, and introduces a two-port network to illustrate how terminal currents and voltages are analyzed. The four key H-parameters—input impedance, forward current gain, reverse voltage gain, and output admittance—are derived and applied across transistor configurations. The lecture concludes with examples of H-parameter nomenclature and assigns homework.

Takeaways

• 📉 The lecture introduces the hybrid model, used for small signal analysis of transistors, which preceded the re (dynamic resistance) model.
• ⚙️ Hybrid parameters (h-parameters) are used to describe transistors under general operating conditions, while re-model parameters are defined by actual conditions.
• 🔄 Hybrid means 'mixed,' referring to the mixed dimensions of the hybrid parameters, which is why the term 'H' is used in this model.
• 🧩 A transistor circuit is treated as a two-port network, focusing on terminal currents and voltages (i1, i2, V1, V2) for analysis.
• 📐 The key equations for small changes in voltage and current, representing the relationships between i1, V1, i2, and V2, are central to the hybrid model.
• 🔍 Hybrid parameters include h11 (input impedance), h12 (reverse voltage gain), h21 (forward current gain), and h22 (output admittance), with each parameter having specific physical units or being dimensionless.
• 📊 By setting certain conditions, such as V2=0 or i1=0, the h-parameters can be calculated and understood in terms of impedance, gain, and admittance.
• 🔁 These parameters are applicable to different transistor configurations like common base, common emitter, and common collector.
• 📝 The nomenclature of h-parameters involves two letters: one representing the parameter (e.g., input impedance) and the other representing the transistor configuration (e.g., common emitter or common base).
• ✏️ Homework involves determining the nature of parameters and transistor configurations for given h-parameter notations, such as hfb.

Q & A

What is the hybrid model in the context of transistors?

The hybrid model is an equivalent model of transistors used in small signal analysis. It was widely used before the popularity of the re model and is also referred to as the h-parameters model. The model uses a set of parameters with mixed dimensions, which are called hybrid parameters.

What is the difference between the hybrid model and the re model?

The key difference between the hybrid and re models lies in the parameters used. The hybrid model defines parameters in general terms, suitable for any operating conditions, while the re model (Dynamic Ameter Resistance model) defines parameters based on the actual operating conditions, making it more precise for specific situations.

Why are the parameters in the hybrid model called 'hybrid'?

The parameters in the hybrid model are called 'hybrid' because they have mixed dimensions. Hybrid means 'mixed,' and these parameters combine different types of measurements like impedance, admittance, and dimensionless quantities.

What is a two-port network, and why is it important in the context of transistors?

A two-port network is a model that consists of two input and two output terminals. It's used to analyze circuits by focusing only on terminal currents and voltages, ignoring internal operations. Transistor circuits can be treated as two-port networks, making it easier to calculate small signal parameters for analysis.

What are the four key quantities in the hybrid model for a two-port network?

The four key quantities are i1 (input current), I2 (output current), V1 (input voltage), and V2 (output voltage). The relationships between these quantities define the hybrid parameters.

How are the hybrid parameters derived from a two-port network?

The hybrid parameters are derived by expressing small changes in V1 and I2 as total differentials. By taking V1 and I2 as dependent quantities, and i1 and V2 as independent quantities, the differentials are calculated with respect to each other, yielding the hybrid parameters.

What does h11 represent in the hybrid model?

h11 represents the input impedance when the output is short-circuited (V2 = 0). It is the ratio of V1 (input voltage) to i1 (input current) under these conditions.

What is the significance of h21 in the hybrid model?

h21 represents the forward current gain when the output is short-circuited (V2 = 0). It is the ratio of I2 (output current) to i1 (input current) and is denoted as Hf, where 'F' stands for forward current gain.

How is h12 defined, and what does it signify?

h12 represents the reverse voltage gain when the input is open-circuited (i1 = 0). It is the ratio of V1 (input voltage) to V2 (output voltage) and is denoted as HR, where 'R' stands for reverse voltage gain.

What is the role of h22 in the hybrid model?

h22 represents the output admittance when the input is open-circuited (i1 = 0). It is the ratio of I2 (output current) to V2 (output voltage) and is denoted as Ho, where 'O' stands for output admittance.