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.

Outlines

00:00

🔍 Introduction to Hybrid Model and its Parameters

The lecture introduces the hybrid model, which is used for small signal analysis of transistors and was widely used before the re model (Dynamic Meter Resistance Model). The hybrid model has parameters defined for any operating conditions, whereas the re model parameters are specific to actual operating conditions. The lecture emphasizes the importance of understanding both models in the course. It explains that the 'H' in 'H-parameters' stands for 'hybrid,' highlighting that these parameters have mixed dimensions. Before transistors, vacuum tubes were used, and only impedance or admittance parameters were needed. With transistors, hybrid parameters were introduced for better analysis.

05:01

📐 Mathematical Representation of Hybrid Parameters

The paragraph delves into the mathematical formulation of hybrid parameters using a general two-port network. It describes the network with currents and voltages at two ports (i1, i2, V1, V2). It explains that the four quantities can be defined with two as dependent and the other two as independent variables. The changes in voltage and current are expressed as differentials, with specific units assigned to these derivatives. The derivation introduces h11, h12, h21, and h22 parameters, corresponding to different relationships between voltage and current, and categorizes them based on their dimensional properties such as impedance and admittance.

10:03

⚙️ Deriving and Understanding the H-Parameters

This paragraph details the derivation of the four primary H-parameters for transistors: h11 (input impedance), h21 (forward current gain), h12 (reverse voltage gain), and h22 (output admittance). By setting certain variables to zero, it explains how to calculate each parameter in different conditions. For instance, h11 is calculated as input impedance when the output is short-circuited, while h21 is derived as the forward current gain under similar conditions. The paragraph uses equations to show these relationships and introduces specific notations (hi, hf, hr, ho) for these parameters to represent their roles in various transistor configurations.

15:04

📊 Nomenclature and Notation for H-Parameters

The paragraph focuses on the nomenclature and notation used to represent H-parameters for different transistor configurations. It explains the double-script notation where the first letter indicates the nature of the parameter (input impedance, forward current gain, etc.), and the second letter indicates the transistor configuration (common emitter, common base, common collector). Examples are provided to illustrate this notation: 'hie' for input impedance of a common emitter configuration, and 'hrb' for reverse voltage gain in a common base configuration.

Keywords

💡Hybrid model

The hybrid model is a small-signal equivalent model of transistors, used to analyze transistor behavior. It was widely used before the introduction of the re model. The term 'hybrid' refers to the fact that the parameters used in this model have mixed dimensions, combining different types of electrical properties. The model simplifies the representation of a transistor in different configurations, as discussed in the lecture.

💡H-parameters

H-parameters (also known as hybrid parameters) are the key components of the hybrid model used to describe transistors. These parameters represent a mix of impedances, admittances, and dimensionless ratios. The script explains the calculation of these parameters and their importance in constructing the equivalent circuit for small-signal analysis of transistors. The four H-parameters are hi (input impedance), hf (forward current gain), hr (reverse voltage gain), and ho (output admittance).

💡re model

The re model, also known as the dynamic resistance model, is an alternative to the hybrid model. Unlike the hybrid model, the parameters of the re model are defined based on the actual operating conditions of the transistor, making it more precise in certain scenarios. The script contrasts the hybrid and re models, emphasizing the need to study both in the course.

💡Impedance

Impedance is the resistance to the flow of alternating current, represented in the H-parameters as h11 or input impedance. The script describes how impedance is one of the key electrical properties used to calculate the H-parameters. In this context, impedance is related to how voltage and current interact at different points in the transistor's operation.

💡Admittance

Admittance is the measure of how easily a circuit allows the flow of electric current. It is the inverse of impedance and is represented in the hybrid model by the H-parameter h22 (output admittance). The lecture explains that admittance is used to describe the output characteristics of the transistor in small-signal analysis, specifically when calculating how the transistor responds to changes in voltage and current.

💡Two-port network

A two-port network is a system with two pairs of terminals, one for input and one for output. The transistor, as explained in the script, is modeled as a two-port network where the input and output currents and voltages can be measured. This network serves as the basis for analyzing transistor behavior using H-parameters.

💡Small-signal analysis

Small-signal analysis is the method used to analyze the behavior of circuits when subjected to small input signals. The hybrid model discussed in the lecture is specifically used for small-signal analysis of transistors. This technique simplifies the equations and models by superimposing small AC signals over the larger DC operating points.

💡Forward current gain (h21 or hf)

Forward current gain, represented by h21 or hf, is one of the four H-parameters in the hybrid model. It defines the ratio of the output current to the input current, assuming the output is short-circuited. This parameter is crucial in determining how much the current is amplified from the input to the output of a transistor.

💡Reverse voltage gain (h12 or hr)

Reverse voltage gain, represented by h12 or hr, describes how much the input voltage is affected by the output voltage when the input current is zero. It measures the feedback from the output to the input in a transistor circuit, and is another essential H-parameter used in the hybrid model.

💡Common emitter configuration

The common emitter configuration is one of the three main transistor configurations (along with common base and common collector) mentioned in the script. In this setup, the emitter terminal is shared by both the input and output sides of the circuit. This configuration is widely used because it provides significant voltage and current amplification, and it is one of the configurations to which the hybrid model equations apply.

Highlights

Introduction of the hybrid model as a small-signal equivalent model for transistors, emphasizing its historical significance before the RE model.

Explanation of how hybrid parameters (H-parameters) are defined in general terms for any operating conditions, unlike the RE model, which depends on actual operating conditions.

Significance of the term 'hybrid': The parameters are called hybrid because they have mixed dimensions, such as impedance and admittance, making them versatile for analysis.

Introduction of a general two-port network model to understand the relationship between currents and voltages at the terminals.

Breakdown of the four key quantities in a two-port network: input current (i1), output current (i2), input voltage (V1), and output voltage (V2).

Definition of dependent and independent quantities in the two-port network: For hybrid parameters, V1 and I2 are considered dependent, while V2 and i1 are independent.

Derivation of hybrid parameter equations: Expressing changes in V1 and I2 as total differentials of i1 and V2, establishing the foundation for H-parameter calculations.

Identification of the four hybrid parameters: h11 (input impedance), h12 (reverse voltage gain), h21 (forward current gain), and h22 (output admittance).

Illustration of the physical significance of each hybrid parameter: h11 is the input impedance when the output is short-circuited, and h21 is the forward current gain under similar conditions.

Clarification of h12 as the reverse voltage gain when the input is open-circuited, and h22 as the output admittance with an open-circuited input.

Naming conventions of hybrid parameters: Explanation of the double subscript notation, where the first letter denotes the nature of the parameter (e.g., input impedance, reverse voltage gain) and the second letter indicates the transistor configuration (e.g., common emitter, common base).

Practical examples to reinforce the nomenclature: Representing input impedance in a common emitter configuration as hie and reverse voltage gain in a common base configuration as hfb.

Application of hybrid parameters in all three transistor configurations: Common emitter, common base, and common collector configurations.

Highlight of the advantages of using hybrid parameters in small-signal transistor analysis due to their general applicability across different configurations.

Summary of the lecture and introduction to the next topic: Calculation of the equivalent circuit using hybrid parameters, highlighting the continuity of the subject.

Transcripts

from this lecture we will start the

hybrid model I will explain how to

calculate the edge parameters of hybrid

model hybrid model is the equivalent

model of transistors used in a small

signal analysis hybrid model was widely

used in the early years before the

popularity of re model so before re

model we had hybrid model re model is

also called as Dynamic ameter resistance

model and in case of hybrid model the

parameters are defined in general terms

for any operating conditions and in case

of re model parameters are defined by

the actual operating conditions so this

is the advantage of re model but we have

to study both hybrid model and re model

in this course this statement is for

hybrid model or we can say h

model this statement is for

re model hybrid model is also called as

hedge parameters model in hybrid model

we have to calculate the HED parameters

and using this parameters we will draw

the equivalent circuit so the first

thing is calculation of hedge parameters

and we will calculate hedge parameters

in this lecture in the next lecture we

will draw the equivalent circuit so we

have to

calculate H

parameters now why this H is there in h

parameters this is because of hybrid H

stands for hybrid I will write this down

H stands for

highbrid now there is one question the

question is why we call this parameters

hybrid parameters what is the

significance of this word hybrid while

we call these parameters hybrid

parameters hybrid means mixed and these

parameters have mixed Dimensions so the

parameters which we will calculate in

this lectures will have the mixed

dimensions and because of this we call

them hybrid parameters before the

invention of transistors circuits were

designed using vacuum tubes only one out

of impedance or admittance parameters

was required to determine all the

parameters we have four important

parameters

any small signal amplifiers and all

these four parameters can be obtained

using only impedance or we can say Zed

parameters

or admittance or we can say y parameters

but this is true for vacuum tubes in

case of transistors there was problem

determining the Zed parameter and the Y

parameter so we introduced a new set of

parameters called called as hybrid

parameters we will begin with General

two Port Network I will quickly draw the

general two Port

Network this is the port number

one and this is the port number

two this

is Port

one and this

is Port two Port one current is equal to

i1 and Port two current is equal to I2

potential difference between these two

terminals is equal to V1 and potential

difference between these two terminals

is equal to V2 and this is the two Port

network two

Port Network we are only interested in

the terminal currents and terminal

voltages we don't have to do anything

with the currents and voltages inside

this box transistor circuit is also a

two Port Network and this currents and

this voltages are the total currents and

total voltages total current or total

voltage

means AC

Value Plus the DC

value so i1 is equal to AC value of the

input current plus the DC value of the

input current in the same way current I2

voltage V1 and voltage V2 are the sum of

their respective AC and DC values we

have four quantities i1 I2 V1 and V2

these are the four quantities and we can

Define the parameters by taking any two

quantities out of four as dependent and

rest two quantities as independent and

let's say let's say we

1 and

I2 are the dependent quantities

dependent quantities so we are left with

V2 and i1

V2 and i1 so V2 and i1 are the

independent quantities

independent quantities and we can say

that

V1 is the function of

i1 and V2 the two independent quantities

and current I2 current I2 is also the

function of let's say the function is

FS2 i1 and

V2 we can find out the changes in

voltage V1 and current I2 as total

differentials we can easily express

changes in V1 and I2 as the toal total

differentials dv1 that is the small

change in the voltage V1 is equal to

rate of change of V1 with respect to the

current i1 for a small change in the

current i1 plus rate of change of V1

with respect to voltage vs2 for small

change in voltage V2 and let's say this

is equation number one in the same way

small change in current I2 is equal to D

I2 by d

i1 d i1 plus d

I2 by D

V2 dv2 and this is the equation number

two now this quantity D V1 by D i1 is

having the units of impedence voltage by

current is impedence so this

is the parameter having the unit of

impedance and let's

say this is h11 now why we are having 1

one in the representation because

voltage is from the port number one and

current is also from the port number one

and this H stands for the hybrid

parameter in the same way if we find out

other three parameters we find

this parameter is dimensionless this

parameter is

dimensionless dimension less and this is

H1 2 D I2 by D i1 is also dimensionless

because current by current is there and

this is h 2 1 the last parameter D I2 by

D E2 is having the units of admittance

current by voltage is the

admittance

admittance and I will represent it by

H22 so these are the four parameters and

you can see D V1 and D I2 are the AC

values I have already explained you that

we are super

imposing the AC part over the DC part

this is the DC part and we are

superimposing the AC like this dv1 this

means a small change in voltage V1 is AC

because DC is constant similarly D2 is

also AC so these two quantities are AC

and in this plot this is AC part and

this part is the DC part and we already

know the conventions for the

representation of AC values the AC

current the AC

current is

represented by small I and the ac

voltage the ac voltage is represented by

small V so equation number one and

equation number two we can rewrite as we

can rewrite as small V1 equal to h11

small i1

plus H1 1 2 small

V2 small I2 equal to

h21 small i1 plus

H22 V2 and let's say this is equation

number three and this is equation number

four equation number three and equation

number four are applicable to all the

three transistor configurations they are

applicable to all the three

transistor configurations we have three

transistor configurations common base

common emitter and common collector and

these two equations are applicable to

all the three configurations if we make

V2 equal to zero in equation 3 and

equation 4 we can easily find out h11

and h21 so let's make voltage V2 equal

to 0 V2 equal to 0 then from equation

number three three from equation number

three we have

h11 equal to V1 by i1 and this is when

this is when V2 is equal to Z so we can

say that h11 is the input impedance with

output short circuited because V2 is

equal to zero only when the output is

short circuited so h11 is the input

impedence input

impedance when output when

output is short circuited and I will

change the representation I will

represent

h11 as hi I where I represents the input

impedance now we will calculate we will

calculate h21 h21 is equal to

h21 is equal to I2 by

i1 when V2 is equal to Z and this we

have from equation number four

from equation number four h21 is the

forward current gain when the output is

short circuited

h21 is the

forward

current gain when the

output is short circuited I will

represent h21 as H subscript f h

subscript F where F represents the

forward current gain now we will make we

will make current i1 equal to 0 in

equation number three and equation

number four so let's make current i1

equal to 0 and from equation number

three from

equation number three we have h12 equal

to V1 by V2 when i1 is equal to0 so

h12 is equal to voltage V1 by voltage

vs2 when input current i1 is equal to

zero so h12 is the reverse voltage gain

with input open circuited

h12 is the

reverse

voltage gain when the input is open

circuited and I will represent

h12 by

HR where R stands for the reverse

voltage gain now we will calculate the

parameter H22 it is equal

to it is equal to current I2 divided by

the voltage V2 when the input current i1

is equal to zero so H22 is the output

admittance with input open circuited

H22 is the output

admittance with input open circuited and

we are having this from equation number

four from

equation number four and I will

represent H22 I will represent H22 as h

o where o stands for the output

admittance so we have hi HF HR and ho o

as the four h parameters now we will

move to the next part of this lecture

which is the nomenclature it is very

important part in this part I will

explain the nomenclature the

nen

clature of H parameters

par meters the first thing is to write H

which represents the hybrid parameter so

first we will write down H which is a

small H and then we have double script

notation L1 L2 this is the double script

notation the first letter L1 denotes the

nature of parameter whether it is input

impedance forward current gain reverse

voltage gain or the output admittance

the second letter L2 denotes the

transistor configuration whether it is

common amiter configuration common base

conf configuration or common collector

configuration let's try to solve one or

two examples which will clear the

nomenclature of H parameters if we have

the

input

impedance of common emiter transistor

then we will represent it we will

represent it with h and the first letter

is definitely I because we are having

input impedance that is this is the

nature of parameter

the second letter is a small e denoting

the common amiter configuration in the

second example in the second example we

have reverse voltage gain

reverse

voltage

gain of common base transistor and we

will represent

it by small H then the first letter will

be R because of reverse vol volage gain

this is denoting the nature of parameter

and then we have small B for common base

configuration now we will move to the

homework part of this

lecture in the first problem you have to

find out the nature of parameter and the

transistor configuration for H in the

second problem you again have to find

out the nature of parameter and the

transistor configuration for

hfb once you have your answers post them

in comment section in the next lecture

we will find out the equivalent circuit

using the edge parameters so this is all

for this lecture see you in the next one