Hybrid Model (Calculation of h-Parameters)
Summary
TLDRThis 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
🔍 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.
📐 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.
⚙️ 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.
📊 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.
Mindmap
Keywords
💡Hybrid model
💡H-parameters
💡re model
💡Impedance
💡Admittance
💡Two-port network
💡Small-signal analysis
💡Forward current gain (h21 or hf)
💡Reverse voltage gain (h12 or hr)
💡Common emitter configuration
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
浏览更多相关视频
5.0 / 5 (0 votes)