Two port network of Hybrid equivqlent model

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1. e THE HYBRID EQUIVALENT MODEL

Consider the two port network shown in Fig. 3.10. To develope the hybrid equivalent model of
this two port network, let us select , and Y, as independent variables and Y, and /, as dependent
variables.

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620)

ar model. Thus

621

2. AS a e EE ——oo
Aransstr ae Low rrequenues age
‚The parameters fis ia» Pa and A are called the hybrid parameters or h-parameters. The
ame hybrid is due to the fact that they do not have the same units. Let us now. define these
rameters

Set Y, = 0 by short circuiting the output terminals:

From Equation (3.21),

nn

623
h, is called the input impedance with output short circuited and he
From Equation (9.22), ———

| Ben
‘hy isthe short circuit forward transfer current ratio and has no unit
Set J,= 0 by open circ
From Equation (3.21),
li is the open circuit reverse transfer voltage ratio and has no unit
From Equation (8.2, ——
La
n= | 620

hh, is the open circuit output admittance and has the unit mhos.

Note that ——_
h,, has the unit ohms

hh has the unit mhos
4i,, and h,, have no units.
Since these parameters dimensionally differ, they are called hybrid parameters. The double
subscript parameter notation can further be reduced to a single subscript notation as follows:
Let 7 represent 11 denoting input
(© represent 22 denoting output
F represent 21 denoting forward transfer
and represent 12 denoting reverse transfer
Equations (3.21) and (3.22) now become,

ha Abe
AAA 627)
SEA 625)

3. Fi and Fig. 3.12 sho
The ire model base on Equation (32) shown in Fig 3.1 nd e 3.2.0 un
the cireuit model of Equation (3.28). Note that Equation (3.

Equation (3.28) is a KCL equation.
Equation (3.27) has two components:

4, representing a voltage drop across the impedance /, and
4, Y, representing a controlled voltage source.

Equation (3.28) has two components:
4, representing a controlled current source and
hi, Y, representing the current through admittance /,

Combining these two models, we obtain the hybrid model ofthe two-port network as shown
in Fig. 3.13,

Fl E a) A

99-1. Hybrid Parameter Nomenclature for Transistor

de ander to specify the hybrid parameters for a given transistor con
is used
e for CE Configuration

b for CB Configuration
and c for CC Configuration

figuration, a second subscript

This is ilustrated in Table 3.1.

4. Hybrid Parameters

h,
hy
rs

h,

@_3.10 HYBRID MODEL OF CB CONFIGURATION
‘The two port network representation of CB configuration is shown in Fig. 3.14.

— 77

Va Va

5 3
FREE)

Comparing the network of Fig. 3.10 and Fig. 3.14, we can list the equivalent voltages and}
currents as given in Table 3.2.

SS

ENANA
Een peraton

étre]

ss
=

5
a

Equations (3.21) and (3.22) now become
eg = Wale a 025)
AA 2 30)
‘The hybrid model constructed based on Equations (3.29) and (3.30) is shown in Fig. 3.15.

5. 5 hara ETS

FESTA

DORE RENE RENE

© 3.11_HYBRID MODEL OF CE CONFIGURATION
‘The two port network representation of CE configuration is shown in Fig. 3.16.

Je og
en
2 Vou
Ve
es -

E
PAE

Comparing the network of Fi, 3.10 and Fig. 3.16 we can lit the equivalent voltages anc
currents as given in Table3.3.

RESTE Re

BRE

MARTA
A
4
a
4
Equations (3.21) and (3.22) now become
LATE ds
ATA
Based on th the h A 632
ia a “ation, tho Hd model far the CE conf
shown in Fig, 3.17. sean

6. © 2:12 HYBRID MODEL OF CC CONFIGURATION
The two port network representation of CC configuration is shown in Fig. 3.18.

Comparing the networks of Fig 3.10 and 3.18 we can list the equivalent voltages and currents
as given in Table 3.4.

Equations (3.21) and (3.22) now become
Veh Nyt Nae Ma 633)
Le ty the A 634)

Based on these equations, the hybrid model for the CC configuration can be developed as

8. © 3.14 ADVANTAGES OF h-PARAMETERS
‘The advantages of h-parameters are

The parameters are extremely useful in the analysis and design of circuits using
transistors.

At audio frequencies the h-parameters are real numbers whi
This is essentially true because all capacitances have been
low-frequencies.

‘These parameters can be easily determined from the transistor characteristics,
Since, we started the definition of h-parameters, by considerin
two-port, four-terminal device, the models develo
transistors are of npn or pnp type.

Further, once the parameters are graphicall
Irparameters of other configurations can be ob!

h makes computations easy.
treated as open circuits at

i the transistor as a general
ped are independent of whether the

ly obtained for one configuration, the
rained by a simple conversion.

9. $ 347 HYBRID = MODEL

Athigh frequencies the effect of junction capacitances of the transistor has to be considered since
ny cnt aprecie ao Of ren dto thi rs ance, The high frequency model
ofthe transistor in ich these capacitive effects are taken into consideration
is called the hybrid model or GIACOLETTO MODEL and is shown in Fig, 329,

Sh SRG: G rn (Daun,

Eo

Let us discuss the significance of each component in Ihe model shown in Fig, 3.29.

Hybrid st Capacitances
In chapter, 1, we have seen that a forward biased p-n junction exhibits diffusion capacitance and
a reverse biased p-n junction exhibits transition capacitance.

In the model of Fig. 3.29, C, represents the diffusion capacitance of forward-biased
emitter-base junction. This eapacitance is an indicative of excess minority carrier storage in the
base. C, is usually just a few picofarads to a few tens of picofarads

C, represents the transition capacitance of the reverse biased collectorbase junction. C,
‘ypically extends from less than 1 pF to a few Picofarads.

€, and C, are altematively represented by C,, and C,, respectively.

Hybrid ze Resistance:
‘The intemal node 8° is not physically accessible as sho
external base terminal. The resistance r, includes the follow

n in Fig, 3.30, Node B represents the

* the base contact resistance
* the base bulk resistance and
* the base spreading resistance.

Is typically a few ohms to tens of ohms.

10. on

po WW"

3:30 Mer

“The resistors 1, , and, re the resistances between the indicated terminals of the transistor

when the transistor is in the active region.
aoe ere denial to, introduced in he common-emittr , model. The resis

+, represents the feedback from collector to base It fs very large typically in the mega ohm
range.

7 isthe oupatresistance which appears between he collector and emitter terminals. Typically
Heldin tne range of 5 KS to 40 KQ and iis determined from the hybrid parameter eg

Hybrid x Conductance
‘The small signal collector current,
shorted to emitter is accounted by th

the collector and emitter terminals,
pl and ri associated wil hybrid parameters have he following meaning

‘st: comes from the hybrid terminology.
script provides union between collector and base terminal.

¿ue to small change in the voltage Y, with the collector
1 voltage controlled current source g, 7, connected between

A: the element with this su

ybrid e Parameters in Terms ofr, and Ih Parameters

‘The following relations can be used to find the parameters of hybrid xr model using 7, and the
h parameters.
(348)
(3:49)
a à
rs 6.50)

12. (a) Sketch the Giacoletto (hybrid 2) model for a common-emitter transistor given that:

n=4Q C=5pF C= LS pF

mus BRO 140

13. Solution
@

Since h, is not given, let us take

The hybrid xr model is shown below.