h parameter conversion formulas

simply emphasise how to derive h parameter conversion formula of CC and CB from h parameters of CE. Generally BJT manufactures give CE parameters with data sheets and we should be able to convert them to the configuration we are involving. As well as the pure conversion formula we also helpful approximate h parameter conversion formulas with considarable approximations.

1. Small-Signal Transistor
Amplifiers
h Parameter Model
Conversion Formulas
H.A.S. KALHARA
[email protected]

2. Conversion Formulas
CC parameters from CE parameters
!!


To satisfy the condition , place a short circuit across the output terminals.
using KVL we write,

FIGURE 1 - Circuit for obtaining CC parameters from CE
parametersh11=v1i1v2=0hic=vbcibvec=0vbc−hrevce=ibhievce=0∴vbc=ibhievbcib=hic=hie
vce=0

3. !
using KCL we write,
h21=i2i1v2=0
h22=i2v2i1=0
hfc=ieibvec=0ib+hfeib+ie=0ieib=−1+hfe( )=hfc
hrc=vbcvecib=0=vbe+vecvecib=0ib=0,vbe=hrevce=−hrevec∴hrc=1−hre
hoc=ievecib=0ib=0,∴vec=ie⋅1hoeievec=hoc=hoe
h12=v1v2i1=0

4. CB parameters from CE parameters




To satisfy the condition , place a short circuit across the output terminals.
using KVL for input loop,
using KVL for output loop,
h11=v1i1v2=0hib=vebievcb=0vcb=0veb+hrevce=−ibhievce=−vebveb⋅1−hre#$ %&=−ibhieveb−hfeibhoe=−ichoevebhoe+hfe1−hre"# $%vebhie =−ic
FIGURE 2 - Circuit for obtaining CB parameters from CE
parameters

5. using KCL,

!


Leaving the input port open to satisfy the condition ,
and also note that,
h21=i2i1v2=0hfb=icievcb=0hfb=−vebhoe+hfe1−hre( )hie"#$$ %&''vebhoehie+1+hfe( )1−hre( )"# %&hiehfb=−hfe1−hre( )−hiehoe1+hfe( )1−hre( )+hoehieh12=v1v2i1=0hrb=vebvcbie=0ie=0ib=−ic
ie=−ic+ib( )ie=vebhoe+hfe1−hre"# $%vebhie +veb1−hre"# $%hieie=vebhoehie+1+hfe( )1−hre( )"# $%hievebie= hiehoehie+1+hfe( )1−hre( )"# $%=hib

6. using the KVL for input loop,
using the KVL for output loop,

using derived formulas above,
veb+hrevce=−hieib=hieicbut,vce=ichoe+hfeichoe∵ib=−ic"# $%veb=ichie−hrehoe−hfehrehoe"#&& $%''vcb+hfeibhoe+hrevce=ichie+1hoe!"# $%&∴vcb−hfeichoe+hreichoe+ichfehoe!"## $%&&=ichie+1hoe!"# $%&∴vcb=ichie+1hoe+hfehoe−hrehoe−hrehfehoe!"## $%&&hrb=vebvcbie=0hrb= ichie−hrehoe−hfehrehoe"#$$ %&''ichie+1hoe+hfehoe−hrehoe−hrehfehoe"#$$ %&''hrb=hiehoe−hre1+hfe( )hoehie+1+hfe( )1−hre( )

7. summary of the h-parameter conversion equations
!hib= hiehoehie+1+hfe( )1−hre( )hrb=hiehoe−hre1+hfe( )hoehie+1+hfe( )1−hre( )hfb=−hfe1−hre( )−hiehoe1+hfe( )1−hre( )+hoehiehob= hoehoehie+1+hfe( )1−hre( )hic=hiehrc=1−hrehfc=−(1+hfe)hoc=hoe
CB
CC
h22=i2v2i1=0hob=icvcbie=0hob= icichie+1hoe+hfehoe−hrehoe−hrehfehoe"#$$ %&''hob= hoehoehie+1+hfe( )1−hre( )

8. Approximate conversion formulas

conversion formulas derived above can be simplified substantially by neglecting terms that are very
small compared to other terms in the expression. For example, for CE configuration
and hold, and also for CC and hold.
reference:
1)Electronics Devices and circuits - Theodore F.Bogart.
2)Electronics Devices and circuits - principles and applications - N.P. Deshpande
hib=hie1+hfehrb=hiehoe1+hfe−hrehfb=−hfe1+hfehob=hoe1+hfehic=hiehrc=1hfc=−(1+hfe)hoc=hoe
CB
CC
hre≪1hfe+1≫hiehoehrc≈1hoc≈0