- Hybrid-pi model
The hybrid-pi model is a popular
circuit model used for analyzing thesmall signal behavior oftransistors . The model can be quite accurate for low-frequency circuits and can easily be adapted for higher frequency circuits with the addition of appropriate inter-electrodecapacitance s and other parasitic elements.BJT parameters
The hybrid-pi model is a linearized
two-port network approximation to the transistor using the small-signal base-emitter voltage and collector-emitter voltage as independent variables, and the small-signal base current and collector current as dependent variables. (See Jaeger and Blalock. cite book
author=R.C. Jaeger and T.N. Blalock
title=Microelectronic Circuit Design
year= 2004
edition=Second Edition
publisher=McGraw-Hill
location=New York
isbn=0-07-232099-0
pages=Section 13.5, esp. Eqs. 13.19
url=http://worldcat.org/isbn/0072320990] )A basic, low-frequency hybrid-pi model for thebipolar transistor is shown in figure 1. The various parameters are as follows.* is the
transconductance in siemens, evaluated in a simple model (see Jaeger and Blalockcite book
author=R.C. Jaeger and T.N. Blalock
title=Eq. 5.45 pp. 242 and Eq. 13.25 p. 682
isbn=0-07-232099-0
url=http://worldcat.org/isbn/0072320990] ) :where::* is thequiescent collector current (also called the collector bias or DC collector current):* is the "", calculated fromBoltzmann's constant , the charge of an electron , and the transistor temperature inkelvin s . At 300 K (approximately room temperature) is about 26 mV ( [http://www.google.com/search?hl=en&q=300+kelvin+*+k+%2F+elementary+charge+in+millivolts+%3D Google calculator] ).
* in ohms:where::* is the current gain at low frequencies (commonly called hFE). Here is the Q-point base current. This is a parameter specific to each transistor, and can be found on a datasheet; is a function of the choice of collector current.
* is the output resistance due to theEarly effect .Related terms
The reciprocal of the output resistance is named the output conductance:*.
The reciprocal of gm is called the intrinsic resistance:*.
MOSFET parameters
A basic, low-frequency hybrid-pi model for the
MOSFET is shown in figure 2. The various parameters are as follows.*
is the
transconductance in siemens, evaluated in the Shichman-Hodges model in terms of theQ-point drain current by (see Jaeger and Blalockcite book
author=R.C. Jaeger and T.N. Blalock
title=Eq. 4.20 pp. 155 and Eq. 13.74 p. 702
isbn=0-07-232099-0
url=http://worldcat.org/isbn/0072320990] )::::, :where::: is the
quiescent drain current (also called the drain bias or DC drain current):: =threshold voltage and = gate-to-source voltage.The combination:
::
often is called the "overdrive voltage".
* is the output resistance due to
channel length modulation , calculated using the Shichman-Hodges model as :::,using the approximation for the channel length modulation parameter λcite book
author=W. M. C. Sansen
title=Analog Design Essentials
year= 2006
page=§0124, p. 13
publisher=Springer
location=Dordrechtμ
isbn=0-387-25746-2
url=http://worldcat.org/isbn/0387257462] :::.Here "VE" is a technology related parameter (about 4 V / μm for the 65 nm technology node) and "L" is the length of the source-to-drain separation.The reciprocal of the output resistance is named the drain conductance
*.ee also
*
Small signal model
*h-parameter modelReferences and notes
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