Infinite divisibility (probability)
The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. Sometimes it is also called "Giacoletto model" because it was introduced by L.J. Giacoletto in 1969.[1] 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-electrode capacitances and other parasitic elements.
Bipolar junction (BJT) parameters
The hybrid-pi model is a linearized two-port network approximation to the BJT 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.[2]
A basic, low-frequency hybrid-pi model for the bipolar transistor is shown in figure 1. The various parameters are as follows.
- is the transconductance in siemens, evaluated in a simple model[3]
- where:
- is the quiescent collector current (also called the collector bias or DC collector current)
- is the thermal voltage, calculated from Boltzmann's constant , the charge of an electron , and the transistor temperature in kelvins, . At approximately room temperature (295K, 22°C or 71°F) is about 25 mV.
- in ohms
- where:
- is the output resistance due to the Early effect ( is the Early voltage).
Related terms
The reciprocal of the output resistance is named the output conductance
The reciprocal of gm is called the intrinsic resistance
Full model
The full model introduces the virtual terminal B' so that the base spreading resistance rbb (the bulk resistance between the base contact and the active region of the base under the emitter) and rb'e (representing the base current required to make up for recombination of minority carriers in the base region) can be represented separately. Ce is the diffusion capacitance representing minority carrier storage in the base. The feedback components rb'c and Cc are introduced to represent the Early effect.[4]
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 the Q-point drain current by (see Jaeger and Blalock[5]):
- where:
- is the quiescent drain current (also called the drain bias or DC drain current)
- = threshold voltage and = gate-to-source voltage.
The combination:
is often called 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 λ[6]
Here VE is a technology-related parameter (about 4 V/μm for the 65 nm technology node[6]) and L is the length of the source-to-drain separation.
The reciprocal of the output resistance is named the drain conductance
See also
References and notes
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- ↑ Giacoletto, L.J. "Diode and transistor equivalent circuits for transient operation" IEEE Journal of Solid-State Circuits, Vol 4, Issue 2, 1969 [1]
- ↑
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Dhaarma Raj Cheruku, Battula Tirumala Krishna, Electronic Devices And Circuits, pages 281-282, Pearson Education India, 2008 ISBN 8131700984.
- ↑
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 6.0 6.1
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534