Subsections

Junction FET

The following table contains the model parameters for the JFET model.

Name Symbol Description Unit Default
         
Vt0 $ V_{Th}$ zero -bias threshold voltage $ \volt$ $ -2.0$
Beta $ \beta$ transconductance parameter $ \ampere / \volt^{2}$ $ 10^{-4}$
Lambda $ \lambda$ channel-length modulation parameter $ 1/\volt$ $ 0.0$
Rd $ R_{D}$ drain ohmic resistance $ \ohm$ $ 0.0$
Rs $ R_{S}$ source ohmic resistance $ \ohm$ $ 0.0$
Is $ I_{S}$ gate-junction saturation current $ \ampere$ $ 10^{-14}$
N $ N$ gate P-N emission coefficient   $ 1.0$
Isr $ I_{SR}$ gate-junction recombination current parameter $ \ampere$ $ 0.0$
Nr $ N_{R}$ Isr emission coefficient   $ 2.0$
Cgs $ C_{gs}$ zero-bias gate-source junction capacitance $ \farad$ $ 0.0$
Cgd $ C_{gd}$ zero-bias gate-drain junction capacitance $ \farad$ $ 0.0$
Pb $ P_{b}$ gate-junction potential $ \volt$ $ 1.0$
Fc $ F_{c}$ forward-bias junction capacitance coefficient   $ 0.5$
M $ M$ gate P-N grading coefficient   $ 0.5$
Kf $ K_F$ flicker noise coefficient   $ 0.0$
Af $ A_F$ flicker noise exponent   $ 1.0$
Ffe $ F_{FE}$ flicker noise frequency exponent   $ 1.0$
Temp $ T$ device temperature $ \degree \mathrm{C}$ $ 26.85$
Xti $ X_{TI}$ saturation current exponent   $ 3.0$
Vt0tc $ V_{Th_{TC}}$ Vt0 temperature coefficient $ \volt/\degree \mathrm{C}$ $ 0.0$
Betatce $ \beta_{TCE}$ Beta exponential temperature coefficient $ \%/\degree \mathrm{C}$ $ 0.0$
Tnom $ T_{NOM}$ temperature at which parameters were extracted $ \degree \mathrm{C}$ $ 26.85$
Area $ A$ default area for JFET   $ 1.0$

Large signal model

Figure 10.6: junction FET symbol and large signal model
\includegraphics[width=0.5\linewidth]{jfet}

The current equation of the gate source diode and its derivative writes as follows:

$\displaystyle I_{GS}$ $\displaystyle = I_{S}\cdot \left(e^{\frac{V_{GS}}{N\cdot V_{T}}} - 1\right) + I_{SR}\cdot \left(e^{\frac{V_{GS}}{N_{R}\cdot V_{T}}} - 1\right)$ (10.37)
$\displaystyle g_{gs}$ $\displaystyle = \dfrac{\partial I_{GS}}{\partial V_{GS}} = \dfrac{I_{S}}{N\cdot...
...}}} + \dfrac{I_{SR}}{N_{R}\cdot V_{T}}\cdot e^{\frac{V_{GS}}{N_{R}\cdot V_{T}}}$ (10.38)

The current equation of the gate drain diode and its derivative writes as follows:

$\displaystyle I_{GD}$ $\displaystyle = I_{S}\cdot \left(e^{\frac{V_{GD}}{N\cdot V_{T}}} - 1\right) + I_{SR}\cdot \left(e^{\frac{V_{GD}}{N_{R}\cdot V_{T}}} - 1\right)$ (10.39)
$\displaystyle g_{gd}$ $\displaystyle = \dfrac{\partial I_{GD}}{\partial V_{GD}} = \dfrac{I_{S}}{N\cdot...
...}}} + \dfrac{I_{SR}}{N_{R}\cdot V_{T}}\cdot e^{\frac{V_{GD}}{N_{R}\cdot V_{T}}}$ (10.40)

Both equations contain the gate-junction saturation current $ I_{S}$, the gate P-N emission coefficient $ N$ and the temperature voltage $ V_{T}$ with the Boltzmann's constant $ k_{B}$ and the electron charge $ q$. The operating temperature $ T$ must be specified in Kelvin.

$\displaystyle V_{T} = \dfrac{k_{B}\cdot T}{q}$ (10.41)

The controlled drain currents have been defined by Shichman and Hodges [13] for different modes of operations.

$\displaystyle g_{m} = \dfrac{\partial I_{d}}{\partial V_{GS}} \;\;\;\;$    and $\displaystyle \;\;\;\; g_{ds} = \dfrac{\partial I_{d}}{\partial V_{DS}} \;\;\;\;$    with $\displaystyle \;\;\;\; V_{GD} = V_{GS} - V_{DS}$ (10.42)

The MNA matrix entries for the voltage controlled drain current source can be written as:

G
S
controlling nodes
D
$ +g_{m}$ $ -g_{m}$  
S
$ -g_{m}$ $ +g_{m}$  
controlled nodes
     

With the accompanied DC model shown in fig. 10.7 using the same principles as explained in section 3.3.1 on page [*] it is possible to build the complete MNA matrix of the intrinsic JFET.

Figure 10.7: accompanied DC model of intrinsic JFET
\includegraphics[width=0.5\linewidth]{dcjfet}

Applying the rules for creating the MNA matrix of an arbitrary network the complete MNA matrix entries (admittance matrix and current vector) for the intrinsic junction FET are:

$\displaystyle \begin{bmatrix}g_{gd} + g_{gs} & -g_{gd} & -g_{gs}\\ -g_{gd} + g_...
...S_{eq}}\\ +I_{GD_{eq}} - I_{DS_{eq}}\\ +I_{GS_{eq}} + I_{DS_{eq}} \end{bmatrix}$ (10.61)

with

$\displaystyle I_{GS_{eq}}$ $\displaystyle = I_{GS} - g_{gs}\cdot V_{GS}$ (10.62)
$\displaystyle I_{GD_{eq}}$ $\displaystyle = I_{GD} - g_{gd}\cdot V_{GD}$ (10.63)
$\displaystyle I_{DS_{eq}}$ $\displaystyle = I_{d} - g_{m}\cdot V_{GS} - g_{ds}\cdot V_{DS}$ (10.64)

Small signal model

Figure 10.8: small signal model of intrinsic junction FET
\includegraphics[width=0.45\linewidth]{spjfet}

The small signal Y-parameter matrix of the intrinsic junction FET writes as follows. It can be converted to S-parameters.

$\displaystyle Y = \begin{bmatrix}Y_{GD} + Y_{GS} & -Y_{GD} & -Y_{GS}\\ g_{m} - ...
...} - g_{m}\\ -g_{m} - Y_{GS} & -Y_{DS} & Y_{GS} + Y_{DS} + g_{m}\\ \end{bmatrix}$ (10.65)

with

$\displaystyle Y_{GD}$ $\displaystyle = g_{gd} + j\omega C_{GD}$ (10.66)
$\displaystyle Y_{GS}$ $\displaystyle = g_{gs} + j\omega C_{GS}$ (10.67)
$\displaystyle Y_{DS}$ $\displaystyle = g_{ds}$ (10.68)

The junction capacitances are modeled with the following equations.

$\displaystyle C_{GD}$ $\displaystyle = \begin{cases}\begin{array}{ll} C_{gd}\cdot \left(1 - \dfrac{V_{...
...ght)}\right) & \textrm{ for } V_{GD} > F_{c}\cdot P_{b} \end{array} \end{cases}$ (10.69)
$\displaystyle C_{GS}$ $\displaystyle = \begin{cases}\begin{array}{ll} C_{gs}\cdot \left(1 - \dfrac{V_{...
...ght)}\right) & \textrm{ for } V_{GS} > F_{c}\cdot P_{b} \end{array} \end{cases}$ (10.70)

Noise model

Both the drain and source resistance $ R_D$ and $ R_S$ generate thermal noise characterized by the following spectral density.

$\displaystyle \dfrac{\overline{i_{R_D}^2}}{\Delta f} = \dfrac{4 k_B T}{R_D} \;\...
...m{ and } \;\;\;\; \dfrac{\overline{i_{R_S}^2}}{\Delta f} = \dfrac{4 k_B T}{R_S}$ (10.71)

Figure 10.9: noise model of intrinsic junction FET
\includegraphics[width=0.58\linewidth]{noisejfet}

Channel noise and flicker noise generated by the DC transconductance $ g_m$ and current flow from drain to source is characterized by the following spectral density.

$\displaystyle \dfrac{\overline{i_{ds}^2}}{\Delta f} = \dfrac{8 k_B T g_m}{3} + K_F\dfrac{I_{DS}^{A_F}}{f^{F_{FE}}}$ (10.72)

The noise current correlation matrix (admittance representation) of the intrinsic junction FET can be expressed by

$\displaystyle \underline{C}_Y = \Delta f \begin{bmatrix}0 & 0 & 0\\ 0 & +\overl...
...ine{i_{ds}^2}\\ 0 & -\overline{i_{ds}^2} & +\overline{i_{ds}^2}\\ \end{bmatrix}$ (10.73)

This matrix representation can be easily converted to the noise-wave representation $ \underline{C}_S$ if the small signal S-parameter matrix is known.

Temperature model

Temperature appears explicitly in the exponential terms of the JFET model equations. In addition, saturation current, gate-junction potential and zero-bias junction capacitances have built-in temperature dependence.

$\displaystyle I_S\left(T_2\right)$ $\displaystyle = I_S\left(T_1\right)\cdot \left(\dfrac{T_2}{T_1}\right)^{X_{TI} ...
...00K\right)}{N\cdot k_B\cdot T_2}\cdot \left(1 - \dfrac{T_2}{T_1}\right)\right]}$ (10.74)
$\displaystyle I_{SR}\left(T_2\right)$ $\displaystyle = I_{SR}\left(T_1\right)\cdot \left(\dfrac{T_2}{T_1}\right)^{X_{T...
...K\right)}{N_R\cdot k_B\cdot T_2}\cdot \left(1 - \dfrac{T_2}{T_1}\right)\right]}$ (10.75)
$\displaystyle P_{b}\left(T_2\right)$ $\displaystyle = \dfrac{T_2}{T_1}\cdot P_{b}\left(T_1\right) - \dfrac{2\cdot k_B...
...- \left(\dfrac{T_2}{T_1} \cdot E_G\left(T_1\right) - E_G\left(T_2\right)\right)$ (10.76)
$\displaystyle C_{gs}\left(T_2\right)$ $\displaystyle = C_{gs}\left(T_1\right)\cdot\left(1 + M\cdot\left(400\cdot 10^{-...
...}\left(T_2\right) - P_{b}\left(T_1\right)}{P_{b}\left(T_1\right)}\right)\right)$ (10.77)
$\displaystyle C_{gd}\left(T_2\right)$ $\displaystyle = C_{gd}\left(T_1\right)\cdot\left(1 + M\cdot\left(400\cdot 10^{-...
...}\left(T_2\right) - P_{b}\left(T_1\right)}{P_{b}\left(T_1\right)}\right)\right)$ (10.78)

where the $ E_G\left(T\right)$ dependency has already been described in section 10.2.4 on page [*]. Also the threshold voltage as well as the transconductance parameter have a temperature dependence determined by

$\displaystyle V_{Th}\left(T_2\right)$ $\displaystyle = V_{Th}\left(T_1\right) + V_{Th_{TC}}\cdot\left(T_2 - T_1\right)$ (10.79)
$\displaystyle \beta\left(T_2\right)$ $\displaystyle = \beta\left(T_1\right)\cdot 1.01^{\beta_{TCE}\cdot\left(T_2 - T_1\right)}$ (10.80)

Area dependence of the model

The area factor $ A$ used for the JFET model determines the number of equivalent parallel devices of a specified model. The following parameters are affected by the area factor.

$\displaystyle \beta\left(A\right)$ $\displaystyle = \beta\cdot A$ $\displaystyle I_S\left(A\right)$ $\displaystyle = I_S\cdot A$ (10.81)
$\displaystyle R_D\left(A\right)$ $\displaystyle = \dfrac{R_D}{A}$ $\displaystyle R_S\left(A\right)$ $\displaystyle = \dfrac{R_S}{A}$ (10.82)
$\displaystyle C_{gs}\left(A\right)$ $\displaystyle = C_{gs}\cdot A$ $\displaystyle C_{gd}\left(A\right)$ $\displaystyle = C_{gd}\cdot A$ (10.83)


This document was generated by Stefan Jahn on 2007-12-30 using latex2html.