Easy Analog Circuit: Voltage divider circuit

We are going to catch "Sv" for voltage divider circuit. "Sv" indicates a stability factor used to discuss stabilization of the circuit during variations in Ic with respect to VBE . Before starting, it's better to take a trip through Stability factor 'S' for voltage divider circuit . Also for getting more idea about stabilization and stability factors, plz visit Stability factors & Biasing circuits .

Stability factor (Sv)

Stability factor indicates the stability of the circuit which is under discussion. Stability means variations in operating point(mainly Ic). To find 'Which are the main components in the circuit that affects stability?' -we always depends upon the equation for the stability factor. Once we get it, we can easily find the components affecting stability and it will then lead us to 'different ways for increasing stability'.
Consider the Thevenin equivalent for Voltage divider circuit. A detailed description is given in the post Voltage divider bias - Stability factor 'S'. For convenience i am including Thevenin's equivalent of input side of voltage divider circuit(fig 1).

fig 1

On writing loop equation, we will get as,

${E_{TH}} = {I_B}{R_{TH}} + {V_{BE}} + {I_B}{R_E} + {I_{_C}}{R_E}$ re-arranging,

${E_{TH}} = {V_{BE}} + {I_{_C}}{R_E} + {I_B}\left( {{R_E} + {R_{TH}}} \right)$ substitute for I_B

${E_{TH}} = {V_{BE}} + {I_{_C}}{R_E} + \frac{{{I_C}}}{\beta }\left( {{R_E} + {R_{TH}}} \right)$ -----(1)

General equations for stability factors are given in Stability factors & Biasing circuits. Definition for the second stability factor 'Sv' is $Sv = \frac{{dIc}}{{dVBE}}$ .
If equation (1) is is differentiated with respect to Ic then we can find an another equation for dIc/dV_BE.

$0 = \frac{{d{V_{BE}}}}{{dIc}} + {R_E} + \frac{1}{\beta }\left( {{R_E} + {R_{TH}}} \right)$

$\frac{{dIc}}{{d{V_{BE}}}} = \frac{{ - 1}}{{{R_E} + \frac{1}{\beta }({R_E} + {R_{TH}})}}$

$\frac{{dIc}}{{d{V_{BE}}}} = \frac{{ - \beta }}{{\beta {R_E} + {R_E} + {R_{TH}}}}$    which is equal to Sv. Therefore,

$Sv = \frac{{ - \beta }}{{(\beta + 1){R_E} + {R_{TH}}}}$

$Sv = \frac{{ - \beta }}{{(\beta + 1){R_E} + {R_{TH}}}}$    re-arrange this equation to include a factor R_TH/R_E.

$Sv = \frac{{ - \beta /{R_E}}}{{(\beta + 1) + \frac{{{R_{TH}}}}{{{R_E}}}}}$     ------(2)

For good stabilization, stability factor Sv should be low. This will happen when (R_TH/R_E) ˂˂ 1+ β and β ˃˃ 1.

During these conditions equ (2) become, Sv =̃ -1/R_E

Sv mainly depends on R_E, when it is low .
Above equation revels that dominant factor in stabilizing Ic against variations in V_BEis the voltage drop across R_E.
Other stability factors for voltage divider circuit are S and S _β.

Easy Analog Circuit

Tuesday 16 September 2014

Voltage divider circuit - stability factor (Sv)

Stability factor (Sv)

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