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Explain collector to base ckt with its stability factor.
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• The collector to base bias ckt is an improvement over the fixed bias ckt.

• The base resistance $R_B$ is now connected to the collector instead of Vcc.

• The current flowing through Rc is the sum of $IC$ and $IB$.

• $R_B$ resistor is connected as feedback element from o/p terminal collector to i/p terminal base.

Analysis of the collector to base ckt:

KVL to i/p.

$Vcc – (I_c + I_B ) R_C – I_B R_B – V_BE = 0$

$Vcc = (R_B + R_c ) I_B + I_C R_c + V_BE$

$\therefore$ $I_B = \frac{Vcc – V_BE}{(R_B + T_C ) + R_C (1 + \beta dc)}$

$I_c = \beta I_B$

KVL to o/p path:

$Vcc – (I_c + I_B) R_c – VCE = 0$

$VCE = Vcc – (I_c + I_B ) R_c$

# Stability factor:

Due to change in $\beta dc$, $Ico$ and $V_BE$ w.r.t temp Q point to transistor gets affected. Hence we need to stabilize Qpt.

$S = \frac{\triangle I_c}{\triangle I_co}$

$S = \frac{1 + \beta dc}{1 - \beta dc [ \triangle I_B/ \triangle I_c]}$

Substituting the value of $\triangle I_c/ \triangle I_c$ in the above equation to et final expression for ‘S’

• To obtain the value of ‘S’ $\triangle I_b / \triangle I_c$ apply KVL to i/p path:

$Vcc = R_c (I_c + I_B) + I_B R_B + VBE$

$\therefore$ $Vcc = I_c R_c + I_B (R_B + R_c ) + VBE$ $\rightarrow$ (1)

To find out stability factor ‘S’ we take into account the change in $I_c$ due to change in ICBO. The other two parameters VBE and $\beta dc$ are assumed to be constant.

Change in $I_c$ is $\triangle I_c, I_B$ is $\triangle I_B$

$\therefore$ equation (1) will be

$Vcc = \triangle I_c R_c + \triangle I_B (R_B + R_c) + VBE$ $\rightarrow$ (2)

$\because$ Vcc and VBE are constant.

Different equation (2) w.r.t $\triangle I_c$ we get,

$0 = R_c + \frac{\triangle I_B}{\triangle I_c} (R_B + R_c ) + 0$

$\frac{\triangle I_B}{\triangle I_c} (R_B + R_c ) = - R_c$

$\frac{\triangle I_B}{\triangle I_c} = \frac{- R_c}{R_B + R_c}$ $\rightarrow$ (3)

$S = \frac{(1 + \beta dc)}{1 - \beta dc [ \frac{- R_c}{R_B + R_c}]}$

$S = \frac{(1 + \beta dc)}{1 + \beta dc ( \frac{R_c}{R_B + R_c})}$

As compared to fixed bias ckt collector to bare bias ckt has much lesser value of ‘S’. this indicates that the Q point stability is better for collector to base bias ckt.