Question

Draw the typical input and output characteristics of an n-p-n transistor in CE configuration. Show how these characteristics can be used to determine (a) the input resistance $\left(r_i\right)$, and (b) current amplification factor $\beta$.

Input charcteristics: It is the graph drawn between input current and input voltage when output voltage is kept constant.

Output characteristics : It is the graph drawn between output current and output voltage when input current is kept constant.

(a) Input resitance $(R_i$

$={\left[\frac{\text{Change in emitter base voltage}(△V_{BE})}{\text{Change in base current}(△I_B)}\right]}_{\text{at constant}{V}_{CE}}$


or $R_i={\left(\frac{△V_{BE}}{△I_B}\right)}_{V_{CE}}$

(b) Current amplification factor, $\left(\beta \right)={\left(\frac{△I_C}{△I_B}\right)}_{V_{CE}}$

= $\frac{△I_C}{△I_E-△I_C}$

= $\frac{\frac{△I_C}{△I_E}}{\frac{△I_C}{△I_E}-\frac{△I_C}{△I_E}}$

= $\frac{\alpha }{1-\alpha }$

$\Rightarrow \beta =\frac{\alpha }{1-\alpha }$

Answer 1

Input charcteristics: It is the graph drawn between input current and input voltage when output voltage is kept constant.

Output characteristics : It is the graph drawn between output current and output voltage when input currentis kept constant.

(a) Input resitance $(R_i$

$={\left[\frac{\text{Change in emitter base voltage}(△V_{BE})}{\text{Change in base current}(△I_B)}\right]}_{\text{at constant}{V}_{CE}}$


or $R_i={\left(\frac{△V_{BE}}{△I_B}\right)}_{V_{CE}}$

(b) Current amplification factor, $\left(\beta \right)={\left(\frac{△I_C}{△I_B}\right)}_{V_{CE}}$

= $\frac{△I_C}{△I_E-△I_C}$

= $\frac{\frac{△I_C}{△I_E}}{\frac{△I_C}{△I_E}-\frac{△I_C}{△I_E}}$

= $\frac{\alpha }{1-\alpha }$

$\Rightarrow \beta =\frac{\alpha }{1-\alpha }$