# Variation of Operating Point

>> Two important factors are two be considered while designing the biasing circuit which is responsible for shifting the operating point ($V_{CE}, I_{C}$).

TEMPERATURE

• Variation in ICO: The flow of current in the circuit produces heat at the junctions. This heat increases the temperature at the junctions.

>> Minority carriers are temperature dependent. They increase with the temperature. The increase in minority carriers increases the leakage current.

>> If temperature increases by 1°, $I_{CO}$  increases by 7%.

>> Specifically $I_{CO}$  doubles for every 10° rise in temperature.

$\displaystyle I_C = \beta I_{B} + (1+\beta) I_{CO}$

>> This excessive increase in $I_C$  shifts the operating point into saturation region.

>> Power dissipation in the transistor is given by :

$\displaystyle P_{T} = V_{CE} \times I_{C}$

>> The increase in collector current increases power dissipation in transistor hence again temperature increases again Collector current increases. The process is cumulative. The excess heat produced at collector junction may even burn and destroy the transistor, this situation is called ‘Thermal Runway’.

• Variation in $\displaystyle V_{BE}$ : Base to emitter voltage decreases with temperature at the rate of 2.5 mV/ °C. Base current depends upon the base to emitter voltage. And Collector current depends on base current. Hence collector current gets changed.

$\displaystyle \frac {\partial V_{BE}}{ \partial T} = -2.5$ mV/ °C

• Variation in $\displaystyle \beta$ : $latex \displaystyle \beta &s=2 &bg=ffffff$ varies either due to transistor replacement or due to variation in temperature.

>> When a transistor is replaced with another transistor, the value of $\beta$ will vary because practically it is difficult to find two transistors exactly having the same $\beta$

As temperature increases → $\beta$ increases.

β = τp / τt (PNP) and β = τn / τt (NPN)

τp and τn : Carrier lifetime (Time upto recombination)

τt : Transition time ( It is the average time a carrier takes to travel through base region )

>> So as temperature increases, carrier lifetime increases hence β increases.

INSTABILITY OF COLLECTOR CURRENT – UNDESIRED EFFECT

1. Variation in operating point along DC load line which may result in distorted output or in worst case >> Operating point may move into saturation region.
2. Thermal runaway can occur which can damage the transistor.