# How to approach the circuit analysis of a BJT in saturation?

There is a question I can't solve.

I know that $\beta\ =50$ and $V_{ce}\ (sat)$ $=0.2$.

I need to find the value of $V_1$ that the BJT is in saturation.

I've tried some KVL/KCL equation using the $V_{ce}\ (sat)$ value but I can't get an answer ($V_1$=3.1V).

What is the way to approach things like that?

• Did you mean to say that $V_{ce}(sat)=-0.2$? Is should be the case if the transistor is PNP. – Vasiliy Oct 7 '13 at 14:12

## 2 Answers

what is the way to approach things like that?

Since $V_E = 0$, the transistor will be saturated when $V_C = -0.2V$. Thus

$I_C = \dfrac{4.8V}{2k \Omega} = 2.4mA$

$I_B = \dfrac{2.4mA}{50} = 48uA$

Then, by KVL:

$V_1 = V_{EB} + 48uA \cdot 50k \Omega = V_{EB} + 2.4V$

So, assuming $V_{EB} = 0.7V$ (a reasonable assumption)

$V_1 = 3.1V$

• OK, that assumption was what I was missing. great solution, much apprecieted! – YNWA Oct 7 '13 at 16:21

The preliminary condition for BJT to be in saturation is that it is not cut-off. This means that you begin by assuming:

$$V_{EB} \approx 0.6V$$

Assumed that, and knowing $V_{EC_{Sat}}$, you're calculating the range of collector current such that:

$$V_{EC} < V_{EC_{Sat}}$$

Since you know $\beta$, you can derive the range of base current from the above range of collector current.

Knowing the base current, it is straightforward to calculate the $V_1$. The answer you quoted is, probably, the lowest limit of $V_1$ such that the BJT is in saturation.