Bjt base current calculation

Question

In a bjt transistor that is used as a switch (maximum saturation, Vce minimum as possible), what is the minimum base current that is required for a corresponding desirable collector current?

Answer 1

First try to read this

The transistor going into saturation isn't a property of the transistor itself, but instead a property of the circuit surrounding the transistor and the transistor, as part of it.

A question about Vce of an NPN BJT in saturation region

For this circuit with ideal transistor (current controlled current source CCCS) any base current large than:

\$\Large I_B > \frac{\frac{V_{cc}}{R_c}}{\beta }\$ will saturate the BJT.

But in real life, ideal transistor don't exist. For any real world transistor, the β is not constant. β varies with Ic, Vce, temperature. And what is worse, every single transistor will have different beta value and beta will changes for different operating conditions also. Also in saturation \$I_C = I_B * β\$ do not hold anymore.

So to overcome this problem with beta and saturation we are forced to use "overdrive factor" or "Forced Beta" trick.

We simply increase the base current well beyond \$I_B > \frac{\frac{V_{cc}}{R_C}}{\beta }\$.

We do this to make sure that we have enough base current to put the transistor well into saturation for every condition we have in our circuit.

Additional most BJT's vendors define saturation region when Ic/Ib = 10 (called Forced Beta). And the most data-sheet show Vce_sat for Ic/Ib = 10

So, to be one hundred percent sure that your BJT will be in saturation region you must use this so-called forced beta technique when choosing base resistor value.

$$\frac{I_C}{I_B} = 10$$

$$R_B = \frac{V_{IN} - V_{BE}}{0.1*I_C}$$

$$R_C = \frac{V_{CC} - V_{CE_{sat}}}{I_C}$$

Or we can use KVL and solve for \$R_B\$

$$I_B=\frac{V_{IN} - V_{BE}}{R_B}$$

$$V_{CE} = V_{CC} - I_C*R_C = V_{CC} - \beta*I_B*R_C = V_{CC} - \beta \frac{V_{IN} - V_{BE}}{R_B} * R_C $$ Solving for \$R_B\$

$$R_B\leqslant \frac{V_{IN_{min}} - V_{BE}}{V_{CC} - V_{CE_{sat}}}*\frac{\beta_{min}}{K}*R_C$$

And K = 3...10 - overdrive factor

Answer 2

There is one formula you need to know to calculate the base curent : \$H_{fe}=\frac{I_c}{I_b}\$. You know from \$I_c\$ from you circuit and \$H_{fe}\$ from the datasheet. That lead to \$I_b = \frac{I_c}{H_{fe}}\$. I suggest you to take \$I_b\$ higher (\$I_b >> \frac{I_c}{H_{fe}}\$).

To fix that base current, you have to remember that \$ V_{BE}\$ will affect the base voltage.

^{simulate this circuit – Schematic created using CircuitLab}

In this exemple, \$I_{R1} = \frac{V_{cmd} - V_{BE}}{R_1}\$

Answer 3

For saturation to occur over all temperature ranges take the hFE(min) and use the equation Ib_minSat = Ic / hFE(min) to find the minimum base current for saturation to occur. You select the desired Ic. Note that you want to make sure your Beta_Forced (i.e. Ic / Ib) is less than the hFE(min) in the datasheet.

If you're confused, see the example in Sedra Smith, Microelectronic Circuits 6th Edition, page 383:

Since β_forced is less than the minimum specified value of β, the transistor is indeed saturated. We should emphasize here that in testing for saturation the minimum value of β should be used. By the same token, if we are designing a circuit in which a transistor is to be saturated, the design should be based on the minimum specified β. Obviously, if a transistor with this minimum β is saturated, then transistors with higher values of β will also be saturated.

Sedra Smith, Microelectronic Circuits 6th Edition, page 383

_{(Image source: ON Semiconductor P2N2222A datasheet)}