BJT Circuits

Q1: What are the states a BJT may be in?
A1: An NPN may have 3 states, which can be linearly modeled as:

1. Cutoff: BE junction is reverse biased
• $i_B=0$, $i_C=0$
• $v_{BE}<v_{D0}$
2. Active: BE junction is forward biased, BC junction is reverse biased
• $v_{BE}=v_{D0}$, $i_B \geq 0$ 
• $i_C=\beta i_B$, $v_{CE}\geq v_{D0}$ 
3. Saturation*: BE junction is forward biased, BC junction is forward biased
• $v_{BE}=v_{D0}$, $i_B \geq 0$ 
• $v_{CE}=v_{sat}$, $i_C < \beta i_B$ 

*There are actually 3 subcategories of saturation: soft saturation, near cutoff saturation, and deep saturation. Here, we'll use saturation to mean deep saturation.

For a PNP, flip the order of the subscript letters for voltages and remember that current directions reverse (relative to the NPN)

For silicon, $v_{sat}=0.2V$

Q2: How can I solve BJT circuits?

A2: To specify the 6 BJT parameters, recall that you only need to find 2 currents and 2 voltages. For example, you might choose to calculate:

1. $v_{BE}$
2. $v_{CE}$
3. $i_{B}$
4. $i_{C}$

To calculate the 4 BJT parameters above, you may use the following algorithm: 

1. Write down the KVL equation for the BE and CE voltages.
2. Assume BJT is off: set $i_B=0$ and $i_C=0$. Check this assumption using the BE-KVL.
• If it follows that $v_BE<v_{D0}$, your assumption is correct. You can then use the CE-KVL to solve for $v_{CE}$
• Otherwise, the BJT has a forward biased BE junction. Set $v_BE=0.7$ to compute $i_B$
3. Assume the BJT is active: set $i_C=\beta i_B$. Check this assumption using the CE-KVL.
• If it follows that $v_{CE} \geq v_{D0}$, your assumption is correct
• Otherwise, the BJT must be in saturation
4. The BJT is in saturation: set $v_{CE}=v_{sat}$. 
• Use the CE-KVL to find $i_C$.