# DC current gain of transistor

I'm having a little thought about how DC current gain comes about. If Ic = Beta x Ib, does that mean the current flowing through collector to emitter and the current from the base i.e beta x Ib is summed up to form the DC resulting current gain?

• The sum of two currents does not make a figure for current gain. DC current gain is Ic/Ib when the transistor is operating in a specific conditions. Oct 6, 2023 at 18:34
• To be a little more pointed, the base current sums into the collector current to create the emitter current. If you want, you could say that the emitter current is 1+beta times the base current, rather than saying that the collector current is beta times the base current. (In active mode, not saturated mode.) And keep in mind that beta, even in active mode, varies a lot from one BJT to another -- even within the same part number family. So you cannot rely on any specific value. Just likely within plus or minus 50% of what someone says is typical. Oct 6, 2023 at 18:42
• So what if a common emitter configuration is implemented on the transistor? Oct 6, 2023 at 18:54
• @RuqayyaSaleh Then it is implemented. Please note that the BJT has no idea about anything. The idea of CE, CC, CB is in the heads of humans. Nature, the universe, and the BJT don't care in the least about what we think. They just do their thing. Oct 6, 2023 at 19:11

The formula $$\I_C = \beta I_B\$$ is correct, but you are also correct when you say the the two currents $$\I_B\$$ and $$\I_C\$$ do combine, by Kirchhoff's Current Law (KCL) to form current $$\I_E\$$ that emerges from the emitter:

simulate this circuit – Schematic created using CircuitLab

Applying KCL here:

$$I_E = I_B + I_C$$

When we talk of current gain, we usually mean the ratio of collector current to base current, ignoring the emitter altogether:

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

However, if you really wanted to know the relationship between emitter current and base current, you just have to rearrange the KCL equation to find $$\I_C\$$, and substitute into the gain equation:

\begin{aligned} I_E &= I_B + I_C \\ \\ I_C &= I_E - I_B \\ \\ \beta &= \frac{I_C}{I_B} \\ \\ &= \frac{I_E - I_B}{I_B} \\ \\ &= \frac{I_E}{I_B} - 1 \end{aligned}

This isn't something we'd use often, but that equation is valid, and defines current gain $$\\beta\$$ in terms of emitter current $$\I_E\$$, instead of collector current.

No, because the beta is the current gain.

• So what if a common emitter configuration is implemented on the transistor? Oct 6, 2023 at 18:55
• Beta is current gain no matter how you connect the transistor. Especially easy in common emitter configuration, you already quoted the correct formula how Ib, Ic relate, and using KCL, that's Ie. Oct 6, 2023 at 19:01
• Alright. I'm going to build a little a circuit and see how it turns out. Thanks by the way. Oct 6, 2023 at 19:15
• @RuqayyaSaleh please stick to the topic - transistor configuration is a different story. Oct 6, 2023 at 20:24

No, you don't sum up Ib and β × I b β×Ib to get the DC current gain. The β × I b β×Ib term gives you Ic directly. The emitter current (Ie) is the sum of the base and collector currents, but that's a different topic. The DC current gain ( β β) is simply the factor by which the base current is amplified to give the collector current.