# Solving for values in an NPN bipolar transistor circuit

simulate this circuit – Schematic created using CircuitLab

I am trying to learn how to apply bipolar transistors in circuit but I cannot figure out how the textbook solved this one.

The book answer for this is Vc = 3.94, Ic = 1.34 mA, and Ib = 6.68 µA, but I cannot figure out how to get these answers. (The gain on Q1 is 200 & the transistor name is as shown; ignore all other data in the transistor info.)

Please walk me through how to approach this problem.

• One approach how to solve this circuit is find “at what Vc it draws maximum power or current”. It is because it always stabilise at this point. Nov 12, 2023 at 23:00
• @MichalPodmanický True, but to replicate the results from the book, it's helpful to know first what model of the transistor is used. For example, the chosen V(BE) voltage matters. Some books use 0.60V, some use 0.65V, some may use the Shockley model with N=1, etc. Nov 12, 2023 at 23:39
• TechD, Just as Kuba says, they assumed that Vbe = 600 mV. From there, it's just one KCL equation for the collector node: $\frac{V_C}{6\:\text{k}\Omega}+\frac{V_C}{500\:\text{k}\Omega}+200\cdot\frac{V_C-600\:\text{mV}}{500\:\text{k}\Omega}=\frac{12\:\text{V}}{6\:\text{k}\Omega}+\frac{600\:\text{mV}}{500\:\text{k}\Omega}$. $V_C$ just drops out as 3.94114888628370 from there. Nov 12, 2023 at 23:44

It would help to know what simplified model of the circuit was used in finding those values. It turns out that the transistor was modeled as a current-controlled current source, with a fixed base-emitter voltage of 0.60V in series:

simulate this circuit – Schematic created using CircuitLab

These simulated measurements match those in your textbook, and thus the circuit you have to analyze is the one above, not the one in the textbook. Perhaps the textbook explained what simplified models are you expected to use. There is no single model that fits everyone's application, so if the textbook does not explain it, it becomes a bit useless. Perhaps their goal was to force you to use a circuit simulator and try a few things to figure out what model they used, and then use the same approximation in your analysis?

Anyway, the circuit as shown above can be analyzed using any circuit analysis method you're likely to know. I presume that at this point you should have learned about how to analyze circuits with voltage and current sources in them. The circuit here has only one slight complication that the current source CCCS2 in parallel with R2 is not a fixed current, but 200x the current flowing through R2. But that's not a problem, as you will see when doing the math.

To calculate IB, and thus IC=200*IB, the voltages V1 and V2 can be merged:

simulate this circuit

Now, the key observation for further simplification is that if you have a resistor R2 in parallel with a current source that draws $$\I_{R_2} \cdot \beta\$$, it's just as-if you had just a resistor with the value $$\R_2/(\beta+1)\$$. If this result was not given in the textbook, you should derive it. So, the simplification you'll apply to further simplify this circuit is:

simulate this circuit

And finally, the total current can be easily determined:

simulate this circuit

• How did you get the constant current value for the transistor? Is that something that is listed in the datasheet? Nov 14, 2023 at 16:27
• @TechDude The current is not constant. The current source is a dependent source. It produces a current 200x larger than the current flowing through R2 (specifically, through the R2.nB node). The beta value of 200 was given in your question. Nov 14, 2023 at 20:43
• Misread the value placed on CCC, thanks for your help btw. Nov 15, 2023 at 15:35