# Bipolar Transistor Inverter Circuit Analysis

I have been trying to understand this question and I'm just not sure what equation to use for the collector current. I'm not sure if I need to be using an output voltage function of time? All I have got is this: Any input or advice will be much appreciated. Thank you for taking your time to read through this.

• First off, since they are explicitly stating that $V_o=\frac12 V_\text{CC}$ it directly follows by sound reasoning that the BJT isn't in saturation. So anything in the question that addresses saturated states of the BJT can be ignored. Do you agree with me on this? – jonk Aug 23 at 20:42
• If Vo=Vi=2.5V, what's the collector current? What's the base current? There's about 2.5V across Rc, and about 1.85 across Rb (assuming a B-E drop of 0.65V). Once you know Ic and Ib, your equation can be used. – Cristobol Polychronopolis Aug 23 at 20:43

You are so very close to answering your question. You want to know how to calculate the collector current and aren't sure how to develop that value. But let's look at the schematic again: simulate this circuit – Schematic created using CircuitLab

Note that I've now included some information that was included in the question that you may have missed that could have helped you. Note that the voltage across $$\R_\text{C}\$$ is specified!! So you already know that there is $$\2.5\:\text{V}\$$ across $$\R_\text{C}\$$, right? From that alone, you can compute the current that must be present in $$\R_\text{C}\$$. And all of the current in $$\R_\text{C}\$$ must also then flow into the collector of $$\Q_1\$$, right? So that's also your collector current.

So you can compute the collector current! And from that, you can now work out everything else from the equations you already wrote about and understand.

I think you are just seconds away from solving your own question.

• Yes! I understand. I should have realised what the voltage drop across Rc was. Thank you @jonk . I was confused by the fact that Vi was given. – Peter Aug 24 at 10:24

Since you need to find the transistor's beta you should calculate what the collector and base current must be for Vi=Vo=(Vcc/2) to be true.

In order for Vo to be Vcc/2 than Rc must have Vcc/2 volts dropped across it. From ohms law you should get the needed current for that to be true.

Using the parameters given for Vbe you should be able to calculate the base current.

From those two currents you can calculate what Beta must be.