Electronic – BJT Biasing with negative voltage

bjtcircuit analysistransistors

BJT biasing schematic

I got this question as a school assignment (1st year electrical engineering). I have to calculate the 3 unknown resistor values. The values which were given are in the schematic. Further \$\beta = 100\$ and the transistor is an NPN BC547B. The problem for me is the negative \$V_{EE}\$ voltage and the \$V_x = 0\$V. I don't really know where to start (already stuck for an hour). Can you give me some hints or an example so I know how to go further? I have already looked at a lot of BJT biasing examples but can't find one (I think) which really fits my problem.

Best Answer

Negative voltages are nothing to be afraid of. They work exactly like positive voltages, just with a minus sign. I'll walk you through the first part, which is to figure out \$R_1\$.

You know the voltage across \$R_1\$ is 15V. If you find the current through \$R_1\$, you can calculate the resistance with Ohm's Law. The current through \$R_1\$ is equal to the current through \$R_2\$ plus the base current. Ohm's Law gives you the current through \$R_2\$:

$$I_{R2} = \frac{0\ \mathrm V - -15\ \mathrm V}{5\ \mathrm{k\Omega}} = 3\ \mathrm{mA}$$

You're given the collector current and \$\beta\$, so you can easily calculate the base current:

$$I_B = \frac {I_C} {\beta} = \frac {1\ \mathrm{mA}} {100} = 0.01\ \mathrm{mA}$$

So the current through \$R_1\$ is:

$$I_{R1} = I_{R2} + I_B = 3\ \mathrm{mA} + 0.01\ \mathrm{mA} = 3.01\ \mathrm{mA}$$

This is almost (but not quite!) equal to \$I_{R2}\$ by itself. In real life, you would probably ignore \$I_B\$ unless \$\beta\$ were lower, but this is homework, so let's do it the hard way. :-)

Now you can calculate \$R_1\$:

$$R_1 = \frac {15\ \mathrm V - 0\ \mathrm V} {3.01\ \mathrm {mA}} = 4.98\ \mathrm{k\Omega}$$

I'll let you handle \$R_C\$ (trivial) and \$R_E\$ (harder) on your own. Please be sure to post the work you've done if you have any follow-up questions.