Electrical – Transistor(BJT) Zenner diode voltage regulator circuit

There are many places we can begin looking at this.

We know that the collector current is 2 mA, and that \$V_{CE}\$ is 5V. Since the emitter is at ground, the collector must be at 5V, and so the voltage across \$R_C\$ is therefore 10V: the difference between 5V and 15V. So \$R_C\$ must be \$10V/.002A = 5K\Omega\$.

Next, \$R_2\$ and \$R_1\$ which span a voltage from \$-15V\$ to \$+5V\$ must form a voltage divider such that the top of \$R_1\$ is at 0.7V (\$V_{BE}\$). Hint: the voltage divider spans a range of 20V, and the 0.7V transistor base voltage is 15.7V above the bottom of the voltage divider.

This approach assumes that we can ignore the base current because it is small. Often when analyzing transistor circuits we can do that, but not in this case because \$R_1\$ is such a high resistor. The voltage divider is not "stiff" at all with regard to the resistance in the base circuit of the transistor (which has no emitter resistor at all).

A more exact answer requires that we account for the base current. The transistor is carrying only 2mA of current, and so is nowhere near hard saturation, and so the base current is only 0.02 mA, or 20 micro-Amperes (2mA divided by \$\beta\$).

Determine how much current is flowing through \$R_1\$ from its resistance, and 15.7 voltage. The current flowing through \$R_2\$ is the sum of the transistor base current (.02 mA) and the current through \$R_1\$. Knowing the current through \$R_2\$ and the voltage across it, we can calculate its resistance.

Your circuit is a half decent regulator and would be good for powering most things that need a small current. The problem, as you quite rightly point out, is the 0.7V lost between input and output.

Low drop-out regulators are really quite common-place and some work really well down to a few milli volts between input and output BUT, they are far more complex than what you think and cannot be made from a couple of transistors, a handful of resistors and a zener diode.

However, in pursuant with your wishes, the best idea I can come up with is to construct a small single transistor colpitts oscillator that runs from the incoming power supply and, via two capacitors and two diodes can create a voltage that is bigger than the incoming voltage - this can then feed the zener diode via a resistor ensuring that the BJT is always biased on at the zener voltage even when the supply is quite close to the zener voltage.

Probably the best you could hope for is a volt-drop across the transistor of 0.1 to 0.2V - but that is better than 0.7V but not as good as some commercially available devices from the usual vendors.