You can easily find transistorized, zener diode based regulator circuits. Mostly for positive voltages, but it will be easy to create one for negative voltages using the same techniques.
I suggest you proceed in steps:
- Create an unregulated input voltage for your regulator. You'll need more than +- 30 V as some voltaeg will be dropped within the regulator. You've done that part quite o.k. in your schematic diagram, but the filter capacitors are a bit on the small side. Look up which filter capacitor size is required for 4 A output current.
- Create the positive adjustable regulator part. If you want to, start with the regulator only (without current limiter), then add the current limiting circuit later. Or use a circuit with current limit from the start.
- Create the negative regulator part. This will involve mainly replacing NPN transistors by PNP transistors (and vice versa if required) and inverting polarities of polarized components (diodes, electrolytic capacitors...)
- Calculate the required heat sink: the regulator will dissipate approx. 30 V × 4 A = 130 W for each polarity when set to a low output voltage! This will require a BIG heatsink - and powerful transistors. One for each polarity.
- Develop the trigger circuit to turn the output voltage on (item #3 from the requirements list) and the LED indicator.
- Build the circuit and a project box to house it.
If you have doubts, present your design steps and ask your questions here in this thread.
Note that it is our policy not to give complete solutions to homework. Rather we will guide you in finding your own solution by pointing out errors and hinting you into the right direction. This may not be what you expect from this forum, but we sincerely think that this method offers you more insight.
