Transistor to amplify dc current and voltage

[LinkZ]

Hi, can someone give me the formulas to calculate how to amplify a dc current and voltage with transistors? For example i have 2vdc 2mA output from a microcontroller and i need to amplify it to 12Vdc and 10mA (of course having an external dc power supply). Can you please provide me the FINAL and usable formulas to calculate all the resistors for the base, emitter, etc. with some schematic if necessary?

[TimFox]

It looks like you want a switch, not an amplifier.
A switch would turn on at +2V at the input, drawing less than 2 mA from the source.
When on, the switch would apply 12 V to the load from the external power supply, and handle at least 10 mA safely.
Past that, you need to specify a few things such as the common connections between the uC, the external power supply, and the load to determine the circuit topology.
For a simple circuit:
Rbase > (2 V - 0.7 V)/(2 mA)
Transistor beta > (10 mA) / [(1.3 V)/(Rbase)].
No emitter resistor required, unless you are trying to determine the output current.  The above equations are for a voltage-output switch that can handle 10 mA.

[LinkZ]

It looks like you want a switch, not an amplifier.
A switch would turn on at +2V at the input, drawing less than 2 mA from the source.
When on, the switch would apply 12 V to the load from the external power supply, and handle at least 10 mA safely.
Past that, you need to specify a few things such as the common connections between the uC, the external power supply, and the load to determine the circuit topology.
For a simple circuit:
Rbase > (2 V - 0.7 V)/(2 mA)
Transistor beta > (10 mA) / [(1.3 V)/(Rbase)].
No emitter resistor required, unless you are trying to determine the output current.  The above equations are for a voltage-output switch that can handle 10 mA.

Excellent! That's what i mean. I don't know what the common connection between the micro is, but his output(s) drives a 7segment led display. My power supply is 12V and i want to drive a bigger segment made from different leds in series.

[TimFox]

You may need to add a resistor in series with the LED string.
LEDs are operated from a given current, with a maximum spec on the voltage for that current on each diode.
That voltage will depend on the LED color, so you need to check either the data sheet or with a simple circuit and voltmeter.
Some LED assemblies include the resistor (or other current limiter), some don't.
If you apply 12 V to a "naked" LED, something will smoke (probably the LED) due to excess power in the device.

[LinkZ]

Thank you. One last question. What specs should i look to choose the proper transistor? Are generic ones good for this purpose?

[TimFox]

For a slow switch these are the important specs.  A generic transistor such as a 2N3904 or 2N3906 (polarity difference) is probably OK.
1.  Collector voltage rating Vceo > 12 V (easy).
2.  Collector current rating > 10 mA (easy).
3.  Current gain > (Icollector)/(Ibase).  Very easy:  almost all transistors have beta > 20.
4.  Polarity:  NPN or PNP according to circuit.  Are you driving positive current from the collector through the LEDs to ground (PNP) or positive current from the power supply through the LEDs to the collector (NPN)?

[Zero999]

You don't need anything special. A generic transistor will do. I like the  BC337 because it's cheap, has a fairly high gain and is good for 500mA.