Current amplifier circuit for vibration motor

Hello!

I am working on a project that utilizes a vibration motor. This particular motor is rated at 3V and 240mA. I know that this is 200mA more than an atmega328 pin can output without damage, which is why I have built a current amplifier (also known as a common emitter amplifier). The circuit I have created is the same as the circuit found in the following LINK

It works, but I would like to know how to properly choose the value for the resistors used in the circuit. I know that the transistor is amplifying the input current and that the resistor value alters the gain, but what is the math behind this? I would like to know what resistor value to use to get the most out of my vibration motor.

Any help will be greatly appreciated!

More information on the vibration motor that I am using can be found in the following LINK

It looks like your "current amp" is actually a switch.

1k base resistor would turn on the transistor fully.

It is being called a "current amp" because it is allowing a greater amount of current to flow in the collector circuit than is being fed into the base circuit. In this sense it is amplifying the base current.

Weedpharma

Use 150 or 220 ohms for the base resistor to get good saturation in the transistor if driving
240mA (base needs 20 to 30mA).

Don't use a resistor in series with the motor at all, that's just wasting power - if the supply
voltage is too high use PWM on the transistor to set the correct drive.

The reason for using a resistor of value 220 or 150 ohms is to keep the amount of current being pulled from the atmega328 between 22.7mA to 33.3mA. The reason for doing this is because I do not want to pull much more current than that because I can damage the atmega328, correct?

By using a 150 ohm resistor, what will my amplified current be? How do I go about calculating this? I am using a P2N2222A transistor.

The transistor will turn full on (saturate) so the current will be determined by the load, not the transistor.
If the motor is spec'ed for 240mA at 3V, and you have:
3V to motor+
motor- to transistor collector
transistor emitter to Gnd

Then the current will be somewhat under 240mA as there is some voltage loss from the collector to emitter, so the motor will only see 2.3 to 2.5V

If you need the motor to see nearly the full 3V, than you need an N-channel MOSFET instead of NPN transistor.
N-channel MOSFET with really low Rds will develop very little voltage across it when it turns on.
For example this part

will have just .0059 ohm of resistance.
With 240mA, Voltage across the MOSFET will be 0.24A x .0059ohm = .0014V, so your motor will run nearly as fast as if you had connected the battery to it directly.