The circuit below is a straight forward way to provide continuous control over the intensity of one or more LEDs using a current regulator circuit based on a crude current mirror.

Linear Regulator LED Intensity Controller

Summary

• Q1 buffers the potentiometer voltage a little.
• Size R2 for maximum current through the LEDs.
• Q3 “mirrors” the current pushed through Q2 despite the voltage drop of the LED string.
• The compliance range of Q3 is the battery voltage less about 1V.
• R3 and R4 are optional, but improve the balance of the mirror by reducing the variability of emitter resistance.
• DS2 is optional, but you should be able to fit as many LEDs as the voltage range allows between 9V and the collector of Q3.
• The lowest 20% or so of potentiometer swing results in insufficient voltage to overcome the two Vbe drops of Q1 and Q2 leaving the upper 80% to control brightness.

Details

Circuit Description
This circuit is simply a voltage to current converter with almost all battery voltage available on the output.

There isn’t a way to reliably control an LED with voltage as it is very much a current device. The attached circuit will take a voltage, set with the pot, buffer it a bit with Q1 and apply that voltage to R2. R2 changes voltage to a current which flows through the left side of the current mirror Q2 and Q3. Q3 will do whatever it takes to draw the same current through the series LEDs. Q3 essentially becomes a linear current regulator, controlled by the voltage made by pot R1, which is exactly what you want to regulate LED brightness.

The current mirror ratio is close to 1:1, but variances in transistors will cause some imbalance. The addition of R3 and R4 help to immunize the current ratio from transistor tolerances and alleviate the need for a matched pair of transistors.

There are simpler ways to create a controllable current regulator, but not by much. This is pretty robust.

R2 Controls Max Current
Note that the max current is governed by R2 which is sized just like you would for an LED in series with a battery. One small difference is Q1 and Q2 both have ~0.7 volt drop so the voltage across R2 is about 9-(2*0.7) or a little over 7V.

Potentiometer Partial Use
The LED is off for the first 20% or so of its setting due to the Vbe of Q1 and Q2. The remaining 80% smoothly controls current through the LED. If this bothers you, place one forward bias diode in series between the bottom of the pot and its ground connection. This will raise the minimum voltage 0.7 V or so and reduce the dead zone a bit. It’s up to you if adding one more component is worth expanding the potentiometer range a tiny bit.

Voltage to Current Converter
This circuit simply converts a voltage appearing on top of R2 to current through the LED, while keeping full voltage available for the LED string. In this example, R1 and Q1 provide the voltage, but any voltage will do.