I am trying to design an oscillator which ranges from a very low value (near 0) to 2kHz. I found an useful lead which I attach below. However, I am not familiar enough with this circuit so I am not sure about how to calculate and modify the range of this circuit. I would appreciate any leads.

Reference: http://www.learnabout-electronics.org/Oscillators/osc42.php

 

The link you supplied does explain the operation of this circuit very well. It even gives you some formulas for the operation frequency.

Best to actually build this circuit and try it. Or you could simulate it in LTspice or similar software. My only comment is that VR1 can be adjusted to zero. The operation will become unpredictable with very low values of VR1. Better to insert a 10k ohm resistor in series so that the total resistance can vary from 10k up to 110k. This should give you a 10:1 frequency range. Change the value of C1 for other frequency ranges.

 

The link you supplied does explain the operation of this circuit very well. It even gives you some formulas for the operation frequency.

Best to actually build this circuit and try it. Or you could simulate it in LTspice or similar software. My only comment is that VR1 can be adjusted to zero. The operation will become unpredictable with very low values of VR1. Better to insert a 10k ohm resistor in series so that the total resistance can vary from 10k up to 110k. This should give you a 10:1 frequency range. Change the value of C1 for other frequency ranges.

Let's say that I am going to use a 33 nF capacitor, and a 100k Trimmer with a 10k resistor in series. According to the formula, I should get as the lower limit about 200 Hz and the higher limit about 2.1 kHz. I think it sounds reasonable, isn't it?

 

How low is "near zero"?

 

How low is "near zero"?

To be more specific I need a very low frequency, but not an exact one, as long as the circuit can provide it. From 1 Hz on, it is okay. Anyways, I would feel good with any lower frequency below 100 Hz.

 

Here's the LTspice simulation of the circuit, modified to have a range of about 5Hz to 2kHz.
The plot shows the output of two superimposed simulations for the two pot positions of 0% (yellow trace) and 100% (green trace).
C2 should be a ceramic or film type capacitor for best stability.
The range with the actual circuit likely will be slightly different, but you should be able to tweak it to get what you want.