Why diameter of telephone cable is exactly 0.44mm and 0.63mm
The characteristic impedance of a telephone cable is very important to get right when it comes to minimizing side-tone (that's the handset microphone producing an amplified sound in your ear). This is achieved by a side-tone cancellation circuit: -



When the line impedance matches Rw in series with Cw there is no microphone signal transferred to the earpiece connected to winding A. The microphone feeds the centre tap between S and P windings.

So, for this to work effectively, the impedance of the telephone line has to "look like" Rw in series with Cw across the range of useful speech frequencies. Here's what a cable impedance might typically look like: -



As you should be able to see, the nominal impedance at 1 kHz is about 600 ohms in magnitude but is in fact similar to the complex impedance mentioned above.

The characteristic impedance of any cable at low frequencies is \$\sqrt{\dfrac{R}{j\omega C}}\$ where R is the series resistance of the loop per metre and C is the parallel capacitance per metre. Any change in conductor spacing or diameter means the capacitance per metre will change and the approximation of Rw in series with Cw won't be as ideal.

Capacitance for twisted pair for example: -



\$C_{twistedpair}\left ( \frac{pF}{inch} \right )=\left ( \frac{.7065}{\ln \left ( \frac{2s}{d} \right )} \right )\cdot \epsilon_r\$