# Phone Line Length Math

Quote of the Day

It was a bold man who first ate an oyster.

— Jonathan Swift

We make ONT products that provide telephone service in addition to data and video services. I was asked today what limits the length of a standard POTS phone line from an ONT. Most ONTs today are specified to drive a phone line less than 1000 feet long. As I started to write down my answer, I thought that this was a nice application of simple DC electronics and was worth documenting here.

The 1000 foot limit is primarily driven by the limited voltage available in an ONT to drive current onto the phone line. Most ONTs drive 25 mA ± 3 mA of current (called loop current) on the phone line when the phone is off-hook. This current powers the phone when a person is talking.

Figure 1 shows a simple electrical model of an off-hook phone.

Figure 1: Simple Electrical Model of an Off-Hook Phone Line.

Our power supply voltage must be greater than the voltage our current generates on the phone line. Equation 1 gives us the line voltage generated by the loop current.

 Eq. 1 $\displaystyle {{V}_{Line}}=\left( 2\cdot \left( {{R}_{\text{Protection}}}+{{R}_{\text{Line}}} \right)+{{R}_{\text{Phone}}} \right)\cdot {{I}_{\text{Line}}}+{{V}_{SLIC}}$

where

• VBAT is the voltage available within the ONT to drive loop current.
• RProtection is the resistance of the surge protection circuitry we always included with a phone line.
• RLine is the resistance of 1000 feet of 26 AWG wire.
• RPhone is the resistance of a standard phone.
• VSLIC is the voltage loss in the Subscriber Line Interface Circuit (SLIC). These circuits have some loss them and we need to account for this loss.

Figure 2 shows my calculations in Mathcad.

Figure 2: Line Voltage Calculations in Mathcad.

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