A telephone line repeater should have a gain equal to the loss of the line section ahead of it, so the voice returns to its starting level and no more, because extra gain can feed back around the two-way loop and make the line oscillate. A voice cannot be re-formed the way a telegraph pulse can, so each repeater also amplifies the noise: for n equal sections the signal-to-noise ratio falls by 10 times log10 of n, which is 7.8 dB for six. A transistor stage with a 1,000 ohm collector and a 100 ohm emitter resistor gives a gain near 10, or 20 dB.
Part of Telecommunications
Amplifying a voice along a long telephone line, the arithmetic of accumulated loss and noise, and why this differs from amplifying inside a receiver.
A Repeater Restores A Level; It Is Not A Volume Control
The wire of a section loses signal level. A repeater placed at the end of the section lifts it back. In decibels the loss and the gain simply subtract, so the repeater is correctly set when:
gain (dB) = section loss (dB)
and the signal then continues at the level it started with. Anything more is wasted at best.
The carrier article’s own design gives the sizes. It specifies a single-transistor repeater with a voltage gain of 10 to 50, notes that a gain of 10 to 20 is typically sufficient for one relay hop, and spaces repeaters 20 to 30 km apart.
- 20 × log₁₀(10) = 20 dB
- 20 × log₁₀(20) = 26 dB
- 20 × log₁₀(50) = 34 dB
If that design is self-consistent, its sections lose roughly 20 to 26 dB over 20 to 30 km, which implies something like 0.7 to 1.3 dB per km (20 / 30 to 26 / 20). This is a consistency check on the carrier’s numbers, not a measured cable property. The corpus gives no attenuation figure in dB per km, so treat the spacing as a starting point and measure your own line with a test tone (Signal Processing).
Two Directions On One Pair Make A Loop That Can Sing
A telephone pair carries both directions of talk. A repeater therefore needs two amplifiers, one for each direction, joined to the two-wire line through a balancing arrangement (the same idea as the anti-sidetone bridge in Anti-Sidetone Network). If the balance is imperfect some of each amplifier’s output leaks into the other’s input, and the signal can circulate: amplifier A feeds B, B leaks back into A.
The condition for trouble is that the round-trip gain reaches or passes zero dB at some frequency while the phase is right. The same condition is behind Feedback Principle’s warning that phase shift can turn feedback positive and make an amplifier oscillate. For an illustration, assume each amplifier gives 20 dB. The pair gives 40 dB, and the leak path through the line and balance network must lose more than 40 dB for stability. If it loses 30 dB, the loop gain is +10 dB and the line howls (in telephone terms, it “sings”). Real designs keep a margin, so the practical gain per repeater is set by how good the balance is, not by what the transistor can do.
Noise Adds At Every Repeater Because A Voice Cannot Be Re-Formed
A telegraph relay in Repeater Stations closes a fresh local circuit, so it throws away the noise and sends a clean on-off pulse. A voice is a continuous waveform; an amplifier has no way to tell voice from noise and amplifies both. Assume n equal sections, each restoring the signal to its starting level S and each adding noise power N at its input. After n sections the signal is still S but the noise has accumulated to n × N. The signal-to-noise ratio falls by:
10 × log₁₀(n) dB
- n = 2 sections: 3.0 dB
- n = 6 sections: 7.8 dB
- n = 10 sections: 10 dB
- n = 100 sections: 20 dB
This assumes equal sections, independent noise and no filtering between them. It is why long analogue chains have to be built to a noise budget and why Data Communication points toward digital regeneration for long runs.
A Repeater Is Not A Receiver Stage
The circuits are the same ones in Amplifier Circuits and Cascading Stages, but the problem is different:
- Bandwidth. A receiver stage amplifies one narrow, selected signal. A repeater must amplify 300 to 3,400 Hz evenly, with a gain that does not vary much across the band.
- Direction. A receiver works one way. A repeater serves two directions on one pair and must not sing.
- Chaining. A receiver has a few stages. A line may have many repeaters in series, so small errors in gain, distortion and noise accumulate.
- Location and upkeep. A repeater sits in the field. The carrier article powers it from a local battery recharged by solar, wind or steam-driven generator.
- Impedance. A line interface is standardly 600 Ω, so transformers are used. A transformer with turns ratio n:1 changes impedance by n², so 10:1 brings 60,000 Ω down to 600 Ω (Impedance Matching).
Worked Example: A 120 km Route
Take 120 km with repeaters every 20 km: 6 sections. Suppose the self-consistent carrier design gives a section loss of 20 dB, and each repeater has gain 10 (20 dB).
- Level: each section loses 20 dB, each repeater restores 20 dB, so the signal arrives at its starting level.
- Noise: 10 × log₁₀(6) = 7.8 dB worse signal-to-noise than a single section.
- Gain from the circuit: with collector resistor 1,000 Ω and emitter resistor 100 Ω, the carrier’s rule gives a gain of about 1,000 / 100 = 10, which is 20 dB.
The carrier’s gain rule is a rough one. Common Emitter shows the real gain depends on the bias current: with a 4.7 kΩ collector resistor, raising the bias from 0.1 mA to 2 mA raises gain from 18 to 362. A repeater built on the rule of thumb must therefore be adjusted against a test tone, not left as calculated.
Negative Feedback Fixes The Gain In Place
Feedback Principle shows that an amplifier with a gain of 100 and a feedback fraction of 0.09 falls to a gain of 100 / (1 + 100 × 0.09) = 10, and gain drift and distortion fall by the same factor. A repeater with feedback has its gain set by resistors, not by the transistor or tube, which suits a chain where every repeater must match its section.
What You Need
- Per direction: a transistor or tube stage, coupling capacitors, and an input and output transformer for the 600 Ω line
- A balance network and a way to adjust it against the real line
- A battery and its charging source at the site
- A test tone and a level meter, since adjustment is by measurement
Common Mistakes
- Setting maximum gain. The line sings, and every other repeater in the chain suffers.
- Ignoring the noise sum. Six good sections can still be too noisy as a chain.
- Skipping the balance network. The two amplifiers then talk to each other.
- Using receiver stages unchanged. A tuned, narrow stage cuts the voice band.
Safety
Supply voltage at the repeater
A tube repeater runs from rectified DC commonly between 150 and 600 V (see Rectification), and a transistor repeater on a 9 V battery is not a shock hazard. Both sit on a line that can carry thousands of volts from a nearby lightning strike (Lightning Protection). Fit a protector and an earth, and discharge tube supplies before servicing.
What’s Next
- Learn next: Filtering, keeping noise out of the band
- Combine with: Reliability Design for the cost of putting many repeaters in series