Cathode Follower

Part of Vacuum Tubes

The cathode follower is a unity-gain buffer stage that transforms high-impedance signals into low-impedance outputs capable of driving cables, loads, and subsequent stages without signal loss.

Why This Matters

Many signal sources in communication systems have high output impedance — the grid circuit of a previous amplifier stage, a detector output, a crystal microphone. Connecting these high-impedance sources directly to a low-impedance load (a long cable, a speaker, another amplifier’s input stage) results in severe signal loss because of the impedance mismatch. The cathode follower solves this problem elegantly.

The cathode follower (called an emitter follower in transistor circuits) takes a signal at its grid and produces nearly the same signal — shifted slightly lower in voltage — at its cathode. The voltage gain is just below 1.0, so there is no amplification. What changes dramatically is the impedance: the high input impedance of the grid is transformed to a low output impedance at the cathode, typically 100 to 1000 ohms. This allows the stage to drive cables and loads without signal loss.

In practical community communication equipment, cathode followers appear wherever you need to drive a long line, buffer a high-impedance source, or connect stages with widely different impedances. Understanding when and how to use the cathode follower simplifies amplifier design and solves a common class of signal level and frequency response problems.

Circuit Topology

The cathode follower differs from the common cathode amplifier in one key way: the plate connects directly to the positive supply (no plate resistor), and the output is taken from the cathode rather than the plate. The cathode resistor becomes the load resistor from which the output signal is extracted.

The signal path is: input signal drives the grid, grid voltage variation controls plate current, plate current variation produces a voltage across the cathode resistor, and this voltage (at the cathode) is the output. Since the grid voltage must stay approximately 1-3V above the cathode (the grid bias), as the input grid voltage rises, the cathode voltage rises to follow it. Hence the name “cathode follower.”

The gain of a cathode follower is:

Av = μ × Rk / ((μ+1) × Rk + Rp)

For large values of Rk and for tubes with moderate to high mu, this simplifies to approximately:

Av ≈ μ / (μ + 1)

For a tube with mu = 20, the gain is 20/21 = 0.952. For mu = 100, gain is 100/101 = 0.99. High-mu tubes give gain very close to unity. The gain is always less than 1, and it is always positive (non-inverting) — the output signal is in phase with the input.

Output Impedance

The cathode follower’s most useful property is its low output impedance. The output impedance looking into the cathode is approximately:

Zout ≈ Rp / (μ + 1)

For a 12AX7 (Rp = 80 kilohms, mu = 100), the output impedance is 80,000 / 101 ≈ 790 ohms. This is much lower than the tube’s plate resistance, and much lower than the output impedance of a common cathode stage with the same tube (which would be the parallel combination of the plate resistor and Rp — typically 50-100 kilohms).

The low output impedance means the cathode follower can drive capacitive loads (long cables) without severe high-frequency rolloff. A 100-meter cable has approximately 5 nanofarads of capacitance. With a 100-ohm source impedance, the -3dB frequency is 1/(2π × 100 × 5nF) = 318 kHz — well beyond the audio range. The same cable driven from a 50-kilohm source would roll off above 637 Hz, making it nearly useless for voice communication.

Practical Applications

Long-line driving is the most common application. When you need to send audio from one building to another — from a microphone amplifier to the transmitter room, from a telephone exchange to a remote repeater — the cathode follower buffers the signal for cable transmission. Connect the cathode follower’s output to the cable through a small series resistor (100-200 ohms) to prevent resonance between the cable capacitance and the inductive elements of the circuit.

Volume control buffering solves a common problem. A potentiometer used as a volume control has an output impedance that varies with the setting — it is highest at the middle of the range and zero at the extremes. This variation interacts with the input capacitance of the following stage, causing the high-frequency response to change as the volume is adjusted. A cathode follower after the volume control eliminates this effect by presenting a constant, low impedance to the following stage regardless of the potentiometer setting.

Plate-to-grid coupling in direct-coupled amplifiers sometimes requires a cathode follower as an intermediate stage. The plate of one tube sits at a high positive voltage (100-200V); the grid of the next tube must sit at a lower voltage with appropriate bias. A cathode follower between stages steps the voltage down while buffering the signal, avoiding the need for large coupling capacitors that would limit low-frequency response.

Driving output transformers: a cathode follower can drive the primary of a small output or matching transformer because its low output impedance is well-suited to the transformer’s reflected load impedance. This is useful in telephone hybrid circuits and line-matching networks.

Design Example and Component Selection

A cathode follower using a triode section of a 12AU7 (mu = 17, Rp = 7700 ohms) suitable for driving a telephone line:

Plate to B+ supply (200V) directly. Cathode through a 10 kilohm resistor to ground. Input at the grid through a 0.1µF coupling capacitor. Grid resistor 470 kilohms to ground. Output from cathode through a 0.1µF coupling capacitor to the line.

At idle, plate current through the 10 kilohm cathode resistor establishes the operating point. With grid-to-cathode bias of approximately −1.5V (the grid is at ground, cathode must be at +1.5V), the cathode current is 1.5V / 10k = 0.15mA. The plate voltage is then 200V − (0.15mA × 0V, plate connects directly to B+, so plate voltage ≈ 200V minus the supply wiring drop) ≈ 199V. The cathode voltage is 1.5V, so the plate-to-cathode voltage is about 197V.

Output impedance: Rp / (mu + 1) = 7700 / 18 = 428 ohms — suitable for driving telephone line impedances.

Gain: 17 / 18 = 0.944 — essentially unity.

This circuit handles audio frequencies without any compensating components and drives cables up to several hundred meters without significant signal degradation.