Common Cathode

Part of Vacuum Tubes

The common cathode configuration is the standard amplifying connection for vacuum tubes, providing voltage gain with signal inversion.

Why This Matters

The common cathode configuration is to vacuum tubes what the common emitter is to transistors — it is the fundamental amplifying connection used in the vast majority of tube circuits. Input goes to the grid, output comes from the plate, and the cathode is the common point (connected to the AC reference, usually ground through a bypass capacitor). This arrangement provides significant voltage gain, moderate input impedance, and moderate output impedance.

Every radio receiver, telephone amplifier, and audio system built with tubes uses common cathode stages as its primary signal amplification mechanism. Learning this configuration in depth — how to calculate gain, how to choose components, how to troubleshoot — is learning the core skill of tube circuit design.

The name “common cathode” describes the AC signal path: both the input circuit (grid-to-cathode) and the output circuit (plate-to-cathode) share the cathode as their common reference. In a properly bypassed circuit, the cathode sits at AC ground even though it may be at a positive DC voltage relative to the physical ground point.

Circuit Elements and Their Functions

A complete common cathode amplifier stage contains five functional blocks, each with a specific purpose.

The plate load resistor connects between the plate and the positive supply rail. It converts the tube’s variable plate current into a variable plate voltage. When plate current increases (grid goes positive), the voltage drop across this resistor increases and the plate voltage falls. The plate voltage is inverted from the grid voltage: a positive-going grid signal produces a negative-going (falling) plate voltage. This inversion is an inherent property of the common cathode connection.

The coupling capacitor blocks DC while passing AC. The plate sits at a high positive voltage (100-250V) which must not reach the next stage’s grid. The coupling capacitor blocks this DC while allowing the AC audio or RF signal to pass through. The coupling capacitor and the following stage’s grid resistor form a high-pass filter that sets the low-frequency response limit.

The grid resistor provides a DC path from the grid to the bias reference (ground or a bias supply). Without this resistor, electrons accumulating on the grid through the grid-cathode capacitance would slowly charge the grid negative, changing the bias. The grid resistor bleeds away this charge. Its value must be high enough not to significantly load the signal source, but within limits set by the tube’s maximum grid resistance rating (typically 1-10 megohms depending on tube type).

The cathode resistor generates self-bias. Plate current flowing through this resistor makes the cathode positive relative to ground. Since the grid connects to ground through the grid resistor, the grid is negative relative to the cathode — the correct polarity for biasing a tube. The cathode resistor value equals the required bias voltage divided by the operating plate current.

The cathode bypass capacitor short-circuits the cathode resistor for AC signals. Without it, AC signal current through the tube also flows through the cathode resistor, generating a negative feedback voltage that opposes the input signal and drastically reduces gain. With the bypass capacitor, the cathode stays at a constant AC voltage (ground) even while the DC voltage adjusts with operating conditions. Choose the bypass capacitor so its impedance at the lowest frequency of interest is much less than the cathode resistor value.

Gain Calculation

The voltage gain of a common cathode stage is given by:

Av = −μ × Reff / (Rp + Reff)

where μ is the amplification factor, Rp is the plate resistance, and Reff is the effective AC load (the plate resistor in parallel with the following stage’s input impedance). The negative sign indicates signal inversion.

For a 12AX7 (μ = 100, Rp = 80kΩ) with a 100kΩ plate resistor driving a 1MΩ grid resistor:

Reff = (100k × 1M) / (100k + 1M) = 90.9 kΩ

Av = −100 × 90.9k / (80k + 90.9k) = −100 × 90.9k / 170.9k = −53.2

This stage amplifies voltage by a factor of about 53, with signal inversion. A 1mV input becomes a 53mV output, inverted in phase.

If the cathode bypass capacitor is removed or if its value is too small to fully bypass the cathode resistor, the gain is reduced by negative feedback:

Av (unbypassed) = −μ × Reff / (Rp + Reff + (μ+1) × Rk)

With a 1.5kΩ cathode resistor unbypassed:

Av = −100 × 90.9k / (80k + 90.9k + 101 × 1.5k) = −100 × 90.9k / 322.4k = −28.2

Removing the bypass capacitor roughly halves the gain in this case but significantly improves linearity and reduces distortion — sometimes a useful trade-off in the final stage before overload.

Input and Output Impedance

The input impedance of a common cathode stage is essentially the value of the grid resistor (for audio and low RF frequencies). At higher frequencies, the grid-to-cathode capacitance of the tube shunts the grid resistor, reducing input impedance. For most audio applications, input impedance is simply the grid resistor value.

The output impedance of a common cathode stage is the parallel combination of the plate resistor and the tube’s plate resistance Rp. For a 12AX7 with an 80kΩ plate resistance and a 100kΩ plate resistor:

Zout = (80k × 100k) / (80k + 100k) = 44.4 kΩ

This relatively high output impedance limits the ability to drive low-impedance loads. Connecting a 600Ω telephone line directly to the plate of a common cathode stage would reduce gain by 99%. A cathode follower output stage or an output transformer is needed to drive low-impedance loads.

Design Procedure

To design a common cathode stage:

1. Select a tube appropriate for the gain needed. High-mu tubes (12AX7, ECC83) give more gain. Medium-mu types (12AU7, 6SN7) give less gain with lower distortion.

2. Choose a supply voltage — typically 150 to 300V for small-signal stages.

3. Select a plate current from the tube’s characteristic curves. For 12AX7: 0.5 to 2mA is typical. Higher current means more headroom before clipping but more heat and a shorter tube life.

4. Choose the plate resistor: supply voltage minus desired plate voltage divided by plate current. For a 200V supply, 100V plate voltage, and 1mA: Rplate = 100V / 1mA = 100kΩ.

5. Calculate the cathode resistor: bias voltage divided by plate current. For −1.5V bias: Rk = 1.5V / 1mA = 1.5kΩ.

6. Calculate the cathode bypass capacitor for the required low-frequency response. For −3dB at 20Hz: C = 1/(2π × 20 × Rk) = 1/(2π × 20 × 1500) = 5.3µF. Use 10µF.

7. Choose the plate coupling capacitor for the required low-frequency response. For −3dB at 20Hz with a 1MΩ following grid resistor: C = 1/(2π × 20 × 1M) = 8nF. Use 22nF for margin.

8. Set the grid resistor: typically 100kΩ to 1MΩ, chosen to be much larger than the source impedance.

Verify the design by checking the actual operating point on the tube’s characteristic curves to confirm the Q-point is where expected and that the supply voltage is adequate.