The Long-Tailed Pair
Two matched tubes sharing a common tail current — the foundation of balanced amplification
A differential pair (or long-tailed pair, LTP) consists of two triodes whose cathodes are tied together through a shared tail impedance. When a signal is applied between the two grids (differential mode), one tube conducts more while the other conducts less — the shared tail current I_tail is steered between the two halves.
The differential gain is half that of a single common-cathode stage because each tube only sees half the input swing. But the key advantage is common-mode rejection: any signal appearing equally on both grids (hum, power supply noise) produces equal currents that cancel in the plate circuit.
The CMRR depends critically on the tail impedance. A simple resistor gives modest rejection (~30-40dB). A pentode CCS tail can achieve 60-80dB, and a cascode CCS can exceed 90dB. This is why high-quality differential stages always use active tail current sources.
Differential Pair Design
Explore how tail impedance affects CMRR and gain
Long-Tailed Pair Topology
Phase Splitter Topologies Compared
Every push-pull amp needs one — which is best for your design?
| Topology | Gain | Balance | Z_out (H/L) | Notes |
|---|---|---|---|---|
| Cathodyne split-load | < 1 | ± 0.5dB | rp/μ / 1/gm | Simplest, but unequal output impedances |
| Long-tailed pair diff pair | μ×RL/(2rp+RL) | ± 0.1dB | RL / RL | Best balance; standard in hi-fi amps |
| Paraphase self-balancing | μ×RL/(rp+RL) | ± 1dB | RL / RL | Feedback derived; used in Fender amps |
| Floating paraphase Williamson | μ×RL/(rp+RL) | ± 0.2dB | RL / RL | Cross-coupled feedback; very good balance |
| Schmitt cathode-coupled | ≈ μ/2 | ± 0.5dB | RL / RL | Used in Mullard 5-20; excellent PSRR |
Designing a Differential Stage
Step-by-step guide with real component values
1. Choose the Tail Current
Start with the desired output swing. For a push-pull driver, you typically need 50-80V peak-to-peak per phase. With 100kΩ plate loads, this means I_tail ≈ 1-2mA. The 12AT7 is ideal here: higher gm than 12AX7 with enough plate dissipation for reliable operation.
2. Tail Impedance Selection
For CMRR > 60dB, you need R_tail > 10 × R_L / (A_diff). With a simple resistor, this means a very large value (470kΩ+) requiring a high B+ voltage. The practical solution is an active current source: a pentode (EF86, 6SJ7) or a MOSFET (DN2540) biased at the desired tail current.
3. Tube Matching
DC balance depends on matched tubes. Measure V_g for equal I_p at the operating point. A 5% gm mismatch causes ~1dB balance error. For critical applications, add a 500Ω trim pot between cathodes (Williamson technique) to null the DC offset. Always use a dual triode (12AT7, 6SN7) for best thermal tracking.
4. Classic Designs
Testez vos connaissances
In a long-tailed pair, what happens to the tail current when a differential signal is applied?
References
- Paul Horowitz & Winfield Hill, The Art of Electronics, 3rd ed., Cambridge University Press, 2015. ISBN 978-0521809269Canonical reference for analog design — covers tubes in Ch. 2.4 & Ch. 3.
- Morgan Jones, Valve Amplifiers, 4th ed., Newnes, 2012. ISBN 978-0080966403Modern engineering treatment of tube audio design.