6/32
← Guides
Circuit Design · 22 min read

Amplifier Topologies

Four fundamental building blocks of tube amplification. Interactive calculators, SVG schematics, and every formula you need — with live results as you adjust parameters.

Select a tube — parameters auto-fill all calculators
12AX7Rich warm midrange. The gold standard.
μ100
rp62.5kΩ
Gm1.6 mA/V
Pd max1.2W
Va max300V
Heater12.6V / 0.15A
ModelKoren SPICE
01 — Voltage Amplifier

Common Cathode

The workhorse of tube electronics. Maximum voltage gain, inverted output, the default topology.

B+RaVoutVinRgRkCkCOMMON CATHODEVoltage Amplifier

The common cathode amplifier is the tube equivalent of a common-emitter transistor stage. Signal enters the grid, the cathode is grounded (AC), and the amplified, phase-inverted signal appears at the plate.

The plate resistor Ra converts the tube's varying current into a voltage swing. Higher Ra = more gain, but less headroom. The cathode resistor Rk sets the DC bias.

With Ck (bypass capacitor), full gain is achieved. Without it, local negative feedback through Rk reduces gain but dramatically improves linearity — a trade-off used constantly in hi-fi design.

PhaseInverted
GainHigh
ZoutHigh
Live Calculator — Common Cathode
Tube12AX7
Pd max1.2W
Heater12.6V
μ100
rp63kΩ
B+250V
Ra100kΩ
Rk1.5kΩ
Voltage Gain61.5(35.8 dB)
Gm1.60mA/V
Output Z38.5kΩ
Quiescent Ia2.46mA
Plate Voltage0V
Cathode Bias3.7V
Plate Dissipation0.00W (0%)
Av = −μ × Ra / (rp + Ra)
Av = −μ × Ra / (rp + Ra + (μ+1)Rk)
Bypassed cathode
Unbypassed cathode
02 — Buffer / Driver

Cathode Follower

Unity gain, very low output impedance, non-inverting. The impedance transformer.

B+VinRgVoutRkCATHODE FOLLOWERUnity Gain Buffer

The cathode follower takes the output from the cathode instead of the plate. The plate connects directly to B+. The result: gain slightly less than unity, but with extremely low output impedance — approximately 1/Gm.

This is 100% negative feedback: the entire output signal is fed back to the input. The tube cancels its own distortion, producing an exceptionally linear transfer function.

Use it between a high-impedance source and a low-impedance load: driving long cables, tone stacks, headphones, or the grid of a power tube that draws current.

PhaseNon-inverted
Gain≈ 1
ZoutVery low
Live Calculator — Cathode Follower
Tube12AX7
Pd max1.2W
μ100
rp63kΩ
B+250V
Rk68kΩ
Voltage Gain0.981(-0.2 dB)
Gm1.60mA/V
Output Z (tube)619Ω
Output Z (eff.)613Ω ∥ Rk
Av = μ·Rk / (rp + (μ+1)·Rk)
Zout = rp/(μ+1) ∥ Rk ≈ 1/Gm
03 — Push-Pull Gain

SRPP

Two triodes stacked: one amplifies, the other regulates. Gain + low impedance in one stage.

B+Rg2Rk2VoutVinRg1Rk1CkSRPPShunt Regulated Push-Pull

SRPP (Shunt Regulated Push-Pull) stacks two triodes vertically. The lower triode (V1) is a common cathode gain stage. The upper triode (V2) acts as a dynamic load — part constant current source, part push-pull partner.

On positive signal swings, V1 conducts more and V2 less. On negative swings, the opposite. The result: push-pull operation from a single-ended input, with partial cancellation of even harmonics.

The magic happens at a specific load impedance (RL ≈ 2 × rp). At this value, distortion cancellation is maximized. Too light or too heavy a load, and the SRPP degenerates into an ordinary common cathode with resistive load.

PhaseInverted
GainMedium-High
ZoutLow
Live Calculator — SRPP
Tube12AX7 × 2
Pd max1.2W / section
μ100
rp63kΩ
B+250V
Rk262kΩ
Voltage Gain33.2(30.4 dB)
Output Z1.2kΩ
Optimal Load125.0kΩ
Gm1.60mA/V
Av ≈ μ × Rk2 / (2rp + Rk2)   |   Zout ≈ 2rp / (μ+1)   |   RL(opt) ≈ 2 × rp
Popular in: Headphone amplifiers (the impedance matches typical 32–600Ω cans), DAC output stages, phono preamps. The Bottlehead Crack is a famous SRPP headphone amp. Works best with low-rp tubes (6922, 6DJ8, 5687) where the optimal load falls in the headphone range.
04 — Active Load

Mu Follower

A constant current source as plate load. Maximum gain approaches μ itself.

B+Rg2CgVoutVinRg1RkCkV2: CCSV1: GainMU FOLLOWERActive Load Amplifier

The mu follower replaces the plate resistor with an active constant current source — the upper triode (V2) with its grid held at a fixed bias. This CCS has an effective impedance of rp × (μ+1), which for a 12AX7 is 6.3 MΩ — impossible to achieve with a real resistor.

Because gain = μ × Ra / (rp + Ra), and Ra is now millions of ohms, the gain approaches the tube's theoretical maximum: μ itself. A 12AX7 mu follower delivers gain ≈ 99 (vs ~60 with a 100kΩ resistor).

The output is taken from the cathode of V2 — a cathode follower output with very low impedance. So you get near-maximum gain AND low output impedance. The best of both worlds.

PhaseInverted
Gain≈ μ
ZoutVery low
Live Calculator — Mu Follower
Tube12AX7 × 2
Pd max1.2W / section
μ100
rp63kΩ
B+300V
Rk1.0kΩ
Voltage Gain99.0(39.9 dB)
Output Z619Ω
CCS impedance6.3MΩ
Gm1.60mA/V
Av ≈ μ²/(μ+1) ≈ μ
Ra(eff) = rp × (μ+1)
Popular in: Audio Note line stages, Shindo preamps, many boutique phono stages. The mu follower is the topology of choice when you want maximum resolution and the most transparent gain from a single tube type. With a 6SN7 (μ=20): gain ≈ 19 with Zout ≈ 367Ω — extraordinary performance from a medium-mu tube.
05 — Head to Head

Topology Comparison

Side-by-side characteristics of all four topologies.

ParameterCommon CathodeCathode FollowerSRPPMu Follower
GainHigh (−μ·Ra/(rp+Ra))< 1 (unity)Medium-HighVery High (≈ μ)
PhaseInverted (180°)Non-inverted (0°)Inverted (180°)Inverted (180°)
Output ZHigh (Ra ∥ rp)Very Low (rp/(μ+1))Low (2rp/(μ+1))Very Low (rp/(μ+1))
Input ZHigh (≈ Rg)Very High (boot.)High (≈ Rg)High (≈ Rg)
LinearityGood (with NFB)ExcellentVery GoodExcellent
Tubes needed1 (½ dual)1 (½ dual)2 (1 dual)2 (1 dual)
Best forVoltage ampBuffer / driverHeadphone ampHigh-gain line
Sonic characterDirect, articulateTransparent, openFast, dynamicLush, detailed

Choosing wisely: The common cathode is your default voltage amplifier. Add a cathode follower when you need to drive a difficult load. Use SRPP when you need gain + low impedance in one envelope (headphone amps). Choose the mu follower when transparency and maximum resolution are the priority — it's the most refined topology, favored by the world's best line stage designers.

06 — Complete Reference

Every Formula You Need

Organized by topology and application. Bookmark this page.

Fundamental
Barkhausen Equationμ = Gm × rp
The three parameters are interdependent
TransconductanceGm = μ / rp = ΔIa / ΔVg
Grid voltage → plate current sensitivity (mA/V)
Amplification Factorμ = ΔVa / ΔVg (at constant Ia)
Intrinsic gain ceiling of the tube
Plate Resistancerp = ΔVa / ΔIa (at constant Vg)
Internal impedance — the tube's output resistance
Common Cathode
Gain (bypassed Ck)Av = −μ × Ra / (rp + Ra)
Maximum gain, inverted output
Gain (unbypassed)Av = −μ × Ra / (rp + Ra + (μ+1)×Rk)
Reduced gain, improved linearity
Output ImpedanceZout = Ra ∥ rp
Parallel combination
Input CapacitanceCin = Cgk + Cgp × (1 + |Av|)
Miller effect — dominates HF rolloff
Cathode BiasRk = Vbias / Ia
Self-regulating — current rise increases bias
Bypass CapCk > 1 / (2π × f₋₃dB × Rk)
Full gain above this frequency
Cathode Follower
GainAv = μ × Rk / (rp + (μ+1) × Rk)
Always < 1, approaches μ/(μ+1)
Output ImpedanceZout = rp / (μ+1) ∥ Rk ≈ 1/Gm
Very low — the whole point
Input ImpedanceZin = Rg / (1 − Av) ≈ Rg × (μ+1)
Bootstrapped — extremely high
SRPP
GainAv ≈ μ × Rk2 / (2rp + Rk2)
For matched triodes
Output ImpedanceZout ≈ 2rp / (μ+1)
Low, but not as low as CF
Optimal LoadRL(opt) ≈ 2 × rp
Best distortion cancellation at this load
Mu Follower
GainAv ≈ μ × rp(μ+1) / (rp + rp(μ+1)) ≈ μ
Near maximum μ — the active load wins
CCS ImpedanceRa(eff) = rp × (μ+1)
Upper tube is a constant current source
Output ImpedanceZout ≈ rp / (μ+1)
Taken from cathode of upper tube
Power & Thermal
Plate DissipationPd = Va × Ia
Must not exceed tube rating
Max Power (SE)Pout = (Vswing × Iswing) / 8
Theoretical Class A max
70% RulePd(idle) ≤ 0.7 × Pd(max)
Safe starting point for bias
Frequency Response
LF −3dB (coupling)fL = 1 / (2π × Cc × Rload)
Coupling cap with next stage grid leak
HF −3dB (Miller)fH = 1 / (2π × Rsource × Cin)
Cin = Cgk + Cgp(1+|Av|)
BandwidthBW = fH − fL
Gain-bandwidth product is ~constant
07 — Practical Wisdom

Design Rules of Thumb

Shortcuts that experienced designers carry in their heads.

Ra = 2–3 × rp
Good compromise between gain and headroom for common cathode
Rk ≈ Vbias / Ia
Start with datasheet typical Ia, calculate Rk from there
Ck > 25μF for audio
Ensures full bass at 20Hz with typical Rk values
Cc = 0.1μF default
Safe starting point for coupling — check fL with actual Rg
Rg ≤ max rated
Exceeding max grid resistance causes bias drift and instability
Pd < 70% max
The thermal safety margin that keeps tubes alive for decades
Miller ≈ Cgp × Gain
Estimate input capacitance — the hidden bandwidth killer
PSRR ≈ Ra/rp ratio
Higher Ra relative to rp = worse power supply rejection
CF after high-Z source
A cathode follower converts impedance — use it at boundaries
SRPP at RL ≈ 2×rp
Distortion cancellation only works at the optimal load
Quiz de synthèse

Test Your Knowledge

Review the key concepts of tube amplifier topologies covered in this guide.

Question 1 / 7

What is the key characteristic of a common cathode amplifier?

In the same category