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  • Output Transformers in Vacuum Tube Push-Pull Amplifiers--Core Size, Power, and the Science Behind the Iron

Output Transformers in Vacuum Tube Push-Pull Amplifiers--Core Size, Power, and the Science Behind the Iron

| 0 comments posted by Vincent Zhang

Published by IWISTAO

A comprehensive technical guide for audiophiles and DIY amp builders

If you have ever opened a vintage vacuum tube amplifier—whether a Dynaco ST-70, a Marantz Model 8B, or a carefully built DIY design—one part immediately dominates the chassis both visually and electrically: the output transformer. It is typically the heaviest component, often the most expensive, and in many ways the part that most strongly shapes the amplifier’s performance.

The job of the output transformer is deceptively simple: it matches the high output impedance of the power tubes, usually in the kilo-ohm range, to the low impedance of a loudspeaker, typically 4, 8, or 16 ohms. Without this impedance transformation, almost no useful power would be delivered to the speaker. But once you ask how this transformation is achieved—and why transformer core size has such a strong relationship to output power and bandwidth—you quickly enter the world of electromagnetic design, magnetic materials, winding geometry, and practical tradeoffs.

This article explores that relationship in detail, from the fundamentals of push-pull operation and Faraday’s law, to core materials, winding structures, primary inductance targets, and real-world design examples for EL84, EL34, KT88, 300B, 845, and related tube families.

IWISTAO 12W Amorphous C-type Core Push-pull Output Transformer 10K for Tube 6P1 6P14 EL84

IWISTAO 12W Amorphous C-type Core Push-pull Output Transformer 10K for Tube 6P1 6P14 EL84

1. Why Push-Pull Operation Matters

1.1 Push-pull fundamentals

In a push-pull amplifier, two output tubes—or two tube pairs in a quad arrangement—are connected to opposite halves of a center-tapped primary winding. One side handles the positive half-cycle of the waveform, while the other handles the negative half-cycle.

  • Tube A conducts during one half-cycle through the upper half of the primary.
  • Tube B conducts during the opposite half-cycle through the lower half.

Because the DC plate currents in the two halves flow in opposite magnetic directions, their DC magnetization largely cancels. In an ideally balanced push-pull transformer, the net DC flux is essentially zero. That is why a push-pull output transformer normally does not require the large air gap that a single-ended transformer does. With no substantial air gap, the core can operate at much higher effective permeability, allowing far higher primary inductance than a similarly sized single-ended design.

1.2 DC balance in real amplifiers

Real amplifiers are never perfectly balanced. Tube tolerances, aging, and slight bias offsets create a residual DC current difference, usually expressed as:

ΔI

That mismatch produces a small net magnetization. Designers typically manage it in three ways:

  • Bias balance adjustment so one tube can be trimmed against the other
  • A very small preventive air gap of about 0.02–0.05 mm to protect against severe imbalance or tube failure
  • High-permeability core materials, especially amorphous and nanocrystalline alloys, which are less sensitive to residual imbalance than conventional steels

2. Core Fundamentals: The Physics Behind the Iron

2.1 Faraday’s law and core size

The basic transformer core-sizing relationship comes directly from Faraday’s law:

E = 4.44 × f × N × Bmax × Ae

Where:

  • E = applied RMS voltage
  • f = frequency in Hz
  • N = number of turns
  • Bmax = maximum flux density in Tesla
  • Ae = effective core cross-sectional area in m²

Solving for core area:

Ae = E / (4.44 × f × N × Bmax)

The crucial point is that frequency sits in the denominator. At low frequencies, a larger core area is required to keep flux density below saturation. This is why transformers designed to reproduce 20 Hz bass need noticeably larger cores than designs intended to roll off at 40–50 Hz.

2.2 Practical core area vs. output power

For push-pull transformers using CRGO silicon steel and targeting roughly a 20 Hz low-frequency limit:

Ae(cm²) ≈ K × √Pout(W)

Typical values:

  • K = 1.0 to 1.5 for ordinary designs
  • K = 1.5 to 2.5 for extended bass designs

Table 1. Core area guideline vs. output power

Output Power Minimum Ae (cm²) Recommended Ae (cm²) Typical Core
10 W 3.2 5–7 EI-48 or EI-57
20 W 4.5 7–9 EI-57 or EI-66
35 W 5.9 8–11 EI-66
50 W 7.1 10–14 EI-75 or EI-86
70 W 8.4 12–17 EI-86
100 W 10.0 16–22 EI-96
150 W 12.2 22–32 EI-114
200 W 14.1 28–42 EI-114 or EI-133

3. Core Geometry: EI, Toroidal, and C-Core Designs

3.1 EI laminated cores

EI cores are built from alternating E-shaped and I-shaped laminations stacked into a three-leg magnetic structure. The windings are placed on a bobbin around the center leg.

Advantages

  • widely available
  • standardized sizes
  • easy to wind
  • mature manufacturing ecosystem
  • relatively economical

Disadvantages

  • butt joints create small discontinuities in the flux path
  • higher stray magnetic field
  • typically higher leakage inductance than toroidal designs

Table 2. EI core size reference

EI Size Tongue Width (mm) Stack Depth (mm) Ae Range (cm²) Window Aw (cm²) PP Power (W) Application
EI-48 16.0 25–32 4.0–5.1 1.6 5–15 EL84 small PP
EI-57 19.0 30–40 5.7–7.6 2.2 10–25 EL84 standard PP
EI-66 22.0 32–50 7.0–11.0 2.9 20–35 EL34 standard PP
EI-75 25.0 40–60 10.0–15.0 3.8 30–50 KT88 entry PP
EI-86 28.7 45–65 12.9–18.7 5.0 40–70 KT88 / 6550 PP
EI-96 32.0 50–75 16.0–24.0 6.2 60–100 KT88 quad / 6550
EI-114 38.0 60–90 22.8–34.2 8.7 80–150 845 / 211 PP
EI-133 44.3 70–100 31.0–44.3 11.8 120–200 833 / GM70 PP
EI-152 50.7 80–110 40.6–55.8 15.4 180–300 Very high power PP

3.2 Toroidal cores

A toroidal transformer uses a continuous ring-shaped magnetic circuit with the windings distributed around the circumference.

Advantages

  • extremely low leakage inductance
  • very low stray field
  • high efficiency
  • compact for a given power rating

Disadvantages

  • difficult to wind
  • high inrush current
  • very difficult to repair or rewind

Table 3. Toroidal core size reference

Outer Dia. (mm) Inner Dia. (mm) Height (mm) Ae (cm²) PP Power (W)
80 40 30 6.0 15–30
100 55 35 7.9 25–45
120 65 40 11.0 40–70
150 80 50 17.5 70–120
180 95 60 25.5 100–180
220 120 75 37.5 160–280

3.3 C-cores

C-cores are made by winding a continuous strip of magnetic material and then cutting the wound body into two matching C-shaped sections.

Key benefit: the grain orientation follows the magnetic path more naturally than ordinary laminated EI stacks, which can lower losses and improve performance.

Table 4. C-core reference

C-Core Size Ae (cm²) PP Power (W) Notes
C-16 8.0 20–40 Low leakage, HiFi grade
C-20 12.5 40–70 Classic KT88 application
C-25 18.0 70–120 High-power KT88 / 6550
C-32 28.0 120–200 845 push-pull
C-40 42.0 200–350 Professional / industrial

4. Core Materials: Silicon Steel, Amorphous, and Nanocrystalline

4.1 CRGO silicon steel

Cold-rolled grain-oriented silicon steel has been the standard material for audio transformers for decades.

Typical properties:

  • Saturation flux density Bsat: about 2.0 T
  • Working Bmax: about 1.2–1.5 T
  • Relative permeability: roughly 3,000–8,000
  • Core loss at 1 T / 50 Hz: about 0.7–1.0 W/kg
  • Useful range: up to roughly 10 kHz before losses rise significantly

4.2 Amorphous alloys

Amorphous metals are made by rapid quenching, which prevents normal crystalline formation and greatly reduces eddy-current losses.

Examples include:

  • iron-based amorphous alloys such as Metglas 2605SA1
  • cobalt-based amorphous alloys such as Metglas 2714A

Compared with CRGO steel, amorphous materials can reduce required core size by about 30–40% for equivalent low-frequency performance because of their much higher permeability.

4.3 Nanocrystalline alloys

Nanocrystalline alloys combine an amorphous matrix with extremely fine crystalline grains, often in the 10–20 nm range.

Typical properties:

  • Bsat: about 1.2 T
  • Working Bmax: about 0.9–1.1 T
  • Relative permeability: 20,000–120,000, sometimes higher after annealing
  • Core loss at 0.5 T / 50 Hz: less than 0.05 W/kg
  • Useful range: from DC to beyond 100 kHz

In practical audio terms, that means either much higher primary inductance with the same turns count, or the same inductance with fewer turns, which lowers leakage inductance and improves high-frequency extension.

Table 5. Material comparison for a 35 W EL34 push-pull transformer at 20 Hz

Core Material Required Ae (cm²) Equivalent EI Core Primary Inductance Frequency Range
Hot-rolled silicon steel 12–16 EI-86 Low 30 Hz – 15 kHz
CRGO silicon steel 8–10 EI-66 / EI-75 Medium 20 Hz – 20 kHz
Iron-based amorphous 6–8 EI-66 High (3–5× CRGO) 15 Hz – 25 kHz
Nanocrystalline 6–9 EI-66 / EI-75 Very high (10–20× CRGO) 5 Hz – 80+ kHz

5. Primary Inductance and Bass Performance

5.1 Why primary inductance matters

The primary inductance L1, together with the source impedance reflected from the output stage, forms a high-pass behavior that sets the low-frequency rolloff:

fL = (Rp || Za) / (2π × L1)

For a push-pull amplifier, a useful minimum estimate is:

L1,min = Za / (4 × 2π × fL)

At fL = 20 Hz, this simplifies to approximately:

L1,min ≈ Za / 502

In practice, at least 3–5× the minimum calculated value is recommended if you want convincing bass under real operating conditions.

Table 6. Primary inductance targets by tube type

Tube Config. Za (Ω) Target fL (Hz) Min L1 (H) Recommended L1 (H)
EL84 × 2 PP 8,000 20 4.0 10–16
EL34 × 2 PP 6,600 20 3.3 8–12
EL34 × 4 PP 3,300 20 1.65 5–8
KT88 × 2 PP 4,000 20 2.0 5–8
KT88 × 4 PP 2,200 20 1.1 3–5
845 × 2 PP 10,000 20 5.0 12–20
211 × 2 PP 8,000 20 4.0 10–15
300B × 2 PP 5,000 20 2.5 6–10
2A3 × 2 PP 4,000 20 2.0 5–8

6. Winding Design: Ratio, Wire Gauge, and Leakage

6.1 Turns ratio

The turns ratio is set by the impedance transformation:

n = N1 / N2 = √(Za / ZLoad)

Table 7. Turns ratio and turns count guide

Tube Config. Za (Ω) ZLoad (Ω) Turns Ratio n N1 (approx.) N2 for 8 Ω
EL84 × 2 PP 8,000 8 31.6 : 1 1,800–2,400 57–76
EL34 × 2 PP 6,600 8 28.7 : 1 2,000–2,800 70–97
EL34 × 4 PP 3,300 8 20.3 : 1 1,600–2,200 79–108
KT88 × 2 PP 4,000 8 22.4 : 1 1,600–2,200 71–98
KT88 × 4 PP 2,200 8 16.6 : 1 1,200–1,800 72–108
845 × 2 PP 10,000 8 35.4 : 1 3,000–4,500 85–127
300B × 2 PP 5,000 8 25.0 : 1 2,000–3,000 80–120

6.2 Wire gauge selection

The wire sizing relationship is:

dwire(mm) = √(4 × I / (π × J)) × 1000

where J is current density, typically about 2–4 A/mm² for audio transformer work.

Table 8. Primary wire guide by tube type

Tube Quiescent Ia (mA) Peak Ia (mA) J (A/mm²) Wire Dia. (mm) AWG
EL84 50 100 3.0 0.21 32
EL34 60 130 3.0 0.24 30
KT88 70 150 2.5 0.28 29
6550 80 170 2.5 0.29 28
845 60 120 2.0 0.28 29
300B 60 100 2.0 0.25 30

Table 9. Secondary wire guide vs. power

Output Power Secondary Current (A) Wire Dia. (mm) AWG
15 W 1.37 1.03 18
25 W 1.77 1.18 17
35 W 2.09 1.28 16
50 W 2.50 1.40 15
70 W 2.96 1.52 14
100 W 3.54 1.67 14

6.3 Leakage inductance and high-frequency rolloff

Leakage inductance represents the part of the primary flux that fails to couple fully into the secondary. It produces a high-frequency rolloff:

fH = Za / (2π × Lleak)

The most effective cure is interleaving, where primary and secondary sections are alternated.

From least to most effective:

  1. P / S
  2. P / S / P
  3. P1 / S1 / P2 / S2
  4. 7-section interleave
  5. 14-section interleave

7. Complete Specifications by Tube Type

7.1 EL34 push-pull, 35 W

Parameter Specification
Output Power 35 W
Supply Voltage 450 V
Za (plate-to-plate) 6,600 Ω
Secondary Impedance 8 Ω (with 4 Ω and 16 Ω taps)
Turns Ratio 28.7 : 1
Primary Turns N1 2,400
Primary Wire 0.22 mm enameled copper
Secondary N2 84T (8Ω) / 59T (4Ω) / 119T (16Ω)
Secondary Wire 1.0 mm enameled copper
Primary Inductance ≥ 10 H; typically 15–25 H
Leakage Inductance < 5 mH
Frequency Response 20 Hz – 40 kHz (-3 dB)
Core EI-66 × 50 mm, 0.35 mm CRGO
Core Weight ~2.5 kg

7.2 KT88 push-pull, 50 W

Parameter Specification
Output Power 50 W
Supply Voltage 500 V
Za 4,000 Ω
Turns Ratio 22.4 : 1
Primary Turns N1 2,000
Primary Wire 0.27 mm × 2 bifilar
Secondary N2 89 turns (8 Ω)
Secondary Wire 1.1 mm enameled copper
Primary Inductance ≥ 8 H; typically 12–20 H
Frequency Response 20 Hz – 35 kHz (-3 dB)
Core EI-86 × 60 mm, 0.35 mm CRGO
Core Weight ~3.5 kg

7.3 KT88 / 6550 quad push-pull, 100 W

Parameter Specification
Output Power 100 W
Supply Voltage 500–550 V
Za 2,200 Ω
Turns Ratio 16.6 : 1
Primary Turns N1 1,600
Primary Wire 0.29 mm × 4
Secondary N2 96 turns (8 Ω)
Secondary Wire 1.4 mm or 2 × 1.0 mm parallel
Primary Inductance ≥ 5 H; typically 8–15 H
Frequency Response 20 Hz – 30 kHz (-3 dB)
Core EI-96 × 70 mm or EI-114 × 60 mm
Core Weight ~5–7 kg

7.4 845 triode push-pull, 60–80 W

Parameter Specification
Output Power 60–80 W
Supply Voltage 1,000–1,200 V
Za 10,000–14,000 Ω
Turns Ratio 35–42 : 1
Primary Turns N1 3,500–4,500
Primary Wire 0.16–0.18 mm
Insulation Requirement Primary must withstand >2,500 V
Primary Inductance ≥ 15 H; ideally 25–40 H
Frequency Response 20 Hz – 25 kHz (-3 dB)
Core Weight 8–12 kg

Safety note: High-voltage output transformers for 845 and 211 amplifiers involve potentially lethal voltages. Insulation margin is not optional.

7.5 300B push-pull, 20–30 W

Parameter Specification
Output Power 20–30 W
Supply Voltage 400–450 V
Za 5,000–6,000 Ω
Turns Ratio 25–27 : 1
Primary Turns N1 2,200–2,800
Primary Inductance ≥ 8 H; ideally 15–30 H
Frequency Response 20 Hz – 40 kHz (CRGO); 5 Hz – 80+ kHz (nanocrystalline)
Preferred Core EI-75 or EI-86 CRGO; nanocrystalline C-core for premium builds

8. Bandwidth vs. Core Size: The Tradeoff That Never Goes Away

8.1 Low-frequency extension

For bass performance, larger cores are genuinely beneficial:

  • larger Ae
  • lower flux density for the same voltage
  • more turns possible
  • higher primary inductance
  • lower low-frequency cutoff

8.2 High-frequency extension

Treble is different. A bigger core often implies more turns, and more turns tend to raise leakage inductance roughly with N². If winding structure is not managed properly, a physically larger transformer can actually lose ground in the top octave.

That is why interleaving strategy often matters more than raw iron size when treble extension is the priority. A carefully wound EI-66 can outperform a poorly wound EI-114 in high-frequency behavior.

Table 10. Bandwidth vs. core size for EL34 PP, 35 W, Za = 6,600 Ω

Core Specification Ae (cm²) N1 L1 (H) Lleak (mH) fL -3dB (Hz) fH -3dB (kHz) Notes
EI-57 × 40 mm 7.6 2,800 6 3.5 44 300 Undersized
EI-66 × 45 mm 9.9 2,400 10 5.0 26 210 Minimum acceptable
EI-66 × 60 mm 13.2 2,200 12 6.0 22 175 Good
EI-86 × 55 mm 15.8 2,000 14 8.0 19 131 Excellent
EI-86 × 75 mm 21.5 1,800 18 10.0 15 105 High-end grade
Toroidal Ø120 × 40 11.0 2,400 13 0.8 20 1,300 Superb treble
Nanocrystalline C-25 18.0 1,600 28 2.0 9 530 Reference grade
Frequency response comparison of EI, toroidal, and nanocrystalline output transformers

9. Practical Design Example: KT88 Push-Pull 80 W Output Transformer

Design targets

  • 80 W output
  • 8 Ω speaker
  • KT88 × 4
  • 500 V supply
  • fmin = 20 Hz
  • fH ≥ 30 kHz

Step 1: Calculate Za

Za = 2 × (450)2 / 80 × 0.5 ≈ 2,500 Ω

Step 2: Turns ratio

n = √(2,500 / 8) = 17.7 : 1

Step 3: Select core and calculate primary turns

Selected core: EI-96 × 70 mm CRGO, with effective core area:

Ae = 21.3 cm²

Target flux density:

Bmax = 1.15 T

Primary RMS voltage:

U1 = √(80 × 2,500) = 447 Vrms

Primary turns:

N1 = 447 / (4.44 × 20 × 1.15 × 21.3×10-4) ≈ 2,060

Step 4: Secondary turns

N2(8Ω) = 2,060 / 17.7 ≈ 116
N2(4Ω) ≈ 82
N2(16Ω) ≈ 164

Step 5: Verify primary inductance

L1 ≈ 87 H
fL = 2,500 / (4 × 6.28 × 87) ≈ 1.1 Hz

Step 6: Wire gauges

  • Primary: 0.35 mm enameled copper
  • Secondary: 1.3 mm enameled copper

Final design summary

Parameter Value
Core EI-96 × 70 mm, 0.35 mm CRGO silicon steel
Effective Ae 21.3 cm²
Za 2,500 Ω
Primary Turns N1 2,060
Primary Wire 0.35 mm enameled copper
Secondary N2 116T (8 Ω) / 82T (4 Ω) / 164T (16 Ω)
Secondary Wire 1.3 mm enameled copper
Primary Inductance ~87 H
Winding Structure 4-section interleave: P1 / S / P2 / S
Estimated Leakage 6–10 mH
Estimated Bandwidth ~8 Hz – 80 kHz (-3 dB)
Estimated Weight ~5.5 kg

10. Rules of Thumb

  1. Core area in cm² is roughly:
    Ae ≈ 1.2 × √Pout(W)
    for CRGO steel, 20 Hz, push-pull design.
  2. Primary inductance should be at least:
    L1 ≥ Za / 502
    at 20 Hz, and ideally 3–5× that value.
  3. Push-pull transformers normally do not require a large air gap.
  4. Toroidal designs can achieve much lower leakage inductance than EI designs.
  5. Nanocrystalline materials can reduce size and weight while extending bandwidth substantially.
  6. Interleaving often matters more than raw core size for treble extension.
  7. Secondary wire is usually much thicker than primary wire because the speaker side runs low voltage and high current.
  8. 845 and 211 transformers need especially careful high-voltage insulation.

Table 11. Quick core selection by tube type

Tube × Count Power (W) Min Ae (cm²) Recommended EI Toroidal OD Za (Ω)
EL84 × 2 PP 15 5.5 EI-57 × 35 mm Ø80 mm 8,000
EL84 × 4 PP 30 7.5 EI-66 × 40 mm Ø100 mm 4,000
EL34 × 2 PP 35 8.0 EI-66 × 50 mm Ø100 mm 6,600
EL34 × 4 PP 70 11.5 EI-86 × 55 mm Ø130 mm 3,300
KT88 × 2 PP 50 9.5 EI-75 × 60 mm Ø115 mm 4,000
KT88 × 4 PP 100 14.0 EI-96 × 65 mm Ø150 mm 2,200
6550 × 4 PP 120 16.0 EI-96 × 75 mm Ø160 mm 1,800
845 × 2 PP 60 18.0 EI-114 × 65 mm Ø160 mm 10,000
211 × 2 PP 50 16.0 EI-114 × 60 mm Ø155 mm 8,000
300B × 2 PP 25 7.5 EI-66 × 50 mm Ø100 mm 5,000
2A3 × 2 PP 15 6.0 EI-57 × 40 mm Ø90 mm 4,000

Conclusion

The output transformer is the true magnetic heart of a vacuum tube push-pull amplifier. Its size is not aesthetic decoration; it is a physical expression of low-frequency voltage swing, saturation margin, inductance, and bandwidth goals. A transformer intended for deep bass needs enough iron to avoid saturation at the bottom octave. A transformer intended for wide treble extension must also control leakage inductance through intelligent winding structure.

That is why no single metric tells the whole story. Core size matters. Core material matters. Interleaving matters. Geometry matters. A beautifully executed CRGO EI transformer can sound superb. A nanocrystalline or amorphous C-core can push performance further. A toroidal design can offer astonishing leakage performance, but only if the rest of the design is equally well judged.

In the end, output transformer design is always a balancing act between physics, materials, manufacturability, and sonic priorities. The iron matters—perhaps more than any other passive part in the amplifier. Choose it carefully, and the rest of the amplifier has a real chance to shine.

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References and Figure Sources

1. Radiotron Designer's Handbook, 4th Ed. — R.G. Langford-Smith (1952), Chapter 15

   URL: https://www.tubebooks.org/technical_files/RDH4.pdf

2. Output Transformer Design and Winding — GEOfex by R.G. Keen

   URL: http://www.geofex.com/Article_Folders/xformer_des/xformer.htm

3. Valve Amplifier Design Considerations, Part 2 — Rod Elliott, Elliott Sound Products

   URL: https://www.sound-au.com/valves/design2.html

4. Lundahl Transformers — LL1620/LL1623/LL1627/LL9202 Datasheet

   URL: https://www.lundahl.se/wp-content/uploads/datasheets/1620_3_7_9202.pdf

5. Sowter Push-Pull Output Transformer Catalogue

   URL: https://www.sowter.co.uk/push-pull-output-transformers.php

6. Erhard Audio — Output Transformer Technical Notes on C-Cores

   URL: https://www.erhard-audio.com/OutputTransformers.html

7. Monolith Magnetics — AmorphCore BA-8/5K Push-Pull Output Transformer Datasheet

   URL: https://www.monolithmagnetics.com/sites/default/files/datasheets/Push-Pull-output-transformers/...

8. Toroidal vs. EI Transformer Comparison — Guangri Winding Machines (2025)

   URL: https://grwinding.com/toroidal-vs-ei-transformers/

9. DIYAudio Forum — Output Transformer Design Discussions

   URL: https://www.diyaudio.com/community/forums/tubes-valves.6/

10. Valve Amps: Output Transformers — Lenard Audio Education

    URL: https://education.lenardaudio.com/en/14_valve_amps_5.html

11. Morgan Jones, Valve Amplifiers, 4th Edition, Chapter 6. Newnes/Elsevier, 2012. ISBN: 978-0080966403

12. AES-5id-1997: AES Information Document for Audio Transformer Standards. Audio Engineering Society, 1997.

blog tags: Amorphous core Audio transformer design C-core transformer Core size calculation EI core EL34 transformer EL84 transformer HIFI DIY Nanocrystalline core output transformer Primary inductance push-pull amplifier toroidal transformer Tube amp output transformer tube amplifier

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