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

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

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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

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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 × B_max × A_e

Where:

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

Solving for core area:

A_e = E / (4.44 × f × N × B_max)

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:

A_e(cm²) ≈ K × √P_out(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

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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

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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 B_sat: about 2.0 T
• Working B_max: 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:

• B_sat: about 1.2 T
• Working B_max: 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

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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:

f_L = (R_p || Z_a) / (2π × L₁)

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

L_1,min = Z_a / (4 × 2π × f_L)

At f_L = 20 Hz, this simplifies to approximately:

L_1,min ≈ Z_a / 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

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

6.1 Turns ratio

The turns ratio is set by the impedance transformation:

n = N₁ / N₂ = √(Z_a / Z_Load)

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:

d_wire(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:

f_H = Z_a / (2π × L_leak)

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

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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

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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 A_e
• 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, Z_a = 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

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

Design targets

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

Step 1: Calculate Z_a

Z_a = 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:

A_e = 21.3 cm²

Target flux density:

B_max = 1.15 T

Primary RMS voltage:

U₁ = √(80 × 2,500) = 447 V_rms

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

f_L = 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

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10. Rules of Thumb

1. Core area in cm² is roughly:
   A_e ≈ 1.2 × √P_out(W)
   for CRGO steel, 20 Hz, push-pull design.
2. Primary inductance should be at least:
   L₁ ≥ Z_a / 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

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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.

Single-Ended Output Transformers Core Size, DC Bias, and the Art of the Air Gap

Published by IWISTAO

A blog-form technical guide for builders of single-ended triode and pentode amplifiers

Figure 1. Why single-ended transformers must deal with continuous one-way DC flux while push-pull cores largely cancel it.

This blog is a faithful long-form adaptation of the source manuscript supplied by the user. It preserves the original technical argument, tables, and formulas while reshaping the material into a publishable article format.

Introduction

Among all parts of a vacuum-tube amplifier, the output transformer is both the most decisive and the most frequently misunderstood. That is especially true in single-ended (SE) amplifiers, where one output tube—or one paralleled output stage—continuously drives the primary winding with DC current present at all times. Unlike a push-pull stage, the transformer cannot assume that the net core magnetization will cancel. Instead, it must survive a standing DC bias current while still passing audio cleanly over the desired bandwidth.

The source article makes one central point: the defining feature of a true SE output transformer is the air gap. Without that gap, the DC component would push the magnetic core into saturation, leaving little room for the audio waveform. Everything else—core size, primary turns, inductance, low-frequency extension, winding geometry, weight, and cost—flows from that constraint.

In practical terms, the DC bias current may be modest, such as about 30 mA for a smaller directly heated triode, or well above 150 mA for large transmitting tubes such as the 845 or GM70. The stronger the standing DC magnetization, the larger the design penalty paid in core size and inductance management.

1. Why Single-Ended Transformers Are Fundamentally Different

In a push-pull output stage, two halves of the primary winding carry equal and opposite DC components. Because these magnetizing forces oppose one another, the transformer core sees very little net DC flux. That makes it possible to use an ungapped core and exploit nearly the full iron cross-section for AC signal swing.

A single-ended stage does the opposite. One active device establishes a quiescent DC current through the primary, and this current never reverses direction. The audio signal is therefore superimposed on top of a standing magnetic offset. The core is already biased before any music arrives.

The original manuscript compares the two topologies in concise engineering terms:

Parameter	Push-Pull	Single-Ended
DC flux in core	≈ 0 (cancels)	Significant
Air gap required	No	Yes—mandatory
Core utilization for audio	Near 100%	Reduced by DC reserve
Transformer size for a given power	Smaller	Typically 1.5× to 3× larger
Even-order distortion	Low	Second harmonic more prominent
Typical sonic reputation	Analytical / controlled	Often described as musical

The source article also illustrates the DC problem quantitatively with the standard field-intensity expression:

H_DC = (N_p × I_DC) / l_e

Here, N_p is the number of primary turns, I_DC is the quiescent current, and l_e is the effective magnetic path length. For a representative 300B SE example using roughly 2,800 primary turns, 80 mA of standing current, and an effective path length around 100 mm, the DC magnetizing field becomes large enough that an ungapped silicon-steel core would be driven into or beyond its usable region. The transformer would no longer behave as a linear audio device.

2. The Air Gap: The Essential Feature of an SE Output Transformer

The air gap solves the DC saturation problem by inserting a controlled non-magnetic reluctance into the magnetic circuit. Air has a relative permeability of about 1, enormously lower than that of transformer steel. As a result, even a small physical gap dominates the reluctance of the magnetic path.

Figure 2. Introducing a gap sharply reduces effective permeability, but it also prevents the standing DC bias from driving the core into saturation.

The source text uses the familiar approximation that the effective permeability of a gapped core is roughly proportional to l_e / l_g when the intrinsic permeability of the steel is much higher than that ratio. This is the heart of the tradeoff: the gap saves the core, but it also lowers primary inductance. Since low-frequency response depends on inductance, every increment of gap has a price.

The article further gives the design equation for the required total gap length:

l_g = (μ₀ × N_p × I_DC) / B_max − l_e / μ_r

Using the worked 300B example from the manuscript—EI-66 core, about 2,800 primary turns, 80 mA DC, and a chosen DC flux density target around 0.9 T—the total gap comes out close to 0.30 mm. For a conventional EI stack, that corresponds to about 0.15 mm shim thickness on each side.

3. Core Size and Output Power

The next major theme of the original article is that single-ended transformers are not sized by power alone. They must simultaneously survive DC bias and still provide enough primary inductance for the target low-frequency cutoff. A useful rule from the manuscript is that core area and window area together set the practical power-handling envelope, and the usable output tends to scale approximately with the square of the core cross-section area.

Figure 3. Typical SE power capability rises steeply as core cross-section area increases.

Core	A_e (cm²)	Typical P_out (W)	Common tubes	I_DC (mA)	Gap total (mm)
EI-48	1.44	0.5–1.5	45, 71A, PX4	25–40	0.05–0.10
EI-57	2.04	1.5–3	2A3, 45, EC8010	35–60	0.10–0.15
EI-66	2.72	3–6	2A3, 300B, PX25	60–90	0.15–0.25
EI-76	3.61	5–9	300B, 6L6 SE, EL34 SE	70–100	0.20–0.30
EI-86	4.62	8–14	845, 211, 300B parallel	90–130	0.25–0.40
EI-96	5.76	12–20	845, GM70, 211	100–150	0.30–0.50
EI-114	8.12	18–30	Parallel 845, GM70×2	150–250	0.40–0.70

One practical design lesson emerges clearly: in SE work, 'more iron' is rarely wasted. Larger cores allow more DC headroom, more low-frequency inductance, and lower flux density stress for a given power level. That is why high-quality 845, 211, and GM70 transformers quickly become physically large and expensive.

The source manuscript also discusses toroidal and cut-core approaches. Because a toroid does not naturally have a joint where a gap can be inserted, manufacturers must cut the core and insert a precision spacer or gap it at manufacture. Amorphous and nanocrystalline materials can improve inductance for a given size, but they do not remove the need to manage DC bias carefully.

4. Primary Inductance: The Real Gatekeeper of Bass Performance

The blog source makes a point that many hobbyists overlook: surviving DC is not enough. An SE transformer also needs adequate primary inductance, because the primary inductance and the source impedance of the output tube form the low-frequency high-pass behavior of the output stage.

The lower cutoff frequency can be approximated by:

f_L = (R_a || R_L′) / (2π × L_p)

For a 300B example with plate resistance around 700 Ω and a reflected primary load of 5 kΩ, the effective source resistance becomes about 609 Ω. Hitting 20 Hz therefore requires a minimum primary inductance a little under 5 H, while more conservative designs aim for roughly 5–8 H or more to preserve authority in the lowest octave.

Once the gap is chosen, the achievable inductance is approximately:

L_p = (μ₀ × N_p ² × A_e) / (l_g + l_e / μ_r)

The original calculation for an EI-66 300B transformer gives an inductance of roughly 10 H with a 0.30 mm total gap—comfortably above the minimum and consistent with strong low-frequency extension.

Tube	R_a (Ω)	Typical Z_a (Ω)	Min L_p @20Hz (H)	Recommended L_p (H)	Typical N_p
45	1,600	1,600	12.7	20–30	3,500–4,500
2A3	800	2,500	6.4	10–18	2,500–3,500
300B	700	3,500–5,000	5.6	8–15	2,200–3,200
845	1,700	5,000–7,000	13.5	20–35	3,000–4,000
211	1,650	5,000–7,000	13.1	20–35	3,000–4,000
GM70	2,000	3,500–5,000	15.9	25–40	3,500–4,500
EL34 (triode SE)	1,000	3,000	7.9	12–20	2,500–3,200
KT88 (pentode SE)	13,000	3,500	17.2	30–50	3,500–5,000

5. Turns Ratio, Secondary Design, and Load Matching

The original manuscript next walks through the familiar impedance-transformation relationship between primary and secondary:

n = √(Z_a / Z_L)

For a 300B driving an 8 Ω loudspeaker from a 3.5 kΩ primary load, the required turns ratio is about 20.9:1. With roughly 2,800 primary turns, that yields about 134 turns on the 8 Ω secondary. From there, wire size is chosen according to current density. In the example, an 8 W / 8 Ω load produces about 1 A RMS, implying a secondary conductor area near 0.286 mm².

The source also notes that many commercial transformers include 4 Ω, 8 Ω, and 16 Ω taps. These are established by the square-law relationships of turns and impedance, not by arbitrary choice. Correct load matching is central to getting the intended power, distortion, and damping behavior from the output tube.

6. High-Frequency Response: Leakage Inductance and Distributed Capacitance

At the top end, transformer behavior is dominated not by primary inductance but by leakage inductance and distributed capacitance. The source article explains the tradeoff elegantly: better interleaving improves coupling and pushes high-frequency rolloff upward, but additional layering can increase interwinding capacitance.

Figure 4. Interleaving the primary and secondary reduces leakage inductance and extends high-frequency bandwidth, though usually at the cost of increased distributed capacitance.

Winding configuration	Relative L_leak	Typical HF -3 dB	Relative C_dist
Simple P-S	1×	30–60 kHz	1×
½P – S – ½P	~0.25×	80–150 kHz	2×
¼P – S – ½P – S – ¼P	~0.06×	150–300 kHz	4×

In other words, transformer design is always a controlled compromise. Bass extension, DC tolerance, copper loss, leakage inductance, capacitance, and manufacturability all pull in different directions. Good transformers are not optimized by a single variable; they are balanced.

7. Worked Design Examples from the Source Article

To make the theory concrete, the original manuscript provides three useful design snapshots. They are reproduced below in blog form.

Design	Core	Primary Z	I_DC (mA)	Primary turns	Gap total (mm)	L_p (H)	Low -3 dB	Weight
300B SE	EI-66 M6	3,500 Ω	80	2,700	0.30	~10	~9 Hz	~450 g
845 SE	EI-96 GO steel	6,000 Ω	75	3,400	0.25	~22	~10 Hz	~950 g
2A3 SE	EI-57 M6	2,500 Ω	60	2,200	0.15	~7	~14 Hz	~280 g

These examples reinforce the article's central theme. A 300B transformer that looks modest on paper still needs careful gap management and enough turns to achieve around 10 H. Step up to an 845, and both core mass and winding effort rise dramatically. Drop down to a 2A3, and everything becomes a bit more compact, but the same magnetic logic still applies.

8. Practical Mistakes Warns Against

• Under-gapping the core. This leaves the iron too close to saturation and causes abrupt distortion on peaks.
• Over-gapping the core. This preserves DC headroom but reduces primary inductance, weakening bass and forcing more turns.
• Ignoring primary DC resistance. Excess winding resistance wastes voltage, raises copper loss, and degrades performance.
• Using push-pull transformers in SE circuits. A non-gapped PP transformer is not a substitute for a proper SE unit.
• Ignoring tube plate resistance. Low-frequency requirements depend on the source impedance of the tube, not just on the nominal primary load.

We also stresses lamination orientation, especially with grain-oriented steel, and reminds builders that winding resistance rises with temperature. Those effects do not invalidate the basic design equations, but they matter in serious builds and should not be treated as afterthoughts.

10. Advanced Notes

The manuscript closes its technical discussion with several advanced topics that deserve mention in a complete blog version.

• Feedback windings can be added to improve damping and extend bandwidth, but phase management becomes critical at high frequency.
• Single-ended pentodes can use ultralinear-style screen taps, often around 25–35% of the primary winding, to trade gain for lower distortion.
• Copper resistance rises about 0.393% per °C, so hot transformers behave differently from cold bench measurements.
• At audio frequencies, hysteresis is a major component of core loss; careful material choice and conservative flux density still matter.

Conclusion

The strength of the article lies in how consistently it ties every design choice back to one immutable fact: a single-ended output transformer must carry DC. Once that is accepted, the rest of the design becomes a balancing act among saturation margin, available AC swing, primary inductance, copper loss, leakage inductance, capacitance, and cost.

In concise rule-of-thumb form, the manuscript leaves the reader with three memorable ideas. First, every watt of serious low-frequency SE output requires substantial iron. Second, the air gap is not an optional tweak but the defining feature of the topology. Third, primary inductance must be chosen with the tube's source resistance in mind, not by catalog optimism alone.

For builders, that means the output transformer is never the place to economize blindly. In single-ended design, the iron is not merely a passive coupler. It is one of the principal determinants of the amplifier's final sound, power delivery, and bandwidth.

Shop Output Transformers

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• The Heart of Harmony: A Deep Dive into Push-Pull Output Transformers
• A DIY Guide: Building a Power Transformer for an EL34B Push-Pull Tube Amplifier

References

The following references are reproduced from the source manuscript and retained here to preserve attribution and technical lineage.

1. Turner, Bruce. "Single-Ended Output Transformer Calculator and Design Guide." Turner Audio. https://turneraudio.com.au/se-output-trans-calc-1.html
2. Merlin, Gary. "The Valve Wizard: Single-Ended Output Stages." https://www.valvewizard.co.uk/se.html
3. Sowter Transformers. "Single-Ended Output Transformers Product Range." https://www.sowter.co.uk/single-ended-output-transformers.php
4. Lundahl Transformers. "Tube Amplifier Output Transformers." https://www.lundahltransformers.com/tube-output/
5. Hashimoto Electric. "SE Output Transformer Specifications — H Series." https://acoustic-dimension.com/hashimoto/hashimoto-output-transformers-single-ended.htm
6. Hammond Manufacturing. "Audio Output Transformers — SE Series." https://www.hammfg.com/electronics/transformers/audio
7. Ridley, Ray. "Air Gap Design for Inductors with DC Bias." Ridley Engineering. https://www.ridleyengineering.com/design-center-ridley-engineering/39-magnetics/128-air-gap-design-for-inductors-with-dc-bias.html
8. van der Veen, Menno. "Modern High-End Valve Amplifiers Based on Toroidal Output Transformers." Elektor, 1999.
9. RCA Corporation. "Radiotron 300B Data Sheet." 1938. http://www.duncanamps.com/tube/300b.html
10. Jones, Morgan. "Valve Amplifiers, 4th Edition." Newnes/Elsevier, 2012.
11. Blencowe, Merlin. "Designing Tube Preamps for Guitar and Bass." Wem Publishing, 2009.
12. Langford-Smith, F. (ed.). "Radiotron Designer's Handbook, 4th Edition." Wireless Press, 1952. https://www.tubebooks.org/technical_files/RDH4.pdf
13. Crowhurst, Norman H. "Audio Transformer Design Manual." Gernsback Library, 1958.
14. Wolpert, David. "Design and Construction of High-Performance Audio Transformers." Glass Audio, Vol. 12(3), 2000.
15. National Magnetics Group. "Amorphous and Nanocrystalline Core Materials for Audio Transformers." https://www.natmag.com/