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

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

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

Mar 16, 2026 | 0 comments posted by Vincent Zhang

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.

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References

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

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