Transformer Calculation, Losses and Leakage Inductance

How to calculate transformator, which losses and parasitic parameters are there in the transformer and how can they be measured and subsequently represented in a simulation model?

Transformer calculation starts with a defined turns ratio, measured inductances, winding resistances and parasitic capacitances. This article explains how to characterise a transformer, build a practical LTspice model and calculate its effect on signal bandwidth and return loss, with additional guidance on winding losses, core losses and switched-mode power applications.

Key Takeaways

The following points distinguish the measured transformer parameters from the performance of the complete circuit.

• Measure open-circuit inductance with the other winding open, and measure primary-referred short-circuit inductance with a low-impedance short directly across the secondary terminals.
• Define the turns-ratio convention before referring impedances between windings. With n = Np/Ns, a secondary impedance referred to the primary is multiplied by n².
• Winding losses include DC resistance, skin effect and proximity effect. Core losses require material, waveform, frequency, flux-density and temperature information; a basic coupled-inductor model does not predict them.
• Leakage inductance stores energy. The surrounding converter determines whether that energy is dissipated, recovered or used as part of a resonant circuit.
• Magnetising inductance and leakage inductance strongly influence the illustrated signal-transformer return-loss responses, but winding capacitance, interwinding capacitance, loading and winding resistance must also be evaluated.
• Validate the model in the intended circuit. A model suitable for small-signal return loss is not automatically suitable for saturation, efficiency, temperature-rise or common-mode EMI analysis.

Transformer Calculation: Losses, Parasitic Parameters and Equivalent Circuit

A useful transformer model is only as detailed as the design question requires. Start with the turns ratio and finite winding inductances, then add measured parasitic elements and loss mechanisms as needed.

Idealised coupled-inductor model

LTspice represents a transformer using an inductor for each winding and a mutual-coupling statement. For two windings named Lp and Ls, the directive K1 Lp Ls 1 specifies perfect magnetic coupling. The final number is the coupling coefficient k; k = 1 means no leakage inductance in this model. [1]

Figure 1. Idealised transformer example in LTspice.

Perfect coupling does not make finite inductors equivalent to an ideal transformer with infinite magnetising inductance. Magnetising current remains, and source and load impedances still influence the simulated response. Winding resistance, capacitance, core loss and saturation are absent unless explicitly represented.

Figure 2. Coupling-factor equation plate.

For a linear two-winding coupled-inductor model, mutual inductance M is related to the winding self-inductances Lp and Ls by:

[EQ 1] $M = k\sqrt{L_p L_s}$

Here M, Lp and Ls are in henries, and k is dimensionless. The winding polarity is represented by the dot convention. [1]

Practical equivalent circuit

The equivalent circuit adds the principal winding resistances, leakage inductance and capacitances.

Figure 3. Transformer equivalent circuit.

The following notation is used in the text:

• Lp and Ls: primary and secondary open-circuit self-inductances, measured under stated conditions.
• L_m: magnetising inductance in an explicitly separated equivalent-circuit model.
• L_leak,p: equivalent series leakage inductance referred to the primary.
• R_Cu,p and R_Cu,s: primary and secondary winding DC resistances.
• C_w,p and C_w,s: effective primary-side and secondary-side winding capacitances.
• C_ww: capacitance coupling the primary and secondary winding systems.

Older diagrams use labels such as Ls_prim for stray inductance. This should not be confused with Ls, which denotes the secondary self-inductance in the present text.

The capacitances in a lumped model are effective circuit parameters. A real transformer contains distributed capacitance between turns, layers, windings, core and surrounding conductors; a single capacitor cannot describe every excitation or grounding condition. [2]

Measuring primary and secondary inductance

Measure the primary inductance with the secondary open. Then measure the secondary inductance with the primary open.

Figure 4. Measuring transformer primary and secondary inductance.

Record the measurement frequency, AC test voltage, DC bias, temperature and instrument equivalent-circuit mode. Use the same conditions when comparing samples or extracting a model, and compensate the fixture before measuring small parasitic quantities.

Keep the excitation low enough to avoid driving the core into a nonlinear region. Measurements intended to describe operation under DC bias require the relevant bias condition rather than an assumed zero-bias result.

Calculating the turns ratio

Define the turns ratio n as the number of primary turns Np divided by the number of secondary turns Ns.

Figure 5. Turns-ratio equation plate.

For windings sharing the same effective magnetic path, the inductance ratio provides an estimate of the turns ratio:

[EQ 2] $n = \frac{N_p}{N_s} \approx \sqrt{\frac{L_p}{L_s}}$

The approximation is most useful with strong coupling and measurements made under comparable conditions. If the physical turns ratio is available, use it and check agreement with the measured inductances. [1][2]

For the example values Lp = 939 µH and Ls = 26.87 µH, Equation 2 gives n = 5.9115, or approximately 5.91.

With this convention, a secondary impedance Zs referred to the primary becomes:

[EQ 3] $Z_{s\rightarrow p} = n^2 Z_s$

Conversely, a primary impedance referred to the secondary is divided by n². This rule applies to resistances and to the impedances of reactive elements, provided the equivalent-circuit transformation is performed consistently.

Measuring total primary-referred leakage inductance

Short the secondary terminals with a short, low-impedance connection directly at the transformer. Measure the inductance at the primary terminals.

For the example connection, the secondary short is across pins 5 and 8, while the primary measurement is between pins 1 and 4.

Figure 6. Measuring transformer total primary-referred short-circuit inductance.

The measured short-circuit inductance is commonly used as the equivalent primary-referred leakage inductance when the transformer is strongly coupled and winding resistance and fixture impedance are sufficiently small.

For the lossless linear coupled-inductor model:

[EQ 4] $L_{\mathrm{sc},p} = L_p(1-k^2)$

Here L_sc,p is the inductance seen at the primary with an ideal secondary short. Solving for coupling gives:

[EQ 5] $k = \sqrt{1-\frac{L_{\mathrm{sc},p}}{L_p}}$

Both inductances must refer to the same winding and compatible measurement conditions. Do not combine primary open-circuit inductance with a secondary-referred leakage value. [2]

A long secondary shorting loop adds inductance, which is reflected to the primary approximately by n² in a strongly coupled step-down transformer. This can produce a substantial measurement error.

Leakage inductance represents magnetic field energy that does not link both windings. Winding geometry, separation, layer arrangement, core/window geometry and turn count influence its value. Interleaving and increased winding overlap can reduce leakage, but often increase interwinding capacitance. The design therefore requires a trade-off rather than independent minimisation of every parasitic parameter. [3]

Measuring winding DC resistance

Measure each winding separately and record which terminals belong to each resistance. For low resistances, use a four-wire measurement where practical so that lead and contact resistance do not dominate the result.

The original measurement example gives winding resistance values of 265 mΩ and 858 mΩ. Keep these values associated with their measured winding terminals when entering the simulation; the resistance values alone do not establish the winding assignment.

DC resistance is an input to winding-loss calculations, not a complete high-frequency loss model. AC resistance can exceed DCR because of skin and proximity effects. [2][3]

Measuring interwinding capacitance

Interwinding capacitance provides an electric-field coupling path between the primary and secondary. It can carry displacement current across a galvanic isolation barrier without a conductive connection between the windings.

For a two-terminal structural-capacitance measurement, connect all terminals of the primary winding together, connect all terminals of the secondary winding together, and measure between the two resulting groups. Do not short the primary group to the secondary group.

Figure 7. Measuring transformer interwinding capacitance.

Record the test frequency and the treatment of the core, screens and any additional windings. A measured structural capacitance does not, by itself, fully describe the common-mode current produced by a distributed winding-voltage waveform. [2][5]

Separating the windings, using sectional construction or increasing insulation thickness can reduce direct capacitive coupling, but may increase leakage inductance. An electrostatic screen can redirect electric-field coupling; its effect depends on placement and connection and must be assessed in the actual circuit.

Estimating effective winding capacitance from resonance

An impedance sweep with the opposite winding open can identify a winding’s self-resonant behaviour. A simple parallel LC approximation provides an effective capacitance estimate around the first relevant resonance.

Figure 8. Winding-resonance equation plate.

For inductance L, effective capacitance C and resonant frequency f_r:

[EQ 6] $f_r = \frac{1}{2\pi\sqrt{LC}}$

Rearranging:

[EQ 7] $C = \frac{1}{4\pi^2 f_r^2 L}$

This is a lumped-model estimate. Fixture capacitance, winding losses, inductance dispersion and other coupled capacitances can affect the observed resonance, so the result should be checked against the measured impedance curve rather than treated as a unique physical interturn capacitance. [2]

Figure 9. Resonant-frequency measurement for the example transformer.

Using Lp = 939 µH and f_r = 875 kHz gives an effective primary-side capacitance of 35.23 pF, consistent with the rounded value of 35 pF.

Using Ls = 26.87 µH at the same resonant frequency gives an equivalent secondary-side value of 1.231 nF, consistent with approximately 1.2 nF. These two calculations are alternative referred representations at the same resonance, not proof of two independent physical capacitors.

If separate primary-side and secondary-side capacitors are included in one model, fit them together to the measured responses. Adding both full referred values without checking their combined effect can double-count capacitance.

Building and validating the LTspice model

The measured parameters can be represented by explicit circuit elements around a coupled-inductor transformer.

Figure 10. Simulation equivalent circuit for the real transformer example.

The corresponding transfer response depends on the transformer, source impedance, load impedance and measurement configuration.

Figure 11. Transfer-frequency response of the example transformer.

Compare simulation and measurement using the same source and load conditions. Check both amplitude and phase where they matter, and investigate discrepancies rather than compensating them with arbitrary parasitic values. [2]

LTspice also allows winding series resistance and parallel capacitance to be entered through inductor attributes, while the coupling statement represents imperfect coupling.

Figure 12. LTspice transformer equivalent circuit.

For example:

• The secondary series-resistance attribute represents R_Cu,s.
• A secondary parallel-capacitance attribute can represent an effective C_w,s.
• The coupling coefficient represents leakage within the coupled-inductor model.

Use either a consistent imperfect-coupling model or an equivalent explicit-leakage representation. Adding the same leakage both through k and through extra series inductors counts it twice. [2]

Figure 13. Coupling-coefficient calculation plate.

If the 36.5 µH short-circuit inductance is primary-referred and the primary open-circuit inductance is 939 µH, Equation 5 gives k = 0.98037. With winding names Lp and Ls, the corresponding directive is K1 Lp Ls 0.98037.

Figure 14. LTspice text editor for a transformer coupling directive.

Alternative model with a separate magnetising inductance

An alternative equivalent circuit separates magnetising inductance from explicit leakage inductances and winding resistances. Such a model can be convenient when individual elements must be referred to one side of the transformer.

Figure 15. Simplified transformer equivalent circuit for SPICE simulation.

The associated original equation plates accompany this representation.

Figure 16. Equation plate for the separate magnetising-inductance model.

Figure 17. Inductance-transformation equation plate: first relation.

Figure 18. Inductance-transformation equation plate: second relation.

Figure 19. Inductance-transformation equation plate: third relation.

The measured short-circuit inductance does not uniquely determine a physical split between primary and secondary leakage. State the chosen equivalent-circuit convention and verify that it reproduces the terminal behaviour of interest.

The simplified model does not automatically include core loss, winding capacitance, frequency-dependent winding resistance, saturation or temperature dependence. A satisfactory small-signal fit is not sufficient evidence that the model predicts power loss or temperature rise. [2]

Transformer Loss Mechanisms in Practice

Separate energy storage from irreversible power dissipation. Winding and core losses heat the transformer, while leakage and capacitance also alter how energy moves through the surrounding circuit.

Mechanism	Physical origin	Main dependencies	Design considerations
DC winding loss	Resistive heating in conductors	Current and winding resistance at operating temperature	Conductor area, winding length, connections and cooling
Additional AC winding loss	Skin and proximity effects	Frequency spectrum, conductor dimensions and magnetic-field distribution	Strand or foil dimensions, layer arrangement and interleaving
Core loss	Magnetic-material dissipation under cyclic excitation	Material, flux waveform, frequency, bias and temperature	Core material, core size, turns and flux swing
Leakage-related circuit loss	Dissipation of stored leakage energy in surrounding components	Leakage inductance, transition current and clamp behaviour	Winding arrangement, clamps, snubbers and energy recovery
Dielectric and capacitive circuit loss	Insulation dissipation and circuit-dependent charging or discharge	Voltage waveform, capacitance, dielectric properties and frequency	Insulation system, geometry, screening and switching conditions

Table 1. Transformer loss mechanisms and their design dependencies.

Winding losses

For a winding with RMS current I_rms and resistance R_DC, the DCR-only estimate is:

[EQ 8] $P_{\mathrm{w,DC\ estimate}} = I_{\mathrm{rms}}^2 R_{\mathrm{DC}}$

Use resistance at the expected operating temperature. This estimate omits the additional resistance associated with non-uniform AC current distribution.

For a linear winding-loss model and a periodic current waveform, separate the DC component and harmonics:

[EQ 9] $P_{\mathrm{w}} = I_0^2 R_{\mathrm{DC}} + \sum_{h=1}^{\infty} I_{h,\mathrm{rms}}^2 R_{\mathrm{AC}}(h f_0)$

Here I₀ is the DC current component, f₀ is the fundamental frequency, h is harmonic order and R_AC is the effective winding resistance at each harmonic frequency.

Skin effect crowds current towards conductor surfaces. Proximity effect redistributes current in response to surrounding magnetic fields. Both are winding-loss mechanisms, not additional categories to add again after using a complete AC winding-resistance model. [3]

Conductor choice must account for the current spectrum and winding geometry. Litz wire, foil, rectangular conductors and PCB windings each require appropriate dimensions and layer arrangements; none guarantees low loss independently of the design.

Core losses and thermal limits

Core-loss calculations require the selected material’s data at appropriate frequency, flux density and temperature. For switched waveforms, check whether the manufacturer’s loss model supports the actual excitation rather than assuming sinusoidal data applies unchanged. [2][3]

Flux-density change follows the voltage-time integral:

[EQ 10] $\Delta B = \frac{1}{N A_e}\int_{t_1}^{t_2} v_m(t)\,dt$

Here ΔB is the change in core flux density in teslas, N is winding turns, A_e is effective core area in square metres and v_m is the voltage associated with the core-linked flux, excluding winding-resistance and leakage-inductance voltage drops.

For power and pulse transformers, check startup, reset and transient volt-seconds as well as steady-state operation. A transformer that is satisfactory in a low-level AC test can still saturate in its application. [3]

Balancing core and winding loss can provide a useful starting point in some power-transformer optimisations, but equal losses are not a universal requirement. The relevant constraints are total loss, local hot-spot temperature, efficiency, insulation capability and cooling.

Leakage inductance and energy handling

Leakage inductance stores magnetic energy:

[EQ 11] $E_{\mathrm{leak}} = \frac{1}{2}L_{\mathrm{leak}} I^2$

Here E_leak is stored energy in joules and I is the instantaneous current through the equivalent leakage inductance.

If a circuit dissipates all of this energy once per switching event, its associated power is the energy per event multiplied by the event rate. Do not apply that estimate when energy is recovered, resonantly transferred or only partly dissipated.

In hard-switched converters, leakage can cause voltage overshoot, ringing and additional clamp or snubber loss. In resonant converters, some leakage inductance can be deliberately incorporated into the resonant network. In signal transformers, leakage mainly changes terminal impedance, bandwidth and matching. [3][5]

Leakage depends strongly on winding arrangement. Analytical estimates are useful for suitable geometries; complex structures can require field simulation and prototype measurements. Reducing leakage by tighter interleaving must be weighed against capacitance and insulation requirements.

Interwinding capacitance in fast-switching applications

A capacitance across an isolation barrier carries current when the voltage across it changes:

[EQ 12] $i_{\mathrm{CM}} = C_{\mathrm{eq}}\frac{dv_{\mathrm{CM}}}{dt}$

Here i_CM is common-mode displacement current, C_eq is the effective capacitance of the relevant coupling path and v_CM is the common-mode voltage across it.

This relationship is particularly important for isolated bias supplies and gate-drive systems exposed to fast GaN or SiC switching edges. Interwinding capacitance can be a significant EMI parameter even when it makes little difference to a differential return-loss curve. The effective coupling also depends on winding voltage distribution and circuit connections. [5]

Transformer Application Requirements

Transformer requirements depend on whether the device transfers a signal, measures current, drives a switch or transfers power. Turns ratio and inductance alone do not establish suitability for all of these functions.

Function and application areas

Transformers can provide:

• Galvanic separation between circuits, subject to the construction and specified insulation capability.
• Voltage transformation according to turns ratio.
• Current transformation inversely related to turns ratio in the ideal transformer.
• Impedance transformation according to the square of the turns ratio.

Typical applications include:

• Power conversion: voltage transformation and, where required, safety isolation.
• Current measurement: conversion of current to a usable secondary signal through a defined burden.
• Pulse and gate drive: isolated transfer of time-varying drive waveforms.
• Data and telecom interfaces: signal coupling, isolation and impedance matching.

A flyback magnetic component additionally stores useful energy in its magnetising inductance. Its design therefore differs from a transformer intended primarily for immediate power transfer between windings. [3]

Requirements for data and signal transformers

A data transformer must preserve the required signal over the operating band and under the specified terminations.

Finite magnetising inductance loads the circuit at low frequencies. Leakage inductance and capacitance affect the upper-frequency response, while winding resistance contributes insertion loss and impedance error.

Pulse-like signals contain harmonics, so evaluating only the fundamental is insufficient when rise time, droop or pulse shape matters. Other interfaces use different signal spectra; the required bandwidth must follow the actual application.

Higher magnetising inductance can improve low-frequency loading, but increasing turns can also increase resistance, capacitance and leakage. The objective is adequate inductance under the relevant bias and temperature conditions, not the largest possible inductance. [2]

Toroidal cores, bifilar windings and twisted conductors can be useful constructions, but the choice depends on bandwidth, balance, capacitance, insulation and manufacturing constraints.

Datasheets may specify both component parameters and system-level quantities such as insertion loss and return loss. Compare the stated measurement conditions before comparing values.

Insertion loss

Insertion loss compares power delivered to the load before and after inserting the device under defined source and load conditions.

Figure 20. Insertion-loss equation plate.

With P_ref representing load power in the reference connection and P_DUT representing load power with the transformer inserted:

[EQ 13] $IL = 10\log_{10}\left(\frac{P_{\mathrm{ref}}}{P_{\mathrm{DUT}}}\right)$

For an unchanged resistive load, the corresponding voltage comparison uses 20 log of the reference-to-measured voltage ratio. A simple primary-to-secondary voltage ratio is not, by itself, insertion loss for a transformer with a non-unity turns ratio.

Insertion loss includes effects of both dissipation and mismatch under the measurement conditions. It should not be interpreted directly as transformer heating.

Return loss

Return loss expresses the ratio of incident power to reflected power, in decibels. A larger positive return-loss value indicates a smaller reflected fraction.

Figure 21. Return-loss definition equation plate.

Use a defined port reference impedance and a defined termination at the other winding. Return loss is not an intrinsic scalar property independent of the connected circuit. [4]

Common-mode rejection

Common-mode rejection describes suppression of signals or interference common to both conductors relative to the relevant reference. It is not simply suppression of DC.

Winding balance, capacitance, grounding and any associated common-mode choke influence performance. Galvanic isolation prevents a direct conductive path, but does not eliminate high-frequency capacitive coupling.

Total harmonic distortion

Total harmonic distortion compares the RMS combination of harmonic components with the fundamental component. The test must state signal frequency, amplitude, termination and any bias conditions.

Core nonlinearity can increase distortion even when a low-level linear model predicts acceptable insertion and return loss. A basic linear coupled-inductor model does not predict this behaviour.

Bandwidth

Bandwidth is the frequency range over which the specified performance limits are met.

A 3 dB bandwidth normally refers to attenuation relative to a defined reference or passband level. It is not necessarily the range in which absolute insertion loss is below 3 dB. Signal interfaces may also impose return-loss, balance, distortion or pulse-response limits.

A Transformer’s Effect on Return Loss

Return-loss analysis combines the transformer equivalent circuit with the source or line reference impedance and the actual load. The examples below use a real, resistive reference impedance, so reflected-power interpretation remains straightforward.

Return-loss equations and reference impedance

Figure 22. Return-loss equation plate.

Figure 23. Return-loss equation plate expanded into resistance and reactance.

Let R₀ be the real positive reference impedance and Z_in the complex input impedance of the loaded transformer. The input reflection coefficient is:

[EQ 14] $\Gamma = \frac{Z_{\mathrm{in}}-R_0}{Z_{\mathrm{in}}+R_0}$

Return loss is:

[EQ 15] $RL = -20\log_{10}|\Gamma|$

Writing Z_in = R + jX gives:

[EQ 16] $RL = 10\log_{10}\left(\frac{(R+R_0)^2+X^2}{(R-R_0)^2+X^2}\right)$

Here R and X are the resistance and reactance of the loaded transformer input, and j is the imaginary unit. [4]

For a complex reference impedance, wave normalisation and the distinction between voltage-wave and power-wave definitions require additional care. The simple real-reference formulas should not be extended indiscriminately to complex source impedances.

Reflection coefficient

The reflection coefficient is complex: it contains magnitude and phase.

Figure 24. Reflection-coefficient equation plate.

Figure 25. Complex reflection-coefficient representation.

With ρ = |Γ| and φ denoting reflection phase:

[EQ 17] $\Gamma = \rho e^{j\phi}$

Figure 26. Relationship between return loss and reflection coefficient.

For a passive termination referenced to a real positive impedance, ρ ranges from zero for a perfect match to one for complete reflection. The reflected-power fraction is ρ². Return loss describes the magnitude but does not retain the reflection phase. [4]

Standing-wave ratio

Incident and reflected voltage waves combine to form a standing-wave envelope on a transmission line. Voltage standing-wave ratio, VSWR, compares the maximum and minimum envelope magnitudes.

Figure 27. Standing-wave ratio.

Figure 28. Standing-wave ratio expressed using reflection magnitude.

For the usual lossless-line interpretation:

[EQ 18] $\mathrm{VSWR} = \frac{1+\rho}{1-\rho}$

A perfect match gives VSWR = 1. An open circuit, short circuit or purely reactive lossless termination gives complete reflection and an unbounded VSWR. [4]

Mismatch loss and transmitted power

For a lossless matching network, the accepted-power fraction is 1 − ρ². The associated mismatch loss is:

Figure 29. Transmission-loss equation plate associated with reflection.

[EQ 19] $ML = -10\log_{10}(1-\rho^2)$

Here ML is mismatch loss in decibels. This is not a complete insertion-loss model for a dissipative transformer: winding and core losses can reduce delivered power further.

Relationships and the Smith chart

Return loss, reflection magnitude and VSWR describe related aspects of the same input reflection. A perfect match produces zero reflection, infinite return loss and unity VSWR.

Table 2. Relationship between reflection coefficient, standing-wave ratio, return loss and transmission loss.

The Smith chart displays complex reflection coefficient and normalised impedance. Constant reflection magnitude forms circles centred on the chart origin; those circles also correspond to constant return loss and VSWR.

Figure 30. Smith-chart example.

Maximum power transfer

For a linear source with fixed Thevenin impedance Z_S, maximum available power is delivered when the load equals its complex conjugate.

Figure 31. Complex source and load.

Figure 32. Maximum-power-transfer equation plate.

[EQ 20] $Z_L = Z_S^*$

The asterisk denotes complex conjugation. Conjugate matching to a complex source and zero voltage-wave reflection relative to a transmission-line impedance are different conditions. They coincide in the familiar case of equal real source and line impedances.

Return loss with a matched load

Consider the original illustrative ADSL case with a 100 Ω real line reference and a purely resistive 100 Ω termination.

Figure 33. Return loss with a matched load.

Figure 34. Matched-load return-loss calculation.

For an ideal connection or ideal 1:1 transformer without finite magnetising loading, Z_in = 100 Ω, Γ = 0 and return loss is infinite. The result is frequency-independent within this idealised model.

Real measurements are limited by the test fixture, calibration, component tolerances and residual parasitic elements; an infinite return-loss result is a theoretical limit.

Return loss with an unmatched resistive load

Keeping R₀ = 100 Ω and changing a purely resistive load produces a finite, frequency-independent return loss in the otherwise ideal model.

Table 3. Return loss for mismatched resistive loads.

Figure 35. Return loss versus frequency for resistive mismatches.

Return loss does not indicate whether the resistance is above or below the reference value; reflection phase supplies that information. However, equal absolute resistance deviations above and below 100 Ω do not give exactly equal return loss, because the denominator in Equation 14 also changes.

Reciprocal normalised resistances produce equal reflection magnitudes. Thus “mismatch direction does not matter” must not be interpreted as exact symmetry for equal resistance increments.

Return loss with finite magnetising inductance

Now introduce a 1:1 transformer with a 600 µH primary-referred magnetising inductance, while retaining a 100 Ω load and 100 Ω reference.

Figure 36. Return-loss impedance reduction: load referred to the primary.

The inductive reactance changes with frequency even when the inductance itself is constant. At low frequency, the finite magnetising branch shunts the load more strongly and worsens the input match.

Use the following calculation sequence:

1. Refer the load to the primary using Equation 3. For n = 1, its value remains 100 Ω.
2. Combine the referred load in parallel with the magnetising branch.
3. Calculate Γ and return loss from the resulting input impedance.

Figure 37. Equation plate for combining the magnetising branch with the load.

Figure 38. Return-loss model with the combined input impedance.

With angular frequency ω = 2πf:

[EQ 21] $Z_{\mathrm{in}} = \left(\frac{1}{R_L}+\frac{1}{j\omega L_m}\right)^{-1}$

Here R_L is the primary-referred load resistance. For R_L = R₀, the expression simplifies to:

[EQ 22] $RL = 10\log_{10}\left[1+\left(\frac{2\omega L_m}{R_0}\right)^2\right]$

For L_m = 600 µH and R₀ = 100 Ω, recalculation gives 17.62 dB at 100 kHz and 37.55 dB at 1 MHz.

Table 4. Return loss with 600 µH primary-referred magnetising inductance.

Figure 39. Return loss with 600 µH primary-referred magnetising inductance.

Above the low-frequency transition, the return loss approaches an improvement of 20 dB per decade in this simplified model. Increasing L_m shifts the transition towards lower frequency, provided other parameters remain unchanged.

Return loss with leakage inductance added

Add 1 µH of primary-referred series leakage inductance to the same example. First combine the magnetising branch and reflected load, then add the series leakage reactance.

Figure 40. Return-loss model including leakage inductance.

Figure 41. Equation plate for adding leakage-inductance reactance.

Figure 42. Return-loss model after adding series leakage reactance.

The input impedance becomes:

[EQ 23] $Z_{\mathrm{in}} = j\omega L_{\mathrm{leak,p}}+\left(\frac{1}{R_L}+\frac{1}{j\omega L_m}\right)^{-1}$

For L_m = 600 µH, L_leak,p = 1 µH and R_L = R₀ = 100 Ω, recalculation gives 17.42 dB at 100 kHz and 27.01 dB at 1 MHz.

Table 5. Return loss with 600 µH magnetising inductance and 1 µH series leakage inductance.

Figure 43. Return loss with 600 µH magnetising inductance and 1 µH leakage inductance.

Finite magnetising inductance limits the lower-frequency match, while leakage reactance degrades the higher-frequency match. The resulting useful band also depends on the termination impedances and any capacitance or resistance added to the model.

Return loss with a less-than-ideal transformer

A more complete linear model includes winding resistance, leakage inductance, effective winding capacitance and a representation of core loss.

Figure 44. Return-loss model for a real transformer.

Figure 45. Illustrative ADSL transformer model.

With n = Np/Ns, multiply secondary resistance and load impedance by n² when referring them to the primary. The same convention must be used throughout the impedance reduction.

Interwinding capacitance connects the winding systems across the isolation barrier. It cannot generally be eliminated by the same simple series/parallel reduction used for a capacitor located wholly on one side. Retain the relevant connections in a nodal or SPICE model when that coupling matters.

Return-loss effect of winding DCR

The original ADSL illustration compares primary DCR of 3 Ω with secondary DCR of 1.5 Ω.

Figure 46. Return-loss effect of winding DC resistance.

For a turns ratio n = 2, a nominal 25 Ω secondary load reflects to 100 Ω. The 1.5 Ω secondary winding resistance reflects to 6 Ω, so it produces a larger primary-side impedance change than the 3 Ω primary resistance.

To isolate the resistance effect, take an otherwise perfectly matched circuit:

• Primary DCR alone gives an input resistance of 103 Ω and return loss of 36.61 dB.
• Reflected secondary DCR alone gives 106 Ω and 30.71 dB.
• Both resistances together give 109 Ω and 27.32 dB.

These results explain the original rounded values of approximately 37 dB, 30 dB and 27 dB. A load deliberately offset from 25 Ω changes the results and must be included explicitly when reproducing the complete plotted example.

Return-loss values cannot be added arithmetically in decibels. Combine the circuit impedances first, then calculate the resulting reflection.

Return-loss effect of leakage and distributed capacitance

Figure 47. Return-loss effects of leakage inductance and distributed capacitance.

Leakage inductance and winding capacitance can each degrade high-frequency matching. Over part of a frequency band, their reactive effects can oppose one another and improve the combined input match.

This does not mean capacitance is always beneficial. The outcome depends on component placement, load, frequency and damping. Resonance can produce a narrow improvement in return loss while creating unwanted peaking or ringing elsewhere.

Compare complete complex impedances, not the individual return-loss magnitudes. Cancellation of reactive error does not remove resistive loss or guarantee a satisfactory time-domain response.

Return-loss effect of interwinding capacitance

Figure 48. Return loss and interwinding capacitance.

The illustrated example uses a circuit simulation to include coupling between the primary and secondary.

In some differential signal models, interwinding capacitance makes a smaller contribution to return loss than leakage and magnetising inductance. This is a result to establish for the specified circuit, not a general permission to omit capacitance.

Its significance increases when capacitive coupling becomes appreciable relative to the other impedances. It can also affect common-mode behaviour even when its differential return-loss effect appears small. [2][5]

Return-loss effect of core loss and inductance

Figure 49. Return-loss effects of inductance and a resistive core-loss representation.

A parallel resistance can approximate a core-loss contribution at a specified small-signal operating condition. It should not be treated as a universal core-loss model across frequency, excitation level and temperature.

The illustration compares the effects of finite inductance and a resistive loss branch. Its qualitative lesson is that their contributions need not be equally important for return loss.

For data and audio transformers, evaluate loss together with loading, distortion and excitation level. For power transformers, use an appropriate material-loss model and thermal assessment. A modest return-loss effect does not establish that core heating is acceptable. [2][3]

Return-loss effect of all parameters

Figure 50. Return loss with all illustrated parameters.

The complete model combines magnetising loading, leakage, winding resistance, capacitances and the chosen loss representation.

In the illustrated ADSL-style example, magnetising and leakage inductance strongly shape the lower- and upper-frequency response. Other parameters modify that result and cannot be ranked independently of the circuit conditions.

A closer look at the dominating parameters

Figure 51. Return-loss comparison highlighting magnetising and leakage inductance.

The upper comparison shows the different models against the idealised, slightly mismatched reference case; the lower comparison focuses on the non-ideal cases.

Use this type of sensitivity analysis to decide which parameters require tighter tolerances or more detailed measurement. Vary inductance, leakage, capacitance, resistance and load over their expected ranges rather than relying only on nominal values.

A parameter may be insignificant for differential return loss but important for another requirement. Interwinding capacitance is a clear example because it can determine common-mode coupling in a fast-switching system. [5]

Design and Selection Checklist

Translate the required circuit performance into measurable transformer specifications before comparing components. Use the same test conditions and reference conventions for catalog parts, custom samples and simulation models.

Define the application

• Identify whether the transformer carries data, audio, gate-drive pulses, measurement signals or power.
• Define operating frequency range, waveform, voltage, current, source impedance and load.
• State DC bias, imbalance, startup and fault conditions where relevant.
• Define acceptable insertion loss, return loss, distortion, pulse droop, ringing and common-mode behaviour.
• For power applications, specify efficiency, temperature-rise and hot-spot limits.

Compare datasheet parameters consistently

• Check turns ratio, polarity, pinout and winding connections.
• Compare minimum and maximum inductance under the relevant frequency, amplitude, bias and temperature conditions.
• Confirm which winding the leakage-inductance value is referred to and which other windings were shorted.
• Check DCR for each winding and whether the values are typical or guaranteed limits.
• Compare capacitance using the specified terminal connections and test frequency.
• Check the terminations and fixtures used for insertion-loss and return-loss specifications.
• Confirm that a supplied model covers the intended frequency, loading and excitation range. [2]

Choose catalog or custom construction

A catalog part is appropriate when its guaranteed electrical, mechanical, thermal and insulation characteristics meet the application without relying on unspecified typical behaviour.

Consider a custom design when the required combination of turns ratio, leakage, capacitance, current capability, geometry or insulation cannot be met by a catalog component.

For custom parts, agree on winding construction, materials, acceptance limits, test methods and change control. Specify electrical performance rather than relying only on a nominal inductance and turns ratio.

Check qualification and safety

Galvanic separation alone does not establish a safety-insulation rating.

Confirm working voltage, required insulation category, dielectric-test conditions, creepage, clearance, insulation materials and the applicable end-product requirements. Check operating temperature, environmental exposure and manufacturing processes as part of the complete qualification.

A short-duration dielectric withstand rating is not a substitute for a documented continuous working-voltage capability.

Do not reduce insulation spacing merely to improve leakage or capacitance without reassessing the safety requirements. Insulation construction also consumes winding-window area and affects electrical and thermal performance. [3]

Validate the prototype

• Repeat the parameter measurements with compensated fixtures and documented conditions.
• Measure the loaded transfer response and input match.
• Check time-domain behaviour when pulse shape or ringing matters.
• For power circuits, verify startup, reset, transient flux conditions and temperature in the intended assembly.
• Check common-mode behaviour when fast voltage transitions cross the isolation barrier.
• Test representative component tolerances and operating extremes before releasing the design. [2][3][5]

Conclusion

Transformer calculation requires a consistent link between the application, measured parameters and the chosen equivalent circuit. The turns-ratio convention, measurement conditions and source/load impedances must remain explicit throughout that process.

For the illustrated signal-transformer examples, finite magnetising inductance limits low-frequency matching and leakage inductance degrades high-frequency matching. Winding resistance, capacitance and core-loss representation modify the response, while interwinding capacitance can remain important for common-mode coupling even when its differential return-loss effect is small.

For power and pulse applications, extend the analysis to waveform-dependent winding and core losses, volt-second balance, saturation, insulation and thermal performance. A validated model supports design decisions; it does not replace measurements in the intended circuit.

FAQ

Further Reading

These articles expand the construction, loss, measurement and thermal topics introduced above.

• How to Suppress Leakage Inductance in Transformer Design — Examines how winding arrangement and geometry influence leakage inductance.
• Winding Losses in Transformers and Inductors — Provides further discussion of skin effect, proximity effect and conductor construction.
• Transformer Testing, Parasitic Inductors/Capacitance and Lab Traps — Explains how secondary connections and test wiring can distort leakage measurements.
• Thermal Modeling of Magnetics — Introduces coupled loss and thermal-network analysis for magnetic components.

References

The following documents support the modelling, measurement and application principles used in this article. References marked “n.d.” do not state a publication year on the consulted document.

1. Gabino Alonso, LTspice: Simple Steps for Simulating Transformers, Analog Devices, 2014.
2. Coilcraft, Simulation Model Considerations: Part II — Choose or Create Meaningful Power Transformer Models for SPICE Simulations, Coilcraft, Doc1709, n.d.
3. Texas Instruments, Section 4 — Power Transformer Design, Texas Instruments, SLUP126, n.d.
4. Keysight Technologies, Reflection Measurements, Keysight VNA Help, n.d.
5. Pradeep Shenoy, How Isolated Bias Transformer Parasitic Capacitance Impacts EMI Performance, Texas Instruments, SSZTDB0, September 2025.