Converter Conducted Emissions Estimator
Converter Conducted Emissions Estimator
The differential-mode conducted noise a switching converter will produce before the hardware exists, from the shape of its input current pulse: the trapezoidal Fourier envelope, its two breakpoints, the harmonic amplitudes, and what the LISN turns them into in dB above a microvolt. It is an envelope and it is differential mode only, and the page says so in every place where that matters.
Trapezoidal envelope through a LISN
a 250 kHz converter pulling 3 A pulses at 35% duty with 20 ns edges, looked at through the MIL-STD-461G LISN at 1 MHz
The trapezoid, its coefficients and its bound
envelope(f) = 2 I D · min(1, 1/πf ton) · min(1, 1/πf tr)
breakpoints at f1 = 1/(πton) and f2 = 1/(πtr)
level = 20·log10( envelope · |ZLISN| / √2 / 1 µV )
- 2 I D
- the flat top of the envelope. Halving the duty halves it, which is 6 dB — and moves the first breakpoint up an octave, so the net effect above that breakpoint is nothing at all
- t on
- the pulse width at the HALF-amplitude points, not at the top. With a real trapezoid the two differ by one rise time, and getting it wrong moves the first breakpoint
- t r
- the edge. Everything above 1/(pi t_r) falls at 40 dB per decade instead of 20, so the edge decides the high-frequency content and nothing else does
- root 2
- an EMI receiver reads the RMS value of a CW component and the coefficient is that component’s peak amplitude. Leaving it out is a 3 dB error, always in the pessimistic direction
Worked example
a 250 kHz converter pulling 3 A pulses at 35% duty with 20 ns edges, looked at through the MIL-STD-461G LISN at 1 MHz
The period is 4 µs and the half-amplitude pulse width is 35% of it, 1.4 µs. The flat top of the envelope is 2 x 3 A x 0.35 = 2.1 A
The first breakpoint is 1/(pi x 1.4 µs) = 227.4 kHz, above which the envelope falls at 20 dB per decade; the second is 1/(pi x 20 ns) = 15.92 MHz, above which it falls at 40
1 MHz is between them, so the envelope there is 2.1 A / (pi x 1 MHz x 1.4 µs) = 477.5 mA
At 1 MHz the LISN's 50 uH is 314.2 ohm of reactance and its 8 uF is 19.89 mohm, so the branch back to the power source is a high impedance and what the noise current sees is the 0.25 uF into the 50 ohm port with its 1 kohm bleeder. Solving the whole Figure 6 network gives 47.07 ohm — near enough the 50 ohm the port is terminated in, which it is NOT lower down the band
So the level is 20 log(477.5 mA x 47.07 ohm / root 2 / 1 uV) = 144.0 dB above 1 microvolt
1 MHz is the 4th harmonic of 250 kHz, and the exact coefficient there — the sinc product rather than the bound — is 143.58, which is 0.44 dB under the envelope. That gap is normal, and between breakpoints it can be much larger
What the trapezoid model leaves out, and roughly how much it matters
| Left out | Effect on the real spectrum | What to do about it |
|---|---|---|
| Common-mode current | Often the dominant mechanism above a megahertz; set by parasitic capacitance to chassis, which no schematic contains | Measure it with a current probe round the whole harness, or bound it from a layout extraction. Do not derive it from the circuit |
| Ringing on the switch node | Narrow peaks at the loop’s resonance, tens of megahertz, often 10 to 20 dB above the envelope there | A snubber, or a smaller commutation loop. Section 7.2.2.3 of Paul’s book treats the spectral effect directly |
| The input capacitor and any filter | Both reduce what reaches the LISN. This page predicts the SOURCE, unfiltered | That is the point: this number is the input to a filter design, not a prediction of the measurement |
| Diode reverse recovery | A separate current spike with its own, much faster, edge | Model it as a second trapezoid of its own amplitude and rise time and take the larger envelope |
| The receiver’s bandwidth and detector | A peak detector in a wide bandwidth reads broadband content higher than a narrowband one; the standards specify which | Only the standard’s own bandwidths give a number comparable with the limit |
| Unequal rise and fall times | The slower edge dominates the envelope; the faster one adds content above it | Use the FASTER of the two here if you want a bound, the slower if you want a best case |
Where the spectrum comes from before there is hardware
A switching converter does not draw a smooth current from its supply. It draws a pulse: the switch closes, current flows in from the input for a fraction of the period, and then it stops. On an oscilloscope that pulse is a trapezoid — a rising edge, a flat top, a falling edge — and the whole of the differential-mode conducted emission problem is the frequency content of that shape.
The envelope. A trapezoid’s Fourier coefficients are the product of two sinc functions: one set by the pulse width, one by the edge. Each sinc is bounded by one at low frequency and by the reciprocal of its argument at high frequency, so the whole spectrum is bounded by a curve with two corners. It is flat at twice the current times the duty, breaks at 1/(pi t_on) and falls at 20 dB per decade, and breaks again at 1/(pi t_r) and falls at 40. That is the standard construction, and it is in Paul’s sections 7.2.1 and 7.2.2 and in Ott’s chapter 12. What this page adds to it is the arithmetic, the LISN, and an insistence on the word envelope.
Why envelope is the right word. The bound touches the real spectrum only near the breakpoints. Between them the sinc functions have nulls, and the true coefficients dive tens of decibels below the bound at frequencies where the duty cycle happens to put one. The chart draws both, and the gap between them is not an error — it is the price of having a bound you can trust in the other direction. Design to the envelope and you will over-filter at some frequencies; design to the exact coefficients and one shift in duty cycle moves every null. The chart runs to 100 MHz so that the rise-time breakpoint is visible, and the exact coefficient is drawn clipped 40 dB below the envelope, because a receiver’s resolution bandwidth fills the nulls in and a line plunging to minus infinity would tell you nothing. Above roughly 30 MHz the trapezoid still describes the source; what a receiver reads up there is decided by layout.
What is missing, and it is a lot. This is differential mode. Common-mode current — the current that leaves through parasitic capacitance from switching nodes to chassis and comes back through the ground plane — is not in this model and cannot be put in it, because it depends on the heatsink mounting, the transformer’s interwinding capacitance and where the harness runs, none of which is on a schematic. On a great many real converters it is the bigger of the two above a megahertz. The trapezoid also contains no ringing, and the switch node rings at the commutation loop’s resonance every cycle. And this is the current the converter itself pulls, before the input bulk capacitor and before any filter: it is the noise SOURCE, which is exactly what you want as the input to a filter design and is not what a receiver would read on a built unit.
Take the level from here into the margin page against your own limit breakpoints, turn the shortfall into components on the filter designer, and find out what those components really deliver on the insertion-loss page. The converter itself is designed on the buck, boost and flyback pages, and the edge rate that sets the second breakpoint comes from the gate driver.
Frequently asked questions
Is this what a receiver would actually measure?
No, and in two directions. It is an upper bound rather than a spectrum, so real content sits at or below it, sometimes far below between the breakpoints. And it is the converter’s own pulsed input current before any input capacitor or filter, so a built unit will read lower. What it is good for is knowing how much attenuation the filter has to provide, which is the number you cannot get any other way before hardware exists.
Why does the rise time matter so much?
Because it sets the frequency above which the spectrum falls at 40 dB per decade instead of 20. Doubling the rise time halves that breakpoint frequency, and everything above the old breakpoint comes down by 20 dB per decade of the shift. That is the cheapest conducted-emissions fix there is, and it is paid for in switching loss — which is the trade this page exists to quantify.
Where is the common mode?
Not here, deliberately. Common-mode current is driven by dV/dt on switching nodes acting through parasitic capacitance to chassis: the switch tab to the heatsink, the transformer’s interwinding capacitance, the harness passing the magnetics. None of that is derivable from a circuit diagram — it is a layout and mechanical property — so any page that claimed to predict it from a schematic would be inventing it. Measure it with a current probe round the whole harness.
Why divide by root two?
Because an EMI receiver or spectrum analyser is calibrated so that a continuous wave signal reads its RMS value, and a Fourier coefficient is that component’s peak amplitude. The two differ by root two, which is 3.01 dB. It is a small error and it is always in the direction that makes a design look worse, which is why it survives in so many application notes — but it is still an error.
Does spread spectrum help?
It moves energy between frequency bins without removing any, so what it buys depends entirely on the receiver’s resolution bandwidth relative to the modulation depth. In a wide bandwidth it can buy almost nothing. In a narrow one it can buy 10 dB or more. Since the bandwidth is set by the standard you are testing to, the honest answer is that you have to know the standard’s bandwidth at that frequency before you can say.
What should I use for the LISN impedance?
For MIL-STD-461G, the default: the standard’s own network, drawn on its Figure 6 and plotted on its Figure 7. This page solves that network rather than reading points off the plot — 50 uH in series, 8 uF and 5 ohm to ground on the source side, 0.25 uF into the parallel 50 ohm port and 1 kohm bleeder — and the closed form agrees with the plotted curve to within 1 ohm everywhere between 10 kHz and 10 MHz, comfortably inside the plus or minus 20 per cent the figure states. A commercial LISN to CISPR 16 is a different network and its curve is not reproduced here; measure yours, or enter a fixed value.
Why is the LISN impedance only 5 ohm at 10 kHz?
Because at 10 kHz the 0.25 uF coupling capacitor is about 64 ohm of reactance in series with the 50 ohm port, and the series 50 uH is only 3 ohm — so the EUT port is looking almost straight through the inductor at the 5 ohm resistor and the 8 uF on the source side. That is the whole point of a LISN: it presents a defined, repeatable impedance instead of whatever the laboratory mains happens to be. It also means a flat 50 ohm assumption overstates the predicted level at the bottom of the CE102 band by about 20 dB.
Related calculators
References
- Paul CR. Introduction to Electromagnetic Compatibility, 2nd ed. Wiley, 2006. Chapter 7 Signal Spectra: 7.2.1 The Spectrum of Trapezoidal (Clock) Waveforms, 7.2.2 Spectral Bounds for Trapezoidal Waveforms, with 7.2.2.1 Effect of Rise/Fall Time on Spectral Content, 7.2.2.2 Effect of Repetition Rate and Duty Cycle and 7.2.2.3 Effect of Ringing (Undershoot/Overshoot). The chapter and section numbering was checked against the published table of contents. The coefficient formula and the two-corner bound this page uses are asserted against direct numerical integration of the trapezoid rather than taken from the text.
- Ott HW. Electromagnetic Compatibility Engineering. Wiley, 2009. Chapter 12 Digital Circuit Radiation, 12.1.3 Fourier Series and 12.1.4 Radiated Emission Envelope, for the same envelope construction; Chapter 13 Conducted Emissions, 13.1.1 Line Impedance Stabilization Network, 13.2.1 Common-Mode Emissions, 13.2.2 Differential-Mode Emissions and 13.2.3 DC-To-DC Converters. Section titles checked against the author’s own published contents listing.
- MIL-STD-461G, Requirements for the Control of Electromagnetic Interference Characteristics of Subsystems and Equipment, 11 December 2015, superseding MIL-STD-461F. A work of the US Government, distributed without charge. Figure 6 gives the LISN schematic — 50 uH series inductor, 8 uF and 5 ohm to ground on the power-source side, 0.25 uF from the EUT node to the signal output port, 1 kohm bleeder — and Figure 7 plots the resulting impedance from 10 kHz to 100 MHz with a stated tolerance of plus or minus 20 per cent. Paragraph 5.5.3 requires the receiver to be connected to that port through a 20 dB attenuator, and the unused port to be terminated in 50 ohm, which is why the port is modelled as 50 ohm at both. The default impedance on this page is the closed form of the Figure 6 network, asserted against sixteen points traced off Figure 7.
- Texas Instruments, The Engineer’s Guide to EMI in DC-DC Converters (Hegarty T., How2Power Today, 2018-2019). A ten-part series on the same problem from the converter side: the input current waveform as the differential-mode source, the LISN as the measurement network, and the separation of differential and common-mode paths.