Unloaded LLC converter - will it keep voltage as calculated?

[Miyuki]

Hi folks,
a quick question. Will an unloaded LLC converter behaves as the gain curve tells or is here some parasitic that will make output voltage skyrocket?
I want the converter to keep running even without load to avoid acoustic issues.
It is calculated with a low Q of 0.4 even at full load so removing load and making Q = 0 should not shift the work point much

[sandalcandal]

Output will skyrocket (depending on the switching frequency if operating frequency is excessively low). Simply put, if you keep pumping energy into the resonant tank and there's no where (no load) for that energy to go, what do you think will happen?

The "Q" used in LLC design is
$Q =\frac{Z_0}{R_{ac}}=\frac{\sqrt{L_r/C_r}}{R_{ac}}$

This $Q$ is technically the Q of the RLC of the primary resonant tank coupled to the output load but thinking of this as a "Q" is a bit misleading. Due to the way an LLC works, a lower Q will result in HIGHER gain. [But will remain bounded as long as switching frequency is well above the primary tank + transformer magnetising inductance resonance]

In order to avoid the resonant tank building energy to the point of blowing itself up you need to operate above resonant frequency or otherwise use control methods such as burst mode operation, or phase shift (PWM) control. [Still seems to be an issue in some cases]

Light load operation is one of a main practical challenges using an LLC topology.

Edit: Typos and wording.
Edit2: Was mistaken, gain is bounded. See below.

[sandalcandal]

Look at any LLC design notes (even mine) and you can see gain skyrockets if switched at sub resonant frequency low load (low Q).

Image source: https://www.ti.com/seclit/ml/slup263/slup263.pdf?DCMP=FC&HQS=pwr-null-null-powertips-pwrhouse-20150710-mc-slup263-en

[Miyuki]

Yes but I want to be around fn with Ln 5, which should have nice theoretical chart, that nasty spike is way down from my working point

[sandalcandal]

Yes but I want to be around fn with Ln 5, which should have nice theoretical chart, that nasty spike is way down from my working point
(Attachment Link)

That red line is the minimum load curve for that design. If you go to no load that red line will be much taller still albeit limited by resonant tank parasitic resistance dissipation or the tank just blowing up. [Gain is bounded by the red curve, see below]

You can play around with around with a FHA (first harmonic analysis) model here: https://www.eevblog.com/forum/projects/1kw-resonant-converter-analysis-design-build-and-validation/?action=dlattach;attach=1257541

[sandalcandal]

Also worth noting that resonant tank components (resonant inductor and resonant capacitor) experience peak voltages get MUCH higher than the output voltage. Again can refer to my own notes or just play around with the FHA model.

Personal, practical experience has been that unchecked, low-load, sub-resonant operation blows up the resonant tank capacitors and sometimes takes out the secondary side rectifiers with it.

Edit: Having a play again with the FHA LTSpice, as long as you don't go too far down in frequency, capacitor voltage is limited so I wonder what was happening in our tests... You do still need to be careful of resonant capacitor voltage near the resonant frequency but only a heavy loads.

[sandalcandal]

Whelp I stand corrected.

Gain will be limited to a $Q\rightarrow 0, M_{\infty}$ curve as is the red curve in the plot Miyuki posted. As long as you don't let the switching frequency go too low and watch maximum voltages you'll be fine. The gain and voltage is bounded when frequency remains well above the Primary + transformer magnetising inductance resonance.

[Edit more details]

If I take the gain equation I previously derived:
$$M = \frac{X_m R_{ac}'}{X_m X_p + X_s'(X_m+X_p)+R_{ac}'(X_m+X_p)} \label{eq:M}$$
And solve for the limit as $R_{ac}' \rightarrow \infty$
$$M_{\infty} = \frac{X_m}{X_m+X_p}$$
This will go grow unbounded towards $\infty$ as $X_m+X_p \rightarrow 0$ i.e. we approach primary tank + transformer magnetising inductance resonance

I would conclude Miyuki should not have a problem but personal experience with a real circuit says otherwise.

[TimNJ]

Are you designing your own controller/algorithm? Or are you using an off-the-shelf controller from TI, NXP, ST, etc?

If the latter, don't worry about it too much...they will run at some burst-mode duty cycle to keep the output under control. Burst mode control is usually hysteretic so these controllers should theoretically allow an infinitesimally small duty cycle (if necessary). Without a "discontinuous" burst mode function at light load, the LLC switching frequency tends towards a very high value. In some cases, the natural switching frequency of the tank might even be beyond the switching frequency capability of the gate driver, 500KHz for example. Obviously this is not good from a functional perspective, and is even worse from a switching loss perspective (as alluded to above).

The best efficiency is usually realized by minimizing the number of cycles per burst, i.e. maximizing the amount of energy delivered in each cycle. If you are powering your control circuitry via auxiliary winding on the transformer, and you have a very narrow burst mode duty cycle, you should make sure that your Vcc capacitor can hold up the control circuitry in the time between bursts.

My two cents from the practical end of things. You guys seem to have the math under much better control than I do. 

[Miyuki]

I might go with my own digital controller (but it will mimic off-the-shelf controller as they have it described in the datasheet) or use off-the-shelf with some way to prevent it from entering burst mode.

[sandalcandal]

Are you designing your own controller/algorithm? Or are you using an off-the-shelf controller from TI, NXP, ST, etc?

If the latter, don't worry about it too much...they will run at some burst-mode duty cycle to keep the output under control. Burst mode control is usually hysteretic so these controllers should theoretically allow an infinitesimally small duty cycle (if necessary). Without a "discontinuous" burst mode function at light load, the LLC switching frequency tends towards a very high value. In some cases, the natural switching frequency of the tank might even be beyond the switching frequency capability of the gate driver, 500KHz for example. Obviously this is not good from a functional perspective, and is even worse from a switching loss perspective (as alluded to above).

We blew up our circuit while running tests with open loop (manually set frequency) control.

A normal/off-the-shelf converter will, as you say, possibly try to increase operating frequency towards infinity or do burst mode at low load to keep gain down if the input-output operating condition is such that M<1 is required for regulation.

This issue could potentially be avoided if you can guarantee the system stays in a state where M>1 regulation is required (sub resonant operation, f_sw<f_r)? Actually not sure what happens to the reactive energy when operating sub-resonant  with no load. I guess it should be self-limiting but again, not good experiences there. LTSpice does not want to run the non-linear time-domain simulation for low loads.

[Edit]
To try explaining the behaviour more visually rather than mathematically, I'll go over what the plot Miyuki posted shows.

The x-axis is the $f_n$ "normalised frequency" i.e. the switching frequency as a fraction of the resonant frequency. The y-axis is the $M$ "characteristic voltage gain" which is basically the voltage gain without any gain from the transformer turns ratio. Each blue curve represents the frequency-gain response for a different load condition; the lower curves are for higher loads (lower load resistance $R_{ac}$). The red curve represents the no-load limit (infinite load resistance).

We can figure out our gain at any given load condition by looking for (or plotting) our nearest load curve then reading off the gain at our normalised switching frequency.

To figure out our operating region we first place our $M_{min}$ and $M_{max}$ horizontal lines which are the minimum and maximum gains required to achieve regulation for our required input and output voltage ranges. We then plot the $M$ curve for our maximum load (minimum $R_{ac}$). The region (shaded in green) between our maximum load curve, the red $M_{\infty}$ curve and bounded by our $M_{min}$ and $M_{max}$ horizontal lines is the possible values for frequency and gain for our system.

If our desired minimum gain is too low, then that $M_{min}$ lines drops further below the red $M_{\infty}$ curve meaning the operating region will extend to excessively high frequencies. If our desired maximum gain it too high, then we can go beyond the "peak" of our maximum load curve and we will not be able to achieve maximum required gain at max load. If gain is not properly controlled e.g. we only using a f_min to bound our operating region (no $M_{max}$ control) then gain can also become excessive at low load, $f_n < 1$. Which is probably what happened to me?

Also note this plot is for a particular resonant inductance to transformer magnetising ratio $L_n = 5$ where  $L_n = \frac{L_m}{L_r} = \frac{1}{\lambda}$ some literature uses $\lambda$ instead of $L_n$. For different inductance ratios, the "shape" of the set of curves will change. Typical ratios range from $L_n$ 3 to 15.

This plot comes from/is used in ST's AN2450 Fig 3. This plot and equivalent plots are ubiquitous in LLC study/design.

[Miyuki]

This issue could potentially be avoided if you can guarantee the system stays in a state where M>1 regulation is required (sub resonant operation, f_sw<f_r)? Actually not sure what happens to the reactive energy when operating sub-resonant  with no load. I guess it should be self-limiting but again, not good experiences there. LTSpice does not want to run the non-linear time-domain simulation for low loads.

I hope it will just oscillate with constant amplitude (limited by the input voltage). The math says so.
But this is dangerously close that RF black magic when thing behaves different way.

[sandalcandal]

This issue could potentially be avoided if you can guarantee the system stays in a state where M>1 regulation is required (sub resonant operation, f_sw<f_r)? Actually not sure what happens to the reactive energy when operating sub-resonant  with no load. I guess it should be self-limiting but again, not good experiences there. LTSpice does not want to run the non-linear time-domain simulation for low loads.

I hope it will just oscillate with constant amplitude (limited by the input voltage). The math says so.
But this is dangerously close that RF black magic when thing behaves different way.

The issues we encountered may well have just been us running our system in a stupid region... I'm afraid I haven't done much to alleviate your issues/concerns but maybe atleast you know something to look out for?

Edit: Also apart from current concentrating skin/proximity effects, parasitic oscillations, noise coupling/EMI and non-linear magnetic behaviour in the resonant inductor and transformer, there shouldn't be too much RF level black magic going on, particularly at a high level design... unless you're running at frequencies into the MHz region? ...actually that is a quite few things isn't it but as far as blowing up our circuit RF level behaviour shouldn't be a big issue afaik.

[TimNJ]

You don't want to run in burst mode because..output ripple? Or what?

If you don't need to worry about light load efficiency (i.e. you don't need to comply with some country/region's efficiency requirements), you can just "pre-load" the output to set the maximum frequency and to make sure that regulation is always possible. Not sure what frequencies you're trying to use, but let's say resonance at 100KHz, you can set the pre-load resistor such that you get 150-200KHz when the actual load is disconnected, as an example. Depends if you're willing to burn some power at no load.

[jbb]

I could be mis-remembering, but I think I heard a comment about stray capacitance in the secondary rectifier diodes causing unexpected resonances and surprise voltage gain.

I think you’ll end up with some kind of ballast load if you want to stay out of pulse skipping. It could be done as a voltage clamp which only comes into effect if Vout goes too high.

[Miyuki]

Voltage clamp sounds like a reasonable solution

[Phoenix]

I could be mis-remembering, but I think I heard a comment about stray capacitance in the secondary rectifier diodes causing unexpected resonances and surprise voltage gain.

This is right - it is to do with the secondary diode capacitances. If the LLC keeps switching (even at increased frequency) you will have a an effect that pushes the output voltage (much) higher than the linear gain would expect. (I can't remember if there is an exact limit - it may want to double as in the parasitic elements form a doubler or charge pump type circuit).

The way to deal with this is, as others mentioned, use a burst mode. Once implementation is that if the LLC frequency operating point gets very high to stop switching all together - then as the voltage starts to droop a little the frequency operating point wants to drop and it will start switching again.

Voltage clamp sounds like a reasonable solution

Depending on the size of the converter and parasitic elements it may take a surprising amount of power/load to bring down the voltage.