Equivalent model of a resonant converter - Page 1
Forum section: electronics / beginners

author: warpco
author_rank: Contributor
timestamp: August 10, 2018, 08:33:26 pm
content: Hi everyone! I'm trying to understand how a resonant converter works, but one thing confuses me, and this thing is the derivation of the equivalent model using first harmonic approximation (FHA) method. At first glance it looks quite simple, here is the step-by-step description of this method from one of the app notes from Texas Instruments (Designing an LLC Resonant Half-Bridge Power Converter):QuoteStop. Why is the secondary voltage assumed to be rectangular? I tried to find some information and found this (A Comparison of Half-Bridge Resonant Converter Topologies by Robert Steigerwald):QuoteAnd... This confused me even more. Why parallel resonant converters use an inductor filter and series resonant converters use a capacitive filter? What will happen if I use the wrong filter type? Where do rectangular voltages and currents come from? Is it something specific to resonant converters or just a common way to get an equivalent resistance of a rectifier+filter?I would be very grateful for any help.

author: Paul Price
author_rank: Super Contributor
timestamp: August 11, 2018, 10:47:55 pm
content: The appnote you quote is in error. The output circuit waveform seen on the secondary of the transformer to the rectifiers isnot a bipolar squarewave.It is not a squarewave that is rectified to create the output voltage, it is very close to a sinewave.A "resonant inverter", i.e. a system that converts a DC voltage into a sinusoidal voltage (more generally, into a low harmonic content ac voltage), and provides ac power to a load. To do so, a switch network typically produces a primary square-wave voltage that is applied to a transformer at a resonant frequency.In a resonant convertor, a resonant tank tuned to the fundamental component of the square wave. In this way, the tank will respond primarily to this component and negligibly to the higher order harmonics, so that its voltage and/or current, as well as those of the load, will be essentially sinusoidal or piecewise sinusoidal.A resonant DC-DC converter is able to provide DC power to a load by rectifying and filtering the sinusoidal ac output of a resonantinverter.The post-rectifier outut type of output filter components can be any combination of capacitors and inductors, but a series inductor serves a purpose which is to decouple the output so as to not detune the resonant transformer.Resonant convertors are a good choice to achieve low EMI generation, but at the expense of efficiencyMost commonly, you see this type of convertor in laptops to provide the >1KV HV AC for CCFL displays. A simple test of your digital thermometer will reveal that the HV transformer core in normal operation quickly becomes hot to the touch, showing high magnetic core losses.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 12, 2018, 05:23:25 pm
content: Is there a schematic to go with this?Tim

author: warpco
author_rank: Contributor
timestamp: August 14, 2018, 09:11:30 pm
content: Quote from: T3sl4co1l on August 12, 2018, 05:23:25 pmHere it is. The left one is the LLC resonant half-bridge converter, the right one is the equivalent AC model of this converter.Quote from: Paul Price on August 11, 2018, 10:47:55 pmI really doubt about that. Every application note, article, research paper I read very clearly states that if the input voltage of an LLC resonant circuit is a square wave than the output voltage is also a square wave. I did some research in SPICE simulator and it seems that this is true. As you said the tank will respond primarily to the fundamental component of the square wave, but in real life the higher order harmonics will not be negligible. And if I understand correctly, the lighter the load, the worse the "filtering properties" of a resonant tank. As for the magnetizing inductance Lm, which is parallel to the load, it doesn't smooths the voltage. My simulation have confirmed this. At the light load the output voltage was more like a slightly smoothed square wave, at no load it was a square wave, and only at heavy load the voltage was sinusoidal.5 minutes later...Hmm... But all this articles assume a nominal load when they do the calculations. At the nominal load both the output voltage Vso and current Ios (see Fig. 3b) will be sinusoidal. And we are back to the beginning. Why they say that the output voltage is a square wave?20 minutes later...Aha! The mentioned simulation was for the equivalent model where the LLC tank is connected to a pure resistive load, and as I said both the current and voltage was approximately sinusoidal. When I add a rectifier with a capacitive filter everything has changed. The current was still sinusoidal, but the voltage was really a square wave! Look at my second quote in the first post, it says that a series resonant converter is a current source. When a current source feeds a rectifier with a cpacitive filter, the voltage at the input of the rectifier is rectangular (with the assumption that the capacitance is big enough to maintain a constant voltage).So the answer to my question is that series resonant converter is a current source, and when a current source supplies power to a rectifier with a capacitive filter we see rectangular voltage and sinusoidal current. Now I must understand why it is a current source...