# LLC Converter Gain-Frequency Curve

The gain-frequency curve of an LLC resonant converter is a graphical guide displaying both the gain and operating frequency. At resonance frequency, the gain is certain to be unity. However, at above or below the resonance, the gain is no longer unity. In this article we will cover how LLC converter gain-frequency curve works or how to interpret it and how to make it. So, keep reading.

## How to Plot the LLC Converter Gain-Frequency Curve

In order to plot the curve, you must know the equivalent AC circuit of an LLC resonant converter. For more details on how to derive it, read the article How to Derive LLC Converter AC Circuit.

## Creation of Simulation Circuit

Below is an equivalent AC circuit of an LLC resonant converter. Parts of it are resonant capacitor (Cres), resonant inductor (Lres), magnetizing inductor (Lmag) and the AC resistance. Lmag is the inductance of the transformer. Below circuit is created in LTSpice, it is a free simulator that you can download here. If you are new to LTSpice, read the tutorial here.

## Setting up the Simulation Command

Configure the source voltage as below illustration. Just hover the mouse to the voltage source and right click to display the configuration window.

The Rac is setup with the curly braces. The purpose of it is to assign several values to it and display in the simulations. Left click on the Simulate toolbar then on the Edit simulation Cmd.

On the Edit Simulation Command, left click on the AC Analysis. Type of sweep must be Octave. Then define the number of points, Start frequency and Stop frequency.  After clicking the OK button, the command .ac oct 20 10k 400k will appear to the schematics.

Then we need to setup the Rac. While on the LTspice environment, simply press letter T on the keyboard. Afterwards, below box will show up.

Tick the SPICE directive and type .step param Rac 50 250 50. Click OK so that the command will appear to the schematics. The circuit with the simulation command should look like below.

## Run the Simulations

To run the simulation, simply click the run icon. Waveform window will show up. On the schematics, click on the Lmag junction. The result must look like below.

## How to Interpret the LLC Converter Gain-Frequency Curve

There are 5 plots. The green plot corresponds to Rac value of 50 while the pink one corresponds to the value of 250. The green plot is the biggest load of the LLC while the pink curve is the lightest load of the converter.

On the y-axis, look for the 1V and project it to the curve from left to right horizontally. The point where the projected line intersects to the curves is the resonance frequency, when projected vertically to the x-axis.

In this simulation, the resonance frequency is around 117 kHz.

The five plots are only dictated by different loading scenarios considering the output voltage is fixed. Regardless of the load, the resonance frequency will not change.

During the design of the LLC tank, the left side of the below equation is equated to one. Then the operating frequency is surely landed at the resonance.

Gain = 2 x n x Vout / Vin

However, if either of the turns ratio, output voltage and input voltage is changed, the gain will either higher or lower than unity.

When the gain is below unity, the operation is to the right of the resonance based from the LLC converter gain-frequency curve. On the other hand, if the gain is higher than one, the operation is to the left of the resonance.

Any gain value will correspond to a switching frequency and this can be plotted from the gain-frequency curve

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1. Biswajit says:

Hi sir , could you please make detailed post on magnetics design for LLC Resonant converter with magnetic integration and without magnetic integration

2. electronicsbeliever says:

Hi Biswajit,

For now I am not considering that post, but maybe I will get to that in the future.
Actually, both options are the same in terms of the LLC function or operation. The only difference is on how the resonant inductor is being considered.

Thanks,
eb

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