3 Example: 50W LLC Development Board

The 50W Interleaved LLC Converter Development Board was used in this example to conduct plant measurements. Since the LLC topology utilizes variable frequency control, the BODE-injected signal modulates the switching frequency. The firmware documentation for this development board provides a detailed, step-by-step guide on how to adapt the code for accurate plant measurements.

For further information, please visit www.microchip.com/ev84c64a. Figure 3-1 illustrates the measurement setup on this development board.

Figure 3-1. BODE Measurement Setup Using dsPIC® DP PIM in 50W LLC Development Board

During the BODE measurement process, as illustrated in Figure 3-2 for test points TP2 (injected signal), TP3 (DAC output) and the TP121 on LLC board (V_OUT) in AC analysis mode on the oscilloscope, an inversion of the BODE injected signal is observed at the DAC output. This inversion occurs due to the influence of the on-board operational amplifier.

Figure 3-2. Signal Measurement During BODE Measurement

The plant gain of the LLC converter is quantitatively defined as the ratio of the peak-to-peak AC component of the output voltage to the corresponding DAC output signal, as described in this equation:

Equation 3-1. LLC Plant Gain Based on the Waveform

G a i n = 20 \times \log \frac{{C H}_{3}}{{C H}_{2}} = 20 \times \log \frac{1.454 V}{388 m V} = 20 \times \log 3.7474 = 11.4746 d B

In digital control systems, it is essential to account for the modulator gain when evaluating plant gain measurements. The modulator effectively scales the digital control signal before it is applied as a duty cycle or frequency to the power stage. If the full-scale range of the 12-bit DAC (4095) and modulator does not match, the measured plant gain will not be correct. In this case, the switching frequency is modulated, so the modulator full-scale range is the difference between the PGxPER register value needed to obtain the maximum switching frequency (PGxPER_min) and the PGxPER value needed to obtain the minimum switching frequency (PGxPER_max). The modulator gain is defined as the ratio of (PGxPER_max-PGxPER_min) to the DAC full-scale code, which is 4095. To ensure accurate comparison between calculated and measured gains, and to maintain consistency across different switching frequencies, a correction factor of 20 × log((PGxPER_max-PGxPER_min)/DAC_max) dB should be added to the measured plant gain. This correction ensures the measured gain represents the true control-to-output transfer function, regardless of the digital implementation or modulator configuration. In this case, the maximum and minimum switching frequencies are 1 MHz and 800 kHz, respectively. Given the mode of PWM operation, this equates to PGxPER_min = 4000 and PGxPER_max = 5000.

Considering the modulator gain correction, the gain calculation is as follows:

Equation 3-2. Plant Gain Including Modulation Gain

G a i n = 20 \times \log \frac{{C H}_{2}}{{C H}_{3}} + 20 \times \log \frac{(P G x P E R_m a x - P G x P E R_m i n)}{{D A C}_{\max}} = {20 \times \log \frac{1.454 V}{388 m V}} + {20 \times \log \frac{1000}{4095}} = -0.77 d B

Where:

DAC_max = Maximum digital value of the DAC output (e.g., 4095 for 12-bit DAC)

Analyzing the plant measurements to identify the poles and zeroes that need compensation is crucial, as shown in Figure 3-3. This analysis is essential for designing an appropriate compensator for the system’s topology.

Figure 3-3. Plant Measurement Without Isolation Transformer of 50W LLC Development Board at 2A Load