# SIMBA Benchmark with Analytical Calculations

A benchmark has been realized in order to compare SIMBA simulation results vs analytical calculations from theory for three basic topologies:

• DC-DC Buck converter
• Flyback
• 3-phase Diode Bridge

## DC-DC Buck converter

Let's compare the output voltage accross R1 and RMS current through the inductance L1.

### SIMBA circuit ### Theoritical calculation

#### Output voltage

$ = D \times V_{in}$

with:

• $V_{in}$ = 50 V
• duty cycle D= 0.5

#### Inductance RMS current

$(I_L)_{rms} = \sqrt{\frac{^2 + (\Delta_{i_L})^2}{12}}$

with:

• R = 5 $\Omega$
• L = 0.001 H
• $f_{sw}$ = 5000 Hz

$ = \frac{D \times Vin}{R}$

$\Delta_{i_L} = \frac{D \times (1-D) \times Vin}{L*f_{sw}}$

### SIMBA simulation

The SIMBA output voltage accross R1 and the RMS current through the inductance L1 have been simulated and below the results: Therefore the comparison between SIMBA and Theory has been done by using histogram to have a clear view of the SIMBA's accuracy: The relative difference is negligeable which shows the reliability and robustness of SIMBA's solver.

## Flyback

For this topology, only the average output voltage accross R2 is compared.

### SIMBA circuit ### Theory calculation

#### Output voltage

$ = V_{in} \times m \times \frac{D}{1-D}$

with:

• $V_{in} = 6 V • duty cycle D = 0.25 • $N_2$ = 2 • $N_1$ = 1 • $m = \frac{N_2}{N_1}$ ### SIMBA simulation The SIMBA output voltage accross R2 has been simulated and below the results: Therefore the comparison between SIMBA and Theory for the average output voltage has been realized and we used the "histogram" way to plot those results. ## 3 phase Bridge Diode Download Simba Model For this topology we will compare the output average voltage accross DC1 and the input rms current through AC1. ### SIMBA circuit ### Theory calculation #### Average Output voltage $ = \frac{V_{in} \times 3 \times \sqrt{6}}{\pi*\sqrt{2}}$ with : •$V_{in} = 380 V
• Input RMS current: $(I_{input}){rms} = I \times \sqrt{\frac{2}{3}}$
• DC current $I_{dc}$ = 10 A

### SIMBA simulation

The SIMBA Output Voltage accross DC1 and the input rms current through AC1 have been simulated and below the results: Therefore the comparison between SIMBA and Theory for the average output voltage and the input rms current have been realized. We also plot the results with "histogram" chart. 