# 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.

### Theoritical calculation

#### Output voltage

< $V_{out}$ > $= D \times V_{in}$

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

< $I_L$ > $= \frac{D \times Vin}{R}$

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

### 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.

### Theory calculation

#### Output voltage

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

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

For this topology we will compare the output average voltage accross DC1 and the input rms current through AC1.

### Theory calculation

#### Average Output voltage

< $V_{out}$ > $= \frac{V_{in} \times 3 \times \sqrt{6}}{\pi*\sqrt{2}}$

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.