u/ee_control_z

Hello community,

I am currently attempting to test a compensator using the Simetrix\Simplis software. When I test my design using LTSpice, the design works as expected. That is, it regulates the output voltage to the expected value and is able to handle a relatively large load step without any issues - output is regulated and stable with minimum over/under shoots at the transition points. When attempting to simulate it with Simetrix/Simplis Elements, not so much. It is very sensitive to the op-amps being used.

Has anyone had similar experience?

If anyone is proficient with Simetrix\Simplis , I can attach a screenshot of the schematic.

Thank you.

https://preview.redd.it/uv4rsnwv4bfh1.png?width=567&format=png&auto=webp&s=27c27fa783ef10b046c3c62d8cafe0519e25ce81

Hello community,

I am following along with Application Note - 1162 from International Rectifier (now under Infineon) and specifically with with respect to the Type II compensator design example - the very first example discussed in the app note. For some reason, which I am unable to determine, my results differ from those stated in the app note. You'll notice that their simulation results state a crossover frequency of ~77 kHz with ~53 degrees phase margin. Using my test script, I am experiencing a crossover frequency well over 100 kHz.

This is the circuit that I used for the buck converter to calculate the transfer function. Although they did not explicitly state a load resistance value, R, I extrapolated 0.15 Ohms since they did state Vout = 1.8V and Imax = 12A. The parasitic resistance for the inductor was shown in a schematic earlier in the app note. However, a value was not explicitly stated in the example when listing the buck converter attributes. I added the inductor resistance in the calculations and edited its value to see if perhaps this was the issue but none of the tests spawned any favorable matching results.

Here is the Python code that I am using to simulate the buck converter along with the Type II compensator.

"""
   Infineon Application Note AN-1162
   
   Synchronous Buck Converter
   
"""

import control as ct
import matplotlib.pyplot as plt
import numpy as np

# 1. Define plant in continuous time domain

# Buck converter component values
L = 530e-9; Rl = 0.005   # Inductor
C = 470e-6; Rc = 0.010  # Capacitor
R = 0.15                # Load @ 12A for V = 1.8v
Vosc = 1.8
Vin = 12
Gain = Vin/Vosc  # From eq (15), page 10 in the app note

# Create buck converter transfer function
num = [Gain*C*C*Rc*Rc*R, Gain*2*C*Rc*R, R/(Vosc)]
den = [C*C*L*(2*Rc*R + Rc*Rc), 2*L*C*(Rc+R), L, Rl]
Gbuck = ct.tf(num, den)

# Design Type II compensator
Rf1 = 1200; Rf2 = 768; Rc1 = 7.15e3 #3.6e3
Cc1 = 4.7e-9; Cc2 = 68e-12

K = 1 / (Rf1*(Cc1))
print(f'\nCompensator gain K = {K:,.1f}')

# Create compensator transfer functions
Gcomp = ct.tf([K*Rc1*Cc1, K], [(Rc1*Cc2), 1, 0])

# Define loop transfer function
Ls = ct.series(Gbuck, Gcomp)

test_sys = ct.TransferFunction(Ls, name='Open Loop')
min_log = 3; max_log = 6; num_points = 10000

plt.style.use('dark_background')
omega = np.logspace(min_log, max_log, num_points)
ct.bode_plot(test_sys, omega=omega, dB=True, deg=True, color='cyan', display_margins=True)

# Get the current figure and axes
fig = plt.gcf()
mag_ax, phase_ax = fig.axes

# Enable logarithmic frequency lines when 'display_margins=True'
mag_ax.grid(visible=True, which='both', axis='both')
phase_ax.grid(visible=True, which='both', axis='both')

plt.show()

Buck Converter Output Filter Impedances

Note that here, 'R' is the load resistance and 'Rc' is the capacitor ESR. There are two capacitors of equal value, thus, Rc1 = Rc2, so just used Rc.

In the simulations, I played around with different values of Rl (inductor series resistance), but could never see any favorable test results matching the app note.

Can someone please help with clarifying why my simulation is not matching the test results in the app note.

Currently studying Control Theory using the textbook: Modern Control Systems by Dorf/Bishop. I ran into the following example of which I am not able to figure out how they came to the following result.

https://preview.redd.it/7nff5rfpjy5h1.png?width=757&format=png&auto=webp&s=4ccd7add01c2d4e539eb775f5faa9373a7b5aae9

In the attached screenshot, the solution is provided without the worked out steps - take em' at their word. I referenced the z-transfrom conversion table and included some of the equivalent s to z transforms. The zero-order hold equivalent s-domain transfer function is included as well.

The table does not include 1/s^3 transform so that is out of the question when looking for a potential solution. I tried multiplying Go(s) by (1 + e^-sT) / (1 + e^-sT). Nothing came about this approach. I am not seeing how you would get an additional multiple of T so that in the result you get T^2 in the numerator in addition to an overall factor of 1/2.

Can someone please help.