# Generating a Bode plot from the small signal analysis of a Buck converter LTSPICE

#### Brettjohnson7191

Joined Apr 28, 2022
27
Good evening all,
I am stuck on a homework assignment and seeking your help. The assignment is for a power electronics course. We are given Vout=5v Vin=40v
output inductor is 100uH and the output capacitor is 1000uF with 10 mohms ESR all operated at 600kHz. This is also required to be completed in LT Spice
for my first attempt I decided to make a regular version of the buck converter which is attached as image 1. Then I began creating the small signal model of the buck converter (image2).
I run into issues when trying to figure out the values to enter into the VCVS and the VCCS can anyone point me in the right direction?
Thanks!

Image1

Image 2

#### crutschow

Joined Mar 14, 2008
34,677
Doesn't the circuit need some negative feedback to regulate the output?
As is, it is just an open-loop circuit.

#### Papabravo

Joined Feb 24, 2006
21,256
Doesn't the circuit need some negative feedback to regulate the output?
As is, it is just an open-loop circuit.
Ultimately it does, but you have to break the loop if you want to understand the open loop response. Also, this is a synchronous buck converter, so you need to work out your timing so you don't have both switches on at the same time. That would be a bad bad thing.
Getting the open loop bode plot will be easier if you substitute a Schottky diode for M2.

When looking at a DC-DC converter, the AC analysis in LTspice is quite difficult to use because you are not comparing an AC output to an AC input. You are comparing a duty cycle to and DC output with a very small, high frequency ripple. I've tried to make that work and have been unsuccessful. the method I used in the other thread is documented in the LTspice Help file. Search for "Middlebrook", the name of the developer of the method. Here is the preamble:

How to get a Bode Plot from a SMPS
In the interest of stability, the open loop gain of a negative feedback system operating in closed loop should fall below unity with increasing frequency before too much phase shift occurs unless your aim actually is to make an oscillator[1]. This idea can be applied to the stability analysis of a Switch Mode Power Supply(SMPS). Even though an SMPS is an intrinsically non-linear circuit with no small-signal linear equivalent circuit, there typically is an analog feedback loop operating on the filtered, switched output.

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#### Brettjohnson7191

Joined Apr 28, 2022
27
Ultimately it does, but you have to break the loop if you want to understand the open loop response. Also, this is a synchronous buck converter, so you need to work out your timing so you don't have both switches on at the same time. That would be a bad bad thing.
Getting the open loop bode plot will be easier if you substitute a Schottky diode for M2.

When looking at a DC-DC converter, the AC analysis in LTspice is quite difficult to use because you are not comparing an AC output to an AC input. You are comparing a duty cycle to and DC output with a very small, high frequency ripple. I've tried to make that work and have been unsuccessful. the method I used in the other thread is documented in the LTspice Help file. Search for "Middlebrook", the name of the developer of the method. Here is the preamble:

How to get a Bode Plot from a SMPS
In the interest of stability, the open loop gain of a negative feedback system operating in closed loop should fall below unity with increasing frequency before too much phase shift occurs unless your aim actually is to make an oscillator[1]. This idea can be applied to the stability analysis of a Switch Mode Power Supply(SMPS). Even though an SMPS is an intrinsically non-linear circuit with no small-signal linear equivalent circuit, there typically is an analog feedback loop operating on the filtered, switched output.
I replaced my low side switching fet with a schottky diode and attached my new file to this reply. My transient response
is showing only around 300mV output at my Vout node. I know there should be some switching losses but I would still expect a range in the 3-4V range if it is working properly. I plot my highside fet voltage and see it is switching at the correct time as well. Any other ideas? I appreciate the help.

#### crutschow

Joined Mar 14, 2008
34,677
Ultimately it does, but you have to break the loop if you want to understand the open loop response.
Okay, but here there's no loop to break, along with the compensation elements required for stability with feedback.

#### crutschow

Joined Mar 14, 2008
34,677
My transient response
is showing only around 300mV output at my Vout node.
So does the circuit eventually need to have feedback to stabilize the output voltage or not?

#### Brettjohnson7191

Joined Apr 28, 2022
27
Okay, but here there's no loop to break, along with the compensation elements required for stability with feedback.
Yes I understand that the first step in our homework is to simulate this portion of the buck converter generating a bode plot for this stage then we are to create the compensation network with the pole generating resistor/capacitor network. and simulate the bode plot once again and compare the two results

#### Papabravo

Joined Feb 24, 2006
21,256
Okay, but here there's no loop to break, along with the compensation elements required for stability with feedback.
Understanding the open loop response is just the first step. With a fixed load and a fixed duty cycle the system is stable without feedback. It is certainly not optimal that comes later.

#### Papabravo

Joined Feb 24, 2006
21,256
I replaced my low side switching fet with a schottky diode and attached my new file to this reply. My transient response
is showing only around 300mV output at my Vout node. I know there should be some switching losses but I would still expect a range in the 3-4V range if it is working properly. I plot my highside fet voltage and see it is switching at the correct time as well. Any other ideas? I appreciate the help.
View attachment 279117
It is trying to get somewhere, but has clearly not reached steady state. C1 is a honking big capacitor. Try a longer simulation and then use the parameter in the .trsan menu to start collecting data after the response reaches steady state
. Windows has a native utility to extract .zip files, but if it is not working for you the try down loading the 7zip.exe utility. If you are on a Mac then I don't know what to tell you. Also zoom in on your inductor current to see the inductor charging and discharging cycles.

#### Papabravo

Joined Feb 24, 2006
21,256