# Question about "DC Transformer" and "Large-signal Simulation"

#### BlackMelon

Joined Mar 19, 2015
126
Dear all,

Currently, I am reading a switching power supply book by Basso. The file is attached here. On page 102, the author defines the word "DC Transformer" and I got his point. It works as an ideal transformer but only with DC input/output.
On page 105, he performs large-signal simulation. Basically, he just perturbs the duty cycle (d) of a buck converter and observes the perturbation of vout. Then, plot the bode plot: vout(s)/d(s). However, after perturbation, I think the secondary side's current should be the mixture of DC and AC. So, why does he use the DC transformer here?

Thank You
BlackMelon

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#### sparky 1

Joined Nov 3, 2018
579
He decides on which model to use in the simulation. It satisfies both turns ratio and will produce a bode plot.
The model is a subroutine in the SSA buck DC / DC and it works also for his quantitative analysis.
The waveform is technically DC the (squarish )reciprocating shift in magnetic field is responsible for the DC conversion at the secondary. The perturbation of the system happens at a quantum level.

#### BlackMelon

Joined Mar 19, 2015
126
Sorry, I forgot to clarify what I mean by DC and AC here. Please see the figure below. Suppose my DC/DC converter is running in its steady-state. My time-instantaneous current of an inductor is the triangular wave. The DC value of this current is its average IL(AVG). The AC is something that try to change the average value (perturbation). It could be noises, impulses, sinusoidal, or anything but let's say it is sinusoidal.
In the book x = X + x_hat. Where X is the DC value and x_hat is the AC (perturbation) value.

#### Papabravo

Joined Feb 24, 2006
16,809
Let's be clear about what is going on here. The DC-DC transformer is an abstract model implemented with behavioral voltage and current sources. There is no primary and secondary, just functional relationships between the two sides. What the model allows is the use of linear analysis methods on what is inherently a nonlinear system. The technique of linearization around an operating point is well established in the analysis of non-linear control systems.

It should be self evident that a change in the duty cycle (for the real converter) will change I(max) and I(min) which will change I(avg). So what was there before will be there after, just changed slightly in magnitude. The input to the DC-DC transformer is still just DC it has no AC component. the output will track changes in the input and changes in the duty cycle. If you look at the output in a simulation you will not see the AC component, only the effects. The AC component only shows up if you are using an inductor and a switch.

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#### Papabravo

Joined Feb 24, 2006
16,809
I went back to the simulation of the DC-DC transformer and updated it to show how to measure the magnitude and frequency of the resonance peak that a potential control system would have to deal with. The results are here:

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