# DC Gain of the System

I'm trying to design a feedbcak loop compensator and I'm following the instructions on power supply cookbook.

Book has calculations for DC gain like equations below: in my situation Vin: 40V-60V and Vout:350V, Nsec/Npri:10 (full-bridge)

DC gain becomes 350V/40V: 8.75 and that means peak to peak output voltage of the error amplifier is: 45.7V

question is what is this peak to peak output voltage of the error amplifier? what do we use it for?

bonus question: I'm using sg3525 and I can't find the ramp voltage of it, is there a calculation for it? Here is the datasheet: https://www.st.com/resource/en/datasheet/sg3525.pdf

thank you.

• There are a lot more steps byond just calculating Adc... Usually Adc is used along with the error amplifier gain (60db for your chip) in a few calculations. – MadHatter May 29 '20 at 1:49
• The expression you give is quite strange, where did you get it? Also, what is the converter topology for which you need to plot the ac response? – Verbal Kint May 29 '20 at 6:56
• @VerbalKint I got them from power supply cookbook, it is a full bridge dc-dc converter. – Das D. May 29 '20 at 11:30
• Not sure what cookbook is this? A full-bridge dc-dc converter is a buck-derived topology whose transfer function is that of a forward converter. Is this a voltage- or current-mode control? Let me know and I'll write an answer. – Verbal Kint May 29 '20 at 12:59
• It's marty brown's cookbook page 202, I'm trying to build a full bridge dc-dc converter with voltage mode control @VerbalKint – Das D. May 29 '20 at 21:14

## 1 Answer

What you need to stabilize your converter is the control-to-output transfer function: if a stimulus is applied to the duty ratio input, how does it propagate through the converter and create a response on the output. You can obtain this transfer function in various ways, for instance via a small-signal model like the PWM switch model or by using a piece-wise linear simulator like SIMPLIS. The program lets you simulate a switching circuit (and thus observe the cycle-by-cycle waveforms) and delivers the ac response later on after a few seconds.

The below circuit shows a possible example running with Elements, the free demonstration version: This is a 5-V/100-A full-bridge converter operated in voltage-mode control from a 24-V dc source. The circuit is simplified to let you run it on Elements but a real application would require additional protection circuits like peak current limit for instance. If you run this circuit, you obtain the below transient waveforms confirming the 5-V output: The control-to-output transfer function is immediate and shows a dc gain of 11.1 dB with the classical second-order response of a buck-derived topology: If you want to determine the dc gain analytically, it is that of a forward converter: In this expression, $$\V_p\$$ represents the peak voltage of the pulse-width modulator (PWM) ramp (2 V in this example), $$\V_{in}\$$ is the input voltage and $$\N\$$ represents the transformer turns ratio $$\1:N\$$.

This dc gain is affected by all the ohmic losses, $$\r_{DS(on)}\$$, $$\r_L\$$ etc. which are considered zero here.

You could find many of these converters free templates from my web page. They all run on Elements and will let you explore the transfer functions of these converters.

Now, based on the data-sheet, I would be inclined to think that the peak voltage is around 3.5 V or so because it corresponds to the maximum duty ratio value on one output: which also corresponds to the clock amplitude if I'm not mistaken.

• thank you for the answer sir, but what's the Vp: 2V here? – Das D. Jun 1 '20 at 19:03
• Hello, glad if this could help. $V_p$ is the peak voltage of the PWM ramp. It is 2 V in my example hence a 6-dB attenuation incurred by the modulator alone. If my interpretation of the 3525 data-sheet is correct, $V_p$ should be 3.5 V or so for this controller. – Verbal Kint Jun 1 '20 at 19:12