I need slightly higher voltage on the output of the TPS23756, 5.2V instead of 5V
Is there any way to do it, without changing the whole design?
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You might try adjusting R18 to 43.2K. Possible effects might be slight increase in minimum input voltage (for regulation) at full current or available current at minimum input voltage. A production design will remove R13 which may have a small effect on the output voltage.
Hypothetically speaking, that is a pretty large change in operating point (20%).
The result is in part dependent on your input voltage range and loading requirements. Concerns would be running out of duty cycle at low line, peak current limit, and the voltage / current ratings of the input and output switches.