Electrical Engineering Asked by learn design on December 22, 2021
I would like to find the expression of voltage across Rsense in the circuit below:
The author says in the book:
"A multiplier generates a current which is a product of the rectified line voltage k.Vin(t) and the error amplifier output level Verr". This current generator feeds an offset resistor Rcs connected to the sense element *Rsense in series with DC low side input terminal. Rcs fixes the maximum peak inductor current allowed by the multiplier. For instance, suppose the the multiplier delivers 300 uA and Rcs equals 2 kohm; then the maximum voltage across Rsense reaches 600 mV
(the inductor is just above the transistor connected in a boost configuration with a diode)
$V_{sense} = -1 cdot I_{inductor} cdot R_{sense}$
where $V_{sense}$ is the voltage of the node immediately to the left of $R_{sense}$ and $I_{inductor}$ is the current flowing right to left from the ground symbol towards $R_{sense}$. The diagram is incomplete, but, the current $I_{inductor}$ is coming from the inductor through the MOSFET and is returning to the AC source $V_{in}$ to complete the circuit. The negative sign is to show that the voltage on the left side of $R_{sense}$ is below the voltage of the ground symbol since current is flowing right to left.
The current through the inductor would be steadily increasing while MOSFET is ON and reaches the peak at the instant MOSFET turns OFF. The output voltage of A2 controls when the MOSFET turns OFF. The expression for non inverting input of A2 is
$k(dots) R_{CS} - I_{inductor} cdot R_{sense} $.
i.e,
$I_{inductor} = I_{setpoint}frac{R_{CS}}{R_{sense}}$ if the switch over point is approximated as the instant when non inverting input of A2 reaches zero volts. This is confirmed by the sentence you have quoted : "For instance, suppose the the multiplier delivers 300 uA and RCS equals 2 kohm; then the maximum voltage across Rsense reaches 600 mV".
Answered by AJN on December 22, 2021
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