A New Way to Model Current-Mode Control

May 1, 2007 12:00 PM
By Robert Sheehan, Principal Applications Engineer, National Semiconductor, Santa Clara, Calif.

Current Mode

The same PWM function occurs for current-mode control, except that monitoring the inductor current creates the ramp. This signal is comprised of two parts: the ac-ripple current and the dc or average value of the inductor current. The output of the current-sense amplifier is summed with an external ramp (VSLOPE) to produce VRAMP at the inverting input of the comparator.

In Fig. 6, the effective VRAMP = 1 V, which was used for the voltage-mode modulator. With VIN = 10 V, the modulator voltage gain KM = 10.

The linear model for the current loop is an amplifier (Fig. 7), which feeds back the dc value of the inductor current, creating a voltage-controlled current source. This is what makes the inductor disappear at dc and low frequencies (Fig. 8) while the ac-ripple current sets the modulator gain.

The current-sense gain (RI) is usually expressed as the product of the current-sense amplifier gain (GI) and the resistance of the sense resistor (RS):

RI = GI × RS.

The current-sense gain is an equivalent resistance, the units of which are V/A. The current-loop gain is the product of the modulator voltage gain and the current-sense gain, which is also in units of V/A. The modulator voltage gain is reduced by the equivalent divider ratio of the load resistor (ROUT) and the current-loop gain KM × RI. This sets the dc value of the control-to-output gain. Neglecting the dc loss of the sense resistor:

This is usually written in factored form:

The dominant pole in the transfer function (ωP) appears when the impedance of the output capacitor (COUT) equals the parallel impedance of the load resistor and the current-loop gain:

The inductor pole (ωL) appears when the impedance of the inductor equals the current-loop gain:

The current loop creates the effect of a lossless damping resistor, splitting the complex-conjugate pole of the output filter into two real poles. For current-mode control, the ideal steady-state modulator gain may be modified, depending on whether the external ramp is fixed or is proportional to some combination of input and output voltage. Further modification of the gain is realized when the input and output voltages are perturbed to derive the effective small-signal terms. However, the concepts remain valid despite small-signal modification of the ideal steady-state value.

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