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 Operation

Whether the current-mode converter uses the peak, valley, average or sample-and-hold method is of secondary importance to the operation of the current loop. As long as the dc current is sampled, current-mode operation is maintained. The current-loop gain splits the complex-conjugate pole of the output filter into two real poles, so that the characteristics of the output filter are set by the capacitor and load resistor. Only when the impedance of the output inductor equals the current-loop gain does the inductor pole reappear at higher frequencies.

To understand how this works, voltage-mode operation is first examined. The basic concept of pulse-width modulation (PWM) is used to establish the criteria for the modulator gain. This allows a linear model to be developed, illustrating the dc- and ac-gain characteristics.

Having established the basic modulator concept, the current loop is added by sensing the inductor current and feeding the sensed signal back to the modulator. For simplicity, the buck regulator is used to illustrate the operation.

Voltage-Mode Control

Fig. 1 shows a voltage-mode PWM circuit. It uses a comparator to modulate the duty cycle (D). The fixed-frequency operation of this circuit is shown in Fig. 2, where a sawtooth voltage ramp (VRAMP) is presented to the inverting input. The control or error voltage is applied to the noninverting input. The modulator gain (FM) is defined as the change in control voltage (VC), which causes the duty cycle to go from 0% to 100%:

The modulator voltage gain (KM), which is the gain from the control voltage to the switch voltage (VSW), is defined as:

where VIN is the voltage applied to S1 in Fig. 3.

For voltage-mode operation, the control-to-output transfer function is found by multiplying the modulator voltage gain by the output-filter response. With VIN = 10 V and VRAMP = 1 V, KM = 10, which is 20 dB. Figs. 3, 4 and 5 show the schematic, the linear model and the frequency response plot for a voltage-mode buck regulator, respectively. The complex-conjugate pole of the LC output filter is clearly seen, with the resulting 180-degree phase shift occurring at approximately 8 kHz.

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© 2007 Penton Media, Inc.