I'm designing a boost converter that boosts a 9V battery to about 10.5V. The objective is to maintain 10.5V despite the V_in reduction due to battery dissipation, e.g. boost 6V to 10.5V. This boost converter works great under steady loads such as when I hook a resistor from V_out to GND. The problem arises when I hook it up to the desired load which is a cellular modem. This modem draws somewhere around 100mA for normal operation but when transmitting it jumps to about 1.2A for 500ms at a time. This causes a massive ripple (really a dip) in my output voltage to as low as V_in. The minimum input to the modem is 8V before it shuts down so these ripples often cause the modem to restart.
Below is my schematic and board design using the LM2731 boost converter IC.
I've tried various inductances (10uH, 22uH, and 33uH) and they all yield the same result. I've also increased the ceramic output capacitors with only a marginal increase in stability. For fun I tried a 1000uF electrolitic between V_out and GND and that helped keep the modem on but still yielded ripples on the order of 1 to 2V which I'd like to reduce to the several hundred mV range.
Does anyone have any insight into how to reduce ripples with short bursts of draw?