Self-learning switching DC-DC convertersII
Knowing the inductance
How can IC designers know the impedance? They can’t…but the circuit can learn it during start-up and/or through power-on reset events; in other words, the system can measure the inductance-ESR impedance during down-times. Figure 1 illustrates how this approach can be applied to a buck (step-down) DC-DC converter using the above-described continuous filter scheme, where VSense is directly proportional and calibrated against inductor current IL. The shaded block is the Gm-C filter whose gain-bandwidth product is tuned with transconductor gm1 and DC gain calibrated with resistor R2 during a system down-time, aided by transistors Ma and Mb, both of which are off during normal operating conditions. The rest of the circuit is simply the power train of the switching supply, comprised of inductor L and its ESR RL, output capacitor Co, and high and low power MOS transistors ML and MH. Once the gain-bandwidth product and DC gain are properly adjusted (that is, filters are matched), the values are digitally stored and the DC-DC converter is allowed to power up and operate normally. Since the learning cycle only affects start-up, their associated power losses are non-existent during normal operating conditions, which is why this scheme is considered lossless.
Figure 1. Self-learning current-sensing Gm-C filter
.
The design and self-learning goal of the filter scheme is to match the series impedance of the inductor-RL combination with the R2C filter during the learning cycle. Following Ohm’s law, inductor current IL is inversely proportional to its series impedance and directly proportional to the voltage across it (VL):
(1)
The R2C network, in this case, is a Gm-C filter with output voltage VSense equal to:
(2)
Consequently, adjusting R2 to ensure inductor current bandwidth RL/L equals filter bandwidth 1/R2C sets VSense to:
VSense = (gmlR2RL) IL how does this look?
(3)
and if gm1R2RL is tuned to a known constant RSense, VSense is a direct measure of inductor current IL,
(4)