1. The Ideal Current Controller The ideal current controller causes the average inductor current to follow the control input: Large-signal and small-signal averaged switch models, buck example:

50. High-frequency pole (from the accurate averaged model (4))

51. Compare to first-order approximation of the sampled-data control-to-current model Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at Model (4) is consistent with the sampled-data small-signal model

54. DC gain of line-to-output G vg-cpm (based on model (4))

55. Example CPM buck converter: V g = 10V, L = 5  H, C = 75  F, D = 0.5, V = 5 V, I = 20 A, R = V/I = 0.25 , f s = 100 kHz Inductor current slopes: m 1 = (V g – V)/L = 1 A/  s m 2 = V/L = 1 A/  s D = 0.5: CPM controller is stable for any compensation ramp, m a /m 2 > 0 Select: m a /m 2 = M a /M 2 = 1, M a = 1 A/  s

56. Example (cont.) Duty-cycle control Peak current-mode control (CPM)

57. Compare to first-order approximation of the high- frequency sampled-data control-to-current model Control-to-inductor current response behaves approximately as a single-pole transfer function with a high-frequency pole at

58. 2 nd -order approximation in the small-signal averaged model