ECEN4797/5797
Pulse Frequency Modulation (PFM) of a Cell-Phone Buck Converter
The figure below shows a buck converter used to supply a microprocessor load (modeled as R) in a cell
phone from a single-cell Lithium-Ion battery, Vg = 3.6 V. As illustrated by the waveforms shown, the
converter is operated in discontinuous conduction mode as follows: at the start of a switching period
MOSFET Q1 is turned ON. At the time when the inductor current reaches Ipk, Q1 is turned OFF and
synchronous rectifier Q2 is turned ON. Q2 is then turned OFF at the time when the inductor current drops
to zero. Both Q1 and Q2 are OFF for the rest of the switching period. To regulate the DC output voltage at
V = 1 V, a controller (not shown) varies the switching frequency fs = 1/Ts. The variable-frequency control
method described here is referred to as peak-current controlled Pulse-Frequency Modulation (PFM). You
can assume all components are ideal; losses can be neglected in this problem.
Q1
i
Q1
i
L
Io
L
!
Vg
+
Vg– +
–
i
i
!
vgs1
v
gs1
+
+
+
vgs2 +
vgs2
!
+
Q2
!
Q2
C
C
v
!
Io
+
v R R
!
Ipk I
pk
vgs1 v
gs1
vgs2 v
gs2
t1 t
1
t2 t
2
t
t
t
t
t
t
Ts T
s
(a) Find an expression for fs as a function of L, Ipk, Io, V, and M = V/Vg. Show that fs is proportional to Io*
(b) Given Vg = 3.6 V, V = 1 V, 1 mA ≤ Io ≤ 200 mA: find Ipk, L, and C so that
•
•
The maximum switching frequency is fsmax = 4 MHz. When fs = fsmax, the converter operates at the
boundary of discontinuous conduction mode and continuous conduction mode.
The peak output voltage ripple is Δv ≤ 5 mV
(c) What is the minimum switching frequency?
*Note that this implies that converter losses are proportional to output power which, in turn, implies that the
converter can maintain high efficiency over very wide range of loads. This is an essential feature in portable batterypowered applications.