Download ECEN 5807. Boost converter with average current mode control

ECEN 5807. Boost converter with average current mode control
Figure 1 shows a boost with average current mode control of the inductor current. In the
design, the op-amp and the converter can be considered ideal. The circuit parameters are
as follows:




Vg = 50-200 V, C = 100 F, L = 500 H, R = 160 , switching frequency
fs = 200 kHz, current sensing resistance Rf = 0.02 
The output voltage is regulated by an outer voltage feedback loop (not shown) at a
constant value, V = 400 V.
The pulse-width modulator employs a saw-tooth waveform vt(t) with an
amplitude of VM = 2 V.
The power MOSFET gate driver is a non-inverting circuit, i.e. the MOSFET is on
when the gate-drive signal c(t) is logic high.
L
iL
+
Vg
+
–
C
R
v

Rf
R1
c(t)
Cp
R2
vc
Cz
10R1
_
+
vm
PWM
Figure 1: Boost converter with average current mode control
(a) Sketch the PWM comparator (showing polarities of the comparator inputs), and
the waveshape of the PWM saw-tooth waveform vt(t) to ensure proper operation
of the average current-mode controller, i.e. so that negative current feedback loop
is obtained in the circuit of Fig. 1.
(b) For the specified range of operating conditions, find the range of steady-state
current-command voltages Vc.
(c) Assuming R1 = 10 k, design the average current loop compensator, i.e., choose
R2, Cz, Cp, according to the following specifications:

The current-loop compensator must have a high-frequency pole at fp = fs.


During the MOSFET off-time, the slope of the signal vm(t) must not be
greater than the slope of the saw-tooth waveform (in absolute value).
The phase margin mi for the current feedback loop must be at least 60o.
(d) For the current-loop compensator designed in part (c), for each of the two
operating points corresponding to the extreme values of the input voltage Vg,
Vg = Vgmin = 50 V, and Vg = Vgmax = 200 V,
 find the cross-over frequency fci, and the phase margin mi
 sketch and label the steady-state waveforms vm(t) and vt(t) during one
switching period
 find approximate expressions for the control-to-output transfer function
Gvc  vˆ / vˆc and determine values of the corner frequencies and gains.
 Verify your results using Spice simulations: plot the magnitude and phase
responses of Gvc  vˆ / vˆc . Make sure that the DC operating points are set
correctly for Vgmin = 50 V, and for Vgmax = 200 V.
For the op-amp you may use your own ideal op-amp model (a voltagecontrolled voltage source having a large gain), an ideal model “opamp”
(included in the LTspice library), a real op-amp model such as LT1368
(included in the LTspice library), or LM324 (included in the PSpice
evaluation version). You may assume that auxiliary DC supply voltages
are available to supply the op-amp.