Introduction to Digital Power Conversion
XMC4000/1000 Family
Control Loops
Application Guide
83
V1.0, 2015-01
7.4
Open Loop Gain Stabilization (Frequency Compensation)
Here we look at how power converter frequency properties and stability is affected by the control
modes; i.e. voltage mode versus current mode control.
Voltage Mode Control, Open Loop Gain (See
Peak Current Mode Control with Slope Compensation, Open Loop Gain (See
Merged Fundamentals in Control Loops ABC
This example is a simplification of some merged basics in loop control, with essential concepts and
terms, generalized in
Note:
The same function block colors are used in the Voltage Mode respective Current Mode Control.
Figure 67
Open Loop Gain vs. Closed Loop Gain
– Fundamentals (ABC)
A
– Principle of Transfer Functions in a Feedback Loop
The output V
OUT
of the conversion functions in H
CF
is (via the ADC H
ADC
feedback path) compared
with the input V
REF
. The difference (error) is forced towards 0 by the closed open-loop-gain path.
H
ADC
can have delay and gain impact, but this is assumed to be out of scope in this example; i.e.
H
ADC
=1.
B
– Open Loop Gain versus Closed Loop Gain: Concept Definitions
‘Open loop gain’ should be understood as the total gain along the loop, from any imagined cut point.
‘Closed loop gain’ is the resulting input-to-output transfer function gain ratio V
OUT
/ V
REF
(Input
=
V
REF
).
C
– Bode-Plot of Open Loop Gain: Stability Terms and Frequency Compensation
The Bode-Plot diagram is logarithmic; vertically by gain (dB) and horizontally by frequency. The
product of absolute values of the transfer functions will appear asymptotically as a line, consisting of a
sum of straight lines. If this line-slope exceeds -40 dB/decade at the 0-dB level, it will cause instability.
The -40 dB/decade is due to poles (each one contributing with -20 dB/decade). The general rule is to
‘eliminate’ one pole by +20 dB/decade frequency compensation by a zero in H
I
, for a phase-margin.
