Page 233 - Rashid, Power Electronics Handbook

222 D. Czarkowski

The output current in PWM dc-dc converters is either equal to control loop. Signal transformers or optocouplers are used for
the average value of the output inductor current (buck-derived isolating feedback signals.
Á
and Cuk converters) or is a product of an average inductor Dynamic characteristics of closed-loop dc-dc converters
current and a function of the duty ratio. In practical imple- must ful®ll certain requirements. To simplify analysis, these
mentations of the current-mode control, it is feasible to sense requirements are usually translated into desired properties of
the peak inductor current instead of the average value. As the the open loop. The open loop should provide a suf®cient

peak inductor current is equal to the peak switch current, the (typically, at least 45 ) phase margin for stability, high band-
latter can be used in the inner loop, which often simpli®es the width (about one-tenth of the switching frequency) for good
current sensor. Note that the peak inductor (switch) current is transient response, and high gain (several tens of decibels) at
proportional to the input voltage. Hence, the inner loop of the low frequencies for small steady-state error.
current-mode control naturally accomplishes the input The open-loop dynamic characteristics are shaped by
voltage-feedforward technique. Among several current-mode compensating networks of passive components around the
control versions, the most popular is the constant-frequency error ampli®er. Second- or third-order RC networks are
one that requires a clock signal. Advantages of the current- commonly used. Because the converter itself is a part of the
mode control are the input voltage feedforward, the limit on control loop, the design of compensating networks requires a
the peak switch current, the equal current sharing in modular knowledge of small-signal characteristics of the converter.
converters, and the reduction in the converter dynamic order. There are several methods of small-signal characterization of
The main disadvantage of the current-mode control is its PWM dc-dc converters, and the most popular ones provide
complicated hardware, which includes a need to compensate average models of converters under the assumptions of high
the control voltage by ramp signals (to avoid converter switching frequency. The averaged models are then linearized
instability). at an operating point to obtain small-signal transfer functions.
Among other control methods of dc-dc converters, a Among analytical averaging methods, state-space averaging
hysteretic (or bang-bang) control is very simple for hardware has been popular since the late 1970s. Circuit-based averaging
implementation. However, the hysteretic control results in is usually performed using PWM switch or direct replacement
variable frequency operation of semiconductor switches. of semiconductor switches by controlled current and voltage
Generally, a constant switching frequency is preferred in sources. All these methods can take into account converter
power electronic circuits for easier elimination of electromag- parasitics.
netic interference and better utilization of magnetic compo- The most important small-signal characteristic is the
nents. control-to-output transfer function T . Other converter char-
p
Application speci®c integrated circuits (ASICs) are acteristics that are investigated are: the input-to-output (or
commercially available that contain the main elements of line-to-output) voltage transfer function, also called the open-
voltage- or current-mode control schemes. On a single 14- loop dynamic line regulation or the audio susceptibility, which
or 16-pin chip, there is an error ampli®er, comparator, describes the input-output disturbance transmission; the
sawtooth generator or sensed current input, latch, and PWM open-loop input impedance; and the open-loop dynamic load
drivers. The switching frequency is usually set by an external regulation. Buck-derived, boost, and buck-boost converters are
Á
RC network and can be varied from tens to hundreds of second-order dynamic systems; the Cuk converter is a fourth-
kilohertz. The controller has an oscillator output for synchro- order system. Characteristics of buck and buck-derived
nization with other converters in modular power supply converters are similar to each other. Another group of conver-
systems, and a constant voltage reference is generated on the ters with similar small-signal characteristics is formed by
chip as well. Additionally, the ASIC controller may be boost, buck-boost, and ¯yback converters. Among parasitic
equipped with various diagnostic and protection features; components, the ESR of the ®lter capacitor r C introduces
for example, current limiting, overvoltage and undervoltage additional dynamic terms into transfer functions. Other para-
protection, soft start, dead time in case of multiple PWM sitic resistances usually modify slightly the effective value of
outputs, and duty ratio limiting. In several dc-dc converter the load resistance. Sample characteristics in what follows are
topologies, for example, buck and buck-boost, neither control given for nonzero r , neglecting other parasitics.
C
terminal of semiconductor switches is grounded (so-called The control-to-output transfer function of the forward
high-side switches). The ASIC controllers are usually designed converter is
for a particular topology and their PWM drivers may be able

to drive high-side switches in low-voltage applications. v ðsÞ
o
T ðsÞ
p
However, in high-voltage applications, external PWM drivers dðsÞ v s ðsÞ¼0
must be used. External PWM drivers are also used for switches V Rr C s þ1=Cr c
I
with high input capacitances. To take full advantage of the ¼ 2
nLðR þ r Þ s þsðCR þLÞ=LCðRþr ÞþR=LCðRþr Þ
C
C
C
C
input-output isolation in transformer versions of dc-dc
converters, such an isolation must be also provided in the ð13:40Þ