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參數(shù)資料
| 型號： | LM2633MTDX/NOPB |
| 廠商： | NATIONAL SEMICONDUCTOR CORP |
| 元件分類： | 穩(wěn)壓器 |
| 英文描述： | SWITCHING CONTROLLER, 275 kHz SWITCHING FREQ-MAX, PDSO48 |
| 封裝： | TSSOP-48 |
| 文件頁數(shù)： | 26/40頁 |
| 文件大?。?/td> | 1350K |
| 代理商： | LM2633MTDX/NOPB |
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Control Loop Design (Continued)
(39)
The value of f
p can be determined by comparing the denomi-
nators of
Equation (35) and Equation (27). The result is:
(40)
From the above expressions, it can be seen that the
control-output transfer function has three poles and one
zero. Of the three poles, one is a real pole (f
p) that is located
at low frequency, the other two are either complex conju-
gates that are located at half the switching frequency (f
n), or
are separated real poles, depending on the Q value. When Q
value is less than 0.5, the two high frequency poles will
become two real poles.
From
Equation (34) it can be told that Q will become nega-
tive when m
c
< 1/(2D’). A negative Q value means an
unstable system because the control-output transfer function
will have a right-half-plane pole.
Example: L = 1.5 H, C = 2 mF, R
e =9 m,Rds =10 m,
V
in = 10V, Vout = 1.6V, R = 0.4. For LM2633, f = 250 kHz,
S
e = 0.25V, ρ =5.
R
j = 10m x 5 = 50m
S
e = 0.25V x 250kHz = 62.5mV/s
f
n = 250kHz ÷ 2 = 125kHz
The resulting gain plot is shown in
Figure 9 as the asymptotic
plot. The plots of the actual gain and phase as computed by
Equation (27) are also shown.
It should be noted that load resistance only changes the low
frequency gain. This causes the location of the low fre-
quency pole to change with load.
Frequency Compensation Design
The general purpose to compensate the loop is to meet
static and dynamic performance requirements while main-
taining stability. Loop gain is what is usually checked for
small-signal performance. Loop gain is equal to the product
of control-output transfer function (or so-called ’plant’) and
the output-control transfer function (i.e. the compensation
network transfer function). Different compensation schemes
result in different trade-offs among static accuracy, transient
response speed and degree of stability, etc.
Generally speaking it is a good idea to have a loop gain
slope that is 20dB/decade from a very low frequency to well
beyond cross-over frequency. The cross-over frequency
should not exceed one-fifth of the switching frequency, i.e.
50kHz in the case of LM2633. The higher the bandwidth, the
potentially faster the load transient response speed. How-
ever, if the duty cycle saturates during the load transient,
then further increasing the small signal bandwidth will not
help. In the context of CPU core or GTL bus power supply, a
small-signal bandwidth of 20kHz to 30kHz should be suffi-
cient if output capacitors are not just MLCs.
Since the control-output transfer function usually has very
limited low frequency gain (see
Figure 9), it is a good idea to
place a pole in the compensation at zero frequency, so that
the low frequency gain especially the DC gain will be very
large. A large DC gain means high DC regulation accuracy
(i.e. DC voltage changes little with load or line variations).
The rest of the compensation scheme depends highly on the
plant shape. If a typical shape such as shown in
Figure 9 is
assumed, then the following can be done to create a
20dB/decade roll-off of the loop gain.
Place the first zero at f
p, the second pole at fz, and the
second zero at f
n, then the resulting loop gain plot will be of
20dB/dec slope from zero frequency up to f
n (half the
switching frequency).
Figure 10 shows the gain plot of such a two-pole two-zero
(more accurately, a lag-lag) compensation network, where
f
z1,fz2 and fp2 are the first zero, second zero and second
pole frequencies. The first pole f
p1 is located at zero fre-
quency.
20000863
FIGURE 9. Example Control-Output Transfer Function
Bode Plot
LM2633
www.national.com
32
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