Frequency response and loop compensation

AN2495

18/36

Doc ID 13127 Rev 5

7

Frequency response and loop compensation

The transfer function in the complex frequency domain of the discontinuous current mode

(DCM) flyback converter with L6565 driver is given by:

Equation 36

The parameters and values are listed in Table 3.

It is worth noting that the transfer function has one pole and one zero on the left half plane

and an additional zero on the right half plane. The RHP zero is very difficult, if not

impossible, to compensate and therefore must be kept well beyond the closed-loop

bandwidth. As a result, the transient response of such a system will not be extremely fast.

Poles and zeros are given in Equation 37 and Equation 38:

Equation 37

A good line and load regulation implies a high DC gain, thus the open loop gain should have

a pole at the origin. Normally in this case we need a feedback network like the one in

Figure 7.

Table 3.

Transfer function main parameters

Parameter

Description

Value

n

Primary/secondary turn-ratio

10

Sensing resistor

0.8

Ω

Maximum duty-cycle

0.5

ESR

Electrolytic series resistance

16 m

Ω

Output load

7.2

Ω

Output capacitance

2 mF

Primary inductance

1.56 mH

G

()

V

out s

()

V

com p s

()

-----------------------

nR

out

•

1D

max

–

()

•

2R

S

•

1D

ma x

+

()

•

--------------------------------------------------------

1s

C

ou t

•

ESR

•

+

() 1s

L

n

2

R

–

()

2

-------------------------------------------------

•

–

⎝⎠

⎜⎟

⎛⎞

1s

C

1D

ma x

+

-----------------------

•

+

---------------------------------------------------------------------------------------------------------------------------------

•

=

=

f

p

25Hz f

Z1

3.5

10

5

Hz f

Z2

;

•

510

3

•

Hz

=

=

;

=