March 2009

11

M9999-032409

MIC2169

Micrel

100

150

100

50

0

0

180

1000000

100

f

Figure 5. Phase Curve for G(s)

It can be seen from the transfer function G(s) and the gain

curve that the output inductor and capacitor create a two pole

system with a break frequency at:

f

1

2L C

LC

OUT

=

××

π

Therefore, f

By looking at the phase curve, it can be seen that the output

capacitor ESR (0.025

Ω) cancels one of the two poles (LC

system by introducing a zero at:

f

1

2

ESR C

ZERO

OUT

=

××

×

π

Therefore, F

From the point of view of compensating the voltage loop, it

is recommended to use higher ESR output capacitors since

they provide a 90° phase gain in the power path. For com-

parison purposes, Figure 6 shows the same phase curve

with an ESR value of 0.002

Ω.

100

150

100

50

0

0

180

1000000

100

f

Figure 6. The Phase Curve with ESR = 0.002

Ω

It can be seen from Figure 5 that at 50kHz, the phase is

approximately –90° versus Figure 6 where the number is

–150°. This means that the transconductance error ampli-

fier has to provide a phase boost of about 45° to achieve a

closed-loop phase margin of 45° at a crossover frequency

of 50kHz for Figure 4, versus 105° for Figure 6. The simple

RC and C2 compensation scheme allows a maximum error

amplifier phase boost of about 90°. Therefore, it is easier to

stabilize the MIC2169 voltage control loop by using high ESR

value output capacitors.

g

It is undesirable to have high error amplifier gain at high

frequencies because high frequency noise spikes would be

picked up and transmitted at large amplitude to the output,

thus, gain should be permitted to fall off at high frequencies.At

low frequency, it is desireable to have high open-loop gain to

attenuate the power line ripple. Thus, the error amplifier gain

should be allowed to increase rapidly at low frequencies.

The transfer function with R1, C1, and C2 for the internal

g

equation:

Error Amplifier(z)

g

1R1 S C1

sC1 C2 1 R1

C1 C2 S

C1 C2

m

=×

+× ×

×+

+

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

⎥

The above equation can be simplified by assuming

C2<<C1,

Error Amplifier(z)

g

1R1 S C1

s

C1 1 R1 C2 S

m

=×

+× ×

×

×

()

⎡

⎣

⎢

⎤

⎦

⎥

From the above transfer function, one can see that R1 and

C1 introduce a zero and R1 and C2 a pole at the following

frequencies:

Figures 7 and 8 show the gain and phase curves for the above

transfer function with R1 = 9.3k, C1 = 1000pF, C2 = 100pF,

and g

amplifier exhibits approximately 45° of phase margin.

20

40

60

60

.001

10000000

1000

f

Figure 7. Error Amplifier Gain Curve