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loop gain. The impedance peaks at the filter resonant frequency. Equation 17 calculates the resonant frequency

of the filter.

fres= 1

2π× LIN×CF

(17)

The purpose of RD is to reduce the peak output impedance of the filter at the resonant frequency. Capacitor CD

blocks the DC component of the input voltage to avoid excessive power dissipation in RD. Capacitor CD must

have lower impedance than RD at the resonant frequency with a capacitance value greater than that of the input

capacitor CIN. This prevents CIN from interfering with the cutoff frequency of the main filter. Add damping when

the output impedance of the filter is high at the resonant frequency (Q of the filter formed by LIN and CIN is too

high). Use an electrolytic capacitor CD for damping with a value given by Equation 18.

CD≥4×CIN

(18)

Use Equation 19 to select the damping resistor RD.

RD= LINCIN

(19)

8.1.2 Error Amplifier and Compensation

Figure 8-2 shows a Type-ll compensator using a transconductance error amplifier (EA). The dominant pole of the

EA open-loop gain is set by the EA output resistance, ROEA, and effective bandwidth-limiting capacitance, CBW,

as shown by Equation 20.

GEAopenloop s = − gm×ROEA

1+s×ROEA×CBW

(20)

The EA high-frequency pole is neglected in the above expression. Equation 21 expresses the compensator

transfer function from output voltage to COMP, including the gain contribution from the feedback divider.

Gcs = vcsvouts = − VREFVOUT × gm×ROEA× 1+ sωz1

1+ sωp1 × 1+ sωp2

(21)

where

• VREF is the feedback voltage reference

• gm is the EA transconductance

• ROEA is the EA output impedance

ωz1= 1

RCOMP×CCOMP

(22)

ωp1=

ROEA× CCOMP+CHF+CBW ≅ 1

ROEA×CCOMP

(23)

ωp2=

RCOMP× CCOMP CHF+CBW ≅ 1

RCOMP×CHF

(24)

The EA compensation components create a pole close to the origin, a zero, and a high-frequency pole. Typically,

RCOMP << ROEA and CCOMP >> CBW and CHF, so the approximations are valid. Figure 8-2 circles the poles in red

and the zero in blue.

LM65680

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