UCC28C53_V01 datasheet(35/48 Pages) TI

35 / 48 page

GTL431 :s; =

lRCOMPz +

s(f) × CZCOMPz p

RFBU

(47)

A compensation pole is required at the frequency of right half plane zero or the ESR zero, whichever is lowest.

Based previous the analysis, the right half plane zero (fRHPz) is located at 7.07 kHz and the ESR zero (fESRz)

is at 1.68 kHz; therefore, for this design, the compensation pole must be put at 1.68 kHz. The opto-coupler

contains a parasitic pole that is difficult to characterize over frequency so the opto-coupler is set up with a

pull-down resistor (ROPTO) equal to 1 kΩ, which moves the parasitic opto-coupler pole further out and beyond the

range of interest for this design.

The required compensation pole can be added to the primary side error amplifier using RCOMPp and CCOMPp.

Choosing RCOMPp as 10 kΩ, the required value of CCOMPp is determined using Equation 48.

CCOMPp =

2 × N × fESRz × RCOMPp

= 9.46 nF

(48)

A 10-nF capacitor is used for CCOMPp setting the compensation pole at 1.59 kHz.

Adding a DC gain to the primary-side error amplifier may be required to obtain the required bandwidth and

helps to adjust the loop gain as needed. Using 4.99 kΩ for RFBG sets the DC gain on the error amplifier to 2.

At this point the gain transfer function of the error amplifier stage (GEA(s)) of the compensation loop can be

characterized using Equation 49.

GEA

:s; = lRCOMPp

RFBG p

1 + s

:f;×C

COMPp × RCOMPp G

(49)

Using an opto-coupler whose current transfer ratio (CTR) is typically at 100% in the frequency range of interest

so that CTR = 1, the transfer function of the opto-coupler stage (GOPTO(s)) is found using Equation 50.

GOPTO (s) =

CTR × ROPTO

RLED

(50)

The bias resistor (RLED) to the internal diode of the opto-coupler and the pull-down resistor on the opto emitter

(ROPTO) sets the gain across the isolation boundary. ROPTO has already been set to 1 kΩ but the value of RLED

has not yet been determined.

The total closed loop gain (GTOTAL(s)) is the combination of the open-loop power stage (Ho(s)), the opto gain

(GOPTO(s)), the error amplifier gain (GEA(s)), and the gain of the TL431 stage (GTL431(s)), as shown in Equation

51.

TOTAL :s; =

OPEN :s;

× G

OPTO :s;

× G

EA :s;

× G

TL431 :s;

(51)

The required value for RLED can be selected to achieve the desired crossover frequency (fBW). By setting the

total loop gain equal to 1 at the desired crossover frequency and rearranging Equation 51, the optimal value for

RLED can be determined, as shown in Equation 52.

LED Q

OPEN :s;

× CTR × C

OPTO

× G

EA :s;

× G

TL431 :s;

(52)

A 1.3-kΩ resistor suits the requirement for RLED.

Based on the compensation loop structure, the entire compensation loop transfer function is written as Equation

53.

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SLUSER8 – JUNE 2022

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