SMALL-SIGNAL ANALYSIS AND CONTROL DESIGN OF ISOLATED POWER S

SMALL-SIGNAL ANALYSIS AND CONTROL DESIGN OF ISOLATED POWER SUPPLIES WITH

OPTOCOUPLER FEEDBACK

Yuri Panov and Milan Jovanovi

Power Electronics Laboratory Delta Products Corporation P.O. Box 12173, 5101 Davis Drive Research Triangle Park, NC 27709, USA

Abstract - Optocouplers are widely used in isolated power supplies to transfer the feedback signal from the secondary to the primary side. In many power supplies, the feedback amplifier is supplied from the output voltage that creates additional feedback path which should be accounted in the control design. The paper compares two possible loop gains corresponding to breaking the feedback loop at different locations. These loop gains are analyzed and are shown to have an unequal value for the design. Dynamic limitations of the TL431 shunt regulator and the optocoupler are discussed. Practical guidelines for the error amplifier design and a design example are presented.

I. INTRODUCTION

Generally, offline and telecom power supplies require the galvanic isolation between a relatively high input voltage and low output voltages. The most widely used devices to transfer signals

optocouplers. The typical isolated power supply with the primary-side PWM control is shown in Fig. 1. The feedback signal is transferred from the secondary to the primary side through the optocoupler OC1. The feedback circuit shown in Fig.1 is very popular in low-power / low-cost power supplies which usually do not have the standby converter to supply the TL431 shunt regulator but use output voltage VO for this purpose. It is well known [1-7] that by supplying the TL431 from the output voltage an additional feedback path is introduced. Therefore, in the control circuit in Fig. 1 two loop gains which correspond to breaking the loop at locations A and B can be considered. The existence of two loops immediately raises the question which loop gain should be analyzed and measured in order to meet the power supply stability and dynamic response specifications. From the general control theory, each loop gain of the entire control system yields the same characteristic polynomial and, therefore, reveals the system stability. However, depending on the chosen loop gain, error amplifier (EA) design is different which leads to different stability margins and different dynamic performance. So far, these issues have not been addressed in the literature.

The purpose of the paper is to present comparative analysis of the loop gains corresponding to points A and B and to provide design guidelines to power supply engineers. Section II of the paper provides general loop gain analysis and interpretation. Section III presents the comparative analysis of loop gains TA and TB for the power supplies with the voltage-mode and the current-mode controls. Section III also discusses EA design limitations of the TL431 shunt regulator and of the optocoupler circuit. Sections

respectively, whereas Section VI summarizes the paper.

II. LOOP GAIN ANALYSIS AND INTERPRETATION

A. Loop Gain TA

The small-signal block diagram corresponding to breaking the loop at point A is shown in Fig. 2. Figure 2 contains following blocks: KD – output voltage divider gain,

- error amplifier transfer function, G= V

EA

K

X

- optocoupler circuit gain, AOC=VCR1

- control-to-output transfer function, GVC=VOC - open-loop audio susceptibility, GVV(OL)=VOIN ZO(OL)=VOiO - open-loop output impedance.

At point A in Fig. 2, the feedback signal is confined to a single

path. Loop gain TA, corresponding to breaking the loop at point A is derived as: TA=AOC GVC (1+KD GEA) (1) The plant transfer function that provides the basis for the EA design is defined as

It should be noted that the EA is not connected in series with

the plant and zeroes of GEA generally do not translate into the same Generally, since loop B contains the inner feedback loop, the zeroes of the loop gain TA. However, in many cases, KD·GEA >> 1 design of loop gain TB is a two-step procedure. Namely, prior to within the loop bandwidth and loop gain TA can be written as loop gain TB analysis, TINNER gain must be examined for stability. TA≈GPL(A) KD GEA. (3) The inner loop gain is relatively low because it does not contain For loop gain TA given in (3), the EA design procedure does the high-gain EA and its stability rarely becomes a practical not differ from that for the implementation where the optocoupler problem. It should be noted that TINNER can be compensated by is supplied from the fixed voltage. If condition KD·GEA >> 1 is not connecting network Z3 on the primary side, as shown in Fig. 1, so satisfied within the loop bandwidth, the relationship between the that the design of loop gain TB can be further optimized. The zeroes of terms KD·GEA and [1 + KD·GEA] can be very complex, analysis and implementation of the inner loop compensation was particularly, when the EA transfer function has more than two presented in [8] in the context of the magamp control. In fact, the poles. To simplify the EA design in this case, it is recommended to control of the isolated power supply with optocoupler supplied keep the order of the EA transfer function not higher than two, but from the output voltage is similar to the magamp control where the to add necessary poles and zeroes by connecting compensation magamp reset circuit is supplied from the output voltage [8, 9].

Equations (1), (5) and (6) are used to derive the relationship network Z3 on the primary side, as shown in Fig. 1. There is one

more reason to connect compensation network Z3 on the primary between TA and TB:

TA=TINNER+(1+TINNER) TB. (7) side. Term [1 + KD·GEA ] in (1) has the slope of 0 dB/dec at high

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