Investigation of Multi-Output Single-Switch Forward Converter in Terms of Cross-Regulation Using Weighted Control Method

Abstract

In a single-switch forward converter, which is a type of single-input multiple-output (SIMO) DC–DC converter, voltage changes are observed at the outputs due to the current passing through the diodes, the difficulty of winding the transformer in full and half windings, differences in resistance in the windings, the presence of leakage inductance and the existence of common inductance between the windings. These voltage changes are undesirable, and cross-regulation techniques have been developed to keep the outputs at the desired value. One of these techniques, the weighted control method, in which voltage information is received from many outputs, is addressed in this article. The reason we apply this technique is to avoid additional components and their control problems. In addition, this technique is simpler and cheaper than other cross-regulation techniques. In this way, we will contribute to the literature on cross-regulation, showing that cross-regulation remains below 3.33% and circuit efficiency reaches 86.83% by using the weighted control method.

1. Introduction

The interest in DC–DC types of forward converters is reflected in the plethora of publications on the subject, including academic research, industry, and manufacturer publications [1,2,3,4,5,6,7,8,9,10,11]. The multi-output single-switch forward converter, a member of the DC–DC converters family, which is single-input multiple-output (SIMO), also offers isolated topology. Single-switch multi-output forward converters are used from 50 W to 300 W. In short, multi-output forward converters are an option for lower powers [12]. Some of the advantages of forward converters are galvanic isolation between the input and output, their simple structure and their low cost [13].

Cross-regulation is a technique for achieving desired output voltages in multiple-output DC–DC power supplies at desired output voltages. There are many research articles that touch upon the issue of cross-regulation in SIMO converters [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]. In some of these studies, the desired output voltages were achieved by developing a new strategy [14,16,17,20,21,22,23,28]. In others, the desired output voltages were achieved by changing diodes or transformer changes, etc. [15,18,19,26]. Frankly, since there is not much research on a multi-output forward converter cross-regulation, we can consider the multi-output flyback converter as a suitable candidate for investigating cross-regulation, due to its low power. Therefore, we will examine and discuss flyback converter cross-regulation issues more meticulously. For instance, in a dual-output 40 W flyback converter [24], the current is limited by being shifted, thus 0.2% cross-regulation is observed. It is used for digital control. Thus, this approach increases additional costs. In another study [25], a flyback converter containing multi-output windings with a synchronous rectification (SR) function to achieve good cross-regulation was utilized, with a cascade structure created by recruiting a few MOSFETs. In addition, 2.26% cross-regulation was achieved, and 87% maximum efficiency was observed. However, there is a problem with most of these cross-regulation techniques. The use of lots of MOSFETs and their controls in the circuit are macro problems. Additionally, the use of additional drivers for controls will increase costs. In a similar study [29], by utilizing PSR control, the relative output voltage deviation was relatively reduced, to below 5%. In another study [30], the output voltage variation ratio was reduced from 17% to 8% with a stacked output flyback topology design. In a similar study [31], cross-regulation up to 0.294% was achieved under same loading. By not using DSP in this article, the authors have avoided the control complexity of the circuit to be designed. In other words, a simple analogue control method of a designed low-power converter is demonstrated.

2. Circuit Description

The working principles of forward converters have been mentioned in previously published articles and books [13,32,33,34]. To briefly describe the circuit, the signal coming from the PWM controller closes the switch inside itself and the current flows through the primary inductance. During this time, since the secondary inductance has the same polarity as the primary inductance, it transfers its energy to the load through the secondary diode. When the PWM signal is pulled to zero, the MOSFET opens, and, in this case, no current flows through the primary side, so the energy transfer to the secondary side stops thanks to the diodes on the secondary side. One of the points that should be taken into consideration is that when the transformer enters saturation, there is only a certain amount of energy transfer. Therefore, it is necessary to operate the transformer in the linear region. Figure 1 shows the basic circuit of a three-output forward converter, and Figure 2 shows the waveforms of the currents and voltages of this circuit.

As can be seen from Figure 1, rectifier diode D_R, flywheel diode D_F, and magnetic-reset clamping diode D_M are fast switching speed diodes. M₁ is the power MOSFET. L1, L2 and L3 are couplings among themselves. The inductances shown for the winding are couplings among themselves. The output capacitors are electrolyte capacitors.

The point we need to pay attention to here is the appropriate design of the reset winding, as can be seen in Figure 2. This issue is touched upon in Section 3. The reset winding must be smaller than the primary winding; otherwise, it is not possible for the circuit to work correctly.

3. Mathematical Modelling of Multi-Output Forward Converter with Weighted Control

In this section, we will additionally mention the mathematical calculations of the design stages using Equation (1) to Equation (26). The circuit diagram of a multi-output forward converter with weighted control is shown in Figure 3 [25,33]. We also recommend that readers look at the datasheets of the FS7M0880, PC817 and KA431 commercial integrated circuits used in the design.

First and foremost, the system properties of the forward converter must be determined. In our design, we have taken the outputs as follows: First Output: 15 V–1 A; Second Output: 12 V–2 A; and Third Output: 3.3 V–2 A. Moreover, the input range is 50 V–80 V. However, the minimum input voltage of the circuit is designed to be 48 V. The expected efficiency is thought to be around 75%. This is calculated by taking the lowest efficiency predicted for the load changes at the outputs when designing the relevant circuit. In this way, a suitable circuit that will work stably is designed. In this case, the expected maximum power consumption is 60.8 W. Another step is to determine the auxiliary winding reset of the transformer. One criterion of the forward converter is that the transformer needs to be reset during the switching-off period. Therefore, an additional reset auxiliary must be recruited. The efficiency of the circuit will be increased with the auxiliary winding reset method. However, it is a disadvantage that this method brings an additional winding to the transformer. One of the design stages should be selected as 50% below the duty ratio to prevent saturation in the transformer.

Generally, a duty max ratio of 45% is selected [33]. The maximum voltage for the MOSFET and the maximum duty ratio are given by the following equations:

$${{\mathrm{V}}_{\mathrm{d}\mathrm{s}}}^{\mathrm{m}\mathrm{a}\mathrm{x}}={{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{a}\mathrm{x}}(1+{\displaystyle \frac{{\mathrm{N}}_{\mathrm{P}}}{{\mathrm{N}}_{\mathrm{r}}}})$$

(1)

$${\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\le {\displaystyle \frac{{\mathrm{N}}_{\mathrm{p}}}{{\mathrm{N}}_{\mathrm{p}}{+\mathrm{N}}_{\mathrm{r}}}}$$

(2)

One of the most important issues in a forward converter is that the PWM control (IC) operates up to a certain current. One of the factors that determines this current is the output current ripple factor. The current ripple factor (K_RF) is selected to be as low as possible. Thus, drain current is reduced. It is reasonable to set K_RF = 0.1~ 0.2. We chose K_RF = 0.1 in our experiment.

$${{\mathrm{I}}_{\mathrm{d}\mathrm{s}}}^{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}={\mathrm{I}}_{\mathrm{E}\mathrm{D}\mathrm{C}}(1+{\mathrm{K}}_{\mathrm{R}\mathrm{F}})$$

(3)

$${{\mathrm{I}}_{\mathrm{d}\mathrm{s}}}^{\mathrm{r}\mathrm{m}\mathrm{s}}=\sqrt{{\mathrm{I}}_{\mathrm{E}\mathrm{D}\mathrm{C}}(3+{K_{RF}}^2){\displaystyle \frac{D_{max}}{3}}}$$

(4)

$$\mathrm{where} {\mathrm{I}}_{\mathrm{E}\mathrm{D}\mathrm{C}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{i}\mathrm{n}}}{{{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}$$

(5)

Another issue is that the winding must be wound on the primary side, to prevent the transformer from saturating. Where Ae = 173 mm², ΔB was taken as 0.3 Tesla for ETD 44.

$${{\mathrm{N}}_{\mathrm{P}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}={\displaystyle \frac{{{{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{A}}_{\mathrm{e}}{\mathrm{f}}_{\mathrm{s}}\mathsf{\Delta }\mathrm{B}}} {10}^6$$

(6)

The next step is to determine the number of turns for each winding of the transformer and the auxiliary winding reset.

$$\mathrm{n}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{P}}}{{\mathrm{N}}_{\mathrm{S}1}}}={\displaystyle \frac{{{{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{V}}_{\mathrm{o}1}+{\mathrm{V}}_{\mathrm{F}1}}}$$

(7)

$${\mathrm{N}}_{\mathrm{s}\left(\mathrm{n}\right)}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{o}\left(\mathrm{n}\right)}+{\mathrm{V}}_{\mathrm{F}\left(\mathrm{n}\right)}}{{\mathrm{V}}_{\mathrm{o}1}+{\mathrm{V}}_{\mathrm{F}1}}}{\mathrm{N}}_{\mathrm{S}1}$$

(8)

$${\mathrm{N}}_{\mathrm{a}}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{F}\mathrm{a}}+{{\mathrm{V}}_{\mathrm{C}\mathrm{C}}}^{\mathrm{*}\mathrm{*}}}{{{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}}}{\mathrm{N}}_{\mathrm{r}}$$

(9)

We will now explain the stages in order; the points to be taken into consideration are stated in the previous steps. The next stages, respectively, are to determine the wire diameter for each transformer winding based on the rms current, to determine the proper core and the number of turns for the output inductor, to define the wire diameter for each inductor winding based on the rms current, to determine the diode on the secondary side based on the voltage and current ratings, to determine the output capacitor by taking into consideration the voltage and current ripple, to design the reset circuit, and to design the feedback loop, which is essential [33].

Another step is to calculate the wire diameter for each transformer winding based on the rms of the current. This is obtained using Equations (10) and (11). The results are given in

Table 1. Diameter for each transformer winding based on the rms current for the first transformer.

Parameters	Diameter	Parallel	Irms (A)	A/mm2	Turn
Primary Winding	0.445 mm	9	1.89	1.29	22 T
Reset Winding	0.445 mm	1	0.07	0.42	11 T
Vcc Winding	0.445 mm	1	0.1	0.62	4 T
First Output Winding	0.445 mm	4	0.67	1.03	16 T
Second Output Winding	0.445 mm	8	1.34	1.03	13 T
Third Output Winding	0.445 mm	8	1.34	1.03	4 T

.

$${{\mathrm{I}}_{\mathrm{s}\mathrm{e}\mathrm{c}\left(\mathrm{n}\right)}}^{\mathrm{r}\mathrm{m}\mathrm{s}}={\mathrm{I}}_{\mathrm{o}\left(\mathrm{n}\right)}\sqrt{\left(3+{{\mathrm{K}}_{\mathrm{R}\mathrm{F}}}^2\right){\displaystyle \frac{{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{3}}}$$

(10)

$${{\mathrm{I}}_{\mathrm{R}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{t}}}^{\mathrm{r}\mathrm{m}\mathrm{s}}={\displaystyle \frac{{{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{i}\mathrm{n}}{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{L}}_{\mathrm{m}}{\mathrm{f}}_{\mathrm{s}}}} \sqrt{{\displaystyle \frac{D_{max}}{3}}}$$

(11)

For copper cables longer than 1 m, the current density is typically 5 A/mm² [33]. However, the transformer windings were chosen to be less than 2 amperes so that they would not heat up. Additionally, we cannot neglect the skin effect in our copper cable selection. An ETD44 core was selected as the transformer and wrapped with copper wire. After this stage, it is necessary to determine the proper core and the number of turns for the output inductor.

$${\displaystyle \frac{{\mathrm{N}}_{\mathrm{s}\left(\mathrm{n}\right)}}{{\mathrm{N}}_{\mathrm{s}1}}}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{L}\left(\mathrm{n}\right)}}{{\mathrm{N}}_{\mathrm{L}1}}}$$

(12)

$${\mathrm{L}}_1={\displaystyle \frac{{\mathrm{V}}_{\mathrm{o}1}({\mathrm{V}}_{\mathrm{o}1}+{\mathrm{V}}_{\mathrm{F}1})}{2{\mathrm{f}}_{\mathrm{s}}{\mathrm{K}}_{\mathrm{R}\mathrm{F}}{\mathrm{P}}_{\mathrm{o}}}} (1-{\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}})$$

(13)

$${{\mathrm{N}}_{\mathrm{L}1}}^{\mathrm{m}\mathrm{i}\mathrm{n}}={\displaystyle \frac{{\mathrm{L}}_1{\mathrm{P}}_{\mathrm{O}}\left(1+{\mathrm{K}}_{\mathrm{R}\mathrm{F}}\right){10}^6}{2{\mathrm{V}}_{\mathrm{o}1}{\mathrm{B}}_{\mathrm{s}\mathrm{a}\mathrm{t}}{\mathrm{A}}_{\mathrm{e}}}}$$

(14)

$${{\mathrm{I}}_{\mathrm{L}\left(\mathrm{n}\right)}}^{\mathrm{r}\mathrm{m}\mathrm{s}}={\mathrm{I}}_{\mathrm{O}\left(\mathrm{n}\right)}\sqrt{{\displaystyle \frac{(3+{{\mathrm{K}}_{\mathrm{R}\mathrm{F}}}^2)}{3}}}$$

(15)

ETD 44 cores were used in the circuit. The minimum windings that must be wound on the core are calculated as 15.8 turns by using Equations (13) and (14). L1 inductance has been selected as 24 windings.

Table 2. Diameter for each transformer winding based on the rms current for output inductances (second transformer).

Parameters	Diameter	Parallel	Irms (A)	A/mm2	Turn
Winding for L1	0.445 mm	5	1	1.23	24
Winding for L2	0.445 mm	10	2	1.23	19.5
Winding for L3	0.445 mm	10	2	1.23	6

was prepared using Equations (12) and (15). For saturation, the maximum magnetic field has been taken to be 0.3 tesla. The cross sectional area of the inductor core is 173 mm².

Another next step is to determine the diode on the secondary side, based on the voltage and current ratings. The maximum voltage and the rms current of the rectifier diode of the n-th output are calculated as follows:

$${{\mathrm{I}}_{\mathrm{D}\left(\mathrm{n}\right)}}^{\mathrm{r}\mathrm{m}\mathrm{s}}={\mathrm{I}}_{\mathrm{o}\left(\mathrm{n}\right)}\sqrt{\left(3+{{\mathrm{K}}_{\mathrm{R}\mathrm{F}}}^2\right){\displaystyle \frac{{\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{3}}}$$

(16)

$${\mathrm{V}}_{\mathrm{D}\left(\mathrm{n}\right)}={{\mathrm{V}}_{\mathrm{D}\mathrm{C}}}^{\mathrm{m}\mathrm{a}\mathrm{x}}{\displaystyle \frac{{\mathrm{N}}_{\mathrm{s}\left(\mathrm{n}\right)}}{{\mathrm{N}}_{\mathrm{P}}}}$$

(17)

The reverse voltage and rms current of the diodes are given in

Table 3. Reverse voltage and rms current for diode selection.

Parameters	Reverse Voltage (V)	Rms Current (A)
Vcc Diode	31	0.1
First Output Diode	43	0.67
Second Output Diode	35	1.34
Third Output Diode	11	1.34

.

Another next step is to determine the output capacitor, taking into consideration the voltage and current ripple.

$${{\mathrm{I}}_{\mathrm{C}\left(\mathrm{n}\right)}}^{\mathrm{r}\mathrm{m}\mathrm{s}}={\displaystyle \frac{{\mathrm{I}}_{\mathrm{o}\left(\mathrm{n}\right)}{\mathrm{K}}_{\mathrm{R}\mathrm{F}}}{\sqrt{3}}}$$

(18)

$${\mathsf{\Delta }\mathrm{V}}_{\mathrm{o}\left(\mathrm{n}\right)}={\displaystyle \frac{{\mathrm{I}}_{\mathrm{o}\left(\mathrm{n}\right)}{\mathrm{K}}_{\mathrm{R}\mathrm{F}}}{4{\mathrm{C}}_{\mathrm{o}\left(\mathrm{n}\right)}{\mathrm{f}}_{\mathrm{s}}}}+2{\mathrm{K}}_{\mathrm{R}\mathrm{F}}{\mathrm{I}}_{\mathrm{o}\left(\mathrm{n}\right)}{\mathrm{R}}_{\mathrm{c}\left(\mathrm{n}\right)}$$

(19)

where Rc(n) is the effective series resistance (ESR) for n-th output capacitor, and Co(n) is the capacitance of the n-th output capacitor.

The ripple voltages and current ripples for the output capacitors are given in

Table 4. Ripple voltages and current ripples for output capacitors.

Parameters	Esr (mΩ)	Current Ripple (A)	Voltage Ripple (V)
First Output Capacitor	40	0.1	0.01
Second Output Capacitor	40	0.1	0.02
Third Output Capacitor	40	0.1	0.02

. The electrolytic capacitors’ ESRs are around 40 mΩ.

In some cases, it is impossible to meet the voltage ripple with a single output capacitor, because of the high ESR of the electrolytic capacitors. Thus, an additional LC filter (post-filter) can be utilized. If using this LC filter, for the stability of the circuit, the corner frequency of the filter should be between 1/5 and 1/10 of the switching frequency.

SRP6050CA-1R2M model inductances have been used as the output inductances in the filter design for the 12 V and 15 V outputs. The filter output capacitors have been selected as electrolyte 330 uF/25 V capacitors for the 12 V and 15 V outputs.

By using these values in the design, we have already equalized a very small voltage ripple to a value so low that it cannot be taken into consideration. We can mention that the output voltages are full dc voltages, which are completely non-ripple.

The first key power stage parameters of the forward converter with a weighted control are given in

Table 5. First key power stage parameters of forward converter with weighted control.

Parameters	Value
DC Input Voltage	50–80 V
DC Output Voltage/Current	15 V/1 A, 12 V/2 A, 3,3 V/2 A
Np, N1, N2, N3, Np, Naux	22, 16, 13, 4, 22, 8 turn
IC PWM Controller	FS7M0880
DR1, DR2, DR3	MBR40250TG Schottky Diode
DF1, DF2, DF3	MBR40250TG Schottky Diode
Dreset	UF4007 Diode
CO1, CO2, CO3	2200 µF/25 V
CP1, CP2	330 µF/25 V
LP1, LP2	1.2 µH/10 A
Fixed Operating Frequency	67 kHz
Output Power under Full Load	45.6 W

.

An FS7M0880 integrated circuit has been used in the design, and it has its own control design. In addition, it contains a power MOSFET. Furthermore, it is a control IC that is compatible with the existing forward converter, which has features such as overload protection, over-voltage protection (OVP) and over-current protection (OCP).

After determining the power stage parameters of the forward converter with weighted control, it is necessary to design a suitable output that can control the power stage. Figure 4 shows a multi-output forward converter closed-loop control system. A voltage divider, compensator and optocoupler constitute the main structure of the circuit, which is called output-to-control. The remaining structure is regarded as the power stage, or control-to-output.

Our feedback control design is made to control the PWM on the primary side by isolating the voltage information received from the secondary side. Since KRF = 0.1 is taken in our circuit, it works in CCM mode. Gvc is the control-to-output transfer function of the forward converter.

$${\mathrm{G}}_{\mathrm{v}\mathrm{c}}=\mathrm{K}{\mathrm{R}}_{\mathrm{L}}{\displaystyle \frac{{\mathrm{N}}_{\mathrm{P}}}{{\mathrm{N}}_{\mathrm{S}1}}}{\displaystyle \frac{1+\mathrm{s}/{\mathrm{w}}_{\mathrm{z}}}{1+\mathrm{s}/{\mathrm{w}}_{\mathrm{p}}}}$$

(20)

$$\mathrm{where} {\mathrm{w}}_{\mathrm{z}}={\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{c}1}{\mathrm{C}}_{\mathrm{o}1}}}, {\mathrm{w}}_{\mathrm{p}}={\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{o}1}}}$$

R_L is the effective total resistance of the controlled output, defined as ${V_{o1}}^2$/Po, which is the voltage to current conversion ratio of the FPS, and corresponds to I_pk/V_FB, where I_pk is the peak drain current and VFB is the feedback voltage for a given operating condition. The output-to-control transfer function of Figure 4 is defined as follows:

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{F}\mathrm{B}}}{{\mathrm{V}}_{\mathrm{o}1}}}={\displaystyle \frac{{\mathrm{w}}_{\mathrm{i}}}{\mathrm{s}}}{\displaystyle \frac{1+\mathrm{s}/{\mathrm{w}}_{\mathrm{z}\mathrm{c}}}{1+\mathrm{s}/{\mathrm{w}}_{\mathrm{p}\mathrm{c}}}}$$

(21)

$$\mathrm{where} {\mathrm{w}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{R}}_{\mathrm{B}}}{{\mathrm{R}}_1{\mathrm{R}}_{\mathrm{D}}{\mathrm{C}}_{\mathrm{F}}}}, {\mathrm{w}}_{\mathrm{z}\mathrm{c}}={\displaystyle \frac{1}{{(\mathrm{R}}_1{+\mathrm{R}}_{\mathrm{F}}){\mathrm{C}}_{\mathrm{F}}}}, {\mathrm{w}}_{\mathrm{p}\mathrm{c}}={\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{B}}{\mathrm{C}}_{\mathrm{B}}}}$$

Table 6. Second key compensation network parameters for forward converter with weighted control.

Parameters	Value
Voltage divider resistor (R1,R2)	22 kΩ
Voltage divider resistor (Ro)	2.49 kΩ
Optocoupler diode resistor (RD)	1 kΩ
KA431 Bias resistor (RBias)	0.68 kΩ
Feedback pin capacitor (CB)	39 nF
Feedback capacitor (CF)	47 nF
Feedback resistor (RF)	1 kΩ

and

Table 7. Third key control parameter results of forward converter with weighted control.

Parameters	Value
Control-to-output DC gain	9
Control-to-output DC zero	1809 Hz
Control-to-output pole	15 Hz
Feedback integrator gain (fi)	462 Hz
Feedback zero (fz)	147.3 Hz
Feedback pole (fpo)	1361 Hz

summarize the compensation network parameters for the forward converter with weighted control. KA431 is used as the Voltage Reference IC, and PC817A is used as the optocoupler.

The control parameter results of the forward converter with weighted control and the compensation network parameters for the forward converter with weighted control are designed in this context. Bode plot curves are required to gain information about the stability of the designed circuit. We examined the system stability by entering the necessary data in the MATLAB 2024a software environment.

In Figure 5, the blue, pink and green lines, respectively, are the control-to-output, output-to-control and open-loop curves. The crossover frequency (fc) of the circuit with weighted control is 431 Hz. When an additional LC filter (post-filter) is applied, the crossover frequency should be set below 1/3 of the corner frequency of the post-filter for introducing a −180 degrees phase drop [33]. This condition is met in both of our circuits.

A Type-II compensator is used in our proposed design. Power stages’ crossover frequency (control-to-output) is 133 Hz and power stages’ phase margin 101°. If a type II control was not designed or a feedback system was designed without using compensator, the phase margin of the system would be 101° and there wouldn’t be fast response in the system to design. However, thanks to the type II compensator, the open loop crossover frequency is increased to 431 Hz and open-loop PM is reduced to 68.9°, as shown in

Table 8. Fourth key system control parameter results of forward converter with weighted control.

Parameters	Crossover Frequency (fc)	PM	GM
Control-to-Output	133 Hz	101°	Inf
Open-Loop	431 Hz	68.9°	Inf

. Briefly, the system’s stability has been made faster by allowing slightly overshoot. As can be seen from Figure 5, the type-II compensator is used boosting 53.6° at 431 Hz which is also the crossover frequency designed for this system. (see Appendix A)

Thanks to weighted averages, the design works by obtaining suitable voltage references, and thus, the desired cross-regulation is obtained. To briefly mention the weighted control method, Figure 6 shows in detail the voltage information received from two outputs of a three-output forward converter.

To create our optimal design, we first needed to obtain information about the output voltages by using the classical control format. A random selection of weights may not benefit the experiment in cross-regulation. For example, if the converter to be tested has four winding outputs, classical control is provided from only one winding. Then, the windings which have the most positive voltage change and the most negative voltage change are selected as references. Then, the design is made. The multi-output forward converter is designed with resistors at the desired rates. Thanks to the advantages provided by our design, we applied our design by taking, to a certain extent, the weighted voltage supply from each of the 15 V and 12 V outputs. Thanks to Equations (22) and (23), the output weights of our converter can be adjusted by using W₁, W₂ and W₃ = 0, in other words, ${\mathrm{i}}_3$ = 0.

$${\mathrm{i}}_{\mathrm{o}}={\mathrm{i}}_1+{\mathrm{i}}_2+{\mathrm{i}}_3={{\mathrm{w}}_1\mathrm{i}}_0+{{\mathrm{w}}_2\mathrm{i}}_0+{{\mathrm{w}}_3\mathrm{i}}_0$$

(22)

$${\mathrm{w}}_1+{\mathrm{w}}_2+{\mathrm{w}}_3=1$$

(23)

KA431 is a 2.5 V reference amplifier. If we use R_o (2.49 kΩ), ${\mathrm{i}}_0$ is approximately 1 mA. We did not receive voltage information from the third output. The expected voltages for V₁ and V₂ are 15 V and 12 V, respectively. By choosing R₁ (22 kΩ) and R₂ (22 kΩ) in Equation (24), we have determined that ${\mathrm{i}}_0$ is approximately 1 mA. As in this design, the desired R1 and R2 can be selected to satisfy Equation (24). That is, another R1 and R2 could have been chosen that satisfied Equation (24):

$${\mathrm{i}}_{\mathrm{o}}={\mathrm{i}}_1+{\mathrm{i}}_2={\displaystyle \frac{V_1-2.5}{{\mathrm{R}}_1}}+{\displaystyle \frac{V_2-2.5}{{\mathrm{R}}_2}}$$

(24)

R_bias and R_D must be designed to satisfy the following conditions:

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{O}}-{\mathrm{V}}_{\mathrm{O}\mathrm{P}}-2.5}{{\mathrm{R}}_{\mathrm{D}}}}>{\mathrm{I}}_{\mathrm{F}\mathrm{B}}$$

(25)

$${\displaystyle \frac{{\mathrm{V}}_{\mathrm{O}\mathrm{P}}}{{\mathrm{R}}_{\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}}}}>1\mathrm{m}\mathrm{A}$$

(26)

where V_OP is optodiode forward voltage drop, which is typically 1 V for PC817A, and I_FB is the feedback current of the FPS, which is typically 0.9 mA for FS7M0880.

4. Simulation and Experiment Analysis

The designed multi-output forward converter with weighted control demonstrates better cross-regulation and efficiency. A suitable prototype was developed based on the design discussion in the previous discussion, and its testing is described in this section.

We designed our circuit using the weighted average method on 15 V and 12 V outputs.

Table 9. Experimental input 50 V/DC load change.

	3.3 V			12 V			15 V
Load (%)	Load (A)	Voltage (V)	Pout (W)	Load (A)	Voltage (V)	Pout (W)	Load (A)	Voltage (V)	Pout (W)
10%	0.2	3.41	0.68	0.2	12.04	2.41	0.1	14.98	1.50
25%	0.5	3.37	1.69	0.5	12.02	6.01	0.25	14.99	3.75
50%	1	3.31	3.31	1	12.01	12.01	0.5	15.00	7.50
75%	1.5	3.26	4.89	1.5	12.01	18.02	0.75	14.99	11.24
100%	2	3.23	6.46	2	12.01	24.02	1	14.98	14.98

and

Table 10. Experimental Input 80 V/DC load change.

	3.3 V			12 V			15 V
Load (%)	Load (A)	Voltage (V)	Pout (W)	Load (A)	Voltage (V)	Pout (W)	Load (A)	Voltage (V)	Pout (W)
10%	0.2	3.41	0.68	0.2	12.04	2.41	0.1	14.98	1.50
25%	0.5	3.37	1.69	0.5	12.02	6.02	0.25	15.00	3.75
50%	1	3.30	3.30	1	12.01	12.01	0.5	15.01	7.51
75%	1.5	3.26	4.89	1.5	11.99	17.99	0.75	14.99	11.24
100%	2	3.23	6.46	2	11.99	23.98	1	14.98	14.98

show the voltages occurring in the output voltage at various loads, according to the input voltage. Precise measurements were made using an electronic load.

It is clear how stable these voltage changes remain. It can be observed that the voltage change for the 3.3 V output is greater than for the other outputs in percentage. The reasons why this third output (3.3 V) has more voltage change are as follows.

(1)

In the multiple-output forward converter, the information of voltage value for this winding was not received.

(2)

The current passing through the diode in its winding always changes under different loads.

(3)

The internal resistance on the transformer of the winding is proportionally different to the resistance in the other windings.

(4)

The secondary winding to which it is connected causes voltage changes due to common inductance.

(5)

When designing the transformer winding, the obligation of making a half winding or full winding causes voltage value changes.

(6)

Primary and secondary windings can never be perfectly coupled. There is leakage inductance between the windings.

In fact, if we had not created a 3.3 V third winding in our design, and had only taken the voltage values from the fist and second outputs in our design, then the cross-regulation would be expected to be only ±0.33%. This shows us how high-quality the design is. In other words, this proposed study proves its quality under certain loads in terms of good cross-regulation.

Figure 7 shows the voltages obtained at the output. These images show the quality of the output voltages. Also, even if the output is not filtered, the worst ripple on the outputs is around 20 mV. Less rippled voltages were obtained by using an extra filter on the 12 V and 15 V outputs. In this case, the ripple voltage is mitigated to less than 1%. We should also point out that since electronic load was used, precise measurements were taken.

Figure 8 shows the V_DS voltage at 50 V underfull load and 80 V under full load. At 80 V under full load, the maximum peak voltage is approximately 250 V. Since the integrated circuit used has a drain-source breakdown voltage of 800 V, it works flawlessly.

As can be seen from Figure 9a, there is a 200 mV jump during the transition from full load to 50% load at the 15 V output voltage, which has a jump rate of 1.33%. Figure 9b shows the initial transition at full load with an output voltage of 15 V. These show us the dynamic behaviour of the control. The results are exactly as we expected. It can also be seen from Figure 9a that the phase margin is 68.9°. The results are exactly as we expected.

Figure 10 shows the current waveforms of the proposed converter at 80 V under full load. These current waveforms match the waveforms shown in the circuit description. When the waveforms of the I_DF2 current waveform and the I_DR2 current waveform are examined, one of them shows a current flow while the other does not, and when the pulse is triggered, while the I_DM1 and I_DR2 currents flow, the I_DF2 current does not flow. When the pulse is off, the I_DR2 and I_M1 currents do not flow; on the contrary, the I_DF2 current flows. The I_L2 current is continuous, and is the sum of the I_DF2 and I_DR2 currents, according to Kirchoff’s current law. As for the I_DM current, we can see from Table 1 that it is a 70 mA rms current. Since this waveform contains high noise at small currents, it is not given as an additional figure.

Figure 11 shows the efficiency of the experimental three-output forward converter with weighted control from 10% load to 100% load. Thanks to the Schottky diode, the efficiency of the circuit of the three-output forward converter with weighted control is around 84%, and the efficiency varies between 80.2 and 86.8%. Moreover, it can be observed that the circuit works stably at full, half, quarter and 10% load. In terms of efficiency, more efficiency is achieved at quarter load. Efficiency decreases gradually from quarter load to full load, and diminishes at less than quarter loads.

The top side of the experimental prototype is shown in Figure 12a. Figure 12b shows that the diode temperature settles around 58.0 °C under full loads.

As can be seen from

Table 11. Simulated input 50 V/DC load change.

	3.3 V		12 V		15 V
Load (%)	Voltage (V)	Cross-Regulation (%)	Voltage (V)	Cross-Regulation (%)	Voltage (V)	Cross-Regulation (%)
10%	3.56	7.88	12.02	0.17	14.92	−0.53
25%	3.54	7.27	12.01	0.08	14.94	−0.40
50%	3.51	6.36	12.01	0.08	14.90	−0.67
75%	3.50	6.06	12.00	0.00	14.89	−0.73
100%	3.49	5.76	12.00	0.00	14.89	−0.73

and

Table 12. Simulated input 80 V/DC load change.

	3.3 V		12 V		15 V
Load (%)	Voltage (V)	Cross-Regulation (%)	Voltage (V)	Cross-Regulation (%)	Voltage (V)	Cross-Regulation (%)
10%	3.55	7.58	12.01	0.08	14.95	−0.33
25%	3.54	7.27	12.01	0.08	14.95	−0.33
50%	3.53	6.97	12.04	0.33	14.98	−0.13
75%	3.51	6.37	12.05	0.42	14.98	−0.13
100%	3.51	6.36	12.05	0.42	14.96	−0.27

, cross-regulation is low at the 12 V and 15 V outputs, which are the feedback from which voltage information is received. The copper resistances formed by the windings in the transformer were neglected in the simulation.

There is a similarity between the application and simulation results. In the simulation study, the diodes are ideal, and the transformer copper winding resistances and core losses are neglected. Figure 13 shows the simulation study.

Finally, in this research, a different approach and method were used compared to other studies, as shown in

Table 13. Comparison table.

Reference	[24]	[25]	[31]	This Work
Converter type	Flyback converter	Flyback converter	Flyback converter	Forward converter
Total output winding	2	3	2	3
Output power	40 W	68 W	8.5 W	45.6 W
Cross-regulation	%0.2	%2.26	below 5%	3.33%
Peak efficiency	86.9%	87%	none	86.8%
Switching frequency	600 kHz	30 kHz	1 MHz	66 kHz

. Transformer and diode selections were made meticulously. It is understood that 0.3% cross-regulation has been observed at 50% loading.

5. Conclusions

This research was designed to address the cross-regulation challenge in a three-output forward converter using a weighted control method. The circuit description and mathematical modelling have been explained in detail. The proposed model reduces the change in voltages to a certain extent if appropriate weights are selected. In the experiment, cross-regulation improvement was observed under various loads.

Also, in this research, notable points are that under different loads, efficiency reaches up to 86.8%, and cross-regulation falls within 3.33%. It is obvious that cross-regulation is 0.42% at the controlled output voltages. From the results, it can be observed that the winding ratios and diode selections are important parameters for cross-regulation. The cross-regulation of low-voltage windings, such as the +3.3 V output, changed relatively greatly compared to other windings, because no reference output was received. In summary, this experiment, which gave a result of only 0.09–3.33% cross-regulation under different loads, exhibited magnificent performance.

Moreover, this proposed circuit does not contain any additional components such as MOSFETs, and does not require an additional control circuit. To put it briefly, this circuit is simpler, cheaper, and has good cross-regulation.