Subcontract No: QSS-05-S-246

Early Oscillation Detection for Hybrid DC/DC Converters

Bright L. Wang Goddard Space Flight Center, Greenbelt, MD National Aeronautics and Space Administration January 2009

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ACKNOWLEDGMENTS

The author would like to thank Jelila S. Walker, the Task Monitor, and Bruce D. Meinhold, the Task Lead, for their support throughout the project. Thanks also to Jeanne Beatty and Richard S. Williams for reviewing and editing the manuscript.

Available from:

This report is available in electronic form at http://nepp.gafc.nasa.gov

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SUMMARY A novel technique for detecting early oscillation of hybrid DC/DC converters has been developed. The technique utilizes a signal spectral analysis method to catch the oscillation signal at its early stage from a wide range of input voltage noise, and to identify the signal base on RF signal AM/FM modulation theories. Thirty-four space-grade converters of 17 types from three major manufacturers were tested to verify the effectiveness of this technique. As a result, over half of those test samples were found to present oscillations at the early stage to some degree. Applications of this technique include acceptance and qualification tests of hybrid DC/DC converters, especially for those not equipped with remote-sense terminals. It is also essential to monitor oscillation in system-level environmental tests to avoid catastrophic test failures. 1.0 INTRODUCTION The electrical power system of a spacecraft plays a very critical role for mission success. Such a modern power system may contain numerous hybrid DC/DC converters inside the power system electronics (PSE) units and many of the flight electronics modules onboard. Reliability of the entire system depends upon reliability of every individual converter unit. To achieve a goal of zero-failure in the power system, long-term efforts have been made by parts engineers to inspect the quality of all incoming converter modules for radiation tolerance, workmanship, and electrical performance. Although electrical failures caused by converter oscillation represented a relatively small portion of total failures during past NASA space flight missions, they still pose a serious threat to mission safety because of the random nature of oscillation occurrence related to hybrid DC/DC converter inherent quality issues, user system design deficiency, and lack of real-time detection methods. Using gain and phase margins of feedback control loops to determine potential stability problems of DC/DC converters has been a practical method for many years. This method provides an efficient tool for design verification of the control circuits by using a frequency response analyzer (FRA) to measure control loop gain and phase angle at an appropriate loop-breaking point, and comparing the gain and phase with stability criteria so that the degree of stability can be determined. However, the gain/phase margin method exhibits some drawbacks for testing hybrid and space-grade DC/DC converters, which include (1) the cases of hybrid converters cannot be opened to probe an FRA to the loop-breaking point on the final products. Although for some types of converters the remote-sense terminals can be used to probe the FRA, the majority of converters are not equipped with remote-sense terminals; (2) the converter cannot be tested in real time during system-level extreme environmental test due to inaccessibility of the remote-sense terminals; (3) the margins of gain and phase are not able to indicate low-level instability that may break the converter into a serious oscillation under some dynamic and transient power conditions; and (4) the gain/phase method that forces the converter to oscillate at a large scale of frequency range could overstress the space flight unit, which has not been studied adequately. In this report, a novel technique is presented to show how to detect a small signal as a potential oscillation that may affect the stability of DC/DC converters. This technique was developed based on the principle of oscillation, the noise spectral analysis method, and theories of RF signal AM/FM modulations. It is particularly useful for all hybrid DC/DC converters with or without remote-sense pins. Furthermore, a comprehensive stability index (CSI) has been defined using the channel power at a characteristic frequency (CF) that is unique to every type of converter. Thirty-four space-grade converters of 17 types from three major vendors were tested to verify the effectiveness of this technique, and their CF was identified for future test reference.

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2.0 THE PROPOSED EARLY OSCILLATION DETECTION TECHNIQUE Differing from the traditionally adopted gain/phase margin measurement to determine stability of DC/DC converters, the proposed early oscillation detection (EOD) technique entails obtaining a specified noise power spectrum at the power-line input of the DC/DC converter in normal operation conditions, and identifying any abnormal signal amplitude at certain frequencies that may be caused by either front-end oscillations or feedback-loop oscillations of the converter. It has been found that the frequency of feedback-loop oscillation correlates with the frequency at which the phase curve in the Bode plot of the gain/phase-margin method rolls across the zero-phase shift point at 0° (or 360°), and strength of the oscillation maintains a strong correlation with the channel power amplitude [1]. Therefore, an oscillation indicator using the signal amplitude at the phase-crossover frequency can be established to determine stability levels of DC/DC converters. Figure 1 illustrates functions of a stability determination system (SDS) using this technique.

Figure 1: The function diagram of a stability determination system.

As indicated in the diagram, an Agilent N9320A spectrum analyzer was used to measure signal amplitude and frequency Fourier components. This analyzer is capable of measuring a small signal as low as -105 dBm while the pre-amplifier is on; thus, it is beneficial for this system to detect an oscillation at its early stage. Key factors in developing this technique generally involve in three aspects: (1) identify frequency Fourier components that are unique to individual types of DC/DC converters to indicate an oscillation, (2) determine the oscillation frequencies that represent front-end oscillations or feedback-loop oscillations, and (3) establish reliable signal-amplitude scales to describe degrees of the oscillations. With these three goals in place, some fundamentals for causing instability of DC/DC converters have been investigated. 2.1 DC/DC Converter Instability Considerations 2.1.1 The Control Loop Transfer Functions

Switching-mode DC/DC converters, as used in all space flight electronic hardware, have potential instability issues due to the output voltage control concept of using negative feedback with loop compensation. Figure 2 shows the closed-loop block diagram of a typical DC/DC converter with negative feedback control. This model includes three key transfer functions within the converter: G1(s), the AC transfer function of the modulator including power transistors and transformer;

Hybrid DC/DC Converter

HP 6060B Electronic

Load, 300W

Agilent E3436A 50V/200W

Power Supply

Tektronics OP4000A

Oscilloscope

Agilent N9320A

Spectrum Analyzer

Computer for Data Acquisition

and Analysis

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(Modulator) Vin E(s) Vout R(s) + Ea(s) C(s) B3

B(s) - G1(s) G2(s)

(Feedback Loop) B2 B1 (Start at 0°

(180° EA lag + 90° comp. lag) phase lag) H(s)

Figure 2: Closed-loop block diagram of a typical DC/DC converter with negative feedback control.

G2(s), the transfer function of the output filter; and H(s), the transfer function of the error amplifier with the compensation network. Similarly, B(s) = H(s) C(s) represents output of the error amplifier, and Ea(s) is a measure of the error of the closed-loop system and is equal to the error E(s) = R(s) - C(s) when H(s) = 1 [2]. The output of the open-loop system, as B1, B4 opened, is

C(s) = G1(s) G2(s) R(s). (1) The output of the closed-loop system, as B1, B4 closed, is

C(s) = G1(s) G2(s) Ea(s) = G1(s) G2(s) [R(s) – H(s) C(s)], (2)

and therefore

C(s) = R(s). (3) It is clear that the H(s) in the denominator of equation (3) plays a critical role in controlling the system output, but it is also the main source of causing system to be unstable. Although the H(s) can be designed with an adequate compensation means for a stable system, a practical verification method must be followed throughout design, manufacture, and user application cycles for DC/DC converters to minimize the impact on stability from real-world variations within the cycles. 2.1.2 Effects of Control Loop Gain and Phase on Stability

According to the feedback control theory, each transfer function block shown in Figure 2 has its associated gain and phase around the feedback loop when viewed over a range of frequencies. The total closed-loop gain of a DC/DC converter is designed to have a gain roll-off rate to a -1 slope, i.e., -20 dB per decade, when passed across the unity gain (0 dB) region. At this point, the phase shift is designed to be less than 360° (180° from the EA plus 90° from the compensation, and plus 90° from the -1 slope), a condition for a stable system. When the phase shift passes across 360° (or 0° in a Bode plot), the gain is designed to be more than -15 dB, another condition for a stable system. Obviously, the 90° from the compensation is an adjustable value at the design stage to force the total phase shift to be less than 360°. However, any one of the three phase shift elements around the loop can significantly cause the total shift to become close to 360°, the primary condition for oscillation.

Power Processing

Error Amplifier (EA) w/ Compensation

Output Filter

G1(s) G2(s) 1 + G1(s) G2(s) H(s)

B4 (90° lag) (End of < 360° lag)

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Frequency response of the control loop is an effective measure for study of the system performance, and it can be plotted into a Bode plot to illustrate the gain and phase-shift behaviors against frequencies. Figure 3 includes two pairs of the typical Bode plot obtained from some of the DC/DC converters under test.

Figure 3: Typical Bode plots obtained from two of the DC/DC converters under test at 25°C, showing the normal and unstable operations of the converters.

The plot A pair shows not only the gain and phase values that meet the stability requirement, but also indicates adequate gain/phase margins for stable operation of the converter at potential extreme transient conditions. As can be seen from the plot A pair, the -2 slope gain starts to roll off +45 dB at 100 Hz and changes to -1 slope gain as a Zero at its corner frequency, fz (A). The -2 slope roll-off is mainly contributed by the output Lo/Co filter for forward-type converters, and is heavily dependent on the equivalent series resistance (ESR) of the output load (RL) for the flyback-type converters. The roll-off corner frequencies can be calculated as fLC = 1/2π (LoCo) ½

and fRC = 1/2πRLCo, respectively. Similarly, the zero corner frequency, fz (A), is contributed by the equivalent series resistance (ESR) of the output capacitor and the capacitance value itself [3]. It can be described as

fz (A) = 1/2πRESR Co. (4)

In the meantime, the phase shift governed by the R-C compensation network has achieved a 66° gain margin away from 0° (or 360°) at the unity gain (0 dB) and the gain crossover frequency fcog (A) of 1.0 kHz. The gain continues to boost to the largest value of 80° at about 5.5 kHz, and starts to roll across the 0° at about 47 kHz, which is called zero-phase frequency as fzp (A). At this point, there is still a -24 dB gain to guarantee the stability of the system. On the contrary, the plot B pairs reveal an extremely unstable response of a DC/DC converter, in which the R-C compensation network has been intentionally altered to place a zero, fz (B), as shown in gain plot B in Figure 3. The gain rolls off in a -1 slope manner and changes to 0 dB/decade just before the unit gain crossover frequency fcog (B), and remains flat for the next 50-kHz range before it rolls off again. But it becomes too late for the gain to keep a larger margin when the phase shift rolls across the 0° (or 360°) point. Despite the phase shifting 122° away

Phase plot A Gain plot A

Phase plot B Gain plot B

66 ° margin

122 ° margin

-24 dB margin

-8.6 dB margin

fcog (B)

fLC and fRC

-1 gain slope 20 dB/decade

M

fzp (A)

fzp (B)

Plot A - from a DVTR283R3S

Plot B - from a modified QV24-5-25

-2 gain slope 40 dB/decade

fZ (A) fcog (A)

-1 gain slope 20 dB/decade

fZ (B)

-3 gain slope 60 dB/decade

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from the 0° (or 360°) at gain crossover, it goes down sharply as the frequency increases because there is no longer an adequate gain to boost the phase shift. In this particular situation, some noise signals generated from the entire loop of the converter with 8-kHz to 60-kHz frequencies (see point M in Figure 3) began to travel through B1-B2-B3 and feed back to B4 (see Figure 2) with exactly the same amplitude as at B1 to cause the converter to become very unstable. This converter may not oscillate at this point, because the phases within the frequency range are still large enough to keep the converter stable. However, there must be some noise signals with the zero-phase frequency (fzp) that could appear on the input of the control loop and become in phase with the output of feedback signals of the same frequency. It could make the converter break into oscillation even though this frequency still has a small gain of -8.6 dB. It has been proved that a DC/DC converter will become very unstable or oscillate if the feedback loop gain is close to the unity (0 dB), which means the same signal amplitude at its input and output, and if the phase shift rolls to 0° (or 360°), which means the signal at input and output are in phase [4]. 2.1.3 Effects of Converter Front-End Oscillation on Stability

With few similarities to the feedback oscillation, the converter front-end oscillation is caused by interactions of abnormal impedance at the converter input due to mismatch with external input LFCF filters or excessive input inductance (LL) and capacitance (CL) along the power input line. The oscillation can occur at the input filter resonant frequency, fFω or at the power input line resonant frequency fLω, and is in the form of a sine wave [1]. The resonant frequencies can be calculated as

fFω (Lω) = 1 / [LF(L) CF(L)]½ . (5) It was noted that the sine-wave oscillation at the front end of the converter, no matter how high the amplitude goes as observed during the tests of this project, normally may not be able to force the feedback loop to break into oscillation. This is because the input impedance section is not directly within the feedback loop. Therefore, it may not alter the transfer function of the feedback loop, as long as the output impedance of input filter Zo is much smaller than input impedance of the converter input Zi (Zo << Zi) and resonant frequency at Zo is lower than that at Zi (fZo < fZi) [5]. However, excessive Zo existing in the input filter or power input line can change the feedback loop transfer function and thus cause the converter to become unstable and even oscillatory [6]. Figure 4 shows a front-end oscillation waveform detected by an oscilloscope from a test in this study. A noise injection transformer secondary winding with inductance of 1.1 mH was inserted

Figure 4: Front-end oscillation waveform of MFL2812S at 31.9 Vin, 1 A load @ 25 °C.

1.72 kHz Vin (AC) = 2V

Vout (AC) = 0.1V

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into the power input line, and the converter operated under 31.9 V input and 1 A load when it ran into oscillation. The oscillation was determined to be a front-end oscillation because the output waveform of the converter was still normal. The feedback loop was determined to be stable by checking the gain and phase margins. A spectrum analyzer is suitable to measure the oscillation, but the bandwidth of the analyzer must be small enough to measure the low frequency. 2.2 The Approach of Detecting Early Oscillation The early oscillation within hybrid DC/DC converters behaves as a conditional stable situation, in which the converter may remain within normal operation but shows some signs of potential oscillation that could occur at some worst-case conditions such as turn-on line input transient and sudden load changes. The early signs of the oscillation typically are small-amplitude electronic signals related to an oscillation as well as some unusual gain/phase margins of a Bode plot, and they are normally obscured in a large amount of background noise. The approach of the early oscillation detection technique is to effectively identify the weak oscillation signal without disturbing the control loop performance of the converter. Indeed, frequency analysis of the input noise signal is adopted to study the oscillation noise profile in the frequency domain to determine a possible early oscillation. 2.2.1 Determining the Characteristic Frequency of the Oscillation

When a DC/DC converter oscillates, it runs at a specific frequency or a certain frequency range. Thus, the oscillation frequency can be one of the important characteristics for identifying the oscillation. As described in Figure 2, if there is a moment in which a noise signal within the control loop starts from the B1 with 0° phase lag, and then travels through B1 - B2 - B3 until B4 with a 360° phase delay, the initial signal at B1 and the final signal at B4 are in phase. The loop will oscillate if, at the same moment, the noise gain within the loop becomes close to 0 dB, which means the signal amplitudes at B1 and B4 are equal [7]. The specific frequency at which the phase is 0 degree can be defined as a characteristic frequency (fc) of the oscillation. To demonstrate the principle of oscillation frequency, an open-frame DC/DC converter was modified on the feedback loop R-C network, in which the 3,900 pF capacitor was replaced by a 560 pF capacitor, and the resistor was adjusted from its original 1.0 kΩ to 6.8 kΩ. Two Bode plots were obtained for the normal condition with R = 1.1 kΩ and for the 5.6 kΩ condition that was just before the start of the oscillation. As seen in Figure 5(a), the plot for normal conditions shows adequate gain and phase margins, but the plot of pre-oscillation condition displays a very

(a) (b)

Figure 5: Bode plots showing zero-phase frequencies fzp at normal and pre-oscillation

conditions (a), and switching/output noise waveforms showing the fc (b).

foc =51.5 kHz

52.2 kHz

fzp

Switching Voltage, VGS

Output Noise Voltage, Vout (AC)

Oscillated

Normal

68.2 kHz

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different picture. That is, the gain is very close to 0 dB when the phase lag reaches 0° (or 360°), the one of absolutely necessary conditions for a feedback loop oscillation. By continuously increasing the resistor value to 6.8 kΩ, the gain dropped to 0 dB and the control loop became completely unstable. Some noise signals around the zero-phase frequency (fzp = 52.2 kHz) at this movement existed at the input of the loop and were in phase with signals at the output of the loop. At power on, the converter ran into serious oscillation at fc = 51.5 kHz (19.4 μs in period) as shown in Figure 5(b). Note that the zero-phase frequency fzp and the oscillation characteristic frequency fc, at this condition agree perfectly with each other. 2.2.2 Amplitude and Frequency Modulations of the Oscillation

Referring to radio frequency (RF) theory, modulation is the process of using specific circuits to impose information contained in a lower-frequency electronic signal onto a higher-frequency signal [8]. In the case of DC/DC converter oscillation, a process very similar to the RF modulation occurs around every circuit fraction of the converter feedback loop. The higher-frequency switching signal as a carrier is modulated by the lower-frequency feedback-loop oscillating signal or the front-end oscillating signal. If the oscillating signal (Vo) causes amplitude of the switching signal (Vsw) to vary, the amplitude modulation (AM) occurs. In a different aspect, the frequency modulation (FM) occurs if the oscillation signal with the fc causes the switching frequency (fsw) to vary. For DC/DC converter oscillations, the AM and FM may occur at the same time and may be mixed together. The equation describing the voltage of the AM wave (υAM) may be written as

υAM = Vsw sin2πfsw t + ½Vo [cos2π (fsw - fc) t] - ½Vo [cos2π (fsw + fc) t] (6)

and the frequency of the FM wave (fFM) may be described in an equation as

fFM = fsw + ∆f sin2π fc t (7)

where ∆f is the frequency deviation, the maximum change in frequency that the modulated wave undergoes. As can be seen from equation (6), the AM-type oscillation generally contains three frequency components: the switching frequency, fsw; the lower-sideband frequency, fsw - fc; and upper-sideband frequency, fsw + fc. Since the waves of the oscillation have a rather complex wave shape and can be considered as a sum of a set of pure sine waves, each of the sine waves that makes up the complex oscillation wave will have both sideband frequencies. The waveforms in Figure 6 illustrate the amplitude modulation observed during one of the tests in this study. In Figure 6(a) is a time-domain switching waveform that is modulated and thus has an amplitude swing of 59.9 kHz. The spectrum of Fourier analysis in Figure 6(b) indicates the oscillation frequency of 59.1 kHz and a switching frequency of 565.2 kHz, as well as two sideband frequencies about 59 kHz apart from both sides of the switching frequency. This is a typical AM modulation because there is only one pair of sideband frequencies appearing in the spectrum. In contrast, Figure 7 presents a case of frequency modulation that shows a jitter-like switching waveform in Figure 7(a) and a Fourier spectrum revealing the oscillation frequency and multiple sidebands of the FM frequency (fFM) in Figure 7(b). The switching waveform has a frequency swing of ∆f ≈ 52 kHz, resulting in the Fourier spectrum of the switching frequency that has an infinitive number of side frequencies (fosc) spaced apart on both sides of the resting frequency (fsw). However, most of the side frequencies do not appear in the spectrum, because of the less significant amount of power they contain.

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fc fsw-fc fsw fsw+fc

(a) (b)

Figure 6: Amplitude modulation (AM) occured in a case of oscillation. Input voltage noise waveform showing the characteristic frequency (fc) (a), and the noise Fourier spectrum showing the oscillation frequency as well as upper and lower sideband frequencies of the oscillation (b).

fc fsw-2fc fsw-fc fsw fsw+fc fsw+2fc (a) (b)

Figure 7: The frequency modulation (FM) occured in a case of oscillation. The converter’s switching waveform showing the switching frequency and the maxmum frequency swing, Δf (a), and the Fourier spectrum showing oscillation frequency and multiple sidebands of the oscillation (b).

2.3 The Indicator of Early Oscillation Early oscillation of hybrid DC/DC converters has been defined as periodic variations of a very low-level noise signal presented within the feedback loop of the converter, due to a natural phenomenon in which one of the Fourier components of the noise exists in phase and has a close-to-zero gain at the loop input and output. The periodic variation means that the noise signal changes in amplitude, frequency, or both at the same time. The early oscillation exists in every type of power converter with a negative feedback control scheme, but the degree of the oscillation strongly depends on the total noise level contained within the converter. In fact, space-grade hybrid DC/DC converters almost always have a lower level of early oscillation because of their superior design regarding noise-level reduction. The oscillation frequency is also unique for every type of converter, since the design on total loop performance for a specific type has defined exactly when the phase should come to zero degree and thus the oscillation frequency has been predetermined. An early oscillation signal (EOS) at normal conditions may be too small to affect performance of the DC/DC converter. In extreme conditions, however, the gain of the EOS may reach zero and therefore make the converter run into a fatal continuous oscillation. Figure 8(a) reveals an early oscillation signal in a power spectrum for the QV24-5-25 converter, which corresponds to the normal condition of the loop performance shown in Figure 5(a) with

∆f fsw=306.6 kHz

foc=59.9kHz 59.1 kHz

507.8 kHz

622.6 kHz

565.2 kHz

53.3 kHz

2υAM

310.4 kHz 368.0 kHz

422.0 kHz

252.4 kHz

197.3 kHz

fsw =565 kHz

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a zero-phase frequency fzp = 68.2 kHz. This is the only significant signal magnitude in this power spectrum besides a pulse at switching frequency, which represents the early oscillation at the fzp due to some of the Fourier components of the noise within the loop that have gains very close to 0 dB. By carefully analyzing all possible noise sources within the entire converter circuit, no significant periodic signal other than the early oscillation signal has been found. Therefore, the evidence of using oscillation characteristic frequency fc for the spectrum analysis method to represent the zero-phase frequency fzp in the frequency response method seems obvious. Figure 8(b) is a closer-look image with a 120-kHz narrow span for examining the early oscillation signal. With the gain of the noise signal being closer to 0 dB at fzp, the must-oscillating condition, the amplitude of the EOS increased and the sideband signals emerged as shown in Figure 8(c). Note that there is only one pair of sideband signals, and the frequencies spaced apart on both sides of the switching frequency are equal roughly to the EOS frequency (51.1 kHz). This clearly indicates an AM-type feedback loop oscillation. Otherwise, it could be an FM-type oscillation or a front-end oscillation, if there are multiple sideband signals around the switching frequency or if the spaced sideband frequencies are much lower than the EOS frequency. Figure 8(d) is the narrow-span power spectrum to represent EOS in 8(c). It can be seen that the signal increase in amplitude from -58.4 dBm in 8(b) to -51.1 dBm in 8(d) clearly implies the development of the oscillation from its early stage to the mature stage. Unfortunately, the signal change of -7.0 dBm (0.45 mV) in amplitude seems too small to be detected by traditional electronic oscilloscopes. Based on detailed studies on the new approach described in previous sections, an early oscillation indicator for hybrid DC/DC converters can be established by efficiently detecting the early oscillation signal at its characteristic frequency (fc) and the sideband signal amplitudes around the switching frequency (fsw). High-sensitivity power spectra shown in Figure 8 are capable of separating the EOS from its background noise, and therefore can provide a more effective tool to

(a) (b)

(c) (d)

Figure 8: A power spectrum in 540-kHz span showing power amplitudes and frequencies of swtching signal and the EOS (a). Amplitude and frequency of the EOS in 120-kHz span (b). The increased EOS and emerging sideband signals indicate a growing feedback loop oscillation (c). The increased EOS showing in the spectrum with a narrow span (d).

62.4 kHz

310.5 kHz

62.9 kHz

53.1 kHz 56.7 kHz 309.4 kHz

368.0 kHz

251.4 kHz

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identify an oscillation at the early stage. Using channel power (CP in dBm/Hz) of the spectrum as a measure for signal-level quantity measures can be another advantage for identifying low-level signal. Channel power at oscillation characteristic frequency (CPcf) and channel power at the switching frequency with all significant sideband frequencies in count (CPsw) are the two effective oscillation indicators. The early oscillation signals are multi-frequency signals containing numeric harmonics, and the channel power works exactly to measure the total energy of the signal within the frequency range. Therefore, the channel power could provide more distinguishable results when comparing among similar signals. 2.4 The Proposed Comprehensive Stability Index (CSI) In order to accurately assign a degree of stability to a specified hybrid DC/DC converter, a quantitative measure to represent the stability condition should be well established. The comprehensive stability index is thus proposed to evaluate the DC/DC converters’ stability performance based on measurement data of early oscillation signals from the power spectrum. As a comprehensive index, the data contains measured channel power at oscillation characteristic frequency (CPcf (m)) and measured channel power at the switching frequency with all significant sideband frequencies (CPsw (m)), both in dBm. The index can be considered as a ratio of CPcf (m) and CPsw (m) of the measured EOS to CPcf (n) and CPsw (n) of the normal EOS, so that the measured EOS can be evaluated against the normal EOS. Clearly, a normal EOS level of a specific DC/DC converter module should be pre-determined by conducting experimental tests on the module or collecting the data from related vendors. The comprehensive stability index, then, can be defined as

]. (8) The comprehensive stability index in equation (8) is dimensionless, and has a value from 0 to 1. Thus, a CSI value of zero would indicate a normal stable situation, in which both measured CPcf and CPsw equal the normal CPcf and CPsw. Note that the measured CSI value shall not be smaller than the normal CSI value in all circumstances, or a measurement error could be involved. As a guideline for future applications, DC/DC converters with CSI values of 0 to 0.5 should be considered acceptable [9].

CPcf (m) -CPcf (n) CPcf (m) +CPcf (n)

CSI =1/2 [ ]+1/2 [ CPsw (m)-CPsw (n) CPsw (m)+CPsw (n)

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3.0 STABILITY ANALYSIS FOR SOME FLIGHT DC/DC CONVERTERS To verify the effectiveness of the early oscillation detection technique, 34 flight-grade hybrid DC/DC converters of 17 models from four vendors were tested as individual parts for their degree of stability. Oscillation characteristic frequency (fc) of the 13 models was identified, and channel power at oscillation characteristic frequency (CPcf) and channel power at switching frequency (CPsw) of those modules were documented. Specifically, the following analyses provide for every individual model an overall status of stability in different power conditions at ambient temperature. Some of the modules were tested through extreme temperatures to study their oscillation behaviors beyond the ambient temperature. The related test data in forms of curves, spectra, and waveforms are shown in Figure 1 through Figure 35 in the Appendix. Model QV24-5-25 (Figure A1)

This 125 W open-frame DC/DC converter was modified to construct an oscillation simulator to study the development behaviors of oscillations because of the possible adjustment on control loop parameters compared to hybrid modules. The images shown in Figure A1 accurately illustrate the complete development process of an oscillation that occurred in this converter. The switching waveforms and the output noise waveforms on the left side provide straightforward time-domain information, while the power spectrums on the right side reveal analytical frequency-domain information on the frequency distributions of the oscillation signal. Note that one of the oscillation indicators at the characteristic frequency fc= 59.4 kHz in Figure A1(b) rapidly increased as the oscillation became more serious. It can be seen how accurately the 52.1 kHz of fc and the 51.5 kHz of oscillation frequency (fosc) in Figure A1(h) and (i) represent each other. Similarly, Figure A1(j) shows a Bode plot created by a frequency response analyzer (FRA) at the same condition as in Figure A1(e) and (f), which has a zero-phase frequency (fzp) of 52.2 kHz and agrees with the fc and fosc in Figure A1(h) and (i). Besides, another one of the oscillation indicators at the switching frequency (fsw) shows multiple sidebands spaced about 52 kHz apart on both sides of the fsw, and their amplitudes also rapidly increases as the oscillation is enhanced. Because of the multi-sideband appearance, it clearly indicates an FM oscillation for this converter. The main pulse at fc=59.4 kHz in Figure A1(b) is an early sign that the oscillation occurred, which means the pulse is at an oscillation-vulnerable frequency (the loop phase is zero) and the amplitude of the pulse is high enough to post an alert. Small value increase in the pulse amplitude could permanently change the seemingly stable situation to an unstable phase. This critical pre-oscillation condition, however, cannot be identified by the time-domain waveform on an oscilloscope as shown in Figure A1(a). Model AFL2805SX/ES (Figure A2)

Figure A2 shows the input noise spectrums of an AFL series 100 W engineering module equipped with remote-sense terminals. This test module runs relatively stable at 28 V input, 15 A load, and at the ambient temperature as shown in Figure A2(b) and (f) with a fsw of 573.9 kHz and fc at about 33 kHz. Figure A2(b) is a spectrum in a 75-kHz narrow span showing a 33.3 kHz fc and its possible low-order harmonic at 63.2 kHz. Its channel power CPcf is at a very low level of -43 dBm (7.1 μV), so the occurrence of an oscillation is very unlikely at the ambient temperature. Tested at an extended temperature range from -55 °C to +125 °C, this module did not reveal a possible early sign of oscillation, except at -48 °C with 28 Vin and no load; some low-order harmonics appeared as shown in Figure A2(i). This is a distortion of the feedback control loop due to the zero-load condition, but it will not cause a stability problem if the converter does not

13

run under an absolute no-load condition. Note that with the increase of the test temperature, the fc value tends to decrease, and vice versa. This agrees with the measurement using the FRA method as shown in Figure A2(a). Model AHE2815SF/CH (Figures A3 to A5)

Besides the characteristic frequency fc, this 20 W push-pull-type converter has two other major frequencies that reflect the combined switching frequencies of two MOSFETs at 250 kHz and the pulse-width-modulator (PWM) controller output frequency (fPWM) of 125 kHz (half of the switching frequency). Therefore, a power spectrum of this type of DC/DC converter may contain at least three frequency components as shown in Figure A3(d) for module SN022. At a stable condition with a zero load, the fc is rarely seen in Figure A3(b), and the switching frequency at 253.3 kHz is modulated by the fPWM at 127.2 kHz so that sidebands are spaced about 127 kHz apart on both sides of the fc. As a result, the frequency component at fPWM also contains left-side sideband component of fc and the fc component also contains the first-order harmonic of the fPWM. At a stable condition with full load, the much greater switching noise causes the fc component to increase as can be seen in Figure A3(d). The fc component of 23.8 kHz continues to increase at 115 °C and causes an internal resonation at 43.5 kHz so that both fsw and fPWM are modulated by the resonant frequency, as shown in Figure A3(g) and (h). There were two other modules (SN059 and SN060) under test with similar results to those of SN022. For SN059, early oscillation situations were detected at ambient temperature and at temperatures above 90 °C as shown in Figure A4(d), (g), (h), and (j). At lower temperature such as -25 °C and -45 °C, this module seems very stable. The data for SN060 shows the best among the three modules. It only has early oscillation signs in a 40 V full load at +125 °C, the worst case of the converter operation. Model AHF2812S/ES (Figures A6 to A8)

All three modules of this converter model show significant input noise at no load and almost all input voltage settings. The noises are in low frequency at about 10 kHz and seem to modulate the main switching frequency as can be seen in Figure A6(b), (d), and (e) for each module. The low-frequency noises exhibit multiple sidebands on those power spectrums, and thus this type of FM oscillation is confirmed to be caused by internal input filter resonation due to the no-load condition. It is noticed that at 28 V input, 0 A load, and room-ambient conditions, all three of the modules present sidebands spaced about 280 kHz apart on both sides of the 558-kHz switching frequency. At the 1.0 A full load, the three modules perform normally with clean channel power amplitudes at fsw and low channel power amplitude at fc. Figure A8(i) and (j) show the early signs of oscillation at high temperature by presenting higher CP amplitudes at fc and obvious sideband around the fsw. Model AMR2805S/EM (Figure A9)

This 30 W engineering module has a 37-kHz early oscillation that can barely be seen in Figure 9A(b), but is clearly shown in the spectrum of Figure A9(d). In the same power condition but at a high temperature of 110 °C, the oscillation frequency changes to half the fsw or about 170 kHz, and the oscillations become even more severe at no-load conditions as shown in Figure A9(e) and (g). At ambient temperature, a low-level 290-kHz sideband appears in the Figure A9(j) spectrum when the power condition is set to 40 V input and no load. Model ATR2815DF/CH (Figures A10 to A12)

In Figure A10(c) and (d), module SN011 of this converter model shows normal operation with a low CP amplitude at a characteristic frequency (fc) of 39 kHz, and at full load and ambient temperature. At no-load condition, the CP at the fc increases more than 10%, and a 280-kHz

14

sideband is formed. This indicates an input voltage noise enhancement but not a front-end or a control loop oscillation. With the temperature rise to above 100 °C, the CP at the fc increases from -70.6 dBm to -35.7 dBm, a 50% increase in amplitude; and an early oscillation of 32 kHz appears as sidebands around the fsw. Figure A10(g) reveals a typical early sign of oscillation with an increasing fc and emerged 30-kHz sideband at 125 °C. At 35 V input, a 139-kHz oscillation is noted to add to the early oscillation so that this module is now considered unstable as shown in Figure A10(h). A very similar situation happens at the low temperature of 0 °C, when 30-kHz and 147-kHz oscillations occur at 28 Vin/full load and 25 Vin/full load, respectively. These can be viewed in Figure A10(i) and (j). The oscillations for module SN063 occur at very low temperatures from -24 °C to -50 °C, which encounters 160-kHz to 190-kHz frequencies dependent on different input voltages, as shown in Figure A11(g), (h), and (j). However, it has been noted in Figure A11(i) that the oscillation can be detected as early as when the temperature drops to -3 °C. Among the three modules, the SN075 presents stable operation at ambient temperature and some high-temperature conditions, but lacks test data at low-temperature ranges to prove its stability for all operation conditions. Model ATW2805SES (Figure A13)

This is a 30 W, push-pull topology DC/DC converter with a pulse-width-modulator output frequency (fPWM) specified at 135 kHz and a dual-MOSFET switching frequency specified at 270 kHz (2 x 135 kHz). The spectrums shown in Figure A11(a) through (j) illustrate oscillation characteristic frequencies (fc) ranging from 47 kHz to 68 kHz that seem to correspond with the Bode plot data obtained by using the frequency response analyzer. Figure A11(b) shows only the switching frequency (fsw) of 280.2 kHz and its first-order harmonic of 585.8 kHz because of the 1 A load that makes the fsw signal noise become dominant. Figure A11(d) and (f) show the fPWM, fsw and their harmonics, which seem to overlap but provide no indication of any kind of oscillations. At a high temperature of 125 °C, an early sign of oscillation can be seen as in Figure A11(j) with 53-kHz and 148-kHz sidebands as a clear indicator for an unstable situation. Model DVFL2812S (Figure A14)

The Bode plot and the input noise waveform in Figure A14(a) and (b) all indicate oscillation at frequencies close to 47 kHz. The characteristic frequency (fc = 43 kHz) for this module is also shown on the spectrums of Figure A14(c) and (d) at 17 Vin/4 A and ambient temperature conditions. CP amplitude at the fc is -54.8 dBm, which seems high enough to predict an early oscillation. The reason for this oscillation is obvious, because control loop gain at the fc is too small to keep the loop stable. At full load and higher input voltage up to 40 V, there are sidebands at about 40 kHz that can be observed in Figure A14(h) and (j). The oscillation could become more severe when temperature of the module changes to either of the extremes. Model DVHF2815D (Figures A15 and A16)

Figure A15(a) and (c) show a 10-kHz oscillation under operation conditions of 40 Vin/0 A and 25 °C. This oscillation is caused by internal input filter resonation of this module due to its operation in the discontinuous mode at very light load. The same measurement results can be seen in Figure A16(a) through (d) for module SN0102. The module SN0077 comes into light oscillation at 50 V input and no load conditions, with higher CP amplitude at the fc and a sideband at about 70 kHz around the fsw. The characteristic frequency (fc) for this model is determined to be around 65 kHz. Overall, these two modules exhibit stable control loop performances at with-load and ambient temperature conditions.

15

Model DVTR283R3S (Figure A17)

This 20 W flyback-mode module presents stable operation at a no-load condition as shown in Figure A17(a), although this is a DC/DC converter model that will actually run into discontinuous mode without a load. This is probably (but not confirmed) because this model has an internal pre-load resistor installed in order to eliminate the no-load oscillation problem. The curves in Figure A17(b) demonstrate the trend of zero-phase frequencies affected by the input voltages and load currents, with the Bode plot data generated by FRA to verify the fc. At full load and all major input voltages, this module presents early signs of oscillation shown in Figure A17(d), (f), (h), and (j). The fc of this module is within the range of 34 kHz to 44 kHz, depending on the power and ambient temperature conditions. Model M3G2805S/EM (Figure A18)

This 40 W module demonstrates stable operation throughout different power and temperature conditions. The characteristic frequency (fc) of the module is in the range of 88 kHz to 107 kHz, corresponding to the range illustrated in the Bode plot of Figure A18(a). At 17 V input and 0 A load, this module shows a light oscillation; the sideband in half of the switching frequency (fsw) appeared on both sides of the fsw. However, this light oscillation will not cause a major stability problem for the module, because it is due to the internal filter resonation at the no-load condition. Model MFL2812S (Figure A19)

From the spectrum of Figure A19(c), one can immediately recognize a serious AM/FM-mixed-type oscillation that occurs under a no-load condition at 28 V input voltage and 0 °C temperature. The channel power amplitudes at about 36 kHz are spaced equally apart from both sides of the switching frequency (fsw), and form multiple sidebands of the fsw. It also can be seen that the oscillation characteristic frequency (fc) is followed by a series of harmonics gradually dropped to zero in amplitude. This oscillation has been clearly verified by the input noise voltage waveform shown in Figure A19(b), in which the amplitude of the switching noise in fsw is modulated by the oscillation noise in fc to form the AM portion of the oscillation. However, the FM portion of the oscillation is not obviously presented in this waveform to indicate the FM actions. Figure A19(f), (g), (j) presents the oscillations of different levels due to certain operation conditions. At its early stage, the oscillation can be detected by identifying the increased CP amplitude at fc and the presentations of the sideband around the fsw. Figure A19(d), (h), and (i) clearly reveals the early signs of the oscillation for this case. Model MFLHP2815S (Figures A20 and A21)

As can be seen in both waveforms (b) in Figures A20 and A21, this 100 W high-power model has the potential to oscillate at low frequencies such as 20 kHz and 29 kHz for the two test modules. It is the internal filtering resonation that, as described before, causes the oscillation sideband that appeared on the input noise spectrum at all no-load conditions. With load applied, operations of the modules seem relatively stable, especially at lower input voltages. The 40-kHz frequency for the CP amplitude represents the characteristic frequency fc, as shown in Figure A20(f), (h) and (j). With increasing the input voltage to 40 V, the fc changes to a higher value, which corresponds to the data in the Bode plot in Figure A20(a) and A21(a). Model MHD2805S (Figures A22 through A24)

At 40 V input, very light load, and ambient temperature, two of the three modules of this model exhibit some degrees of noise oscillation. A 153-kHz and a 172-kHz CP amplitudes that appear in Figures A22(b) and A23(b) cause sidebands around the CP amplitudes at fsw. They disappear

16

when the light load is ether removed or increased as seen in the figures. This model has a roughly 45 kHz fc, which also can cause a sideband as shown on some spectrums in figures such as Figure A23(b) and (f). At ambient and most of the load conditions, the modules’ performance seems stable, except the 40 V/3 A condition in Figures A22(j) and A24(j) in which an early sign of oscillation can be recognized by the 45-kHz low-amplitude sideband. Model MHF+2812S (Figures A25 through A31)

This is a popular 15 W model of a low-power category, with considerably high output current and a smaller package. However, quite a large amount of test data has indicated significant potential oscillation problems with this model. Figure A25(c) shows that at ambient temperature, 25 V input and 1.25 A full load, the early sign of oscillation exists with appearance of the 53.9-kHz low-amplitude sideband. This early oscillation can be excited further by disconnecting the ground line from the case of the module so that the CP amplitudes of both fc and fsw sidebands rise much higher as can be seen in Figure A25(e). The waveform in Figure A25(a) confirms this oscillation by showing the same frequency value as the fc in time domain. This experiment implies that once an early sign of oscillation has existed, there is always a potential for this model to become seriously oscillated if interfering signals, such as noise increase and power condition changes, are injected into the feedback circuits. This phenomenon can be found throughout the seven figures. Furthermore, the oscillation may be found to become better or worse when testing those modules at the two extreme limits of operational temperatures. Model MSA2815D (Figures A32 and A33)

This is also a low-power model rated to only 5 W. The flyback-topology model inherently makes itself quite noisy at a no-load condition, except for one condition at 16 V/0 A for the SN0083 module due to its operation into discontinuous mode. In fact, the test data for both of the two modules shows that they are in oscillations of different levels at various operational conditions. The time-domain waveforms of Figure A32(a) and Figure A33(a) reflect the test results in the spectrum of frequency domain. Figure A33(e) illustrates a result of a detected early oscillation for this module. With input voltage changes, the CP amplitudes of fc and fsw change in their intensities as shown in Figure A33(f) through (j). Model SMFL2805S/KP (Figure A34)

This is a class K 80 W module, which has a Bode plot from FRA analysis to indicate the gain and phase margins. The zero-phase frequency (fzp) in the Bode plot shows 33.6 kHz at 28 V/5 A and ambient temperature. In the same test conditions, a spectrum analysis reveals the oscillation characteristic frequency fc of 35.9 kHz as the equivalent value to fzp, which can be seen in Figure A34(c). Overall, this module shows it is stable at ambient under all power conditions. Model VI-J2L-EV (Figure A35)

To demonstrate an application of the early oscillation detection technique, this non-metal-hermetic, military-grade, 50W DC/DC converter presents some significant figures with clearly marked fc, fsw, and their harmonics. It is noted that the fsw of this model varies from 110 kHz to 450 kHz at different power conditions, rather than a fixed frequency. The fc also changes with a small range of 22 kHz to 31 kHz. As shown in Figure A35(f), an oscillation of about 27 kHz causes the module some FM sidebands so that an unstable operation condition at 24 V/1 A and ambient temperature is expected. Figure A35(h) shows an early sign of the oscillation, while Figure A35(i) indicates a later stage of the oscillation as the input voltage is increased. Figure A35(j) displays a series of CP amplitudes of the fsw fundamental and its continuously strong harmonics. It may imply an intensive existence of switching noise instead of an oscillation.

17

4.0 CONCLUSION Based on this study, the following conclusions are drawn: 1. The study has confirmed that feedback-loop oscillation of a DC/DC converter occurs at the

frequency where both signals at input and output of the feedback loop are in phase and are within zero dB difference of their amplitudes. This frequency can be recognized in a Bode plot of FRA analysis as zero-phase frequency (fzp), where the phase curve reaches 0 degree. The fzp theory is adopted as the fundamental of the early oscillation detection technique.

2. Analytical study of early signs of oscillation shows that there is always a micro-level

oscillation at the fzp for every DC/DC converter, which can be caused by any kind of noise signal and their harmonics involved within the loop. It has been found that a power spectrum is very suitable to display the early signs of the oscillation that is a measure of small channel power amplitude at fzp. Since every DC/DC converter module has its unique oscillation frequency, a characteristic frequency (fc) is defined to use in the spectrum analysis method. Under this circumstance, the fc is equivalent to fzp.

3. Based on the early-sign study, indicators of the early oscillation have been established to

efficiently and accurately measure and monitor the oscillations, especially in their early stage. The indicators include CP amplitudes at fc and switching frequency (fsw) as well as its sidebands. Increasing the amount in CP amplitudes at fc and fsw sideband from a normal level would indicate an ongoing oscillation and can be utilized to determine the types, intensity, and change tendency of the oscillation.

4. Assessment of the degree of stability of a hybrid DC/DC converter can be realized using the

comprehensive stability index. The CSI is a dimensionless value from 0 to 1 to describe the stability levels from normal to severely unstable.

5. The early oscillation detection technique has been proved to be effective in the respects of

determining oscillation frequency, discovering oscillation initiative, and eliminating background noise. Of a total of 34 DC/DC converter modules tested using this technique, 23 modules were detected as having early signs of oscillation, and four modules have been found severely unstable because of high-amplitude CPs at fc, fsw, and a large amount of sidebands. Overall, only eleven of the 34 modules were found oscillation-trouble-free and thus stable at all tested conditions.

6. The EOD technique shows significant advantages over the frequency response analysis

method in terms of detection sensitivity, measurement accuracy, real-time ability, and test probing flexibility. This technique does not disturb the structure and performance of the converter; thus, it is very suitable for system or in-circuit testing and monitoring. Because there is no need to inject a disturbing signal into the converter circuit, as the FRA method does, the EOD technique is the only stability measurement method for hybrid DC/DC converters not equipped with remote-sense terminals.

18

5.0 RECOMMENDATIONS The following recommendations are made based on the test results: 1. Develop a comprehensive stability evaluation test procedure based on the early oscillation

detection technique for Class K type DC/DC converters, including requirements for standard test equipment, setup for test pass/fail criterion, test data processing, and test article safety precautions.

2. Update relevant MIL standard and NASA power system design and test guidelines to require

the testing and monitoring of DC/DC converter stability at part, board, and subsystem test levels.

3. Work with the converter manufacturers to establish a database to gather stability-related

critical data, such as normal level of CP amplitude at fc, gain and phase margins, and input/output impedance for all DC/DC converters and filter modules used by NASA.

4. Use the proposed stability determination system to test all flight DC/DC converters for

stability before delivering them to flight mission end-users, and provide them with the test data and application guidelines.

5. Provide guidelines to integration and test (I&T) test personnel to monitor early oscillation

signals on relevant flight cards, boxes, and systems during electromagnetic interference (EMI) test and all other environmental tests.

19

REFERENCES

1. Bright L. Wang, DC/DC Converter Stability Testing Study, NASA/CR-2008-214163, 2008, National Information Service, 5282 Port Royal Road, Springfield, VA 22161; NASA Center for Aerospace Information, 7115 Standard Dr., Hanover, MD 21076; http://-nepp.gsfc.nasa.gov, pp. 20-24.

2. George C. Chrysis, High-Frequency Switching Power Supplies, Theory and Design,

McGraw-Hill, New York, 1984, pp. 233-244. 3. Marty Brown, Power Supply Design Cookbook, Motorola, 2001, pp. 145-167. 4. Abraham I. Pressman, Switching Power Supply Design, McGraw-Hill, New York (ISBN: 0-

07-050806-2), 1991, pp. 427-470. 5. R. D. Middlebrook, Input Filter Considerations in Design and Application of Switching

Regulators, IEEE Industry Applications Society Annual Meeting (IEEE Publication 76CH1122-1-IA), 1976 Record, pp. 336-382.

6. Fred C. Lee and Yuan Yu, Input-Filter Design for Switching Regulators, IEEE Transactions

on Aerospace and Electronic Systems, Vol. AES-15, No.5, 1979, pp.627-634. 7. Venable Industries, New Techniques for Measuring Feedback Loop Transfer Functions in

Current Mode Converters, Venable Technical Paper #8. 8. Lloyd Temes, Theory and Problems of Electronic Communication, Schaum’s Outline Series,

McGraw-Hill, New York (ISBN: 0-07-063495-5), 1979. 9. L. Wang, N. Zhang, J. W. Slocombe, and D. K. Kuhlman, Measurement of Spray

Distribution Uniformity for Agricultural Nozzles Using Spectral Analysis, Pesticide Formulation and Application Systems, 13th Volume, ASTM STP 1183, American Society for Testing and Materials, Philadelphia, 1993, pp. 265-279.

20

APPENDIX

Figure A1: QV24-5-25_SN0811_D/C0711 (RO Associations, Inc.) Vin = 18V~36V, Vout = 5V @ 25A, fSW = 310 kHz, Forward

(a) 28V, 5A, normal, R = 1.1k (b) 28V, 5A, early sign of oscillation, R = 1.1k

(c) 28V, 5A, low jitter, R = 2.0k (d) 28V, 5A, low level oscillation, R = 2.0k

(e) 28V, 5A, high jitter, R = 5.2k (f) 28V, 5A, mid level oscillation, R = 5.2k

(g) 28V, 5A, severely oscillated, R = 6.5k (h) 28V, 5A, high level oscillation, R = 6.5k

(i) A still image of the severe oscillation (j) The Bode plot, high jitter at R=5.2k

59.4 kHz

251.4 kHz

197.3 kHz

53.1 kHz

52.2 kHz

309.4 kHz

368.0 kHz

255.4 kHz

310.4 kHz 252.4 kHz

52.3 kHz

368.0 kHz

51.5 kHz

310.6 kHz

303.6

303.6 k

310.5 kHz

422.0 kHz

Gain

Phase VGS

Vout (AC)

VGS

VGS

VGS

VGS

Vout (AC)

Vout (AC)

Vout (AC)

Vout (AC)

fzp

51.1 kHz

21

Figure A2: AFL2805SX/ES_SN0710044 (International Rectifier) Vin = 16V~40V, Vout = 5V @ 16A, fSW = 550 kHz, Forward

(a) Bode plot showing fZP @∆T (f) 28Vin, 15A, 25°C, normal, 600 kHz Span

(b) 28Vin, 15A, 25°C, 33 kHz fc (g) Normal, 24Vin, 0A, -3°C, 117 kHz fc

(c) 28Vin, 1A, 110°C, 95 kHz fc (h) Normal, 24Vin, 0A, -20°C, 135 kHz fc

(d) 24Vin, 0A, 15°C, 103 kHz fc,100 kHz Span (i) 26Vin, 0A, -48°C, 146 kHz sideband

(e) 24Vin, 0A, 15°C, 103 kHz fc (j) 24Vin, 0A, 49°C, 94 kHz fc, 100 kHz span

32.6 kHz

583.4 kHz 135.7 kHz

117.4 kHz

578.3 kHz

103.1 kHz

573.9 kHz

580.4 kHz

146.5 kHz

93.5 kHz

586.7 kHz

33.3 kHz

94.7 kHz

103.1 kHz

537.8 kHz

63.2 kHz

429.7 kHz

283.6 kHz

22

Figure A3: AHE2812SF/CH_SN022 (International Rectifier) Vin = 17V~40V, Vout = 12V @ 1.6A, fSW = 250 kHz, Push-Pull

(a) 28Vin, 0A Load @ 25 °C (b) 28Vin, 0A Load @ 25 °C, 500 kHz span

(c) 28Vin, 1.6A Load @ 25 °C (d) 28Vin, 1.6A Load @ 25 °C, 500 kHz span

(e) 40Vin, 0A Load @ -55 °C (f) 40Vin, 1.6A Load @ -55 °C, 500 kHz span

(g) 28Vin, 1.6A Load @ 115 °C (h) 28Vin, 1.6A Load @ 115 °C, 500 kHz span

(i) 28Vin, 1.6A Load @ 60 °C (j) 28Vin, 1.6A Load @ 125 °C

253.3 kHz

379.3 kHz

252.2 kHz 379.5 kHz

127.8 kHz

254.3 kHz 508.7 kHz 763.0 kHz

29.4 kHz 127.2 kHz 253.3 kHz

378.3 kHz

23.3 kHz

43.5 kHz 130.4 kHz 259.8 kHz

216.3 k 302.2 k 389.1 kHz 87.0 k

172.8 k 345.7 k

23.9 kHz

22.79 kHz

22.7 kHz

127.2 kHz

24.1 kHz 44.4 kHz

24.1 kHz

23

Figure A4: AHE2812SF/CH_SN059 (International Rectifier) Vin = 17V~40V, Vout = 12V @ 1.6A, fSW = 250 kHz, Push-Pull

(a) 28Vin, 0A Load @ 25 °C (b) 28Vin, 0A Load @ 25 °C, 500 kHz span

(c) 28Vin, 1.6A Load @ 25 °C (d) 28Vin, 1.6A Load @ 25 °C, 500 kHz span

(e) 40Vin, 1.6A Load @ -25 °C (f) 40Vin, 1.6A Load @ -45 °C, 500 kHz span

(g) 28Vin, 1.6A Load @ 90 °C (h) 28Vin, 1.6A Load @ 115 °C

(i) 28Vin, 1.6A Load @ 125 °C (j) 28Vin, 1.6A Load @ 125 °C, 500 kHz span

258.7 kHz 130.4 kHz

252.2 kHz 382.6 kHz

128.3 kHz

130.4 kHz 259.8 kHz

389.1 kHz 29.4 kHz

130.2 kHz 259.3 kHz

389.3 kHz

381.8 kHz

33.7 kHz 139.1 kHz 278.3 kHz

244.6 k 310.9 k

415.2 kHz 107.6 k

165.3 k

381.5 k

319.6 k 24.1 k

192.4 k 64.2 k 446.7 k

450.0 k

400.0 kHz

266.3 kHz 133.7 kHz

33.7 kHz

101.1 k

171.7 k

245.6 k 301.7 k

29.7 kHz

65.2 k

127.2 kHz 254.3 kHz

285.7 k 223.5 k

165.3 k

41.3 kHz

33.7 kHz

30.0 kHz

30.0 kHz

388.0 kHz

24

Figure A5: AHE2812SF/CH_SN060 (International Rectifier) Vin = 17V~40V, Vout = 12V @ 1.6A, fSW = 250 kHz, Push-Pull

(a) 28Vin, 0A Load @ 25 °C (b) 28Vin, 0A Load @ 25 °C, 500 kHz span

(c) 28Vin, 1.6A Load @ 25 °C (d) 28Vin, 1.6A Load @ 25 °C, 500 kHz span

(e) 36Vin, 1.6A Load @ 110 °C (f) 40Vin, 0A Load @ 122 °C, 800 kHz span

(g) 40Vin, 1.6A Load @ 125 °C (h) 40Vin, 1.6A Load @ 125 °C, 1.0 MHz span

(i) 28Vin, 1.6A Load @ 125 °C (j) 28Vin, 1.6A Load @ 125 °C, 1.0 MHz span

254.4 kHz

379.3 kHz

252.2 kHz

378.3 kHz

126.1 kHz

64.2 kHz

67.8 kHz 267.8 kHz

26.1k 267.4 kHz

534.8 kHz

400.0 k

534.8 k

800.0 kHz

134.8 k

317.4 k 665.2 k

129.2 kHz

23.9 kHz

52.2

215.2 k 932.6 k

267.4 kHz

802.2 kHz 134.8 kHz

667.4 k 23.9 k

24.0 kHz

24.0 kHz

24.2 kHz

25.4 kHz

23.7 kHz

25

Figure A6: AHF2812S/ES_SN029 (International Rectifier) Vin = 16V~40V, Vout = 12V @ 1.0A, fSW = 550 kHz, Forward

(a) Normal, 28Vin, 1A @ 25 °C, 100 kHz span (b) Input noise, 28Vin, 0A Load @ 25 °C

(c) 28Vin, 0A Load @ 25 °C, 1 MHz span (d) 28Vin, 0A Load @ 25 °C, 9.4 kHz fc

(e) 28Vin, 0A Load @ 25 °C, 9 kHz sideband (f) 28Vin, 0A Load @ 75 °C, 16 kHz sideband

(g) 19Vin, 1A Load @ 110 °C, 62.6 kHz fc (h) 28Vin, 0A Load @ 110 °C, 19 kHz sideband

(i) 28Vin, 0A Load @ -40 °C, 65.2 kHz fc (j) 28Vin, 0A Load @ -40 °C, 11 kHz oscillation

553.2 kHz

9.65 kHz

556.5 kHz

834.8 kHz 280.4 kHz

62.6 kHz

56.5 kHz

553.0 kHz

21.7 kHz

603.5 k

553.0 kHz 53.9 kHz

273.0 k

566.3 kHz 544.3 k

19.1 k

535.7 k

32.6 kHz 558.3 kHz 65.2 kHz

500.9 k

562.3 k 571.2 k

580.1 k

535.5 k

526.3 k

549.3 kHz 532.4 kHz

568.7 kHz

556.5 kHz

11.0 kHz

9.4 kHz 54.5 kHz

26

Figure A7: AHF2812S/ES_SN030 (International Rectifier) Vin = 16V ~40V, Vout = 12V@1.0A, fSW = 550 kHz, Forward

(a) 28Vin, 0A @ 25 °C, 10.1 kHz noise (b) Input Noise, 28Vin, 0A Load @ 25 °C

(c) 28Vin, 0A @ 25 °C, 10 kHz sideband (d) 28Vin, 1A @ 25 °C, 10 kHz sideband

(e) 28Vin, 0A @ 25 °C, sideband in ½ fsw at 276 kHz (f) 40Vin, 0A @ 100 °C, 20 kHz sideband

(g) 33Vin, 0A Load @ 118 °C (h) Normal, 19Vin, 1A @ 112 °C, 62.6 kHz fc

(i) 33Vin, 0A @ 122 °C, 19 kHz sideband (j) Normal, 33Vin, 1A @ 122 °C, 69.6 kHz fc

555.6 kHz

10.1 kHz

558.7 kHz

839.1 kHz 276.1 kHz

62.6 kHz

58.7 kHz

553.0 kHz

53.9 kHz

54.2 kHz 18.9 kHz

572.6 kHz

545.2 k

558.3 kHz 559.8 kHz

69.6 kHz

566.3 k

576.0 k 586.6 k

535.3 k 524.6 k

552.0 kHz

532.4 kHz

10.1 kHz 54.7 kHz

20.2 k 30.0 k

545.2 kHz

554.8 kHz

507.8 k 608.7 k

575.7 k 540.9 k

566.3 kHz

27

Figure A8: AHF2812S/ES_SN031 (International Rectifier) Vin = 16V~40V, Vout = 12V @ 1.0A, fSW = 550 kHz, Forward

(a) 28Vin, 0A @ 25 °C, 12.5 kHz fosc, 48 kHz fc (b) Input Noise, 28Vin, 0A Load @ 25 °C

(c) 28Vin, 0A @ 25 °C, 12 kHz sideband (d) Normal, 40Vin, 1A @ 125 °C, 64.3 kHz fc

(e) 28Vin, 0A @ 25 °C, sideband in ½ fsw at 278 kHz (f) 28Vin, 0A @ 120 °C, 22 kHz sideband

(g) Normal 18Vin, 1A @ 106 °C, 62.6 kHz fc (h) 19Vin, 0A @ 103 °C, 57 kHz sideband

(i) 40Vin, 0A @ 110 °C, 47 kHz sideband (j) 33Vin, 0A @ 110 °C, 45 kHz sideband

554.8

11.9 kHz

558.7 kHz

832.6 kHz 278.3 kHz

62.6 kHz

48.7 kHz

554.8 kHz

64.3 kHz

600.0 k

553.0 kHz

57.4 kHz

615.7 kHz

542.8 k

-52.4 dBm

561.7 kHz

556.5 kHz 45.2 kHz

500.9 k

566.8 k

578.6 k 531.1k 519.1 k

558.3 kHz 22.6 k

12.5 kHz 48.0 kHz 24.3 k

36.0 k

70.7 k 59.2 k

606.5 k

578.6 k

506.5 k

-72.5 dBm

278.30 k 502.6 k

539.1 k 577.4 k 59.1 k

47.0 kHz

511.3 k 601.7 k

513.0 k 598.3 k

554.8 kHz -51.3 dBm

-77.0 dBm -80.9 dBm

-40.2 dBm

-71.3 dBm -76.2 dBm

28

Figure A9: AMR2805S/EM_SN 0534036 (International Rectifier) Vin = 18V~40V, Vout = 5V @ 6.0A, fSW = 550 kHz, Forward

(a) Bode plot showing fZP @ 25 °C (b) 37.3 kHz input noise, 18Vin, 6A @ 25 °C

(c) 18Vin, 0A Load @ 25 °C, 221 kHz OSC (d) Early OSC, 18Vin, 6A @ 25 °C, 37 kHz fc

(e) 18Vin, 0A @ 110 °C, 193 kHz sideband (f) 18Vin, 6A @ 110 °C, 169 kHz sideband

(g) 40Vin, 0A @ 110 °C, 197 kHz sideband (h) Early OSC, 40Vin, 6A @ 110 °C, 41 kHz fc

(i) 40Vin, 0A Load @ 25 °C, 39 kHz sideband (j) 40Vin, 6A Load @ 25 °C, 43 kHz fc, 290 kHz sideband

37.3 kHz

587.0 kHz

784.8 k 193.5 kHz

43.5 kHz

39.1 kHz

589.1 kHz

37.0 kHz

589.1 kHz

41.3 kHz

768.7 kHz

613.0 k

352.2 kHz

41.7 kHz

602.2 kHz 39.1 kHz

391.3 k 435.3 kHz

988.4 k

169.6 k

121.7 kHz

39.0 kHz

556.4 k 800.8 k

589.1 kHz

393.5 k 784.8 kHz

197.8 k

982.6 kHz

152.2 k 221.7 k

350.1 k 589.1 kHz

801.9 k 858.7 k

587.0 kHz

84.8 k

589.1 kHz

43.5 kHz 102.2 kHz

293.5 k 873.3 k

29

Figure A10: ATR2815DF/CH_011 (International Rectifier) Vin = 16V~40V, Vout = ±15V @ ±1.0A, fSW = 550 kHz, Forward

(a) 28Vin, 0A @ 25 °C, 37 kHz fc (b) 28Vin, 0A @ 25 °C, 280 kHz sideband

(c) Normal, 28Vin, ±1A @ 25 °C, 38.5 kHz fc (d) Normal, 28Vin, ±1A @ 25 °C, 39 kHz fc

(e) 28Vin, ±1A @ 100 °C, 35.1 kHz fc (f) 28Vin, ±1A @ 110 °C, 32 kHz sideband

(g) 25Vin, ±1A @ 125 °C, 30 kHz sideband (h) 35Vin, ±1A @ 125 °C, 40 kHz and 139 kHz sidebands

(i) 28Vin, ±1A @ 0 °C, 30 kHz sideband (j) 25Vin, ±1A Load @ 0 °C, 148 kHz sideband

39.1 kHz 554.3 kHz

29.6 kHz 560.0 kHz

550.0 kHz

553.0 kHz 40.3 k

582.7 k

556.5 kHz

41.3 k

38.5 kHz

553.2 kHz 32.6 kHz 35.1 kHz

525.3 k

147.8 kHz 30.4 kHz

139.1 k

963.0 k

554.3 kHz

85.2 k

587.8 k 57.4 k

615.7 k

530.4 k

280.4 k 830.4 k

37.0 kHz

39.1 kHz

415.7 k 690.4 k

704.3 k

513.0 k 593.0 k

63.0 k 526.1 k 587.0 k

493.5 k 617.4 k

408.7 k

30

Figure A11: ATR2815DF/CH_063 (International Rectifier) Vin = 16V~40V, Vout = ±15V @ ±1.0A, fSW = 550 kHz, Forward

(a) 28Vin, 0A Load @ 25 °C, 35.8 kHz fc (b) 28Vin, 0A @ 25 °C, 285 kHz sideband

(c) 28Vin, ±1A @ 25 °C, 37.7 kHz fc (d) Normal, 28Vin, ±1A @ 25 °C, 1 MHz Span

(e) 28Vin, ±1A @ 125 °C, 38.0 kHz fc (f) Normal, 28Vin, ±1A Load @ 90 °C

(g) 18Vin, ±1A @ -24 °C, 35.8 kHz fc and 182 kHz sideband (h) 18Vin, ±1A @ -50 °C, 189 kHz fosc and harmonics

(i) 40Vin, ±1A @ -3 °C, 150 kHz sideband (j) 40Vin, ±1A @ -50 °C, 160 kHz sideband

35.8 kHz 560.9 kHz

39.1 kHz

567.4 kHz

556.5 kHz

546.1 kHz

40.0 kHz

378.3 k

565.2 kHz

43.5 k

37.7 kHz

189.1 kHz

42.6 kHz

38.0 kHz

567.4 k

160.9 kHz

43.5 kHz 967.4 k

565.2 kHz

952.2 k 387.0 k

745.7 k

182.6 k

285.4 k 856.0 k 35.8 kHz

39.1 kHz

723.9 kHz

150.0 k 415.2 k 717.4 k

404.3 kHz

754.3 k 943.50 k

978.3 k

31

Figure A12: ATR2815DF/CH_075 (International Rectifier) Vin = 16V~40V, Vout = ±15V @ ±1.0A, fSW = 550 kHz, Forward

(a) 28Vin, 0A @ 25 °C, 33 kHz fc (b) 28Vin, 0A @ 25 °C, 186 kHz sideband

(c) 28Vin, ±1A @ 25 °C, 38.3 kHz fc (d) Normal, 28Vin, ±1A @ 25 °C, 1 MHz Span

(e) 28Vin, ±1A @ 125 °C, 39.4 kHz fc (f) Normal, 28Vin, ±1A @ 90 °C

(g) 28Vin, ±1A @ 60 °C, 37.3 kHz fc (h) Normal, 28Vin, ±1A @ 60 °C

(i) 28Vin, 0A @ 25 °C, Liner Scale, 188 kHz sideband (j) Normal, 28Vin, ±1A @ 25 °C, Liner Scale

35.8 kHz 556.7 kHz

37.3 kHz

554.3 kHz

546.1 kHz

40.0 kHz

557.1 kHz

38.2 kHz

38.3 kHz

40.0 kHz

39.4 kHz

38.2 kHz

742.4 k

557.1 kHz

371.6 k 743.9 k

33.3 kHz

38.2 kHz

371.8 k

188.3 k 371.8 k

188.3 k

546.1 kHz

742.5 k

186.5 k

926.8 k

32

Figure A13: ATW2805SES_021 (International Rectifier) Vin = 19V~40V, Vout = 5V @ 6.0A, fSW = 270 kHz, Push-Pull

(a) Bode plot, 28Vin, various load @ 25 °C (b) 28Vin, 1A @ 25 °C, 585.8 kHz harmonic.

(c) 28Vin, 0.1A @ 25 °C, 40.7 kHz fc (d) 28Vin, 0A @ 25 °C, 140 kHz fPWM and 280 kHz fsw

(e) 28Vin, 6A c@ 25 °C, 52.4 kHz fc (f) 28Vin, 6A @ 25°C, 55.4 kHz fc , 140 kHz fPWM and the fsw

(g) 40Vin, 0A @ 125 °C, 66.9 kHz fc (h) 40Vin, 0A @ 125 °C, low noise @ fsw =283 kHz

(i) 40Vin, 6A @ 125 °C, 52.2 kHz fc (j) 40Vin, 6A @ 125 °C, 53.0 kHz and 148 kHz fPWM sideband

280.2 kHz

66.9 kHz

280.4 kHz

279.3 kHz

55.4 kHz

588.7 kHz

53.0 kHz

47.0 kHz

67.8 kHz

52.4 kHz

881.4 k

283.1 kHz

294.3 k

52.2 kHz 148.3 k

741.5 k

585.8 k

140.2 k 418.5 k 19.6 k

140.8 k 418.2 k

934.3 k 830.4 k

445.8 k

33

Figure A14: DVFL2812S_SN 4431 (DELTA/VPT) Vin = 16V~40V, Vout = 12V @ 9.0A, fSW = 500 kHz, Forward

(a) Bode plot, 28Vin @ 25 °C (b) Input voltage noise, 46.7 kHz @17Vin, 4A, 25 °C

(c) 17Vin, 4A Load @ 25 °C, 43.0 kHz fc (d) 17Vin, 4A @ 25 °C, noise at 43.5 kHz.

(e) 28Vin, 0.2A @ 25 °C, 42.6 kHz fc (f) Normal, 28Vin, 0.2A @ 25 °C, 800 kHz Span

(g) 28Vin, 8A @ 25 °C, 40.9 kHz fc (h) 28Vin, 8A @ 25 °C, 41 kHz sideband

(i) 40Vin, 8A @ 25 °C, 45.9 kHz fc (j) 40Vin, 8A Load @ 25 °C, 45 kHz sideband

46.7 kHz

42.6 kHz

43.5 kHz 553.3 kHz 43.0 kHz

553.8 kHz 45.2 kHz

43.5 kHz

40.0 k

157.3 kHz

553.3 kHz

45.9 kHz

40.9 kHz

554.8 kHz

492.2 k

598.2 k 499.1 k

10 mV/Div

34

Figure 15: DVHF2815D_SN 0077 (DELTA/VPT) Vin = 15V~50V, Vout = ±15V @ ±0.65A or 1.33Amax total, fSW = 450 kHz, Flyback

(a) 10.1 kHz input noise, 40Vin, 0A @ 25 °C (b) 54.3 kHz input noise, 50Vin, ±0.65A @ 25 °C

(c) 40Vin, 0A @ 25 °C, 10.2 kHz fosc, 58.7 kHz fc (d) Normal, 50Vin, ±0.65A @ 25°C, 66 kHz fc

(e) 40Vin, ±0.65A @ 125 °C, 50 kHz fc (f) 50Vin, 0A @ 25 °C, 70 kHz sideband

(g) 28Vin ±0.65A @ 25 °C, 61 kHz fc (h) 28Vin, ±0.65A @ 25 °C, early sign of OSC

(i) 17Vin, ±0.65A @ 25 °C, 60 kHz fc (j) Normal, 17Vin, ±0.65A @ 25 °C, 600 kHz Span

426.5 kHz

61.3 kHz

426.5 kHz

10.1 kHz 54.3 kHz

422.6 kHz

61.3 kHz

367.8 k

60.2 kHz

490.4 k

69.6 kHz

356.5 k

62.6 kHz

50.2 kHz

10.2 kHz 20.0 kHz 58.7 kHz

77.2 kHz

423.9 kHz

66.5 kHz

35

Figure A16: DVHF2815D_SN0102 (DELTA/VPT) Vin = 15V~50V, Vout = ±15V @ ±0.65A or 1.33Amax total, fSW = 450 kHz, Flyback

(a) 35Vin 0A Load @ 25 °C, 17.4 kHz noise (b) 50Vin, 0A @ 25 °C, 10.6 kHz noise

(c) 35Vin, 0A load @ 25 °C, 17.0 kHz fosc (d) 50Vin, 0A Load @ 25 °C, 11.1 kHz fosc

(e) 35Vin, ±0.5A @ 25 °C, 62.6 kHz fc, (f) Normal, 50Vin, ±0.5A @ 25 °C, 66.1 kHz fc,

(g) Normal, 15Vin, 0A @ 25°C (h) Normal, 25Vin, 0A @ 25 °C, 59.1 kHz fc

(i) Normal, 15Vin, ±0.5A @ 25°C, 59.1 kHz fosc, (j) Normal, 28Vin, +0.9A/-0.7A @ 25 °C

10.6 kHz

17.0 kHz

420.9 kHz 420.9 kHz

60.9 kHz

420.9 kHz

66.1 kHz

423.9 kHz

62.6 kHz

420.9 kHz

21.5 k

420.9 kHz

33.3 kHz 11.1 kHz 49.4 kHz

59.1 kHz

63.1 kHz

59.1 kHz

81.5 kHz

17.4 kHz

31.7 k 42.2 k 52.6 k 63.3 k

94.6 k

36

Figure A17: DVTR283R3S_SN3925 (DELTA/VPT) Vin = 15V~50V, Vout = 3.3V @ 6.0A, fSW = 475 kHz, Flyback

(a) 28Vin, 0A @ 25 °C, 43.0 kHz fc (b) Zero phase frequency, fzp vs. Vin , Iout (Bode plot data)

(c) 18Vin, 5A load @ 25 °C, 43.0 kHz fc (d) 18Vin, 5A @ 25 °C, 34 kHz sideband

(e) 28Vin, 5A Load @ 25 °C, 37.1 kHz fc (f) 28Vin, 5A @ 25 °C, 38 kHz sideband

(g) 40Vin, 5A Load @ 25 °C, 40.9 kHz fc (h) 40Vin, 5A @ 25 °C, 40 kHz sideband

(i) 50Vin, 5A Load @ 25 °C, 44.7 kHz fc (j) 50Vin, 5A Load @ 25 °C, 44 kHz sideband

40.9 kHz

527.0 kHz

37.8 kHz

527.9 kHz

486.5 kHz

37.1 kHz

40.4 kHz

44.7 kHz 44.3 kHz

43.0 kHz

33.9 kHz

(V)

530.0 kHz

528.3 kHz

529.7 kHz

565.9 k

33.7 kHz

564.7 k

563.3 k

561.2 k

37

Figure A18: M3G2805S/EM_SN044 (International Rectifier) Vin = 18V~50V, Vout = 5V @ 8.0A, fSW = 500 kHz, Forward

(a) Bode plot showing the fzp @ 25°C (b) 17V, 0A Load @ 25 °C, 259 kHz sideband

(c) 28Vin, 0A @ 25 °C, 88 kHz fc, (d) Normal, 17Vin, 6A Load @ 25 °C

(e) 28Vin, 8A Load @ 25 °C, 99 kHz fc (f) Normal, 50Vin, 8A Load @ -33 °C

(g) 28Vin, 8A @ 125 °C, 107 kHz fc, low Psw (h) Normal, 50Vin, 8A Load @ 0 °C

(i) 50Vin, 0A @ 125 °C, 102 kHz fc, low Psw (j) Normal, 50Vin, 8A Load @ 100 °C

107.0 kHz

520.4 kHz

517.8 kHz 258.7 kHz

101.7 kHz

97.8 kHz

107.0 kHz

25.9

516.8 kHz

107.0 kHz

88.3 kHz

98.9 kHz

97.1 k

517.4 kHz

523.1 kHz

517.3 kHz

523.1 kHz

522.5 kHz

518.5 kHz 104.3 kHz

776.5 kHz

38

Figure A19: MFL2812S_SN 0102 (Interpoint) Vin = 16V ~40V, Vout = 12V@ 5.0A, fSW = 600 kHz, Forward

(a) Bode Plot Showing the fpc (b) 37.7 kHz OSC , 28V, 0A Load @ 0 °C

(c) 28Vin, 0A @ 25 °C, 36 kHz sideband (d) 28Vin, 4A @ 25°C, 36 kHz and 200 kHz sidebands

(e) 26Vin, 0.1A @ 25°C, 38.5 kHz fc, unknown 346 kHz (f) 26Vin, 4A Load @ 25 °C, 34 kHz sideband

(g) 40Vin, 0A @ 25 °C, 38 kHz sideband (h) 40Vin, 0.1A @ 25 °C, early sign of 36 kHz OSC

(i) 40Vin, 3A @ 25 °C, early sign of OSC (j) 40Vin, 4A @ 25 °C, 38 kHz and 200 kHz sideband

38.0 kHz

605.7 kHz

616.5 kHz 34.1 kHz

38.0 kHz

346.2 kHz

36.5 kHz

36.5 k

605.8 kHz

39.7 kHz

640.0 k

38.5 kHz 584.3 k

570.4 k 605.2 kHz

610.1 kHz

610.3 kHz

608.8 kHz 605.7 kHz

36.5 kHz

37.7 kHz

640.8 k 200.9 kHz 404.8 kHz

200.9 kHz

569.1 k 642.2 k

650.3 k

570.6 k

570.5 k 645.0 k

406.3 kHz 570.7 k 642.2 k

650.0 k 570.1 k

20 mV/Div

39

Figure A20: MFLHP2815S_SN 0132 (Interpoint) Vin = 19V~40V, Vout = 15V @ 6.7A, fSW = 600 kHz, Forward

(b) Bode Plot Showing the fpcs at 25°C (b) 19.6 kHz OSC, 28V, 0A @ 25 °C

(c) 28Vin, 0A @ 25 °C, 19.2 kHz fosc and 34.7k fc (d) 28Vin, 0A @ 25 °C, 19 kHz sideband

(e) 28Vin, 5A @ 25 °C, 38.3 kHz fc (f) Normal, 28Vin, 5A Load @ 25 °C

(g) 19Vin, 4A @ 25 °C, 36.1 kHz fc (h) Normal, 19Vin, 4A @ 25 °C, 36.1 kHz fc

(i) 40Vin, 5A @ 25°C, 42.0 kHz fc (j) Normal, 40Vin, 5A Load @ 25°C

19.8 kHz

596.5 kHz

593.0 kHz

38.3 kHz

41.7 kHz

38.3 kHz

36.5 kHz 594.8 kHz

42.0 kHz

19.2 kHz

36.1 kHz

593.0 kHz

36.5 kHz

19.6 kHz

578.3 k 613.3 k

628.2 k 561.5 k

34.7 kHz

20 mV/Div

40

Figure A21: MFLHP2815S_SN 0133 (Interpoint) Vin = 19V~40V, Vout = 15V @ 6.7A, fSW = 600 kHz, Forward

(i) Bode Plot Showing the fpcs at 25°C (b) 29.2 kHz OSC, 28V, 0A Load @ 25 °C

(c) 28Vin, 0A Load @ 25 °C, 30 kHz FEO (d) 28Vin, 0A Load @ 25°C, 30 kHz sideband

(e) 40Vin, 0A @ 25 °C, 35 kHz fc (f) 40Vin, 0A Load @ 25 °C, 17 kHz sideband

(g) 28Vin, 5A @ 25 °C, 39.8 kHz fc (h) Normal, 28Vin, 5A @ 25 °C

(i) 22Vin, 0A @ 25°C, 33.7 kHz fc (j) 22Vin, 0A @ 25°C, 154 kHz sideband

34.8 kHz

603.5 kHz

598.5 kHz

36.5 kHz

39.8 kHz

17.5 kHz

40.0 kHz 603.5 kHz

34.5 kHz

30.0 kHz

605.2 kHz

154.2 kHz

33.7 kHz

765.2 kHz

29.6 kHz

29.2 kHz

467.8 kHz

88.7 kHz 179.1 kHz

634.8 k 575.7 k

17.4 kHz

125.2 kHz 217.4 kHz

622.6 k 586.1 k

20 mV/Div

88.0 kHz

41

Figure A22: MHD2805S_SN 0619 (Interpoint) Vin = 16V~40V, Vout = 5V @ 3.0A, fSW = 625 kHz, Forward

(a) 17V,3A @25°C, 43 kHz fc, normal (b) 40V, 0.02A Load @ 25 °C, 253 kHz sideband

(c) 28Vin, 3A @ 25°C, 41.7 kHz fc, normal (d) 25Vin, 0.05A @ 25 °C, 153 kHz sideband

(e) 40Vin, 0A @ 25 °C, 45.7 kHz fc (f) 40Vin, 0A @ 25 °C, 30 kHz, 45 kHz sidebands

(g) 40Vin, 2A Load @ 25 °C, 45 kHz fc (h) Normal, 40Vin, 2A @ 25°C, 800 kHz Span

(ii) 40Vin, 3A Load @ 25°C, 47 kHz fc (j) 40Vin, 3A @ 25°C, early sign of 45 kHz oscillation

34.8 kHz

606.5 kHz

605.2 kHz

45.2 kHz

563.5k

43.5 kHz

605.2 kHz

45.2 kHz

41.7 kHz

44.9 kHz

41.3 kHz

43.5 kHz

152.2 kHz

304.3 k 910.9 k

760.9 k

47.3 kHz

111.3 k

45.7 kHz

655.7 k 558.3 k

38.3 kHz

607.0 kHz

607.0 kHz

579.1 k

607.0 kHz

636.5 k 650.4 k

29.6 k

608.7 kHz 153.0 kHz

455.7 k 758.3 k

42

Figure A23: MHD2805S_SN 0620 (Interpoint) Vin = 16V~40V, Vout = 5V @ 3.0A, fSW = 625 kHz, Forward

(a) 40V, 0.02A @25 °C, 45.8 kHz fc (b) 40V, 0.02A @ 25 °C, 43.5 Khz sideband

(c) 25Vin, 0.05A @ 25°C, 41.9 kHz fc (d) 25Vin, 0.05A @ 25 °C, ½ fsw sideband

(e) 40Vin, 0A Load @ 25°C, 44.7 kHz fc (f) 40Vin, 0A Load @ 25 °C, 60 kHz sideband

(g) 28Vin, 3A @ 25 °C, 44.4 kHz fc (h) Normal, 28Vin, 3A @ 25°C, 800 kHz Span

(i) 40Vin, 3A @ 25°C, 47.6 kHz fc (j) 40Vin, 3A@ °C, 52.2 kHz sideband

608.7 kHz

600.0 kHz

52.2 kHz

50.0 kHz

600.2 kHz

43.5 kHz

41.9 kHz

44.3 kHz

41.3 kHz

43.5 kHz

304.3 kHz 910.9 kHz

47.6 kHz

44.7 kHz

652.0 kHz

45.8 kHz

542.6 k

605.2 kHz

666.1 k

172.2 k

607.0 kHz 85.2 k 563.5 k 648.7 k

434.8 k 777.4 k

43

Figure A24: MHD2805S_SN 0621 (Interpoint) Vin = 16V~40V, Vout = 5V @ 3.0A, fSW = 625 kHz, Forward

(a) 16Vin, 3A @ 25 °C, 40.3 kHz fc (b) 16V, 3A Load @ 25°C, normal

(c) 28Vin, 3A @ 25 °C, 43 kHz fc (d) 28Vin, 3A Load @ 25 °C, normal

(e) 40Vin, 0A Load @ 25 °C, 44.6 kHz fc (f) 40Vin, 0A Load @ 25 °C, 45.3 kHz sideband

(g) 40Vin, 2A @ 25 °C, 42.3 kHz fc (h) 40Vin, 2A Load @ 25°C, normal

(i) 40Vin, 3A Load @ 25°C, 43.4 kHz fc (j) 40Vin, 3A Load @ °C, normal

34.8 kHz

601.7 kHz

603.5 kHz

43.5 kHz

41.7 kHz

605.2 kHz

45.3 kHz

43.0 kHz

42.3 kHz

43.5 kHz

40.0 kHz

43.4 kHz

44.6 kHz

43.5 kHz

40.3 kHz

563. 3 k

605.2 kHz

648.7 k

607.0 kHz

44

Figure A25: MHF+2812S_SN 0143 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 25V,1.25A @ 25 °C, Input noise waveform (b) 17V,1.25A Load @ 25 °C, normal

(c) 25V,1.25A @ 25 °C, early sign of oscillation (d) Normal, 28Vin, 1.25A Load @ 25 °C

(e) 25V,1.25A @ 25 °C, case not earth grounded (f) 32Vin, 1.25A @ 25°C, 45.2 kHz sideband

(g) 36Vin, 1.25A Load @ 25 °C (h) 36Vin, 1.25A @ 25°C, 48.7 kHz sideband

(i) 40Vin, 1.25A @ 25°C, 54 kHz sideband (j) 40Vin, 1.25A Load @ 25°C, normal

No output-COM to case connection

34.8 kHz

568.7 kHz

553.0 kHz

62.6 kHz

87.0 k

48.7 kHz 561.7 kHz

45.2 kHz

53.8 kHz

47.1 kHz

60.9 kHz

47.0 kHz

673.0 k

607.0 k

509.6 k 53.9 kHz

53.9 kHz

563.5 kHz

513.0 k 613.9 k

528.7 k

572.2 kHz

613.9 k

619.1 k

561.7 kHz

563.5 kHz

608.7 k

514.8 k

518.3 k

55.7 kHz

567.0 kHz

45

Figure A26: MHF+2812S_SN 0152 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 32V, 1.25A @25 °C, Waveform (b) 16V,1.25A Load @ 25 °C, normal

(c) 32Vin, 1.25A @ 25 °C, 47.7 kHz sideband (d) 28Vin, 1.25A Load @ 25 °C, normal

(e) 35.6Vin, 1.25A @ 25 °C, early sigh of 45 kHz oscillation (f) 34Vin, 1.25A Load @ 25 °C, normal

(g) 35Vin, 0A Load @ 25 °C, 94 kHz sideband (h) 35Vin, 1.25A Load @ 25°C, normal

(i) 36Vin, 1.25A @ 25°C, 47 kHz sideband (j) 40Vin, 1.25A Load @ 25°C

93.9 kHz

558.3 kHz

558.3 kHz 48.7 kHz

57.4 kHz

567.0 kHz

60.9 kHz

90.4 k

469.6 k

57.4 kHz

561.7 kHz

57.4 kHz

607.0 k

520.0 k

47.0 kHz

45.2 kHz

47.2 kHz

607.0 kHz

653.9 k

558.3 kHz 47.0 k 514.8 k

469.6 k 601.7 k

645.2 k

563.5 kHz 567.0 kHz

518.3 kHz

90.4 k

565.2 kHz

60.9 k

565.2 kHz

476.5 k

90.4 kHz 600.0 kHz 514.8 k

643.5 k 471.3 k

46

Figure A27: MHF+2812S_SN 0154 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 16V, 1.25A Load @25 °C, 57.6 kHz fc (b) 16V, 1.25A @ 25 °C, early sign of oscillation

(c) 25Vin, 1.25A Load @ 25 °C (d) 16Vin, 0A Load @ 25 °C, 52 kHz sideband

(e) 25.2Vin, 1.25A @ 25 °C, 36 kHz sideband (f) 24.3Vin, 1.25A @ 25 °C, 52 kHz sideband

(g) 24Vin, 1.25A @ 25°C, 42 kHz sideband (h) Early sign of 54 kHz OSC, 28Vin, 1.25A @ 25°C

(i) 40Vin, 1.25A @ 25°C, input noise waveform (j) 40Vin, 1.25A Load @ 25 °C, normal

62.6 kHz

567.0 kHz

36.7 k

36.5 kHz 52.2 kHz

551.3 kHz

52.2 kHz

62.5 kHz

49.6 kHz

53.9 kHz

102.6 k

41.7 kHz

516.5 k

525.2 k 603.5 k

565.2 kHz

615.7 k

572.2 kHz

605.2 k 535.7 k

567.0 kHz

615.7 k 518.3 k

57.4 kHz

565.2 kHz

511.3 k

102.6 k

558.3 kHz

57.6 kHz

617.4 k

606.3 k 608.7 k

47

Figure A28: MHF+2812S_SN 0157 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 16V, 1.25A Load @25 °C, 41 kHz fc (b) 16V, 1.25A @ 25 °C, early sign of 42 kHz OSC

(c) 16.1Vin, 1.25A Load @25°C, normal (d) 17.8Vin, 1.25A@25 °C, no Earth ground

(e) 21Vin, 1.25A @ 25°C, 23.5 kHz front-end OSC (f) 19Vin, 1.25A @ 25 °C, early sign of 35 kHz OSC

(g) 29Vin, 0A Load @ 25 °C, 49 kHz sideband (h) 33Vin, 1.25A Load @ 25°C, 38 kHz sideband

(i) 38Vin, 1.25A @ 25°C, 57 kHz sideband (j) 28Vin, 1.25A Load @ °C, normal

48.7 kHz

584.3 kHz

558.3 kHz

52.2 kHz

23.5 k

97.4 kHz

554.8 kHz

38.3 kHz

509.6 k

50.4 kHz

556.5 kHz

41.7 kHz

608.7 k

664.3 k

497.4 k

57.4 kHz

36.5 kHz

46.5 kHz

41.1 kHz

605.2 k

92.2 k

57.4 kHz

76.5 k

518.3 k 589.6 k

563.5 kHz

638.3 k

69.3 k

563.5 kHz 601.7 k

113.0 k

527.0 k

567.0 kHz

488.7 k

553.0 kHz

608.7 k

443.5 k

527.3 k

48

Figure A29: MHF+2812S_SN 7429 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 16V, 1.25A Load @25 °C, 57 fc kHz (b) 16V, 1.25A Load @ 25 °C, normal

(c) 28Vin, 1.25A Load @ 25 °C (d) 25Vin, 1.25A Load @ 25 °C, normal

(e) 38Vin, 0A Load @ 25°C, 62 kHz fc (f) 38Vin, 1.25A @ 25 °C, 106 kHz sideband

(g) 40Vin, 0.01A @ 25 °C, 61 kHz sideband (h) 40Vin, 1.25A Load @ 25°C, normal

(i) Oscillation, 40Vin, 0A Load @ 25°C (j) 40Vin, 0A Load @ 25°C, 800 kHz span

60.9 kHz

573.9 kHz

62.1 kHz

64.4 k

97.4 kHz

579.1 kHz

62.6 kHz

106.1 kHz

521.7 k

57.4 kHz

579.1 kHz

59.1 kHz

640.7 k 518.3 k

62.6 kHz

62.6 kHz 579.1 kHz

56.7 kHz

605.2 k

687.0 k

57.4 kHz

33.0 k

520.0 k 600.0 k

575.7 kHz

645.2 k

473.0 k

575.7 kHz

586.1 kHz

474.8 k

588.9 kHz

49

Figure A30: MHF+2812S_SN 7430 (Interpoint) Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 16V, 1.25A Load @25 °C, 56.2 kHz fc (b) 16V, 1A Load @ 25 °C, normal

(c) 28Vin, 1.25A @ 25 °C, 57.6 kHz fc (d) 28Vin, 1.25A Load @ 25 °C, normal

(e) 40Vin, 0A @ 25 °C, 58 kHz fc (f) 32Vin, 1.25A Load @ 25 °C, normal

(g) 40Vin, 1.25A @ 25°C, 59.8 kHz fc (h) 40Vin, 1.25A Load @ 25°C, normal

(i) 57.5 kHz input noise, 40Vin, 0A @ 25°C (j) 40Vin, 0A Load @ 25°C, 116 kHz sideband

12.1 kHz

563.5 kHz

58.4 kHz

57.5 kHz

60.9 kHz

60.6 kHz

57.4 kHz

57.4 kHz

59.8 kHz

680.0 k Vin (AC)

59.1

565.2 kHz

56.2 kHz

23.7 k

57.6 kHz

47.0 k 35.2 k

558.3 kHz

116.5 k

575.7 kHz

565.2 kHz 450.4 k

50

Figure A31: MHF+2812S_SN 7431 (Interpoint)

Vin = 16V~40V, Vout = 12V @ 1.25A, fSW = 550 kHz, Forward

(a) 16V, 1.25A Load @25 °C, 56.7 kHz fc (b) 16V, 1.25A Load @ 25 °C, normal

(c) 60 kHz input noise, 24.9Vin, 1.25A @ 25 °C (d) ESO, 24.9Vin, 1.25A @ 25 °C, 59 kHz sideband

(e) 28Vin, 0A Load @ 25 °C, 58.7 kHz fc (f) ESO, 28Vin, 1.25A @ 25 °C, 110 kHz sideband

(g) 40Vin, 1.25A @ 25 °C, 59 kHz fc (h) 40Vin, 1.25A Load @ 25°C, normal

(i) 61 kHz input noise, 40Vin, 0.9A @ 25°C (j) 40Vin, 0.9A Load @ 25°C, 60 kHz sideband

60.9 kHz

567.0 kHz 58.1 kHz

61.0 kHz

62.6 kHz 59.3 kHz

514.8 k

59.1 kHz

563.5 kHz

55.7 kHz

62.6 kHz

565.2 kHz

459.1 k

59.1 kHz

114.8 k 622.6 k

671.3 k

59.9 kHz

109.8 k

603.5 k

507.8 k

570.4 kHz

567.0 kHz

56.7 kHz

51

Figure A32: MSA2815D_SN 0083 (Interpoint) Vin = 16V~40V, Vout = ±15V @ ±0.167A, fSW = 550 kHz, Flyback

(a) 32V, ±0A Load @25 °C, 41 kHz noise (b) 33V, ±0A @ 25 °C, 44 kHz sideband

(c) 20Vin, ±0A Load @ 25 °C, unknown 140 kHz (d) 20Vin, ±0.08A Load @ 25 °C. 19 kHz sideband

(e) 22Vin, ±0.16A @ 25 °C, 19 kHz sideband (f) 28Vin, ±0.16A @ 25 °C, normal

(g) 39Vin, 0A @ 25 °C, normal (h) 39Vin, ±0.16A @ 25°C, 38.3 kHz sideband

(i) ) 16V, 0A Load @ 25 °C, normal (j) Back ground noise at power off @ 25°C

38.3 kHz

469.8 kHz

467.8 kHz

34.7

41.3 kHz

481.7 kHz

174.8 kHz

114.8 kHz

139.1 k

43.5 kHz

711.3 kHz

43.5 kHz

481.7 kHz

516.5 k

19.0 kHz

140.9 k

38.3 k

500.9 k

19.1

140.9 kHz 447.0 k

499.1 k

113.8 k

467.8 kHz

476.5 kHz

464.2 k

471.3 kHz

424.3 k 151.3 k

471.3 kHz

233.7 k

464.3 k

514.8 k

57.4 k

140.9 kHz

52

Figure A33: MSA2815D_SN 0085 (Interpoint) Vin = 16V~40V, Vout = ±15V @ ±0.167A, fSW = 450 kHz, Flyback

(a) 35 kHz input noise, 39V, ±0.16A Load @25 °C (b) 39V, ±0.16A Load @ 25 °C, 38 kHz sideband

(c) 17Vin, ±0.08A Load @ 25 °C, 233 khz sideband (d) 17Vin, ±0.16A @ 25 °C, 238 kHz sideband

(e) Early sign of 42 kHz, 24Vin, ±0A @ 25 °C (f) 25Vin, ±0A @ 25 °C, 42 kHz sideband

(g) 28Vin, ±0A Load @ 25 °C, 43 kHz sideband (h) 28Vin, ±0.16A @ 25°C, 233 kHz sideband

(i) 32Vin, ±0A Load @ 25°C, 42 kHz sideband (j) 32Vin, ±0.16A @ 25°C, 118 kHz sideband

455.7 kHz

459.1 kHz

154.8 kHz

347.8 k

35.5 kHz

481.7 kHz

118.3 kHz

41.7 kHz

132.2 k

43.5 kHz

38.3 kHz

41.7 kHz

455.8 kHz

685.2 k

41.7 kHz

697.2 kHz

233.0 k

497.4 k

497.4 k

127.0 kHz

233.0 kHz

238.3 k

459.1 kHz

415.7 k

462.6 kHz

464.3 kHz

415.2 k

462.6 kHz

417.4 k 127.0 k

459.1 kHz

693.9 k 500.9 k

420.9 k 499.1 k

579.1 k 693.9 k

231.2 k

424.3 k 495.7 k

53

Figure A34: SMFL2805S/KP_SN 0703 (Interpoint) Vin = 16V~40V, Vout = 5V @ 16A, fSW = 550 kHz, Forward

(a) Body Plot showing fzp, 5A Load @25 °C (b) 40V, 13A Load @ 25 °C, 41.9 kHz fc

(c) 28Vin, 5A Load @ 25 °C, 36 kHz fc (d) 28Vin, 6A Load @ 25 °C, normal

(e) 28Vin, 0A Load @ 25 °C, 38.3 kHz fc (f) 28Vin, 13A Load @ 25 °C, normal

(g) 16Vin, 0A Load @ 25 °C, very low noise (h) 16Vin, 10A Load @ 25°C, normal

(i) 40Vin, 0A Load @ 25°C, 43.5 kHz sideband (j) 40Vin, 13A Load @ 25°C, normal

38.3 kHz

603.5 kHz

605.2 kHz

35.5

41.7 kHz

43.5 kHz

38.3 kHz

601.7 kHz

38.3 kHz

605.2 kHz 38.3

36.5 kHz

342.6 k

35.9 kHz

603.5 kHz

603.5 kHz

601.7 kHz

41.9 kHz

561.7 k 647.0 k

54

Figure A35: VI-J2L-EV, SN723 (Vicor Corp.) Vin = 21V~50V, Vout = 28V @ 1A, fSW = 170 kHz~450 kHz

(a) Body Plot showing fzp, @25 °C (b) 40V, 1A Load @ 25 °C, 22.1 kHz fc

(c) 21Vin, 0A Load @ 25 °C, 27 kHz fc (d) 21Vin, 1A Load @ 25 °C, normal

(e) 33Vin, 1A Load @ 25 °C, 22.2 fc (f) 24Vin, 1A Load @ 25 °C, 27 kHz sideband

(g) 50Vin, 1A Load @ 25 °C, 29.7 kHz fc (h) 40Vin, 1A Load @ 25°C, 25 kHz

(i) 50Vin, 1A Load @ 25°C, 31 kHz fc (j) 50Vin, 1A @ 25°C, 112 kHz fsw and harmonics

25.0 kHz

426.5 kHz

31.3 kHz

459.1 k

65.0 kHz

112.2 kHz

30.7 kHz

22.2 kHz

170.7 kHz

22.1 kHz

27.4 kHz

545.2 kHz

148.5 k

452.6 k

28.7 kHz

113.5 kHz

399.1 k

27.4 kHz

220.4 k

336.5

241.3 kHz

503.5 k

43.7 kHz

262.2 k

193.3 k

29.7 kHz

83.2 k 143.2 k

448.7 k

560.9 k

224.3 k

480.0 k 371.7 k

481.3 kHz