# [023] Frequency Response Measurement Part I: Wide Band of Frequencies

The needed frequency range of power supply design and analysis is explored.

### Introduction

In this article, Dr. Ridley starts a series of three articles on switching power supply frequency response. The first article introduces the frequency ranges of interest in a switching power supply, and some of the difficulties of frequency response analysis.

### Switching Power Supplies – Ultra Wide Band Circuits

Switching power supplies have a reputation for being difficult circuits to design, troubleshoot, and manufacture. Some of the reasons for this have been covered in past articles in Power Systems Design Europe [1]. There is another fundamental issue encountered with power supplies that makes them a special class of electronics: they generate an extraordinarily wide range of frequencies.

Sometimes it is easy to point at RF fields and be in awe at the extremely high frequencies encountered, in the multi-GHz range. Anyone who has worked in these fields is familiar with the critical parameters of circuit layouts, microwave circuit elements, matching networks, and other specialties. The 100 kHz switching power supply seems relatively easy by comparison.

A major challenge of the switching power supply design is encountered in the extreme range of frequencies that must be considered. Figure 1 shows the typical frequency bands for a switching power supply.

There are two significantly separate regions of Figure 1. The first region concerns the frequencies up to half of the switching frequency. These are the relevant control frequencies of the converter, where the control loop responds to changes in the system such as changing loads, or changing input voltages.

The second region is from the switching frequency and up. For these frequencies, the power supply is a noise or EMI generator. The power supply is not expected to respond to a control stimulus in these frequency ranges, and the job of the power supply designer is to suppress and manage the high frequency noise components.

### Control Frequencies

Control Frequencies of a power supply can extend down as low as 0.01 Hz, and as high as several hundred kHz, depending on the switching frequency (typically in the range of 20 kHz to 2 MHz.)

Many power supplies are now designed with two stages of power conversion – a switching power factor correction circuit (PFC) which shapes the AC input current waveform, and a switching DC-DC power supply which isolates and regulates the output from the input source power.

The function of the PFC circuit is to make the input of the system look like just a resistive load, even though there are large bulk capacitors to be charged at the input. To achieve this, the primary purpose of the PFC circuit is to shape the input current into a rectified AC waveform. (A feedback loop from the output capacitor after this circuit is used to set the average current level during the AC line cycle.)

If the input current waveform is to have low distortion, the feedback signal setting the current level must remain essentially constant during a single line cycle. This means that the loop around the PFC circuit must be slow – with a bandwidth of perhaps no more than 1 Hz. This PFC circuit requirement sets the first two bands of Figure 1 – the PFC loop gain is typically measured in the range from 0.01 Hz to 10 Hz.

10 Hz is typically where a loop gain Bode plot is initiated for the switching power supply. This frequency is chosen since it is below the significant noise frequency caused by the AC input line. The AC input line generates noise at 50 or 60 Hz with a single-diode rectifier, and at 100 or 120 Hz with a bridge rectifier. The control of the power supply is expected to respond to prevent the line-frequency harmonics from appearing on the output of the power supply.

The resonance of the LC filter of a switching power supply is typically around 100 times lower than the selected switching frequency. For a 100 kHz power supply, a resonance of 1 kHz is typical.

The loop gain of the converter can be as high as about 1/10th the switching frequency [2], and as low as perhaps 100 Hz. While the actual crossover itself is not a design objective, raising the crossover frequency is usually a method to improve performance without making significant changes to power components. Loop gain measurements are continued above the crossover frequency and up to the switching frequency, to verify the gain margin of the system.

### Noise Frequencies

The switching frequency of the power supply is both the carrier of the control and power information. It is a generator of noise which must be attenuated before it gets to the output and input lines of the system. Since PWM converters are designed to be as efficient as possible, the rise and fall times of the square-wave waveforms are very fast.

The fast edges of switching action generate harmonics from the fundamental of the switching frequency out to 10 MHz and beyond.

The abrupt switching also excites resonances in the circuit due to magnetics and junction capacitances, and peaks in the EMI spectrum can be seen at frequencies in the multi-MHz range.

### Control Signal and Noise All At Once

Once of the specially challenging aspects of switching power supplies is that the noise frequencies from 50 Hz up to 100 MHz all coexist at the same time. When probing the circuit with an oscilloscope, you must use many different time bases in order to see the frequencies that you are looking for, and to troubleshoot system issues.

Specialized equipment is used in addition to a high-performance oscilloscope. A spectrum analyzer is used to detect individual frequencies that make up a waveform, and to accurately show magnitudes at very low signal levels in order to verify EMI compliance.

Below the switching frequency, a frequency response analyzer is used to generate a low-level sinusoidal stimulus, one frequency at a time, and measure the response of the system to the single stimulus. This must be done in the presence of noise which can far exceed the measured signals. In addition, the frequency response analyzer must compare two signals in the system, both in terms of their amplitude and phase difference. This will be discussed further in the next article in this series.

Fig. 2 shows the challenge encountered in with power supply waveforms. Fig 2a shows the output voltage of a flyback power supply, with the time base set at 20 ns per division. Multiple high frequencies can be observed in this waveform, and a spectrum analyzer would be needed to separate and measure them.

Fig 2b is set at 2 μs/div, showing the switching frequency noise and harmonics. Notice that the high frequency noise dominates the waveform amplitude.

Fig. 2c shows the same waveform at 20 ms/div, a time base six decades away from Fig. 2a. A low frequency envelope can be seen in the waveform of Fig. 2c, but it is buried in the switching noise of the converter. A frequency response analyzer will be needed to measure this signal properly to obtain control amplitude and phase information.

 Figure 2a: Power Supply Output Noise 20 ns/div Figure 2b: Power Supply Output Noise 2 μs/div Figure 2c: Power Supply Output Noise 20 ms/div

### Summary

Switching power supplies generate noise, and must respond to controls at frequencies which cover a range with  10 orders of magnitude. Controls respond from dc to half the switching frequency, and noise is generated from the switching frequency up to 100 MHz. One of the major challenges of the power supply designer is to separate the signal from the noise in order to create a rugged and stable system. In the next few articles, this column will explore further the control measurement and design issues involved in this process.

### References

• Join our LinkedIn group titled “Power Supply Design Center”. Noncommercial site with over 7000 helpful members with lots of theoretical and practical experience.
• “Design Tips”, Dr. Ray Ridley,Power Systems Design Magazine, Design Tips Archive
• “Loop Gain Crossover Frequency”, Dr. Ray Ridley.

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