# [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.

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