# [060] Input Impedance Measurements and Filter Interactions Part I

The proper place to apply Middlebrook's stability criteria for input filters.

### Introduction

In this article, Dr. Ridley continues the discussion of input impedance measurements, and shows the effect of properly locating all of the input filter components. Middlebrook's input filter stability criteria only apply to the system measured with the filter components in the correct location.

### Input Impedance Measurements

As discussed in the last article, an input impedance measurement gives information about the characteristics of the power supply input terminals. The measurement is usually a requirement of the documentation package in the aerospace industry. The input impedance measurement is very useful for anyone that has to add components to the basic power supply design. This can include an input EMI filter, or another power supply that preconditions the input voltage rail.

Figure 1 shows a block diagram of a switching power supply connected to an input filter. Dr. Middlebrook, in his famous paper on input filter interactions, said that the if the input impedance of a converter, Zin, is always greater than the output impedance of the filter, Zout, then a stable power supply will remain stable when the filter is connected [2]. Measurements of both the filter output impedance, and the power supply input impedance are useful for predicting the stability of the resulting power system.

Fig. 1: Power supply with input filter module

The impedances can be measured with the diagram shown in Figure 2. An ac voltage source is connected in series between the filter and the switching power supply. The input impedance is measured from the ratio of the input voltage of the supply and the current into the terminals. The output impedance of the filter can be measured with the same injection setup with the voltage probe at the output of the filter. The filter output impedance can also be measured with power removed from the circuit, as will be described in the next article.

The practical implementation of the voltage injection and measurement is described in detail in [1].

Fig. 2: Voltage injection into the power rail for impedance interaction measurements

The Middlebrook criteria require that the power supply block of Figure 2 contains only the switching cell, and none of the input filter components. However, it is usually a practical necessity that at least one filter component is included in the power supply block to filter high-frequency pulsating currents. Without this, measurements can be too noisy and the converter may not operate properly. Also, in many cases, the internal circuit nodes for measurement are inaccessible, and the power supply input impedance measurement will include several filter components.

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