The concept of impedance is a very broad one that can be applied to fields such as electricity, communications, optics, sound, and vibration. Covering all of these is beyond my capabilities, so I will provide a basic explanation.
When a force (or pressure) is applied to something, a certain quantity changes. The ratio of the applied force (or pressure) to the amount that changes is defined as impedance. In simpler terms, when a force (or pressure) is applied, a certain quantity moves or flows, and impedance represents the resistance to that movement or flow. Incidentally, the word impedance means "to delay" or "to hinder."
Generally, impedance has two quantities—magnitude (also called gain or magnitude) and phase—which are functions of frequency, and is therefore expressed as a complex number.
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Figure 1: AC current flowing through an impedance
In an electrical circuit, impedance is the ratio of the voltage across its terminals to the current flowing through it, as shown in Figure 1. That is;
This relationship is exactly the same as Ohm's law for direct current, and impedance can be described as resistance that hinders the flow of AC signals.
Just as explained last time, when Z (impedance) in Figure 1 includes a reactance component (i.e., circuit elements such as coils and capacitors), a phase difference occurs between the instantaneous AC voltage and AC current.
AC voltage
alternating current
Therefore, the impedance Z becomes a function of the frequency f;
It can be expressed as follows. From equation (2), we can see that Z is a complex function of frequency f with magnitude V/I and phase -θ (with a negative phase lag).
Now, in order to measure impedance with an FFT analyzer or frequency response analyzer, an AC signal source is needed to drive the impedance system in question. The important point here is that the frequency of the driving signal source and the frequency being analyzed are synchronized.
Two examples of measuring electrical impedance are shown below. The first example is measuring the input impedance (commonly known as load resistance) of an audio speaker (Figure 2).
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Figure 2: Example of a speaker impedance measurement system
The speaker is driven by an AC signal from the analyzer (DS-2000). The voltage signal across the speaker is input to Ch2, and the current signal flowing through the speaker (voltage signal across the shunt resistor) is input to Ch1. The impedance is determined by measuring the transfer function between the channels. Figure 3 shows the measurement results, where the red in the left figure (Bode plot) represents the amplitude ratio of voltage to electric charge (i.e., AC resistance, in Ω), and the blue represents the phase difference (angle, deg).
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Figure 3: Example of speaker output impedance measurement data
The second example is measuring the output impedance (commonly known as internal resistance) of a battery such as a fuel cell (Figure 4).
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Figure 4. Example of a battery output impedance measurement system.
(Note: This is an example using the ELZ-175 electronic load device from Keisoku Gijutsu Kenkyusho Co., Ltd.)
In this example, an electronic load device is required to absorb the battery's power. By supplying an AC signal from the analyzer (DS-2000) as the load current control signal for the electronic load device, inputting the current signal absorbed by the electronic load device to Ch1 and the voltage signal across the battery to Ch2, and measuring the transfer function in the same way as in Example 1 above, the battery's internal impedance can be measured. Figure 5 shows a measurement example, and the graph on the right is the Cole-Cole diagram.
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Figure 5 Example of internal impedance measurement data for a fuel cell
In mechanical systems, mechanical impedance is used. When an object is vibrated by a vibrator, if the excitation force is F and the vibration velocity of the response is V, then the mechanical impedance Z is:
It can be defined as follows: In other words, Z represents the degree of resistance to vibration.
One method used to determine the loss coefficient of vibration damping materials is mechanical impedance (see the document on vibration damping materials and their performance measurement).
Overall - Glossary of Basic Terms Related to FFT Analysis
The graph in Figure 6 shows an example of mechanical impedance data for a two-layer test specimen. The specific measurement method involves inputting signals from an acceleration sensor to Ch1 and signals from a force sensor to Ch2 to determine the force/acceleration transfer function (also called dynamic mass or apparent mass), and then differentiating it on the frequency axis to obtain the mechanical impedance Z.
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Figure 6. Example of mechanical impedance measurement data for vibration damping material.
In acoustic systems, impedance is also defined. Generally, acoustic impedance is the ratio of sound pressure to volume velocity passing through a specified surface of a medium such as air, and it represents the resistance of the medium to motion. In particular, in the case of an acoustic tube, it can be considered a plane wave, so the ratio of sound pressure to the particle velocity at a single point in the medium is called specific acoustic impedance (or acoustic impedance density).
A system for measuring the sound absorption coefficient with normal incidence using an acoustic impedance tube can determine the specific acoustic impedance of a sound-absorbing material.
Table 1 summarizes the correspondence between each physical quantity in the fields of electrical engineering, mechanical engineering, and acoustics.
| Electrical system | Mechanical Systems | Acoustic system (general space) | Acoustic system (plane wave) |
| Voltage V | force F | Sound pressure p | Sound pressure p |
| current i | speed V | Volume velocity V | particle velocity v |
| Impedance Z = V/i | Mechanical impedance Z = F/V | Acoustic impedance Z = p/V | Relative acoustic impedance Z = p/v |
Table 1. Impedance in electrical, mechanical, and acoustic systems
(Excerpt from the email newsletter issued on September 18, 2008)
