Editing Electrical impedance (section)

== Measurement ==
The measurement of the impedance of devices and transmission lines is a practical problem in [[radio]] technology and other fields. Measurements of impedance may be carried out at one frequency, or the variation of device impedance over a range of frequencies may be of interest. The impedance may be measured or displayed directly in ohms, or other values related to impedance may be displayed; for example, in a [[radio antenna]], the [[standing wave ratio]] or [[reflection coefficient]] may be more useful than the impedance alone. The measurement of impedance requires the measurement of the magnitude of voltage and current, and the phase difference between them. Impedance is often measured by [[Bridge circuit|"bridge" methods]], similar to the direct-current [[Wheatstone bridge]]; a calibrated reference impedance is adjusted to balance off the effect of the impedance of the device under test. Impedance measurement in power electronic devices may require simultaneous measurement and provision of power to the operating device.

The impedance of a device can be calculated by complex division of the voltage and current. The impedance of the device can be calculated by applying a sinusoidal voltage to the device in series with a resistor, and measuring the voltage across the resistor and across the device. Performing this measurement by sweeping the frequencies of the applied signal provides the impedance phase and magnitude.<ref name="LewisJr">{{cite journal |author=George Lewis Jr. |author2=George K. Lewis Sr. |author3=William Olbricht |name-list-style=amp |date=August 2008 |title=Cost-effective broad-band electrical impedance spectroscopy measurement circuit and signal analysis for piezo-materials and ultrasound transducers |journal=Measurement Science and Technology |volume=19 |issue= 10|page=105102 |doi=10.1088/0957-0233/19/10/105102 |pmid=19081773 |pmc=2600501 |bibcode = 2008MeScT..19j5102L }}</ref>

The use of an impulse response may be used in combination with the [[fast Fourier transform]] (FFT) to rapidly measure the electrical impedance of various electrical devices.<ref name="LewisJr"/>

The [[LCR meter]] measures a component's inductance (L), capacitance (C), and resistance (R); from these values, the impedance at any frequency can be calculated.

===Example===
Consider an LC [[LC circuit|tank]] circuit. 
The complex impedance of the circuit is
:<math>Z(\omega) = \frac{j\omega L}{1 - \omega^2 LC}.</math>
It is immediately seen that the value of <math display="inline">{1 \over |Z|}</math> is minimal (actually equal to 0 in this case) whenever 
:<math>\omega^2 LC = 1.</math>
Therefore, the fundamental resonance angular frequency is  
:<math>\omega = {1 \over \sqrt{LC}}.</math>