## Frequency dependent characterization of electrical components (R-L-C)

## Frequency dependent characterization of electrical components

In an electrical circuit, a potential difference between two points induces the flow of current. Impedance is defined as the sum of resistance and, in the case of alternating current supplies, reactance; the effect is to reduce current flow.

If the circuit comprises only resistors, then the impedance is constant at all frequencies and has what is known as ohms law, defined by:

V = IR (where V = voltage, I = current and R = resistance).

Therefore, R = V / I.

In the case of a DC (direct current) circuit that contains a capacitor, current will flow through the capacitor until it becomes fully charged. This rate of charge reduces exponentially as the capacitor charge nears the target voltage.

Conversely, if the circuit is powered by AC (alternating current) such as a mains supply, the current response will oscillate in phase with the voltage and can be seen as a sine wave on an oscilloscope. This current response is at its highest rate early in the capacitor charging cycle, but the constant reversal of current flow that is characteristic of AC supplies actually causes the circuit to behave almost as if the capacitor were not present. This is especially so at high frequencies.

Therefore, the extent and effect of capacitive impedance depend on the AC supply frequency measured in Hertz (cycles per second), the capacitance (measured in micro or millifarads) and any other components connected either in series or in parallel. The type of impedance produced is said to be *reactive* (as opposed to purely resistive) and is a linear function of the frequency, both for pure capacitance and inductance.

Notably, in a purely capacitive circuit, the current response is ninety degrees ahead of the AC voltage. However, in practice, some resistance is always present; capacitors are often also combined with resistors such as in purpose-designed signal noise filters.

In addition, inductors are components that have a reactive response and cause impedance. In a sense, they are the opposite of capacitors in that the current flow through an inductive load **lags** the voltage supply, with a phasing difference of ninety degrees. If the supply frequency is changed, the current response will also increase or decrease.

If we extend the example capacitive circuit further with the addition of an inductor, the different components will all cause phase differences between the voltage applied and the resultant current flow. The net result will be either a capacitive or an inductive circuit load or dynamic impedance. Additionally, if the frequency of the supply is varied, the two opposing effects of leading and lagging responses combine to cancel each other out at a certain point in the frequency range, due to the rising and falling response of the different components at varying frequencies. This distinct point is known as the *resonant frequency* and is where the maximum response is obtained. In these circuits, the terms R, L and C refer resistance, inductance and capacitance (respectively). At maximum dynamic impedance, current flow is minimum and the maximum voltage is produced across the load. This type of electronic engineering can be employed to design and configure high pass and low pass filters.

Impedance analysers measure precisely these frequency-dependent impedance characteristics, between two test points in an electrical system. They measure the phase angle, i.e. how much the current lags or leads the voltage curve. Using trigonometry, an inverse tangent function is employed in algorithms (in a similar manner to vector mathematics calculations) to determine the dynamic impedance, referred to in electrical engineering by the symbol X.

Whether the electrical impedance in the circuit or medium being tested is resistive, capacitive or inductive, its measurement and the recording of any changes in response over time have a number of applications. Impedance measurement is used in geology and soil science for electrical resistivity tomography (ERT) or imaging (ERI), as well as construction engineering and spectroscopy in laboratories. Similarly, in the world of medicine, electrical impedance myography (EIM) is a non-invasive procedure used to assess muscular health, atrophy or hypertrophy along with the diagnosis of neuromuscular disease. Here, the test analyses impedance to low currents flowing through cells and fluids, which have a reactive (capacitive) response. The results across a spectrum of frequencies give a good indication of muscle integrity. Other medical uses include cardiography and phlebography (vein analysis and the diagnosis of thrombosis).

Modern impedance analysers can also be used for the rapid, efficient testing of materials such as polymers, plastics, ceramics and glass in addition to semiconductors and electrolytes. On production lines, pass or fail test parameters can be set, including for components and circuits containing piezoelectric devices which operate at a range of frequencies. A specially designed impedance meter may be required for certain test applications.

The speed and accuracy of the response will depend on the type of meter and its cost. Typically, handheld impedance analysers might measure frequencies ranging from 100 Hertz up to 100 Kilohertz, whereas bench top devices are able to sweep through larger frequency curves at various voltage levels with ease. They can also measure the Q (quality) factor, which is the ratio of resistance to reactivity. These more advanced meters also give greater accuracy when testing DC circuits. In summary, modern impedance meters are capable of testing multiple parameters and offer the advantage of replacing several separate instruments that were previously necessary to provide a similar range of test functionality.

In this section you find following videos (just scroll down) regarding RLC.

**Capacitors and Resistance****Intro to Frequency-Dependent Impedance | Capacitors in Alternating Currents****Physics – RCL Circuits With Reactance and Impedance (1 of 2)****Physics – RCL Circuits With Reactance and Impedance (2 of 2) Resonance Frequency**

## 1. Capacitors and Resistance

##### A first look at a capacitor in series with a resistor. Explain the relationship between frequency and the overall impedance – capacitor in series with resistor is frequency dependent.

Videl length: 15 minutes 41 seconds | Resolution: 480p

## 2. Intro to Frequency-Dependent Impedance | Capacitors in Alternating Currents

##### Capacitors, which are cool in their own special way, become even more interesting if you shake them around electrically. Never shake a baby, though.

More phasors in here.

Video length: 9 minutes 43 seconds | Resolution: 720p (HD)

## 3. Physics - RCL Circuits With Reactance and Impedance (1 of 2)

##### Problem: Find the a) Inductor reach; b) Capacitor reach; c) Total reactance; d) Impedance; e) Phase angle; f) Current; g) Power consumed by the resistor; and others of the RCL circuit with reactance and Impedance.

Video length: 14 minutes 10 seconds | Resolution: 1080p (HD)

## 4. Physics - RCL Circuits With Reactance and Impedance (2 of 2) Resonance Frequency

##### Problem: a) Find the resonance frequency (fo); b) What is the impedance @ fo? c) What is the phase angle @ fo? d) Sketch Z vs f; of the RCL circuit with reactance and Impedance.

Video length: 9 minutes 25 seconds | Resolution: 1080p (HD)

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**SinePhase Impedance Analyzer** and **LCR Meter** are designed for measurements up to 16777 kHz.

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