Molly Ayala
Impedance is a measure of the opposition that a circuit or a part of a circuit presents to electric current. It is denoted by the letter Z and is calculated using the formula that combines resistance and reactance. In an inductive circuit, the current lags the voltage by 90 degrees, while in a capacitive circuit, the current leads the voltage by 90 degrees. Impedance is crucial in designing and analysing circuits in AC systems, where resistance and reactance affect performance.
| Characteristics | Values |
|---|---|
| Definition | The measure of opposition that a circuit presents to a current when a voltage is applied |
| Formula | Impedance is denoted as Z and is calculated using specific formulas that combine resistance and reactance |
| Resistance | The real part of a complex impedance |
| Reactance | The imaginary part of a complex impedance |
| Impedance in AC and DC circuits | In an AC circuit, impedance is observed, whereas in a DC circuit, impedance and resistance are the same |
| Impedance and output quality | Impedance affects the output quality of the circuit and the device that comprises the circuit |
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What You'll Learn
Impedance in series and parallel circuits
Impedance is defined as the measure of opposition that a circuit presents to a current when a voltage is applied. It involves both resistance and reactance. Unlike resistance, impedance varies with the frequency of the applied voltage and has both magnitude and phase.
In a series circuit, the total impedance is the sum of the individual impedances. For example, if there are four components in a series with impedances Z1, Z2, Z3, and Z4, the total impedance ZT is given by:
ZT = Z1 + Z2 + Z3 + Z4
In a parallel circuit, if a single resistance and a single reactance are connected together, the impedance of each parallel branch must be found. If there are only two components in parallel, R and X, the standard equation for two resistances in parallel can be used:
RT = (R1*R2)/(R1 + R2)
In this equation, Z, R, and X are given in ohms.
The analysis of series-parallel AC circuits is similar to series-parallel DC circuits, with the main difference being that all figures and calculations are in complex form. Before simplifying a series-parallel circuit, the impedance of every resistor, inductor, and capacitor must be determined so that all component values are expressed in common terms (Z) instead of an incompatible mix of resistance (R), inductance (L), and capacitance (C).
Vector diagrams can be used to show how resistance and reactance are combined to form impedance. The ohmic values of the circuit, using Z, R, or X, can be used to find the phase angle between the supply voltage and the circuit current.
Understanding Electric Tables: IMC, EMT, and Their Meanings
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Impedance and resistance
Resistance
Resistance is a measure of voltage divided by current in a resistor. It is the purely electrical effect of resisting current flow. The voltage and current in a resistor always overlap perfectly, meaning they are in phase. Resistance is caused by electrons in a conductor colliding with the ionic lattice of the conductor, which results in the conversion of electrical energy into heat. Resistance can be seen in both AC and DC circuits, and its value does not change with the frequency of the DC current. Resistance does not have a magnitude or phase angle.
Impedance
Impedance is the generalized notion of voltage divided by current for any component. It is the combination of resistance and the contribution of magnetic inductance and capacitance in an AC system. Impedance is the measure of the nature of opposition of AC electricity, which is created due to inductance and capacitance. This opposition varies with the frequency of the applied voltage, and impedance has both magnitude and phase. The traditional variable used for impedance is 'Z'.
In an inductive circuit, the current lags the voltage by 90 degrees, while in a capacitive circuit, the current leads the voltage by 90 degrees. In a purely resistive circuit, the current neither lags nor leads the voltage. When a circuit is powered by direct current (DC), impedance and resistance are the same. In AC circuits, impedance is an important factor and should be associated with a specific frequency or frequency band.
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Impedance in inductive and capacitive circuits
Impedance is a measure of the opposition to the flow of current in a circuit when a voltage is applied. It is denoted by the letter 'Z' and is expressed in ohms. In a direct current (DC) circuit, the opposition to current flow is called resistance. In an alternating current (AC) circuit, impedance is the result of both the circuit's resistive (R) and reactive (X) components.
In an AC circuit, impedance includes the effects of the induction of voltages in conductors by magnetic fields (inductance) and the electrostatic storage of charge induced by voltages between conductors (capacitance). The impedance caused by these two effects is collectively referred to as reactance and forms the imaginary part of complex impedance, whereas resistance forms the real part.
In a purely inductive circuit, the current lags the applied voltage by 90 degrees. Inductors are used to temporarily store electrical energy in the form of a magnetic field. The impedance of an inductor can be calculated using the equation: ZL = ωL, where ZL is the impedance of the inductor, ω is the angular frequency, and L is the inductance.
In a purely capacitive circuit, the current leads the voltage by 90 degrees. Capacitors are used to temporarily store electrical energy in the form of an electric field. The effective impedance of a capacitor is dependent on the frequency and for ideal capacitors, it always decreases with frequency.
Vector diagrams can be used to show how resistance and reactance (inductive and capacitive) are combined to form impedance. The phase angle of reactance, either inductive or capacitive, is always 90 degrees out-of-phase with the resistive component. This means that the circuit's resistive and reactive values cannot be simply added together to give the total impedance value.
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Impedance in AC and DC circuits
Impedance is a measure of a circuit's opposition to the current when a voltage is applied. It is denoted by the letter Z and is calculated by combining resistance and reactance. Impedance varies with the frequency of the applied voltage and has both magnitude and phase.
In a purely inductive circuit, the current lags the voltage by 90 degrees, whereas in a purely capacitive circuit, the current leads the voltage by 90 degrees. In a purely resistive circuit, the current and voltage are in phase. When a circuit is powered by direct current (DC), impedance and resistance are the same.
In an AC circuit, the combined effect of reactance and resistance is called impedance. Many AC circuits, such as heating elements and lamps, consist of pure ohmic resistance with negligible inductance or capacitance. In these circuits, Ohm's Law and Kirchhoff's Law can be used to calculate voltage, current, impedance, and power, just as in DC circuits.
The impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals to the complex representation of the current flowing through it. Impedance can be represented as a complex number, with the same units as resistance, the SI unit being the ohm (Ω). Its magnitude and phase can be represented in polar form as |Z|∠θ, or it can be represented using Cartesian complex numbers.
Vector diagrams can be used to show how resistance and reactance are combined to form impedance. The right-angled triangle representation developed by John Ambrose Fleming in 1889 shows resistance, reactance, and impedance as the lengths of the sides of the triangle. This graphical representation is directly analogous to an Argand diagram, allowing for algebraic approaches to problems in impedance calculation.
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Impedance calculations
Impedance is a measure of the opposition that a circuit presents to a current when a voltage is applied. It is denoted by the letter Z and measured in ohms. Unlike resistance, impedance varies with the frequency of the applied voltage and has both magnitude and phase.
There are several methods to calculate the impedance of a circuit:
- Circuit Simulation: This technique uses software to verify the functionality of a board design before manufacturing. Many PCB design software programs now include impedance calculations, allowing users to modify design parameters and perform simulations to optimize their designs.
- Online Calculators: Online impedance calculators can be used to determine controlled impedance or trace parameters. While they may not be as detailed as simulation tools, they can provide reasonably accurate results with minimal adjustments required for manufacturability.
- Practical Formula-Based Approach: Impedance can also be calculated using mathematical formulas. If the circuit has only resistors, the total impedance is simply the sum of the individual resistors' resistances. If there are only inductors or only capacitors, the total impedance is the same as the total reactance. For circuits with both resistance and reactance, the formula Z = R - j/ωC + jωL can be used, where R is the resistance, C is the capacitive reactance, L is the inductive reactance, and ω = 2πf.
It is important to note that impedance calculations should also consider the appropriate parasitic elements that can influence the actual impedance value. Additionally, understanding the reflection coefficient (Γ) is crucial to analyzing the effects of impedance variations on signal transmission.
Frequently asked questions
Electrical impedance is the measure of opposition that a circuit or circuit component presents to a current when a voltage is applied.
Impedance affects the output quality of a circuit and the device that comprises that circuit. For example, speakers with higher impedance than the amplifier will not produce the maximum volume output.
Impedance is calculated using specific formulas that combine resistance and reactance. Resistance is denoted as R and reactance as X.
Unlike resistance, impedance varies with the frequency of the applied voltage and has both magnitude and phase. Resistance is a measure of the extent to which a substance opposes the movement of electrons among its atoms.
Impedance is expressed as a complex, exponential, imaginary number since it expresses two pieces of information: magnitude and phase in response to a unit current. It is denoted as Z.
