When plotted on a chart, AC voltage takes the shape of a sine wave. In one cycle, the AC voltage starts from 0V, rises to its peak, passes back through 0V to its negative peak, and rises back to 0V. As the AC voltage value varies throughout the cycle, it is expressed in its peak V peak and root-mean-square values V rms.

V peak refers to the maximum amplitude of the sinusoidal waveform, while V rms is derived via the following formula:.

Vrms is also identified as V ac. It represents the equivalent voltage delivered by DC. In the US, the mains delivers V ac while the UK uses V ac. The law specifies how electric currents can be induced in a moving coil as it cuts through magnetic flux at the right angle.

The current change is proportional to the rate of change in magnetic flux. They involve rotating a loop of conductors across a magnetic field. As the loop cuts through the magnetic field, the current starts to flow in one direction and it reaches the maximum when the loop is perpendicular to the magnetic field.

The loop continues to rotate until the conductor is in parallel with the magnetic flux, which results in zero current. The current starts to flow in the opposite direction as the loop starts cutting the magnetic flux but in an opposite direction. Just like the difference in solving a single side vs.

Unlike with DC voltages, the behaviors of these components are no longer simple when used with AC voltages. The measurement for resistors is expressed as impedance Z in AC circuits, instead of resistance R for DC circuits. High-voltage direct-current HVDC electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power.

Transmission with high voltage direct current was not feasible in the early days of electric power transmission , as there was then no economically viable way to step the voltage of DC down for end user applications such as lighting incandescent bulbs.

Three-phase electrical generation is very common. The simplest way is to use three separate coils in the generator stator , physically offset by an angle of ° one-third of a complete ° phase to each other. Three current waveforms are produced that are equal in magnitude and ° out of phase to each other.

If coils are added opposite to these 60° spacing , they generate the same phases with reverse polarity and so can be simply wired together.

In practice, higher "pole orders" are commonly used. For example, a pole machine would have 36 coils 10° spacing. The advantage is that lower rotational speeds can be used to generate the same frequency. For example, a 2-pole machine running at rpm and a pole machine running at rpm produce the same frequency; the lower speed is preferable for larger machines.

If the load on a three-phase system is balanced equally among the phases, no current flows through the neutral point. Even in the worst-case unbalanced linear load, the neutral current will not exceed the highest of the phase currents.

Non-linear loads e. the switch-mode power supplies widely used may require an oversized neutral bus and neutral conductor in the upstream distribution panel to handle harmonics.

Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors. For three-phase at utilization voltages a four-wire system is often used.

When stepping down three-phase, a transformer with a Delta 3-wire primary and a Star 4-wire, center-earthed secondary is often used so there is no need for a neutral on the supply side. For smaller customers just how small varies by country and age of the installation only a single phase and neutral, or two phases and neutral, are taken to the property.

For larger installations all three phases and neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. Three-wire single-phase systems, with a single center-tapped transformer giving two live conductors, is a common distribution scheme for residential and small commercial buildings in North America.

This arrangement is sometimes incorrectly referred to as "two phase". A similar method is used for a different reason on construction sites in the UK. Small power tools and lighting are supposed to be supplied by a local center-tapped transformer with a voltage of 55 V between each power conductor and earth.

This significantly reduces the risk of electric shock in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage of V between the two conductors for running the tools.

A third wire , called the bond or earth wire, is often connected between non-current-carrying metal enclosures and earth ground.

This conductor provides protection from electric shock due to accidental contact of circuit conductors with the metal chassis of portable appliances and tools.

Bonding all non-current-carrying metal parts into one complete system ensures there is always a low electrical impedance path to ground sufficient to carry any fault current for as long as it takes for the system to clear the fault.

This low impedance path allows the maximum amount of fault current, causing the overcurrent protection device breakers, fuses to trip or burn out as quickly as possible, bringing the electrical system to a safe state.

The frequency of the electrical system varies by country and sometimes within a country; most electric power is generated at either 50 or 60 Hertz.

Some countries have a mixture of 50 Hz and 60 Hz supplies, notably electricity power transmission in Japan. A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type traction motors for applications such as railways.

However, low frequency also causes noticeable flicker in arc lamps and incandescent light bulbs. The use of lower frequencies also provided the advantage of lower transmission losses, which are proportional to frequency.

The original Niagara Falls generators were built to produce 25 Hz power, as a compromise between low frequency for traction and heavy induction motors, while still allowing incandescent lighting to operate although with noticeable flicker.

Most of the 25 Hz residential and commercial customers for Niagara Falls power were converted to 60 Hz by the late s, although some [ which?

Off-shore, military, textile industry, marine, aircraft, and spacecraft applications sometimes use Hz, for benefits of reduced weight of apparatus or higher motor speeds. Computer mainframe systems were often powered by Hz or Hz for benefits of ripple reduction while using smaller internal AC to DC conversion units.

A direct current flows uniformly throughout the cross-section of a homogeneous electrically conducting wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface.

This is because an alternating current which is the result of the acceleration of electric charge creates electromagnetic waves a phenomenon known as electromagnetic radiation. Electric conductors are not conducive to electromagnetic waves a perfect electric conductor prohibits all electromagnetic waves within its boundary , so a wire that is made of a non-perfect conductor a conductor with finite, rather than infinite, electrical conductivity pushes the alternating current, along with their associated electromagnetic fields, away from the wire's center.

The phenomenon of alternating current being pushed away from the center of the conductor is called skin effect , and a direct current does not exhibit this effect, since a direct current does not create electromagnetic waves.

At very high frequencies, the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths. Even at relatively low frequencies used for power transmission 50 Hz — 60 Hz , non-uniform distribution of current still occurs in sufficiently thick conductors.

For example, the skin depth of a copper conductor is approximately 8. This tendency of alternating current to flow predominantly in the periphery of conductors reduces the effective cross-section of the conductor.

This increases the effective AC resistance of the conductor, since resistance is inversely proportional to the cross-sectional area. A conductor's AC resistance is higher than its DC resistance, causing a higher energy loss due to ohmic heating also called I 2 R loss.

For low to medium frequencies, conductors can be divided into stranded wires, each insulated from the others, with the relative positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique is called Litz wire. This measure helps to partially mitigate skin effect by forcing more equal current throughout the total cross section of the stranded conductors.

Litz wire is used for making high-Q inductors , reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher radio frequency current up to hundreds of kilohertz , such as switch-mode power supplies and radio frequency transformers.

As written above, an alternating current is made of electric charge under periodic acceleration , which causes radiation of electromagnetic waves.

Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation. At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a twisted pair.

This reduces losses from electromagnetic radiation and inductive coupling. A twisted pair must be used with a balanced signalling system, so that the two wires carry equal but opposite currents.

Each wire in a twisted pair radiates a signal, but it is effectively cancelled by radiation from the other wire, resulting in almost no radiation loss. Coaxial cables are commonly used at audio frequencies and above for convenience.

A coaxial cable has a conductive wire inside a conductive tube, separated by a dielectric layer. The current flowing on the surface of the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube. The electromagnetic field is thus completely contained within the tube, and ideally no energy is lost to radiation or coupling outside the tube.

Coaxial cables have acceptably small losses for frequencies up to about 5 GHz. For microwave frequencies greater than 5 GHz, the losses due mainly to the dielectric separating the inner and outer tubes being a non-ideal insulator become too large, making waveguides a more efficient medium for transmitting energy.

Coaxial cables often use a perforated dielectric layer to separate the inner and outer conductors in order to minimize the power dissipated by the dielectric.

Waveguides are similar to coaxial cables, as both consist of tubes, with the biggest difference being that waveguides have no inner conductor.

Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. Because waveguides do not have an inner conductor to carry a return current, waveguides cannot deliver energy by means of an electric current , but rather by means of a guided electromagnetic field.

Although surface currents do flow on the inner walls of the waveguides, those surface currents do not carry power. Power is carried by the guided electromagnetic fields. The surface currents are set up by the guided electromagnetic fields and have the effect of keeping the fields inside the waveguide and preventing leakage of the fields to the space outside the waveguide.

Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility, electrical resistance of the non-ideal metals forming the walls of the waveguide causes dissipation of power surface currents flowing on lossy conductors dissipate power.

At higher frequencies, the power lost to this dissipation becomes unacceptably large. At frequencies greater than GHz, waveguide dimensions become impractically small, and the ohmic losses in the waveguide walls become large.

Instead, fiber optics , which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used. Alternating currents are accompanied or caused by alternating voltages. An AC voltage v can be described mathematically as a function of time by the following equation:.

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak.

Below an AC waveform with no DC component is assumed. The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage.

For this reason, AC power's waveform becomes Full-wave rectified sine, and its fundamental period is half of the one of the voltage's. To illustrate these concepts, consider a V AC mains supply used in many countries around the world.

It is so called because its root mean square value is V. To determine the peak voltage amplitude , we can rearrange the above equation to:.

During the course of one cycle two cycle as the power the voltage rises from zero to V, the power from zero to RW, and both falls through zero. The SIMPLIS Status window offers a peek into how the POP algorithm works. Shown below is the output from the POP simulation run.

You can view the status window text as a file in a new browser window by clicking 1. log :. After each pass through the POP algorithm, the pass number and the measured convergence is output to the SIMPLIS Status Window.

Each pass is a complete loop through the POP algorithm as described above. The final convergence for this circuit is 2. SIMPLIS routinely solves circuits to this level of accuracy, which as you will see in the next section, allows you to run an AC analysis on the time-domain model.

This topic is an overview of the POP analysis. You will learn the details of the POP algorithm in 2. As described in 1. The AC results are then calculated from the time domain response to the perturbation signal. Then the injected signal is stepped to the next frequency to be analyzed and the measurement process is repeated until the entire requested frequency range is covered.

No averaged model is used. All AC analysis results are derived from the time-domain response of the full nonlinear system. SIMPLIS Tutorial 1. A - Define Waveform Persistence 5. SIMPLIS - Time Domain, All the Time SIMPLIS - Piecewise Linear, All the Time What SIMPLIS POP Does and Why it Matters Accuracy of SIMPLIS PWL Models SIMPLIS Basics Advanced SIMPLIS Training Course Outline Installing the Training Course License Getting Started Module 1 - Overview of the SIMPLIS Environment Navigating the Course Material 1.

A - Symbols May Not Represent What You Think Module 5 - Parameterization 5. A - Passing Parameters into Subcircuits Using the PARAMS Property Appendix 5. B - Single Property Parameterization Appendix 5. C - Tabbed Dialog Spreadsheet Tool Module 6 - Modeling 6. Issues with Hierarchical Blocks and Subcircuits SIMPLIS Data Selection - Overview.

KEEP DVM - Design Verification Module DVM Tutorial 1. What is SIMPLIS? Why Simulate? Home Advanced SIMPLIS Training Module 1 - Overview of the SIMPLIS Environment 1.

In this topic:. Key Concepts This topic addresses the following key concepts: The Periodic Operating Point POP analysis is a specialized transient analysis. The POP analysis literally forces the circuit into a steady-state condition by putting an extra control loop around the converter.

Despite AC voltage being more complex, this article will guide you to a better understanding. AC stands for alternating current and it refers to how electrons are moving in an alternating direction in a conductor.

In electronics, electrons move from a negative potential to a positive potential. An alternating current is produced by switching the potential between two terminals in a fixed time interval—the frequency. The difference in potential between the positive and negative terminal is expressed in volts.

Thus, the term AC voltage is used to determine the value of the potential difference between terminals where alternating current flows. When plotted on a chart, AC voltage takes the shape of a sine wave.

In one cycle, the AC voltage starts from 0V, rises to its peak, passes back through 0V to its negative peak, and rises back to 0V. As the AC voltage value varies throughout the cycle, it is expressed in its peak V peak and root-mean-square values V rms.

V peak refers to the maximum amplitude of the sinusoidal waveform, while V rms is derived via the following formula:. Vrms is also identified as V ac. It represents the equivalent voltage delivered by DC.

In the US, the mains delivers V ac while the UK uses V ac. The law specifies how electric currents can be induced in a moving coil as it cuts through magnetic flux at the right angle. The current change is proportional to the rate of change in magnetic flux.

They involve rotating a loop of conductors across a magnetic field. As the loop cuts through the magnetic field, the current starts to flow in one direction and it reaches the maximum when the loop is perpendicular to the magnetic field. The loop continues to rotate until the conductor is in parallel with the magnetic flux, which results in zero current.

The current starts to flow in the opposite direction as the loop starts cutting the magnetic flux but in an opposite direction. Just like the difference in solving a single side vs.

Unlike with DC voltages, the behaviors of these components are no longer simple when used with AC voltages. The measurement for resistors is expressed as impedance Z in AC circuits, instead of resistance R for DC circuits. There is no difference to the resistive value, regardless of the amplitude or frequency of the AC voltage.

The terminology difference exists because of how the phasor difference is considered when expressing resistance as a function of voltage and current. All input sources are considered to be sinusoidal, their frequency is ignored.

If the Function Generator is set to a square or triangular waveform, it will automatically switch internally to a sinusoidal waveform. AC circuit response is calculated as a function of frequency.

Running AC Analysis Consider the circuit shown in Figure 1. Figure 1. Butterworth low-pass filter. ms11 located in the Downloads section.

Open the Oscilloscope front panel and run the simulation. The circuit will attenuate frequencies greater that Hz. Stop the simulation. Select Simulate»Analyses»AC Analysis. The AC Analysis window opens. Table 1 describes the Frequency Parameters tab in detail.

Table 1. Parameters used in AC Analysis. Parameter Meaning Start frequency FSTART Starting frequency of the frequency sweep. It must be greater than zero. Stop frequency FSTOP Ending frequency of the frequency sweep.

It must be greater or equal to the starting frequency. Sweep Type Indicates how the analysis frequency is swept. There are three options: Decade: Log sweep, by decades. Octave: Log sweep, by octaves.

Linear: Linear sweep. Number of points per decade Number of points in the sweep. Its interpretation depends on the Sweep Type. For Linear, is the total number of points spaced evenly from the start to the stop frequency. Vertical scale Controls the y-axis scaling on the output graph.

Note: In SPICE, the command that performs an AC Analysis has the following form:. Configure the Frequency Parameters as shown in Figure 2.

You can reset all the parameters to their default values by clicking the Reset to default button. Figure 2.

Frequency parameters for the AC Analysis. Select the Output tab. Select the Variables in circuit list, select All variables from the drop-down list, and then highlight V out from the list. Click the Add button to move the variable to the right side under Selected variables for analysis , as shown below : Figure 3.

Output variable for the AC Analysis. Click Simulate. The Grapher View window opens. Results are displayed in Figure 4. Figure 4. AC Analysis results. Select View»Show Cursors. On the left side of the Magnitude plot you will see a set of cursors.

Click one of them, drag it to the right and observe the changes on the cursor information dialog. You can use cursors to take precise measurements. References [1] Electric Circuits, James W. Nilsson, Pearson Prentice Hall, , ISBN Related Links Entering Expressions in Analyses in Multisim SPICE Analysis Fundamentals Download a Day Evaluation of NI Multisim Join the NI Circuit Design Community.

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