## Brushing up on ac circuit fundamentals

Compared with dc theory, which was discussed in the May issue, the subject of ac theory is more complex. A dc current flows only one direction, hence the name direct current. With ac, or alternating current, electricity flows back and forth, switching polarity on the circuit conductors.

## Why ac?

There are several benefits to ac, but power transmission is a big one. AC allows higher voltages, which enable significantly lower power losses when transmitting electricity long distances. The power loss in a transmission line is proportional to the square of the current, so if the current increases 10 times, the power loss consequently increases 100 times.

We can do the same amount of work with a high voltage and a low current as we can with a low voltage and a high current. The product of the voltage and the current stays the same, so the ability to do work stays the same. AC allows changing the voltage level with transformers, so we can send thousands of volts down the line with relatively low current. At the other end, transformers reduce the voltage back to the levels needed in homes and factories. Transformers can also easily adjust ac voltage for different applications — from 12 V for a battery charger to 480 V for a large motor.

## The nature of ac

Typically, we represent ac with a sine wave by plotting voltage and current against time (Fig. 1). You can see a representation of ac by looking at the signal with an oscilloscope. The amplitude of the voltage controls the vertical movement of the beam, while a specified time reference controls the horizontal sweep. In this representation of ac, the area above the horizontal line is current flow in one direction, or positive voltage. Conversely, the area below the line is current flow in the other direction, or negative voltage. In order for the signal to be ac, there must be a 0 V reference. The voltage must alternate between positive and negative. The current must reverse direction. Lacking that, it is just pulsating dc.

Although the horizontal axis of graphs depicting voltage and current (as well as an oscilloscope trace) really represents time, it is often labeled in degrees. Think of going around a circle. When we get back to where we started, we have moved 360 degrees. An ac voltage starts at 0 degrees of the sine wave, then increases and decreases in amplitude until it gets back to where it started, ready to start again.

By dividing the sine wave path of the ac voltage into 360 degrees like the circle, we can identify various points on the waveform (Fig. 2). By convention, the starting point is usually at 0 V, just before starting to go positive. One complete rotation — from 0 V to a positive peak, dropping back and crossing through 0 V toward a negative peak, and finally rising back to 0 V — represents one complete cycle. The time it takes to traverse one cycle is called the period of the waveform, and is measured in milliseconds (ms), microseconds (

## Voltage considerations

The voltage at any one particular point in time is the instantaneous voltage. The instantaneous voltage at the most positive point is the peak voltage; from the positive peak to the negative peak is the peak-to-peak voltage. With sinusoidal ac voltage, the peak-to-peak value is twice the peak value. These values are important in considering insulation parameters because the insulation must withstand these peak voltages. The 120 Vac in our homes has a peak-to-peak value of about 340 V.

So where does the 120 value come from? It’s the root mean square (RMS) value of an ac sine wave voltage with a peak value of nearly 170 V. RMS is a steady-state representation of the rapidly varying ac voltage. RMS is the square root of the average of the squares of all the instantaneous voltages in the waveform.

The RMS value of a sine wave is also the dc equivalent voltage. A sine wave ac voltage that has a peak value of 170 V can do the same amount of real work as 120 Vdc. For those of you who need numbers, the RMS value is equal to the peak value divided by 1.414, which is approximately the square root of 2. And for those of you who thrive on formulas:

**Peak = RMS x 1.414**

**Average = Peak x 0.637**

**RMS = Peak x 0.707**

These formulas are based on a pure sinusoidal waveform.

Not all ac voltages are sine waves. An ac signal can ride on a dc voltage, which we call offset. And if the dc voltage is higher than the peak value of the ac voltage, the combination will never go negative. We call this voltage pulsating dc. Many times, usually because of a faulty ground, two ac voltages are at different levels, presenting a voltage between their grounds — sometimes at lethal levels.

## Different waveforms

Generators provide electricity in the form of sine waves. However, in electrical and electronic theory and application, not all waveforms are sinusoidal (Fig. 3).

Square waves represent data in a computer. A square wave rises almost immediately to some voltage value, and then returns to zero after a period of time. Just like sine waves, if a square wave alternates between a positive and a negative voltage, it is ac, even though the waveform is not sinusoidal. If it never changes polarity, it is pulsating dc.

Sawtooth waves slowly rise to a peak, and then rapidly fall back. This type of wave drives the beam across the face of a picture tube in a TV or oscilloscope. Distortion, of course, can alter the shape of any waveform, and will change the way the signal behaves.

## AC power

Power in ac circuits is a measure of the ability of the voltage and current to do real work, and is measured in watts, kilowatts or megawatts. In a pure resistive load, the power is simply the product of the voltage and the current, without regard to polarity. Mathematically, multiply the voltage and the current to obtain the power used in a circuit.

The important point is that power to do work comes from the movement of electrons, regardless of which direction they are moving. The RMS value of an ac sine wave is independent of the instantaneous polarity; it is the magnitude of the voltage and current, not the average. The average of a sine wave ac voltage (or current, for that matter) is zero.

The phase angle is the specific degree of the signal from 0 to 360. The phase angle must be referenced to something else, usually the current waveform of that voltage, or another voltage (Fig. 4).

Phase differences in ac circuits can cause the armature of a motor to continually try to catch up with a magnetic field, as with three-phase power commonly used in industrial plants. At the same time, phase angles between the voltage and current in that same motor can cause power to be wasted and excess demands to be put on the distribution equipment, resulting in penalties from the power company.

Voltage across a purely resistive load and the current through that load are always in phase. The peak of the voltage coincides with the peak in the current flow. Inductive loads, such as induction motors and lighting ballasts, cause the voltage and current to be out-of-phase with each other. The current waveform will lag behind the voltage waveform by 90 degrees in a pure inductance, but something between 0 and 90 with real devices.

With this type of load, there are two components to the power used. There is the real power, or true power, which does the work and acts like the power in a resistive load because the current and voltage are in phase. The other component is the reactive power, which provides the magnetic field in a motor that allows the motor to function. The vector sum of these two components is the apparent power, measured in volt-amps, or VA. A vector sum is necessary because the current in reactive power is out of phase with the voltage, and therefore the reactive power is out-of-phase with the true power. Remember that out-of-phase just means that they are not occurring at the same time. The ratio of true power to total or apparent power is power factor. If all the power is true power the ratio is 1:1, and the power factor is unity, or one.

An inductive load stores the energy in a magnetic field during part of the cycle, and releases it during the balance of the cycle. The watt-hour meter on the building electrical service measures the true power that is used by the load. The reactive power, which is alternately drawn from the utility and then returned during the next half cycle, cancels itself out in the meter, does no real work, and is not measured. But, this reactive power does flow in the wires all the way back to the power station. It causes losses in wires and transformers, and mandates larger components in the switchgear. For these reasons, the power company either charges a penalty for low power factor, or gives a discount for power factors near unity.

A capacitor also stores energy during part of the cycle, and releases it during the rest of the cycle. In a capacitor, the voltage lags the current, exactly the opposite of the inductor. If a capacitor is connected across an induction motor, the power used to build up the magnetic field is released back into the capacitor. During the next half cycle the power in the capacitor is released to build up the magnetic field in the motor. Of course, this is still not a perfect circuit; there are always losses. Choosing the capacitor correctly confines most of the reactive power to the motor-capacitor circuit, instead of sending it back through the wires to the power station.

Some plants locate a large capacitor bank at the incoming power service equipment. The goal is to size the capacitor bank to correct the power factor for the entire facility. In this arrangement, equipment dynamically measures the power factor and automatically switches capacitors in and out as the reactive load, and consequently the power factor, varies.

Some plants install individual capacitors with each inductive load and wire them to switch in and out as required. A combination of overall correction for plantwide loads such as lighting ballasts, which are relatively constant, and individual capacitors sized for each induction motor, is also effective. In either case, it is extremely important to size the capacitor banks properly. If they are too small, they will fail to give optimum correction. If they are sized too large, they will decrease the power factor because of capacitive reactance.

Can we can get too much of a good thing? Absolutely! If power factor correction cancels the inductive reactance exactly, oscillations are likely to occur between the motor and the capacitor. These oscillations can feed on each other just like acoustic feedback in an auditorium. This scenario must be avoided because it could cause heavy damage to both components.

Optimally, about 80% of the reactive power should be cancelled by power factor correction. This provides a safety margin and still can increase the power factor to nearly 0.95 in some cases. Regardless of how well power factor correction circuits perform, the wires, contactors and switchgear between the load and the capacitor bank must be oversized to handle all the power — both real and reactive — that could possibly exist in that specific circuit.

## More Info:

Wendell Rice, Instrument and Controls Engineer, Parsons Infrastructure & Technology, Pasadena, CA, has been a controls engineer for more than 25 years. He can be reached at 765-245-535 or wendell.rice@parsons.com . Mr. Rice currently is assigned to a project in Newport, IN that provides support for the U. S. Army’s chemical weapon neutralization program. Article edited by Jack Smith, Senior Editor, 630-288-8783, jsmith@reedbusiness.com .

## Brief history of Hertz

**Heinrich Rudolf Hertz** studied at the University of Berlin under Gustav Kirchhoff and Hermann von Helmholtz, the foremost physicists of the time. In 1888, Hertz described in an electrical journal how he was able to trigger electromagnetic waves with an oscillator. His experiments dealing with the reflection, refraction, polarization, interference and velocity of electric waves would trigger the invention, soon after, of the wireless telegraph, radio, television, and radar.

In recognition of Hertz’ work, his name is now given to the unit of frequency. One cycle per second is equal to one Hertz and is abbreviated Hz. This replaced the use of cycles per second for the unit of frequency in the late 1960s.