Power Calculations for Pure Sine Waves

Figure 1: For a purely resistive load,
power = voltage * current, with both vectors in phase

Wouldn't it be wonderful if every sine wave we encountered in the real world was pure, with no distortion? It sure would make life easier. Alas, it's pretty much never the case. But in reviewing sinusoidal power calculations, it's best that we begin with the simplest case: a single, pure sinusoidal line voltage and single, pure sinusoidal line current supplying a linear load.

Back to Basics: AC Sinusoidal Line Current

Figure 1: A single-phase AC current
vector rotates at 50 or 60 Hz

We've reviewed the basics of AC line voltage in previous posts. Now we'll turn our attention to the other fundamental component of line power. Regardless of whether you call it "grid," "household," "line," "utility," or "mains," AC sinusoidal current is what flows from the power utility's lines into every home and business.

More Basics of Three-Phase AC Sinusoidal Voltages

Figure 1: In the Wye three-phase
connection, neutral is present but
sometimes inaccessible

Our last post in this series on the essential principles of power covered the basics of three-phase voltages: their composition of three voltage vectors, how they're generated, how they're measured (line-line or line-neutral), and conversion of line-line values to line-neutral values. Here, we'll pick up the thread with more on three-phase AC voltages.

Transmission Lines (Part V): Reverse-Engineering the DUT

Figure 1: Every DUT can be thought of as a Thevenin
voltage source with some internal resistance

There are always two primary elements of any test and/or measurement application: the oscilloscope and the device under test (DUT). Getting valid measurement results depends, first and foremost, on the oscilloscope's capabilities given the task at hand. It also depends on what we'll call "situational awareness," or the operator's understanding of the oscilloscope and of the characteristics of the DUT.

Transmission Lines (Part IV): More Essential Principles

Figure 1: The return current in a transmission line
is as important as the signal current

In our continuing survey of the topic of transmission lines, we'd begun in our last post to cover some essential principles that govern their behavior. We're not quite done with those, so in this post we'll discuss more principles that should be part of the foundation of how you think about interconnects.

Transmission Lines (Part III): Essential Principles

Figure 1: All interconnects are transmission lines with a signal
path and a return path (not ground)

Now that we've covered some of the principles and assumptions that underlie transmission lines in two prior posts, we can now directly address the topic with some essential principles that you need to understand.

Transmission Lines (Part II): More on Bandwidth vs. Rise Time

Figure 1: In the frequency domain (right), a near-ideal
square wave displays predictable 1/f amplitude dropoff

We began this series about transmission lines by thinking about some pertinent principles and relationships that can help form our thinking about the topic. In particular, we'd covered the relationship between bandwidth and rise time and why we have this rule of thumb that says that bandwidth can be estimated using 0.35/10-90% rise time.