#complex power

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More Than You Ever Wanted to Know About Electrical Engineering, Part 26: Complex Power

We’ve been looking at ways to calculated power supplied and dissipated in steady-state AC circuits. So far, our analysis has focused on resistive circuit elements. We know that resistors consume power, while inductors and capacitors just store it temporarily. What this means practically, is that for a circuit with capacitative and inductive elements, at any single instant, there may be energy in the circuit that we can’t account for just by tracking the power supplied by the source and dissipated by resistance - some energy is being stored in the inductors and/or capacitors. When we’re talking about averages, that stored energy works out to a net zero - it’s constantly being stored and released, so all we really care about is what goes in through the source and out through the resistors. If we want an accurate picture of what’s going on moment-to-moment in a circuit like this, though, we need some way to account for energy that’s in temporary storage.

The way we do this is with something called complex power, usually written as S. It has a lot in common with the idea of impedance. When we started looking at impedance, we said that it consisted of a real component, the resistance, which told you about actual blockages to current flow, and an imaginary component, the reactance, which told you about the average impediment to current flow caused by the cyclical charging and discharging of capacitors and inductors. Similarly, complex power will have a real component (real power, P) which accounts for power dissipated in resistive elements, and an imaginary component (reactive power, Q), which accounts for energy in capacitors and inductors.

Like impedance, this is a complex quantity, so there are a number of ways to write this. RMS values will also come in handy here. Here’s a few other ways to write complex power, real power, and reactive power.

The units on S, P, and Q are all technically the same (energy per unit time). However, to clarify whether we’re talking about complex, real, or reactive power, we normally refer to units of complex power as volt-amps (VA), units of real power as watts (W), and units of reactive power as volt-amps reactive (VAR).

Over the next few articles, we’ll look at the reasons complex power is useful and how we can manipulate it in circuits.

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Fundamental parameters of antennas

Fundamental parameters of antennas

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This is my first set of notes for the UofT course ECE1229, Advanced Antenna Theory, taught by Prof. Eleftheriades, covering ch. 2 [1] content.

Unlike most of the other classes I have taken, I am not attempting to take comprehensive notes for this class. The class is taught on slides that match the textbook so closely, there is…

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