|How much power is consumed in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere?|
|A. 70.7 Watts|
|B. 100 Watts|
|C. 141.4 Watts|
|D. 200 Watts|
E5D - AC and RF energy in real circuits: skin effect; electrostatic and electromagnetic fields; reactive power; power factor; electrical length of conductors at UHF and microwave frequencies
In AC circuits–and RF circuits are just a type of AC circuit–capacitors and inductors store and release energy as the voltages and currents change. Because of this, calculating power and energy in an AC circuit is not as straightforward as it is for DC circuits.
Capacitors store electrical energy in an electrostatic field. During the positive portion of an AC cycle, the capacitor stores energy in its electrostatic field, but during the negative portion of the cycle, it returns that energy to the circuit.
Inductors store electrical energy in a magnetic field. The current through the inductor creates the magnetic field. The amount of current determines the strength of a magnetic field around a conductor.
(E5D07) The direction of the magnetic field oriented about a conductor in relation to the direction of electron flow runs in a direction determined by the left-hand rule. (E5D06)
A similar thing happens to the magnetic field created by the current flow through an inductor that happens to the electrostatic field in a capacitor. When the current flows in one direction, a magnetic field is created. When the current changes direction, the energy stored in that magnetic field gets returned to the circuit.
The type of energy that is stored in an electromagnetic or electrostatic field is potential energy (E5D08)
When talking about the power consumed by AC circuits, an important concept is reactive power.
Reactive power is wattless, nonproductive power. (E5D14)
As noted above, during some portions of an AC cycle, inductors and capacitors will draw current and store energy, but during other portions of the cycle, it will return that energy to the circuit. So, what happens to reactive power in an AC circuit that has both ideal inductors and ideal capacitors is that it is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated. (E5D09) In other words, the net power dissipation is zero.
Of course, very few circuits contain only capacitors and inductors. In AC circuits where there is a resistance, that resistance will dissipate real power. For example, in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere, the power consumed is 100 Watts. (E5D13) (P = I2 × R = 1A2 × 100 ohms = 100 W.)
In an AC circuit with inductors and capacitors, the voltage is out of phase with the current. You determine the true power of an AC circuit where the voltage and current are out of phase by multiplying the apparent power times the power factor. (E5D10) For example, if a circuit has a power factor of 0.71 and the apparent power is 500 VA, the watts consumed is 355 W. (E5D18)
The power factor, or PF, is the cosine of the phase angle between the voltage and current. For example, if an R-L circuit has a 60 degree phase angle between the voltage and the current, the power factor is the cosine of 60 degrees, or 0.5 (E5D11) The power factor of an R-L circuit having a 45 degree phase angle between the voltage and the current is the cosine of 45 degrees, or 0.707. (E5D15) The power factor of an RL circuit having a 30 degree phase angle between the voltage and the current is the cosine of 30 degrees, or 0.866. (E5D16)
Let’s look at a few examples:
- If a circuit has a power factor of 0.2, and the input is 100 VAC at 4 amperes, the watts 15 consumed is V × I × PF = 100 V × 4 A × 0.2 = 80 watts. (E5D12)
- If a circuit has a power factor of 0.6 and the input is 200 V AC at 5 amperes, the watts consumed is V × I × PF = 200 VAC × 5 A × 0.6 = 600 watts. (E5D17)
The behavior of conductors at high frequencies
At RF frequencies, the current in a conductor tends to flow near the surface of that conductor. This phenomenon is called the skin effect. The result of skin effect is that as frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface. (E5D01)
At VHF, UHF, and microwave frequencies, the inductance of conductors must be taken into account. The reason for this is that inductive reactance increases with frequency, and at high frequencies, this reactance is no longer negligible. Inductance is a parasitic characteristic that increases
with conductor length. (E5D05) It is, therefore, important to keep lead lengths short for components used in circuits for VHF and above to avoid unwanted inductive reactance. (E5D02)
Another phenomenon that occurs at high frequencies is that printed circuit board traces begin to act like transmission lines instead of just simple conductors. To properly connect components and circuits, printed circuit board designers carefully lay out the traces so that they have a constant impedance.
Microstrips are precision printed circuit leads above a ground plane that provide constant impedance interconnects at microwave frequencies. (E5D03)
At microwave frequencies, it is also import to keep connections as short as possible. Short connections are necessary at microwave frequencies to reduce phase shift along the connection. (E5D04)
Thanks to KB6NU DAN ROMANCHIK