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. 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.
Conductors, such as wires or traces on printed circuit boards have a small inductance and when current passes through the conductor, it creates a magnetic field around the conductor. The higher the current, the stronger the magnetic field. The magnetic field runs in a circle around the conductor.
QUESTION: In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow? (E5D06)
ANSWER: In a circle around the conductor
Reactive power
When talking about the power consumed by AC circuits, an important concept is reactive power. Reactive power is often thought of as nonproductive power because it doesn’t do any work. During some portions of an AC cycle, inductors and capacitors will draw current and store energy, but during other portions of the cycle, they return that energy to the circuit. The energy is repeatedly exchanged between the magnetic field created by current flowing through the inductors and electric fields in the capacitors, but is not dissipated. The net power dissipation is zero.
QUESTION: What is reactive power? (E5D14)
ANSWER: Wattless, nonproductive power
QUESTION: What happens to reactive power in an AC circuit that has both ideal inductors and ideal capacitors? (E5D09)
ANSWER: It is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated
Of course, very few circuits contain only capacitors and inductors. In AC circuits where there is a resistance, that resistance will dissipate real power. Here’s an example:
QUESTION: How many watts are consumed in a circuit consisting of a 100-ohm resistor in series with a 100-ohm inductive reactance drawing 1 ampere? (E5D13)
ANSWER: 100 watts
P = I2 × R = 1A2 × 100 ohms = 100 watts.
This value is called the true power of the circuit because this is the actual amount of power being dissipated by the circuit. But, even though this circuit dissipates 100 watts, it will actually draw more current from a power supply than you would expect because of the inductive reactance. This value is called the apparent power, and is measure in volt-amperes (VA). True power is equal to the apparent power multiplied by a value called the power factor of the circuit.
QUESTION: How can the true power be determined in an AC circuit where the voltage and current are out of phase? (E5D10)
ANSWER: By multiplying the apparent power by the power factor
QUESTION: How many watts are consumed in a circuit having a power factor of 0.71 if the apparent power is 500VA? (E5D07)
ANSWER: 355 W
500 VA x 0.71 = 355 W
The power factor, or PF, is the cosine of the phase angle between the voltage and current. Here are a couple of examples:
QUESTION: What is the power factor of an RL circuit having a 60-degree phase angle between the voltage and the current? (E5D11)
ANSWER: 0.5 (The cosine of 60 degress is 0.5)
QUESTION: What is the power factor of an RL circuit having a 45-degree phase angle between the voltage and the current? (E5D15)
ANSWER: 0.707 (The cosine of 45 degrees is 0.707)
QUESTION: What is the power factor of an RL circuit having a 30-degree phase angle between the voltage and the current? (E5D05)
ANSWER: 0.866 (The cosine of 30 degrees is 0.866)
Now, let’s look at how to calculate the true power dissipated in reactive circuits:
QUESTION: How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100 VAC at 4 amperes? (E5D12)
ANSWER: 80 watts
The apparent power is 100 VAC x 4 A = 400 VA. True power is apparent power x power or factor, or 400 VA x 0.2 = 80 W.
QUESTION: How many watts are consumed in a circuit having a power factor of 0.6 if the input is 200VAC at 5 amperes? (E5D08)
ANSWER: 600 watts
The apparent power is 200 VAC x 5 A = 1000 VA. True power is apparent power x power or factor, or 1000 VA x 0.6 = 600 W.
The behavior of conductors at high frequencies
At RF frequencies, the current in a conductor tends to flow near the surface of that conductor. As the frequency increases, the current flows in an increasingly thinner layer near the surface of the conductor, and the resistance to the RF current increases. This phenomenon is called the skin effect.
QUESTION: What is the result of skin effect? (E5D01)
ANSWER: As frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface
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. Because inductance increases with conductor length, it is, important to keep lead lengths short for components used in circuits at VHF frequencies and above.
QUESTION: Why is it important to keep lead lengths short for components used in circuits for VHF and above? (E5D02)
ANSWER: To avoid unwanted inductive reactance
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 run above a ground plane and have a constant impedance.
QUESTION: What is microstrip? (E5D03)
ANSWER: Precision printed circuit conductors above a ground plane that provide constant impedance interconnects at microwave frequencies
When designing a printed circuit board that will carry signals at microwave frequencies, it is also import to keep connections as short as possible to prevent signal phase shift.
QUESTION: Why are short connections used at microwave frequencies? (E5D04)
ANSWER: To reduce phase shift along the connection
Leave a Reply