2. AC and RF Foundations on The HamStudy Amateur Extra Class HamBook (2024 - 2028)

2.1 Phase and Stored Energy

Mon, 01 Jan 0001 00:00:00 +0000

Section 2.1: Phase and Stored Energy #

Switch off a power supply, and its filter capacitors can hold a dangerous charge until a bleeder resistor drains them. The draining isn’t instant. The stored energy leaves only as current flows through the resistor, and the resistor limits that current. Storing and returning energy takes time in AC circuits too, where it makes voltage and current peak at different times.

Charging Takes Time #

Connect an uncharged capacitor to a DC source through a resistor, and it charges quickly at first. As capacitor voltage rises toward the source voltage, less voltage remains across the resistor. That reduces current, so each further increase takes longer. The voltage curves toward its final value.

2.2 Drawing Complex Impedance

Mon, 01 Jan 0001 00:00:00 +0000

Section 2.2: Drawing Complex Impedance #

Connect an antenna analyzer to a feed line, and it might report $50-j25\ \Omega$ instead of a single number. The extra information lets us distinguish resistance from reactance and tell whether a load is inductive or capacitive. Plotting the reading lets us see those differences and work out their combined effect.

Two Directions, One Impedance #

Resistance and reactance affect phase differently, so we cannot add them along one line to find impedance $Z$ . We draw them in two directions instead, at right angles. A graph that locates each point by how far across and how far up or down it lies uses rectangular coordinates. Here both coordinates are in ohms. A pure resistance has no reactance at all.

2.3 Calculating AC Circuits

Mon, 01 Jan 0001 00:00:00 +0000

Section 2.3: Calculating AC Circuits #

The impedance triangle has given us one number so far: the magnitude. Its angle completes the description, telling how far voltage and current are out of step. One more calculator function finds it, and a little care with signs keeps it pointing the right way once an inductor and a capacitor share a circuit.

An Angle from the Triangle #

In the impedance triangle, the vertical side divided by the horizontal side, $X/R$ , is the tangent of the angle. A calculator’s inverse tangent function works backward: give it that ratio and it finds the angle. Written as a formula for the phase angle $\phi$ (phi),

2.4 Resonance and Q

Mon, 01 Jan 0001 00:00:00 +0000

Section 2.4: Resonance and Q #

Inductive reactance rises with frequency while capacitive reactance falls, so an inductor and a capacitor have one frequency where their reactances are equal. That is their resonant frequency, the one a tuned circuit picks out. In series, the pair draws its greatest current from the source there; in parallel, it draws its least. Either way, the voltages or currents inside the circuit can be much larger than the source’s own.

2.5 Real Components at RF

Mon, 01 Jan 0001 00:00:00 +0000

Section 2.5: Real Components at RF #

You buy an inductor for its inductance, but you get some capacitance and resistance with it at no extra charge. A capacitor brings unwanted inductance too. This chapter’s calculations have treated parts as ideal. At RF, those extras can grow large enough to change the answer, so a correct value on the label does not guarantee the right behavior.

Current Crowds Toward the Surface #

A wire’s DC resistance can underestimate the loss it causes at RF. DC uses the whole cross section evenly, but an alternating current’s own changing magnetic field pushes it toward the conductor’s surface, more strongly as frequency rises. This is skin effect. At 14 MHz, most of the current in a copper wire flows within about 0.02 mm of the surface, a layer thinner than a sheet of paper.