Circuits

Competency 4.0 is the circuit itself: how series and parallel R, L and C behave on DC and AC, how to classify an impedance and write it in polar or rectangular form, resonance and Q, filters, oscillators and multivibrators, RC differentiators and integrators, clippers and clampers, and the phase-locked loop. This page follows ETA's list. Section 12 adds the thyristors (SCR, triac and diac), which ETA lists under Competency 3.6 but which are the switches in AC phase-control circuits, and section 13 is job practice. Build the series and parallel circuits in the Circuits Lab, and see impedance and resonance drawn in the Visual Learning Lab.

Series and parallel circuits on DC and AC

Competency 4.1 asks you to identify and describe common DC circuits, and 4.2 common AC circuits. In a series circuit there is one path, so the same current flows through every part and the voltage divides among them. In a parallel circuit every branch sits across the same two points, so each branch has the same voltage and the currents add. Most real circuits mix the two.

On DC, once the circuit has settled for about five time constants (the sheet's τ = R × C and τ = L / R), a capacitor is fully charged and passes no current, and an inductor drops only what its winding resistance drops, because the sheet's V = L(di/dt) is zero once the current stops changing. On AC the source keeps reversing, so capacitors and inductors keep reacting: their reactances, X_L = 2π × f × L and X_C = 1 / (2π × f × C) on the sheet, change with frequency, and they shift the current's phase. Kuphaldt's rule: every DC law still holds on AC, as long as you work in impedances with their phase angles (sections 3 and 4). Power is the exception.

Competency 4.3 and 4.4 ask how series and parallel R, L and C are used in equipment. ETA's sheet gives every combination:

More practice, step by step, is in the Series Circuits and Parallel Circuits lessons in the Study Hub; the Circuits Lab simulates DC series and parallel circuits and analyzes RC, RL and RLC circuits on AC.

Kirchhoff's laws

Competency 4.10 asks you to explain Kirchhoff's laws and why they matter to a technician. Kuphaldt states them as:

• Kirchhoff's Voltage Law (KVL): the algebraic sum of all voltages in a loop must equal zero. Going around a series loop, the drops add up to the applied voltage.
• Kirchhoff's Current Law (KCL): the algebraic sum of all currents entering and leaving a node must equal zero. What flows into a junction flows out.

Why a technician cares. The two laws turn a meter into a fault finder: if the readings around a loop don't add up to the supply, or the branch currents don't add up to the total, something between the points you measured is not what the schematic says. NEETS uses KVL to explain the RC wave-shaping circuits in section 9: at every instant the resistor's and the capacitor's voltages add up to the input.

Resistive, inductive or capacitive?

Competency 4.7 asks you to classify circuits as inductive, capacitive or resistive. In a series circuit with both kinds of reactance, X_L and X_C work against each other, and NEETS subtracts them: X = X_L − X_C, and the result carries the sign of the larger one. ETA's sheet gives the size of the series impedance, and of R and X in parallel:

The phase angle is the shift between the voltage and the current. A perfect resistor's is 0°, a perfect inductor's +90° (its voltage leads its current) and a perfect capacitor's −90° (its voltage lags). The classification depends on frequency: NEETS shows that a series LC circuit looks capacitive below its resonant frequency and inductive above it, and a parallel (tank) circuit the other way round.

Polar and rectangular notation

Competency 4.9 asks you to describe the polar and rectangular presentations of L, R, C circuits. An impedance has a size and a direction, so it is written as a complex number, in either of two forms (Kuphaldt):

• Rectangular form, R + jX: the real part is the resistance and the imaginary part, marked j, is the reactance. Inductive reactance is +j, capacitive reactance is −j. A 100 Ω resistor is 100 + j0 Ω; an inductor with X_L = 50 Ω is 0 + j50 Ω; a capacitor with X_C = 50 Ω is 0 − j50 Ω.
• Polar form, Z at θ: the magnitude and the phase angle (textbooks print an angle sign between the two; this page writes “at”). The same three parts are 100 Ω at 0°, 50 Ω at 90° and 50 Ω at −90°.

Both describe the same right triangle: R is the adjacent side, X the opposite side and Z the hypotenuse. Converting is trigonometry. Only the magnitude formula is on ETA's sheet (section 3); the angle and the back-conversion are not:

Why two forms? Kuphaldt: rectangular form suits addition and subtraction (add the real parts, add the j parts), which is how series impedances combine; polar form suits multiplication and division (multiply the magnitudes and add the angles; divide the magnitudes and subtract the angles), which is how Ohm's law, I = V / Z, works on AC.

The impedance triangle and phasor views in the Visual Learning Lab draw the same triangle as you change R, X_L and X_C.

Resonance, Q and bandwidth

Competency 4.8 asks you to explain resonance and calculate the resonant frequency. At one frequency X_L equals X_C: a series LC circuit then has its minimum impedance, and a parallel (tank) circuit its maximum. ETA's sheet gives two forms; the second uses kilohertz, microhenries and microfarads:

Competency 4.15 asks how bandwidth and Q relate. Q measures how sharp the resonance is. Kuphaldt gives Q = X / R for the coil's reactance and the circuit's resistance, and the bandwidth, measured between the half-power (70.7%) points, is the resonant frequency divided by Q. Neither formula is on ETA's sheet:

So a high Q means a narrow bandwidth and a selective circuit, and series resistance lowers Q (for a parallel tank, heavier loading, that is a lower shunt resistance, does the same): NEETS notes that less resistance gives a narrower bandwidth, which is better selectivity. In a series resonant circuit the voltage across L or C is Q times the applied voltage (Kuphaldt).

The Resonance lesson in the Study Hub has more on series and parallel resonance, and the resonant frequency calculator is in the Calculator Suite.

Filter circuits

Competency 4.13 asks you to describe filter circuits, why and how they are used. Kuphaldt: a filter separates some frequencies from others in a mixed signal, as in audio equalizers and loudspeaker crossover networks. It works because reactance changes with frequency.

The cutoff frequency is where the output has fallen to 70.7% of the input. For a single RC section it is where X_C equals R, which gives a formula that is not on ETA's sheet but comes straight from its X_C formula:

Power supply filters (L, T and pi) are in the Power Supplies guide, and the Filter Calculator works RC, RL and LC sections for you.

Oscillators, crystals and the piezoelectric effect

Competency 4.5 asks you to explain the purpose of oscillators and the use of crystals. NEETS: an oscillator is an amplifier that provides its own input through feedback, and its purpose is to generate a waveform at a constant amplitude and a specific frequency. It needs three things:

1. Amplification, to make up the circuit's losses.
2. Regenerative (positive) feedback, enough to sustain the oscillation.
3. A frequency-determining device: an LC tank, an RC network or a crystal. Without one the stage oscillates at a random frequency.

LC oscillators (NEETS's Armstrong, Hartley and Colpitts) use a tuned tank; RC oscillators use a phase-shifting RC network. A load that changes pulls the frequency and amplitude, so a stable low-power oscillator is often followed by a buffer amplifier that isolates it from the load.

Competency 4.16 asks you to explain the piezoelectric effect. NEETS: it is the property of a crystal by which mechanical forces produce electrical charges and, conversely, electrical charges produce mechanical forces. Quartz shows it less strongly than Rochelle salt, but it is used for frequency control because it is mechanically stronger. A quartz crystal is a thin wafer ground to a thickness that sets its natural resonant frequency: for a given cut, the thinner the crystal, the higher the frequency.

Multivibrators

Competency 4.6 asks you to tell oscillators from multivibrators. The oscillators in section 7 make sine waves, set by a tank, an RC network or a crystal. A multivibrator is a relaxation oscillator: NEETS describes it as two amplifiers with regenerative feedback, one conducting while the other is cut off, switching quickly between saturation and cutoff. Its output is a square or rectangular wave, and in the astable and monostable types an RC time constant, not a resonant circuit, sets its timing (a bistable is not timed: it waits for a trigger). NEETS classifies multivibrators by their number of stable states:

The 555 timer is the usual IC multivibrator. TI's NE555 datasheet gives its timing, which is not on ETA's sheet: a monostable pulse of t_w = 1.1 × R_A × C, and an astable frequency of 1.44 / ((R_A + 2R_B) × C), with the output high for 0.693 × (R_A + R_B) × C and low for 0.693 × R_B × C.

Try other values in the 555 Timer Calculator.

Differentiators and integrators

Competency 4.11 asks for the purposes and types of differentiator and integrator circuits. NEETS calls them shaping circuits: a series RC (or RL) network whose time constant is chosen against the length of the input pulse, so that it changes the shape of square, rectangular or sawtooth waves. They do not change the shape of a pure sine wave. The names come from calculus, although the RC circuits only approximate the operations.

Uses: the differentiator turns edges into the sharp spikes that timing and trigger circuits need, and the integrator turns a square wave into a sloped, ramp-like wave; NEETS notes the RC integrator is used as a wave-shaping network in communications, radar and computers. An op-amp with a capacitor in its feedback loop makes a true integrator, and one with a capacitor at its input a true differentiator; Kuphaldt: a differentiator gives a constant output for a steadily changing input, and an integrator a steadily changing output for a constant input.

Wave shaping: clippers and clampers

Competency 4.14 asks you to explain wave-shaping circuits and their purposes. Besides the RC shapers in section 9, the two diode circuits ETA expects are the clipper and the clamper.

Clippers (limiters) remove the part of a waveform beyond a set level. NEETS: a limiter keeps some part of a waveform from exceeding a specified value, and is used for wave shaping and circuit protection. In a series limiter the diode is in series with the output; in a parallel (shunt) limiter it is across the output, after a series resistor. Kuphaldt's examples: one silicon diode across the output clips one peak at about 0.7 V; two in anti-parallel clip both peaks at about ±0.7 V; a DC source in series with the diode moves the clipping level to that voltage plus the diode drop; and a zener can replace the diode and the source. Uses: keeping voice peaks from overdriving a radio transmitter, squaring up a sine wave, and protecting IC inputs with diodes to the supply rails.

Clampers (DC restorers) keep the waveform's shape but shift its DC level, so one peak sits at a fixed voltage. A series capacitor and a shunt diode do it: the diode charges the capacitor to the peak on one half-cycle, and the capacitor's charge then adds to the signal. The diode's direction decides which peak is clamped; a DC reference in series with the diode moves the clamp level. NEETS also calls it a base-line stabilizer; Kuphaldt's application is restoring the DC level of composite video in television transmitters and receivers.

An overdriven amplifier clips too, as distortion; see the Amplifiers guide.

The phase-locked loop

Competency 4.12 asks you to describe the sections of a PLL and its uses. A phase-locked loop is a negative-feedback loop that holds a voltage-controlled oscillator at an exact multiple of a stable reference. TI's application note on PLL synthesizers describes the integer-N loop, the classic form, in these blocks:

When the loop is locked, the divided VCO frequency equals the reference, so the output is N times F_r, and the channel spacing is F_r. This is TI's equation, not one on ETA's sheet:

The RF & Communications guide shows where the synthesizer sits in a transmitter and a receiver.

Thyristors: SCR, triac and diac

ETA lists the thyristors under Competency 3.6.1 (identify diacs, triacs and SCRs and explain their operation) and 3.6.2 (compare SCRs with other semiconductors). They are taught here because their main job is switching AC power in phase-control circuits. Kuphaldt and Littelfuse: a thyristor is a four-layer PNPN device that behaves like a PNP and an NPN transistor coupled in positive feedback, so once it turns on it latches, staying on with no further drive, and once off it stays off. Bipolar transistors and FETs don't latch: their output follows the input signal moment by moment.

Phase control. On AC, an SCR or triac turns itself off as the current falls through zero at the end of each half-cycle (natural commutation) and must be fired again in the next. Firing it later in each half-cycle chops more of the sine wave away and delivers less power; a lamp dimmer's RC network delays the firing point. Kuphaldt explains why the diac is there: triacs often don't fire at the same gate voltage in each polarity, and the diac's breakover voltage is much more symmetrical, so it makes the triac fire at the same point on both half-cycles and cuts the harmonics. A gate turn-off thyristor (GTO) is an SCR variant built to be turned off by a reverse gate pulse, which takes a fairly high current (Kuphaldt: typically 20% of the anode current).

The Semiconductor Basics guide covers the diodes and transistors these devices are built from.

On the job: measuring circuits that misbehave

Job practice, not exam content. These checks apply the sections above at the bench. The service manual and your employer's procedures come first.

1. Let Kirchhoff find the fault. Measure the drops around a loop and compare them with the supply. In a dead series string the part that reads the full supply voltage is open (section 2). If one part reads near 0 V while the others read higher than the expected values, that part is shorted.
2. Remember the parallel paths. An ohmmeter across a part still in the circuit reads that part in parallel with everything else connected to the same two nodes, so it reads low. Lift one end before trusting a resistance reading; the Test Equipment guide covers in-circuit testing.
3. Don't let the probe pull the oscillator. NEETS: load changes shift an oscillator's frequency and amplitude, which is why a buffer follows it. Measure at the buffer's output where you can, and use a 10× probe rather than a 1× probe on the oscillator itself (see probe loading in the Amplifiers guide).
4. Off-frequency synthesizer? Check the reference. A locked PLL is only as accurate as its reference (section 11), so a radio that is off frequency on every channel points at the reference oscillator, not the VCO. Follow the radio's service manual for the reference adjustment.
5. Test an SCR with a simple DC circuit. Kuphaldt's test: the SCR in series with a load and a DC supply, a normally open pushbutton from the anode to the gate to latch it, and a normally closed pushbutton in series to unlatch it. It should latch when the gate button is pressed and stay on after it is released, and drop out when the series button breaks the current. If it won't stay latched, the load current may be below the SCR's latching current, the minimum that keeps it on right after the gate signal is removed (Littelfuse); Kuphaldt's test simply calls this drawing less than the holding current.