E7: Practical Circuits

Digital circuits work with just two values, usually written 1 and 0, or "high" and "low." Everything here is built from two kinds of parts: logic gates (which make a decision the instant their inputs change) and flip-flops (which remember a value).

Positive logic and truth tables

First, two definitions you will see in the questions. Positive logic simply means that a high voltage represents a 1 and a low voltage represents a 0. (Negative logic flips that around, but the test wants the positive-logic definition.) A truth table is just a list of every possible set of inputs and the output the device produces for each one. It is a cheat-sheet that fully describes how a gate behaves.

The logic gates

A gate looks at its inputs and produces one output by a fixed rule. Memorize these four behaviors exactly as the pool words them:

• OR gate: it produces a 1 at its output if any input is 1. ("Any one of you is enough.")
• NAND gate (short for "NOT AND"): it produces a 0 at its output only if all inputs are 1. It is an AND gate with the answer flipped, so the only way to get a 0 out is to have every input high.
• Exclusive NOR gate (two-input XNOR): it produces a 0 at its output if one and only one of its inputs is 1. In other words it outputs 1 when the inputs match and 0 when they differ.
• (An AND gate, for completeness, outputs 1 only when all inputs are 1; an XOR outputs 1 when exactly one input is 1.)

Memory trick: the little "N" in NAND and NOR means "NOT", it inverts the normal answer. "Exclusive" means "exactly one."

Flip-flops: the circuit that remembers

A flip-flop is a circuit that holds one of two steady states until something tells it to change. Because it has two stable resting states, it is called bistable. ("Bi" means two; "stable" means it sits still there.) So the answer to "which circuit is bistable?" is a flip-flop. An AND gate or an OR gate has no memory, and a bipolar amplifier is not a logic device at all.

Because a flip-flop can be wired to change state once for every two input pulses, a single flip-flop can divide the frequency of a pulse train by 2. ("Pulse train" just means a steady stream of on/off pulses.) Chain them and each one halves the rate again: 2, then 4, then 8, then 16. So to divide a signal frequency by 16 you need 4 flip-flops (because 2 × 2 × 2 × 2 = 16).

Counters

String flip-flops together with a little logic and you get a counter. A decade counter counts in tens: it produces one output pulse for every 10 input pulses. ("Decade" means ten.) These are the building blocks of digital clocks and frequency counters.

Multivibrators

A multivibrator is a circuit that switches between high and low states. There are three flavors, distinguished by how many of their states are stable:

• An astable multivibrator has no stable state, so it continuously alternates between two states without any external clock signal. It is a free-running oscillator, the source of the on/off beat itself. ("A-stable" = not stable.)
• A monostable multivibrator has one stable state, so when triggered it switches temporarily to an alternate state for a set time and then snaps back. It is a one-shot timer. ("Mono" = one stable state.)
• A bistable multivibrator is just another name for a flip-flop (two stable states).

Memory trick: count the stable states. A-stable = zero (it never settles), mono-stable = one (it settles back after a delay), bi-stable = two (a flip-flop that stays put).

An amplifier takes a small signal and makes a bigger copy of it. The active part doing the work (a transistor or a tube) does not have to be "on" for the whole signal cycle, and how much of the cycle it conducts gives the amplifier its class. The class trades off two things: faithfulness (low distortion) versus efficiency (how little power is wasted as heat).

Amplifier classes

• Class A: the active device conducts during the entire cycle (360 degrees). It is the most faithful but the least efficient. Its operating point (its resting, no-signal condition, called the bias point) sits approximately halfway between saturation and cutoff. ("Saturation" is fully on; "cutoff" is fully off; halfway gives the signal maximum room to swing both ways without clipping.)
• Class AB (push-pull): two devices take turns. Each active element conducts for more than 180 degrees but less than 360 degrees. This is the workhorse for clean SSB linear amplifiers.
• Class C: the device conducts for much less than half the cycle. Very efficient, but badly distorting. Using a Class C amplifier on a single-sideband (SSB) phone signal causes signal distortion and excessive bandwidth, because Class C cannot faithfully reproduce a signal whose amplitude varies. (It is fine for constant-amplitude modes like FM or CW.)
• Class D: a switching amplifier. A Class D amplifier uses switching technology to achieve high efficiency. The device is either fully on or fully off, almost never lingering in between.

Why switching amplifiers are so efficient

A transistor wastes the most power when it is partly on, because it then has both voltage across it and current through it at the same time. Switching amplifiers are more efficient than linear amplifiers because the switching device is at saturation (fully on) or cutoff (fully off) most of the time, and in either of those states it dissipates very little heat. The price you pay is harmonics: chopping a signal hard creates many extra frequencies. So an RF switching amplifier requires a filter at its output to remove the harmonic content before the signal reaches the antenna.

Amplifier configurations

There are three basic ways to wire a transistor, named for whichever terminal is the common reference:

• Common emitter (the one in Figure E7-1, described below): high gain, output inverted relative to input.
• Emitter follower, also called common collector: its hallmark is that the input and output signals are in-phase (it does not invert), and it has high input impedance with low output impedance, making it a good buffer.
• Grounded-grid (the tube version of common-base): its characteristic is low input impedance.

Taming a power amplifier

A high-power RF amplifier can break into unwanted self-oscillation, generating spurious signals. To prevent unwanted oscillations in an RF power amplifier you install parasitic suppressors and/or neutralize the stage. ("Parasitic" oscillations are accidental ones the circuit was never meant to make; a "parasitic suppressor" is a small part that damps them; "neutralizing" feeds back a small canceling signal to keep the stage stable.)

Reading Figure E7-1 (a common-emitter amplifier)

Figure E7-1 shows a single transistor wired as a common emitter amplifier. You can answer all three of its questions from the parts:

• R1 and R2 form a voltage divider bias. Two resistors in series across the supply set a steady voltage on the transistor's base, fixing where the amplifier idles.
• R3 (the resistor in the emitter leg) provides self bias. It stabilizes the operating point automatically: if current tries to rise, R3 raises the emitter voltage and gently reins it back in.
• The whole circuit is a common emitter amplifier.

A filter passes the frequencies you want and blocks the ones you do not. The four basic responses are low-pass (passes low frequencies, blocks high), high-pass (the reverse), band-pass (passes one band, blocks above and below), and notch (also called band-reject, blocks one narrow band). Filters are built from capacitors and inductors arranged in patterns named after the letters they resemble.

Pi, T, and Pi-L networks

• A low-pass Pi-network is shaped like the Greek letter π (pi): a capacitor from the input to ground, another capacitor from the output to ground, and an inductor connecting the input to the output. The two grounded capacitors are the two legs of the pi and the inductor is the bar across the top.
• A T-network with series capacitors and a shunt inductor ("shunt" means connected to ground) gives a high-pass response.
• A Pi-L network is a Pi-network with an additional output series inductor. The reason you add that inductor is greater harmonic suppression, the extra L knocks down high-frequency junk more effectively, which is why Pi-L networks are popular in transmitter output stages.

Impedance matching

An impedance-matching circuit makes a load look like the resistance a transmitter wants to see, so power transfers efficiently. A real-world load is a complex impedance, meaning it has both resistance and reactance (the frequency-dependent opposition of capacitors and inductors). A matching network cancels the reactive part of the impedance and changes the resistive part to the desired value. Think of it as two jobs: zero out the reactance, then scale the resistance.

Named filter families

Engineers tune the capacitor and inductor values to get different trade-offs, and the recipes carry names:

• A Chebyshev filter has ripple in the passband and a sharp cutoff. It accepts a little bumpiness in the pass region in exchange for a steeper edge.
• An elliptical filter has an extremely sharp cutoff with one or more notches in the stop band. Those deliberate notches are what make its edge the steepest of all.

Specialty filters used in radios

• A crystal lattice filter is a filter for low-level signals made using quartz crystals. Quartz crystals act like extremely sharp, stable resonators, perfect for shaping a narrow SSB or CW passband at the IF (intermediate frequency).
• A helical filter (a coil-shaped resonator) is most frequently used as a band-pass or notch filter in VHF and UHF transceivers.
• A cavity filter (a tuned metal chamber) is the filter used in a 2-meter band repeater duplexer. (A "duplexer" lets a repeater transmit and receive on one antenna at the same time; cavity filters keep the strong transmitter out of the sensitive receiver.)

Measuring a filter

The shape factor measures a filter's ability to reject signals in adjacent channels. The closer the shape factor is to 1, the more "brick-wall" the filter, steep skirts that pass your channel but cut off the neighbors.

A power supply turns the AC from your wall into the clean, steady DC a radio needs. The most important part is the voltage regulator, the circuit that holds the output voltage constant even as the load changes. There are two big families: linear and switching.

Linear regulators

A linear electronic voltage regulator works by varying the conduction of a control element to maintain a constant output voltage. Picture a smart valve in a water pipe that opens and closes just enough to keep the pressure downstream rock-steady. There are two arrangements:

• A series regulator puts the control element in line with the load. A common three-terminal voltage regulator (input, output, ground) is a series regulator.
• A shunt regulator sits across (in parallel with) the output and works by loading the unregulated voltage source, drawing off just enough extra current to keep the voltage in check.

Two numbers describe a linear regulator's limits:

• The dropout voltage is the minimum input-to-output voltage required to maintain regulation. Drop below it and the regulator can no longer hold the output steady.
• The power dissipated by a series linear regulator is the voltage difference from input to output multiplied by the output current. That wasted voltage times the current all turns into heat, which is why linear supplies run hot and need heatsinks.

The voltage reference

A regulator needs a fixed, known voltage to compare against. The classic stable reference is a Zener diode, a special diode that holds a nearly constant voltage across itself once it conducts in reverse. So the device used as a stable voltage reference is a Zener diode.

Switching (switchmode) regulators

A switchmode voltage regulator works by varying the duty cycle of pulses input to a filter. ("Duty cycle" is the fraction of time the switch is on.) Instead of burning off the excess as heat, it rapidly chops the input on and off and lets a filter average the pulses into smooth DC. Adjust how long it stays on each cycle and you adjust the output voltage.

Why is a switching power supply less expensive and lighter than an equal linear one? Because its high-frequency inverter design uses much smaller transformers and filter components for an equivalent power output. The trick is frequency: a transformer that handles power at tens of thousands of cycles per second can be a fraction of the size and weight of one running at the 60-cycle line frequency.

Reading Figure E7-2 (a linear regulator)

Figure E7-2 shows a linear voltage regulator. Two parts are asked about:

• Q1 is the pass transistor: it controls the current to keep the output voltage constant. It is the adjustable "valve."
• C2 bypasses rectifier output ripple around D1. (D1 is the Zener reference diode; C2 routes the AC ripple to ground so it does not disturb the reference.)

Batteries, solar, and high-voltage supplies

• Battery operating time is calculated as capacity in amp-hours divided by the average current. A 10 amp-hour battery feeding a 2 amp load lasts about 5 hours.
• An inverter connected to a solar panel exists to convert the panel's output from DC to AC (so you can run normal household AC gear from the panel's DC).
• When filter capacitors are connected in series for high voltage, you place equal-value resistors across each one. The answer to "why" is all these choices are correct, because those bleeder resistors equalize the voltage across each capacitor, help discharge them safely after power-off, and improve voltage sharing.
• A step-start circuit in a high-voltage supply exists to allow the filter capacitors to charge gradually, avoiding a damaging inrush surge at switch-on.

Modulation is the act of stamping your message (your voice, your data) onto a radio carrier so it can travel. Demodulation (or detection) is recovering the message at the far end. This group covers the circuits that do both, plus the mixer, which shifts signals from one frequency to another.

Baseband

Start with one definition. Baseband is the frequency range occupied by a message signal prior to modulation. Your raw voice (a few thousand cycles per second) is baseband; modulation lifts it up to a radio frequency for transmission.

Making FM

FM (frequency modulation) carries the message by nudging the carrier's frequency up and down. One way to do this is reactance modulation of a local oscillator. The circuit that does it is a reactance modulator, which produces PM or FM signals by varying a capacitance. ("Reactance" is the opposition of a capacitor or inductor; vary the capacitance in step with the audio and the oscillator's frequency wobbles in step too.)

FM systems shape the audio for cleaner results:

• A pre-emphasis network is added to an FM speech channel to boost the higher audio frequencies before transmission, which improves the signal-to-noise of the trebly parts.
• De-emphasis is used in the receiver to undo that boost; the reason given is for compatibility with transmitters using phase modulation.

Making SSB

To produce a single-sideband phone signal the classic method is to use a balanced modulator followed by a filter. A "balanced modulator" produces both sidebands while canceling the carrier (a double-sideband suppressed-carrier signal), and then a sharp filter removes one of the two sidebands, leaving the single sideband.

The mixer

A mixer combines two frequencies to produce new ones, the heart of every superheterodyne radio. The principal frequencies at a mixer's output are the two input frequencies along with their sum and difference frequencies. (Feed in 14 MHz and 5 MHz and you get 14, 5, 19, and 9 MHz, and you keep whichever one you want.) But if you overdrive it, trouble follows: when the input signal levels to a mixer are too high, spurious mixer products are generated, unwanted extra signals at frequencies you did not intend.

Demodulators (detectors)

• A frequency discriminator is a circuit for detecting FM signals. It converts frequency wobble back into audio.
• A diode envelope detector functions by rectification and filtering of RF signals. It is the simple detector used for AM: chop off half the waveform with a diode, then smooth it to recover the audio outline ("envelope").
• A product detector is used for demodulating SSB signals. It mixes the incoming SSB with a locally generated carrier to reconstruct the original audio.

Modern radios increasingly do their work in software. DSP stands for digital signal processing: turn a signal into numbers, then filter, mix, and demodulate it with arithmetic. A software defined radio (SDR) pushes this idea as far as it can go.

Direct sampling

Direct sampling means incoming RF is digitized by an analog-to-digital converter without being mixed with a local oscillator signal first. Instead of the traditional approach of shifting the signal down to a lower frequency before measuring it, a direct-sampling SDR measures the radio frequency itself, thousands or millions of times a second, and does everything else in math.

Sampling rules

• How often must you sample? At least twice the rate of the highest frequency component of the signal. This is the famous Nyquist rule: sample too slowly and you cannot faithfully reproduce the wave.
• The sample rate is what determines the maximum receive bandwidth of a direct-sampling SDR. Faster sampling means you can take in a wider chunk of spectrum at once.
• Resolution comes from bits. To sample a 1-volt range at 1-millivolt resolution you need 10 bits (because 2 raised to the 10th power is 1024, just over the 1000 steps needed to slice 1 volt into 1-millivolt pieces).
• The minimum detectable signal level of a direct-sampling SDR (ignoring outside noise) is set by the reference voltage level and the sample width in bits. More bits over a smaller reference voltage lets you resolve fainter signals.

Aliasing, decimation, and the FFT

• Decimation is reducing the effective sample rate by removing samples. Once you have isolated a narrow signal, you no longer need the huge original sample rate, so you throw samples away to lighten the processing load.
• But you must filter first. An anti-aliasing filter is required in a decimator because it removes high-frequency signal components that would otherwise be reproduced as lower frequency components. ("Aliasing" is when a too-fast signal masquerades as a fake slow one after sampling, the same illusion that makes wagon wheels seem to spin backward in old films.)
• A Fast Fourier Transform (FFT) performs the job of converting signals from the time domain to the frequency domain. In plain terms it takes a stream of samples over time and tells you which frequencies are present, exactly what a waterfall display shows.

Digital filters: taps and FIR

• To remove unwanted noise from a received SSB signal, DSP uses an adaptive filter that adjusts itself to the changing noise.
• To generate an SSB signal with DSP, you use a Hilbert-transform filter, and the method combines signals in a quadrature (90-degree) phase relationship to cancel the unwanted sideband.
• A Finite Impulse Response (FIR) filter has a useful property: it can delay all frequency components of the signal by the same amount. (That even delay is called "linear phase" and keeps a complex signal from getting smeared.)
• Taps in a DSP filter provide incremental signal delays for filter algorithms. They are the staged copies of the signal the filter math works on, and using more taps lets a DSP filter create a sharper filter response.

An operational amplifier, or op-amp, is a tiny, extremely high-gain amplifier on a chip. By itself its gain is so large it is unusable raw; you tame it with feedback (a resistor from output back to input) to get a precise, predictable amplifier or filter. The questions here are part definition, part easy arithmetic.

What an op-amp is

An operational amplifier is a high-gain, direct-coupled differential amplifier with very high input impedance and very low output impedance. Break that down: "differential" means it amplifies the difference between its two inputs; "direct-coupled" means it works all the way down to DC. The two impedance facts are tested on their own:

• An op-amp's input impedance is very high (it barely loads down whatever feeds it).
• An op-amp's output impedance is very low (it can drive a load without sagging).

Ideal behavior and real-world limits

• How does the gain of an ideal op-amp vary with frequency? It does not vary with frequency, the ideal has flat, infinite gain everywhere.
• A real op-amp does roll off, described by the gain-bandwidth product, defined as the frequency at which the open-loop gain of the amplifier equals one. ("Open-loop" means with no feedback; "gain of one" means the signal is no longer being amplified at all.)
• Input offset voltage is the differential input voltage needed to bring the open-loop output voltage to zero. It is a small real-world imperfection that you sometimes have to trim out.
• To prevent unwanted ringing and audio instability in an op-amp audio filter, you restrict both gain and Q. ("Q" is sharpness; too much gain or Q makes the filter overshoot and oscillate.)

Figure E7-3: the inverting amplifier

Figure E7-3 shows an op-amp wired as an inverting amplifier. Two resistors set its behavior: R1 is the input resistor and RF is the feedback resistor. There is one easy formula to learn:

voltage gain = RF ÷ R1

The word "inverting" means the output is the negative of the input (flipped in sign). Now the calculations:

• If RF is 470 ohms and R1 is 10 ohms, the gain is 470 ÷ 10 = 47.
• If RF is 68 kilohms (68,000 ohms) and R1 is 1,800 ohms, the absolute gain is 68,000 ÷ 1,800 = about 38.
• If RF is 47 kilohms and R1 is 3,300 ohms, the absolute gain is 47,000 ÷ 3,300 = about 14.
• For an output voltage: with R1 = 1,000 ohms, RF = 10,000 ohms, the gain magnitude is 10. Apply 0.23 volts at the input and the output is 0.23 × 10 = 2.3 volts, but because the amplifier inverts, the answer is negative 2.3 volts.

Adding a capacitor: if you put a capacitor across the feedback resistor RF in Figure E7-3, the circuit becomes a low-pass filter. (At high frequencies the capacitor shorts out part of the feedback, reducing gain for the highs, so only the lows pass at full gain.)

An oscillator turns steady DC into a continuous wave, the source of the carrier and the clock in every radio. It works by positive feedback: a little of the output is fed back to the input in the right phase to keep the wave going, like pushing a swing in time with its motion. This group also covers the modern way to make precise frequencies: the phase-locked loop and the direct digital synthesizer.

The classic oscillators

Three common oscillator circuits are the Colpitts, Hartley, and Pierce. They differ in how they feed the signal back:

• A Colpitts oscillator supplies its positive feedback through a capacitive divider (two capacitors splitting the signal).
• A Pierce oscillator supplies its positive feedback through a quartz crystal, which makes it very stable.
• (A Hartley uses a tapped inductor for feedback.)

Keeping an oscillator steady

Two enemies of a stable frequency are vibration and temperature:

• A microphonic is a change in oscillator frequency caused by mechanical vibration, literally, the circuit picking up bumps and sounds. You reduce it by mechanically isolating the oscillator circuitry from its enclosure (soft mounts and shielding so shocks do not reach it).
• Thermal drift in crystal oscillators (frequency wandering as the temperature changes) can be reduced with NP0 capacitors, a type whose value barely changes with temperature.
• To ensure a crystal runs on its marked frequency, you must provide the crystal with a specified parallel capacitance, the exact load capacitance the manufacturer assumed when they cut it.

The phase-locked loop (PLL)

A phase-locked loop is an electronic servo loop consisting of a phase detector, a low-pass filter, a voltage-controlled oscillator, and a stable reference oscillator. ("Servo loop" means a self-correcting feedback system.) The phase detector compares the controllable oscillator against the rock-steady reference and constantly nudges it to stay locked. A PLL can perform frequency synthesis and FM demodulation. ("Frequency synthesis" means generating many precise frequencies from one reference; the same loop also recovers audio from an FM signal.)

The direct digital synthesizer (DDS)

A direct digital synthesizer builds a waveform out of numbers. It is the synthesizer that uses a phase accumulator, a lookup table, a digital-to-analog converter, and a low-pass anti-alias filter. The lookup table holds amplitude values that represent the desired waveform, basically a stored picture of one cycle of the wave, which the circuit reads out at the right pace to set the frequency. Its main downside: the major spectral impurity components of a DDS are spurious signals at discrete frequencies (specific little unwanted spikes, "spurs," rather than broad noise).

Oscillators for microwave

What technique provides the highly accurate, stable oscillators needed for microwave work? The answer is all these choices are correct, because several methods are used together (such as locking to a GPS-derived reference, using oven-controlled or temperature-compensated crystals, and using rubidium or other atomic references). At microwave frequencies, even tiny errors get multiplied, so stability is everything.