10.2 Op Amps, PLLs, VCOs & Mixers

10.2 Op Amps, PLLs, VCOs & Mixers

Quick Answer: Ideal op-amp: infinite open-loop gain, infinite Zin, zero Zout; feedback sets gain. Inverting gain = −Rf/Rin; non-inverting = 1 + Rf/Rg. PLL = phase detector + loop filter + VCO → lock to reference. VCO frequency follows control voltage. Mixer outputs sum and difference frequencies (heterodyning)—the heart of the superhet.

Passive tanks set frequency and selectivity. Active practical circuits amplify cleanly, lock frequency, tune by voltage, and translate spectra from RF to IF. Element 3 Topic 3-D expects you to recognize these blocks by behavior, not to design a custom IC layout.

Operational amplifiers — the ideal model

An operational amplifier (op amp) is a high-gain differential amplifier with inverting (−) and non-inverting (+) inputs and a single-ended output (classic symbol: triangle).

Ideal op-amp rules used on exams and benches

With negative feedback, the op amp adjusts its output so the differential input voltage is forced nearly to zero (the two inputs are at the same voltage). That single idea unlocks virtual ground and the closed-loop gain formulas.

Inverting amplifier

Signal enters through Rin to the inverting input; feedback resistor Rf from output to inverting input; non-inverting input grounded.

[ A_v = \frac{V_{\mathrm{out}}}{V_{\mathrm{in}}} = -\frac{R_f}{R_{\mathrm{in}}} ]

Why virtual ground? Negative feedback holds the inverting input at the same potential as the grounded non-inverting input—about 0 V—while current through Rin continues through Rf (ideally no pin current).

Worked example — inverting gain

Rin = 10 kΩ, Rf = 100 kΩ:

[ A_v = -\frac{100}{10} = -10 ]

A 0.1 V peak input → −1.0 V peak output (within supply rails). Swap to Rf = 47 kΩ → gain ≈ −4.7.

Non-inverting amplifier

Signal drives the non-inverting input. Feedback divider Rg (ground) and Rf (to output) sets the fraction returned to the inverting input.

[ A_v = 1 + \frac{R_f}{R_g} ]

Worked example — non-inverting gain

Rf = 22 kΩ, Rg = 10 kΩ:

[ A_v = 1 + \frac{22}{10} = 3.2 ]

Op-amp roles in radio equipment

Supply note: Real op amps need power rails (split ± or single-supply with bias). Clipping against the rails is the usual limit when calculated gain × input exceeds available swing—exactly what you see as flat-topped audio on a scope.

Voltage-controlled oscillators (VCOs)

A VCO produces an AC output whose frequency depends on a control voltage. Raise the tuning voltage and f_out rises (or falls, depending on design); the control law is often approximately linear over a design range.

FM connection: If the control voltage carries audio, the VCO becomes a direct FM generator. If the control voltage is a filtered PLL error, the VCO becomes the tunable LO inside a synthesizer.

GROL maintainers meet VCOs as “the LO synthesizer brick” on modern VHF marine, aviation COM, and HF gear: wrong lock voltage, open varactor bias, or contaminated control line → off-frequency or unlocked operation.

Phase-locked loops (PLLs)

A phase-locked loop forces a VCO to track a reference in phase (and therefore in frequency, once locked).

Classic three-block PLL

 Reference ──► Phase ──► Loop ──► VCO ──► Output
               detector   filter     │
                  ▲                  │
                  └────── feedback ──┘
                 (often ÷N in synthesizers)

In frequency synthesizers, a programmable divider (÷N) sits in the feedback path so

[ f_{\mathrm{out}} = N \times f_{\mathrm{ref}} ]

(or a fractional-N variant). Channel step size relates to reference and division architecture—the conceptual Element 3 point is lock the VCO to a stable reference via feedback.

Lock range vs capture range

Shop symptoms of unlock: no transmit on frequency, receiver dead on channel, synthesizer unlock LED/alarm, warbling or multiple spurs. Causes include wrong reference (dead TCXO), bad loop filter caps, VCO not covering band, programming error on ÷N, or supply ripple on the control line.

PLL uses in radiotelephone gear

1. Channelized LO synthesis for RX/TX.
2. Carrier recovery or coherent detectors in some data modes.
3. Clock cleaning / reference distribution on digital radio boards.
4. FM demodulation (PLL discriminator topologies)—advanced but same blocks.

Mixers and heterodyning

A mixer is a nonlinear (or switching) circuit with two inputs that produces output components at the sum and difference of the input frequencies—and usually the originals and harmonics depending on topology.

If inputs are f1 and f2:

[ f_{\Sigma} = f_1 + f_2, \quad f_{\Delta} = |f_1 - f_2| ]

Heterodyning is the process of mixing to translate a signal from one frequency to another. The superheterodyne receiver is named for this: RF is mixed with a local oscillator (LO) to create a fixed intermediate frequency (IF) that is easy to filter and amplify.

Superhet conversion (conceptual)

| Low-side LO | f_IF = f_RF − f_LO |

Image frequency: another RF that also mixes to the same IF. Image rejection is why preselectors and high first IFs exist—preview of receiver chapters, but the mixer sum/difference idea starts here.

Mixer types you will see named

Worked example — IF generation

Marine channel RF 156.8 MHz, LO 146.3 MHz (teaching numbers):

[ f_{\Delta} = 156.8 - 146.3 = 10.5,\mathrm{MHz} \quad (\mathrm{IF}) ]

[ f_{\Sigma} = 156.8 + 146.3 = 303.1,\mathrm{MHz} \quad (\mathrm{filtered, away}) ]

Same LO on transmit chains can up-convert a modulated IF to the antenna frequency—mixers are bidirectional spectral tools, not “RX only” parts.

How the four blocks cooperate on one radio

Walk a modern synthesized VHF transceiver:

1. Reference oscillator (TCXO) feeds the PLL.
2. PLL locks a VCO to N × f_ref → channelized LO.
3. Mixer combines LO with incoming RF → IF.
4. Op amps condition audio, AGC voltages, and squelch analog paths after detection.

Exam-day checklist for op amps, PLLs, VCOs, mixers

1. Ideal op-amp: infinite gain, infinite Zin, zero Zout (analysis model).
2. Inverting: −Rf/Rin; non-inverting: 1 + Rf/Rg.
3. Virtual ground on the classic inverter’s summing junction.
4. PLL locks VCO to reference via phase detect + loop filter.
5. Lock holds; capture acquires—capture often narrower.
6. VCO = voltage steers frequency.
7. Mixer → sum and difference; superhet IF = |LO ± RF| chosen product.

With tanks from §10.1 and these active blocks, you can describe how a radio both selects a frequency and generates/translates it. The final section of this chapter teaches you to read the schematic and signal-flow path that wires all of those pieces together.

The direct digital synthesizer block chain (name every block)

Sub-topic 3-D-031 asks which frequency synthesizer circuit uses a phase comparator, look-up table, digital-to-analog converter, and a low-pass antialias filter. The answer is a direct digital synthesizer (DDS) — and the value of the question is that it names the whole chain. Candidates who can say "DDS uses a look-up table and a DAC" still miss it, because they stop before the filter.

The anti-alias filter is not optional cosmetics. A DAC clocked at f_clk produces not only the wanted output but mirror images at f_clk ± f_out, 2f_clk ± f_out and so on. Without the low-pass filter those images leave the synthesizer as real, radiated spurious emissions.

In a direct digital synthesizer, what are the unwanted components on its output? Spurs at discrete frequencies. Note the contrast the pool draws with the PLL: what spectral impurity components might be generated by a phase-locked-loop synthesizer? Broadband noise. Two different synthesizers, two different failure signatures:

That distinction is directly useful on a spectrum analyzer: discrete pickets either side of the carrier point at a DDS; a raised noise pedestal points at a PLL.