PLL and DDS Synthesizers: How Your Radio Makes Its Frequency

Turn the knob of an old receiver and you move a capacitor plate, changing the frequency of an LC oscillator that drifts as it warms up. Turn the knob of a modern transceiver and you change a number, and a circuit called a PLL synthesizer or a DDS produces exactly that frequency from a single stable crystal. This change is one of the main reasons why a radio today holds its frequency to a few parts per million, tunes in steps of 1 Hz and remembers hundreds of channels. This guide explains how the two main synthesis methods, the phase-locked loop and direct digital synthesis, work in plain terms, what step size, phase noise and spurs mean and why they matter to the amateur who uses the radio.

From the Variable Oscillator to the Synthesizer

The old variable-frequency oscillator, or VFO, was an LC circuit whose frequency depended on the inductance and capacitance. Temperature, supply voltage and vibration all moved it, so operators retuned during a QSO. A synthesizer replaces the free-running oscillator by a system that is locked to a reference. The reference is a crystal oscillator, often a temperature-compensated type with a stability of a few parts per million, and all the frequencies the radio produces are derived from it. The oscillator is no longer the master; the crystal is. That is why a synthesized radio does not drift, and also why its accuracy can be improved at once by using a better reference, as discussed in our article on calibrating a transceiver frequency.

How a PLL Synthesizer Works

A phase-locked loop is a feedback circuit with four main blocks. A voltage-controlled oscillator, or VCO, produces the output frequency. A divider divides that frequency by a number N. A phase detector compares the divided signal with a reference signal, and the difference in phase becomes a voltage. A loop filter smooths this voltage and feeds it to the VCO, correcting its frequency until the two signals agree in phase and frequency. At that point the loop is locked, and the output frequency is exactly N times the reference.

The result is a simple formula: f(out) = N × f(ref). If the reference is 10 kHz and N is 1420, the output is 14.2 MHz. Changing the divider changes the frequency, in steps equal to the reference frequency. This is the step size of the synthesizer. To obtain smaller steps, the reference is divided down first, so that the reference to the phase detector is lower, for example 1 kHz or 100 Hz, but a lower comparison frequency means a slower loop and more noise from the dividers. Designers therefore use tricks such as fractional-N division, in which the divider alternates between two values to create an average number with a fraction, and multiple loops, in which one loop makes coarse steps and another makes fine steps.

How DDS Works

A direct digital synthesizer follows a quite different idea. It builds the waveform from numbers. A phase accumulator, which is a counter, adds a tuning word to its value on every tick of a fixed clock. The value of the accumulator represents the phase of a sine wave and is converted by a lookup table into a sample of the wave. A digital-to-analogue converter turns the samples into an analogue signal, and a filter removes the steps. The output frequency is

f(out) = M × f(clock) / 2ⁿ

where M is the tuning word and n the number of bits of the accumulator. With a clock of 100 MHz and a 32-bit accumulator, the smallest step is 100 MHz divided by about 4.29 billion, which is 0.023 Hz. This is why a DDS can tune in tiny steps and can change frequency almost instantly. The output frequency cannot be higher than about 40 percent of the clock, because the filter needs room above the wanted signal, so a DDS with a 100 MHz clock covers up to roughly 40 MHz.

PLL and DDS Compared

The two methods have complementary strengths. A DDS gives very fine resolution and fast tuning, and it can switch phase and frequency without a glitch, which is useful for digital modes and for frequency-hopping. Its weakness is spurious signals, because the digital steps and the converter create unwanted lines in the spectrum at known offsets from the wanted frequency. A PLL has a cleaner output at close offsets from a good oscillator, but its step size is limited by the reference, and the settling time depends on the loop bandwidth. The table shows the typical features.

Most modern radios combine the two. A common arrangement uses a DDS to generate a clean, finely tunable low frequency, which is then used as the reference for a PLL, or mixed with the output of a PLL. The DDS provides the small steps, the PLL brings the frequency up to the range needed, and filters take away the spurs. This hybrid design uses the advantages of both and covers the weaknesses of each.

Phase Noise: What You Hear

No oscillator is perfectly pure. Its signal has a small random variation of phase, which appears as a skirt of noise on both sides of the carrier. In a synthesizer the phase noise comes from the reference, the VCO, the phase detector and the dividers, and the loop shapes it: inside the loop bandwidth the noise is dominated by the reference and the dividers, outside it by the VCO. If you multiply the frequency of the reference by N, the noise rises by 20 log N decibels, which is why a high division ratio needs a very clean reference.

Why should the operator care? On receive, the noise of the local oscillator mixes with strong nearby signals and creates a noise floor that hides weak signals, an effect known as reciprocal mixing. On transmit, the same noise is added to your signal and appears as a broad pedestal that disturbs your neighbours in a crowded contest band. Specialist reviews of transceivers therefore measure phase noise at offsets such as 2 kHz and 20 kHz. The effect on receiving is explained in our guide to receiver dynamic range, blocking and IMD.

Spurs, Birdies and Clean Signals

A spur is a narrow unwanted line in the output spectrum. In a DDS the spurs have their origin in the truncation of the phase word and in the limited resolution of the converter, and they appear at offsets that depend on the tuning word. In a fractional-N PLL, spurs appear at multiples of the fraction step. A spur on the transmit side may be filtered by the following stages, but a spur that falls inside the receiver passband produces a birdie, a tone that is heard at certain frequencies and does not depend on the antenna. If you hear a steady tone that stays at the same dial position when you disconnect the antenna, it is probably a spur of the synthesizer or a harmonic of a clock inside the radio.

The designers use several methods to make spurs smaller: more bits in the converter, dithering to randomise the error, careful choice of clock frequencies and filtering at the output. The result is judged by the spurious-free dynamic range, the difference in decibels between the wanted signal and the highest spur. A good DDS reaches 60 to 70 dB or better in the area of use. This is an important number for those who build digital VFOs for a homebrew receiver.

Building With Modern Parts

Amateurs have long used synthesizers in home-built equipment, and the parts are cheap. The AD9850 and AD9833 DDS modules are known from Arduino projects, while programmable clock generators such as the Si5351, which contain several PLLs, produce three clock outputs from a crystal and are widely used in QRP transceivers and in software defined radios. A small microcontroller, a crystal and such a chip give you a digital VFO with memories and a display for the price of a few components. If you want to start with a kit, our guide to a first QRP kit build lists the tools needed, and the overview of Arduino projects for hams shows other uses of the same hardware.

When you build, pay attention to the reference. A cheap crystal gives an output that drifts with temperature, which defeats the purpose. A TCXO, and for exacting work a reference locked to GPS, makes the result accurate to a fraction of a part per million. Keep the supply clean with a regulator and decoupling capacitors, and shield the synthesizer, because the clock signals contain harmonics that radiate into the receiver. And keep the leads of the output filter short.

Choosing a Radio With the Synthesizer in Mind

The manufacturer rarely says which method the radio uses, but the behaviour tells you. Very small tuning steps and rapid retuning point to a DDS in the chain. If the data sheet gives reciprocal-mixing dynamic range at 2 kHz and 20 kHz offsets, it is the parameter to watch if you work in contests or in crowded bands. A stable frequency after switching on is a sign of a good reference. And a radio with an input for an external 10 MHz reference lets you lock it to a standard, which is worth having for weak-signal and microwave work.

Synthesizers in Software Defined Radios

In a software defined radio the same ideas appear in a new form. A direct-sampling receiver uses a fixed sampling clock, and the tuning is done by mathematics inside the processor, with a numerically controlled oscillator which is a DDS in software. The quality of the sampling clock then decides the performance, because its jitter becomes noise on all signals. Receivers that mix the signal down first use a PLL-based local oscillator, like a traditional superheterodyne radio. Our comparison of direct sampling SDR and superheterodyne receivers shows how the choice of architecture shifts the burden from analogue to digital circuits.

For the operator, the practical consequence is the same everywhere: a clean, stable clock is the foundation. If you use an external reference with an SDR or a transverter, make sure that the reference is clean and at the right level, and that you do not add noise through ground loops or long unshielded cables. A poor reference can make a receiver with excellent specifications sound worse than a simple one.

How to Check Your Own Radio

You can test a synthesizer without special instruments. For frequency accuracy, listen to a time signal station and compare the dial with the known carrier frequency, as in the calibration method mentioned above. For spurs and birdies, disconnect the antenna, terminate the input with a dummy load and tune slowly across the bands, noting every steady tone; the tones that remain are generated inside the radio. For phase noise, tune to a very strong local signal and listen to the noise at a few kilohertz either side of it; a clean synthesizer shows little increase in noise, while a poor one gives a noticeable hiss that follows the strong signal. These simple observations give a good impression of the quality of your radio.

The Bottom Line

Modern radios generate their frequencies from a stable crystal with a PLL synthesizer, a DDS or a combination of both. A PLL multiplies a reference by a divider ratio and locks a VCO to it, while a DDS builds a sine wave from numbers, giving tiny steps and fast tuning at the cost of spurs. The things that matter to the user are the stability of the reference, the phase noise, which shapes the quality of both receive and transmit, and the level of spurs. Understand these, and you will read a radio review and a data sheet with a more informed eye, and you will know what to improve in a home-built VFO.

Frequently Asked Questions

What is a PLL synthesizer?

It is a feedback circuit that locks a voltage-controlled oscillator to a stable reference through a divider and a phase detector, so that the output frequency is a set multiple of the reference.

How does a DDS differ from a PLL?

A DDS builds a sine wave from numbers with a phase accumulator and a converter, giving very fine steps and fast tuning. A PLL multiplies a reference and generally has lower spurs but coarser steps.

What limits the output frequency of a DDS?

The clock. The usable output is about 40 percent of the clock frequency at most, so a 100 MHz clock covers up to roughly 40 MHz.

Why does phase noise matter to me?

On receive it creates a noise floor next to strong signals, and on transmit it adds a pedestal of noise around your signal that disturbs neighbouring frequencies.

What is a birdie?

A steady tone heard at certain dial settings that does not depend on the antenna. It often comes from a spur of the synthesizer or a harmonic of an internal clock.

Can I improve the accuracy of a synthesized radio?

Yes, by improving the reference. A better TCXO or an external 10 MHz reference locked to GPS makes all the derived frequencies more accurate.