Millimeter-Wave Frequency Synthesizers

This chapter reviews the basics of frequency synthesizer design. It begins with an introduction to frequency synthesizer fundamentals in Section 2.1. The operation of both analog and all-digital phase-locked loops is presented in Section 2.2. Section 2.3 compares two frequency synthesizer topologies that are most commonly employed for mm-wave frequency generation: phase-locked loop (PLL) with a fundamental oscillator and PLL-based harmonic generation. Both of the synthesizer topologies can be made digitally intensive using the architecture and digital techniques that will be described in Chapters 4–8.

Keywords

Phase noise; phase-locked loop (PLL); direct digital frequency synthesizer (DDFS); charge-pump; all-digital phase-locked loop (ADPLL); millimeter-wave; harmonic generation

Contents

2.1 Frequency Synthesizer Fundamentals

A local oscillator (LO) is required in high-performance radio transceivers irrespective of the architecture. It is employed to translate the RF signal down to an intermediate frequency or baseband in receivers, and vice versa in transmitters. The LO has to be tunable across the RF band and the frequency resolution has to be at least equal to the channel spacing. A frequency synthesizer is typically used as the LO in RF transceivers to overcome the drifts in oscillator frequency due to temperature variations. The synthesizer provides a stable RF carrier with high spectral purity, ideally across a wide frequency span. RF frequency synthesizers remain one of the most challenging blocks in many wireless systems (e.g., mobile communications). The choice of frequency synthesis approach depends on factors such as phase noise (PN), permissible spurious output levels, switching rate, frequency resolution, cost, and complexity.

2.1.1 PN in Oscillators

An ideal LO operating at angular frequency c, produces a sinusoidal output versus time of the form (t)=A⋅cos(ωct+φ), where A is the amplitude and is an arbitrary and fixed phase. The zero-crossings occur at integer multiples of the period, c=2π/ωc. In the frequency domain, all of its power is concentrated at a single frequency, c, as shown in Figure 2.1a. However, noise sources inside practical oscillator circuits (e.g., from transistors) perturb the zero crossings randomly. Therefore, both the amplitude and phase vary randomly with time. In most cases, the change in amplitude is removed by a limiting buffer circuit, and therefore only the random deviation of the phase must be considered:

(t)=AL⋅cos(ωct+φn(t)), (2.1)

where n(t) is a small, random phase quantity that causes the zero crossings to deviate from integer multiples of c. Consequently, the oscillator frequency spectrum spreads around c (Figure 2.1b). The phase function n(t) in the time domain is observed as spectral spreading in the frequency domain and is called PN [1].

PN of RF oscillators is normally characterized in the frequency domain. For a small value of the phase fluctuation, φn(t)|≪1 radian, Eq. (2.1) can be simplified to

(t)≈A⋅cos(ωct)−A⋅φn(t)⋅sin(ωct), (2.2)

which means that the spectrum of n(t) is frequency-translated to ωc. Thus, the declining skirts in Figure 2.1b are due to the phase fluctuation n(t). This PN can be quantified by considering a 1-Hz bandwidth at an offset ω from the carrier, calculating the noise power, and dividing that result by the carrier power [2].

(Δω)=10log10noisepowerina1-Hzbandwidthatωc+Δωcarrierpower. (2.3)

This is the single-sided spectral noise density, usually expressed in decibels, with respect to the carrier per hertz bandwidth (i.e., dBc/Hz). The single-sided PN of Eq. (2.3) is one-half of the PN spectrum, which contains both upper- and lower-frequency components (c±Δω). In practice, the PN reaches a constant floor at large frequency offsets (e.g., ω larger than a few tens of megahertz in a typical RF oscillator). The region near the carrier is called “close-in” PN and the region far from the carrier is called “far-out” PN, although the border between the two is vague. In this book, “far-out” PN refers to offsets greater than 20 MHz from the carrier.

Figure 2.2 shows a PN spectrum of a typical oscillator. In this log-log plot, the PN in dBc/Hz is plotted against the offset ω from the carrier frequency c. The PN profile traverses through /ω3, /ω2, and /ω0 slope regions. The region /ω2 is generally referred to as the thermal noise region because it is caused by white or uncorrelated timing fluctuations in the period of oscillation. The 1/f flicker noise of electronic devices is also substantial for lower offset frequencies. It gets up-converted and creates the /ω3 region. Finally, the /ω0 region is typically dominated by the thermal noise added outside the oscillator proper, such as in an output buffer.

In addition, an undesired, systematic fluctuation in the oscillator PN gives rise to a spurious tone. This can be simply explained by considering the effect of a single sinusoidal tone on the phase n(t)=φpsin(ωmt). Then, Eq. (2.2) becomes

(t)≈A⋅cos(ωct)+A⋅φp2[cos(ωc+ωm)t−cos(ωc−ωm)t], (2.4)

which indicates that the single sideband PN has a spurious tone at ω=ωm. Spurious tones (or spurs) in a PN spectrum of an oscillator are normally caused by a parasitic coupling from the frequency reference circuitry, phase/frequency detector (PFD) and the charge-pump in classical phase-locked loop (PLL)-based synthesizers. In the time domain, the presence of systematic timing fluctuations in an oscillator waveform represents a periodic timing error. In the frequency domain, it manifests itself as undesired tones in the frequency spectrum. Ideally, the oscillator output spectrum is centered at a single frequency with no spurious tones, as shown in Figure 2.1a. In reality, the presence of spurious tones causes other frequency components to appear in the oscillator output spectrum (see the spurious tones in Figure 2.1b). The amplitude of spurious tones is specified relative to the LO carrier power (i.e., in dBc) at a specific frequency offset from the carrier. It is simply the ratio of the powers of spurious tone and carrier.

2.1.2 Frequency Synthesizer in a Radio Transceiver

The design of RF synthesizers remains one of the most challenging tasks because the synthesizer must operate at a low supply voltage of today’s CMOS technologies, while meeting stringent PN and switching transient specifications with low cost and power consumption. We can generally evaluate a synthesizer design by considering the following criteria (in order of importance): PN at a specified offset from the carrier, discrete spurious tones levels, switching speed (defined by the time it takes the synthesizer to hop from its stable state f0, by a certain frequency excursion Δf, and converge to the new frequency f0±Δf), frequency and tuning range, level of integration, and portability between technology nodes.

For wireless applications, a transmitter’s PN can cause interference in adjacent bands and distort phase-modulated signals in the process of up/down-conversion, since the PN is indistinguishable from phase or frequency modulation. The resultant constellation points experience small random rotations around the origin, which degrade the error vector magnitude, (EVM; i.e., a measure used to quantify modulation performance of a digital radio transceiver), especially when complex modulation (i.e., I-Q) schemes are employed,...