Design Consideration

An oscillator generates a periodic output. The circuit must entail a self-sustaining mechanism that allows its own noise to grow and eventually become a periodic signal.

According to Barkhausen’s criteria, a positive feedback loop and that the loop gain larger than unity are both vital requirements for oscillation. When design an oscillator for a wireless communication system, there are some important specifications need to take into considerations.

Phase noise: It is a parameter for signal purity in the frequency domain viewpoint. An oscillator’s instabilities are usually characterized in terms of the single sideband noise spectral density shown in Fig. 3.4. It defines that the units of decibels below the carrier per Hertz (dBc/Hz) as

where Psideband(ω0+△ω, 1 Hz) denotes the single sideband power at a frequency offset

△ω from the carrier in a measurement bandwidth 1 Hz, and Pcarrier is the total power at carrier frequency ω0. In the time domain viewpoint, the uncertainty of the transition spacing is known as timing jitter. The clock jitter often dominates the maximum speed of digital circuits and high speed SERDES. A relation between phase noise and cycle to cycle jitter can be derived from the integral of phase noise profile [51]

1 Hz

Fig. 3.4 The phase noise of an oscillator

20 Chapter 3. LC-Type VCO output frequency of a frequency synthesizer, and it must cover the entire frequency band for a communication system. The frequency tuning range usually designs larger than specification to cope with variation of process, voltage and temperature.

VCO gain: For a given noise amplitude on the control line of a voltage-controlled oscillator, the noise in the output frequency is proportional to VCO gain (K_VCO). Hence, to minimize the effect of noise on the control line, K_VCO must be minimized. There has a constraint in direct conflict with the required tuning range. The multiband operation can be adopted to lower the sensitivity of the noise, as illustrated in Fig. 3.5.

Output power: Typically, the output of an oscillator drives next stages of frequency dividers and mixers. Thus large amplitude swing at output is desirable to drive next stages. Besides, it has less sensitivity to noise when output power is large. The amplitude trades with power dissipation, supply voltage and even the tuning range.

Generally, a LC-type VCO has better phase noise and higher operating frequency than a ring-type VCO due to its higher quality factor. The equivalent circuit of a LC oscillator is

Fig. 3.5 Frequency tuning curve with multiband and single band

shown in Fig. 3.6, which is composed of a RLC tank with loss and a positive feedback loop.

To maintain oscillation, the loop gain must be larger than 1. The phase noise performance as well as start-up condition is both relative to effective series resistance in Fig. 3.6, which can be derived as [51]

The above reveals that the more electric power stores in capacitor of tank, the more quality factor can be obtain. Also, effective series resistance can be reduced more to obtain better phase noise performance. A typical phase noise plot for a free running oscillator is illustrated in Fig. 3.7. The second order transfer function of LC-tank converts a flicker and thermal noise of circuits φinto 1/f³ and 1/f² region, respectively. A flat region occurs at the frequency far away from center frequency of LC-tank. To capture how the noise sources

Rp

Fig. 3.6 Equivalent circuit for the LC oscillators

( )

Fig. 3.7 A typical phase noise plot for a free running oscillator

22 Chapter 3. LC-Type VCO

contaminate resonant tank, Fig 3.8 illustrates a diagram in spectrum. Fig 3.8 shows that noise components located near integer multiple of resonant frequency are integrated to form the low frequency sidebands for Sφ(ω). These sidebands in turn become close in phase noise as SV(ω) through phase modulation. The close-in (1/f ³ region) phase noise is mainly caused by the flicker noise of tail current through the mechanism of up-converted single balance mixer performed by cross-coupled pair [53], or a time-variant phase noise model with impulse sensitivity function [51]. Then the 1/f ³ noise due to tail current will be further filter out by LC-tank band pass filter, which is depend on its quality factor. On the other hand, the noise in 1/f ² region is deteriorated by cross-coupled pair and effective series resistance of tank. The [51] derived phase noise in 1/f ² region and 1/f ³ region is described as

Fig. 3.8 Conversion of noise to phase instabilities and phase noise sideband

{ } ₂^{02 2} ₂ ^1/

where Γrms and C0 respectively denote the root-mean-square and DC value of ISF, qmax is the maximum charge stored in tank and ω1/f is the corner frequency of device.

The cross-coupled LC oscillators can be categorized as double-switch-pair oscillator (DSO) and single-switch-pair oscillator (SSO) two types. Fig. 3.9 illustrates the circuit schematics of SSO and DSO both with N-MOS tail current source, and their noise source are contributed from cross-coupled pairs, tail current, and LC tank itself. The phase noise in 1/f² region for DSO and SSO can be respectively derived [54]

( ) ^{10 log 2} _tan ^2B( )^{2 1 n 2 p} γn are equal, and everything else is also the same, except the oscillation amplitudes Adso and

M1 M2

Fig. 3.9 Circuit schematic of a (a) SSO and (b) DSO with N-MOS tail current

24 Chapter 3. LC-Type VCO

Asso. We have seen that, for the same bias current, the DSO has double oscillation amplitude, compared to the SSO and results in a phase noise which is 6 dB lower in the DSO. It figured out that DSO does not have to pay any noise penalty associated to the second switch pair. In fact, what happens is that each switch in the DSO generates only half as much noise as each switch in the SSO, so that the total noise is the same in both oscillators.

Although DSO has better phase noise performance when operating at the same bias current and power supply, the SSO can operate at half power supply and twice bias current to achieve the same FoM of DSO, as summarized in Table 3.1 which the values are normalized to DSO. Therefore, SSO is suitable for low voltage supply than DSO by its nature. On the other hand, if a chip with power management cannot offer an extra half power supply to SSO, DSO is more properly to be adopted in this situation.

To suppress more phase noise, a noise filtering technique can be adopted [53]. As discussed before, noise components located near integer multiple of resonant frequency are

Table 3.1 Comparison with DSO and SSO

DSO SSO

VDD 1 1 0.5

Itail 1 1 2

Phase noise 1 0.25 1

Figure of merit 1 0.25 1

Fig. 3.10 Circuit schematic of a SSO with noise filtering technique

integrated to vicinity of resonant frequency results in close in phase noise. Hence, we can design a filter to filter out the significant noise in 2ω0 to achieve a low noise oscillator. Fig 3.10 illustrates a SSO with noise filtering technique. A top bias with P-MOS has adopted to obtain lower flicker noise floor, a bypass capacitor at node A also utilizes to bypass the noise at 2ω0. Besides, an auxiliary LC-tank is added at the source of cross-coupled pair and resonates at 2ω0 to prevent gds of the switch pair in triode region to degrade the quality factor of LC-tank.

A quadrature VCO (QVCO) and a differential VCO respectively operates at 8.4 GHz and 2.4 GHz is implemented using 180 nm CMOS technology. Under a single 1.8 V power

Iout

26 Chapter 3. LC-Type VCO

supply, both of them are base on a complementary architecture. Fig. 3.11 illustrates the LC tank QVCO and its core cell. Both Cv1 and Cv2 are accumulation mode MOS varactors for fine frequency tuning. In addition, the switched capacitor SC1 and SC2 are added in parallel for coarse tuning to cope with PVT variations. The quadrature output employs anti-phase coupling technique to form a two stage ring oscillator between two differential VCOs. By injecting out phase current to tank through M5 and M6, the oscillation frequency must deviate from ωcenter by a greater amount so that tank provides the required phase shift, as shown in Fig. 3.12. As the frequency is increasingly farther from the resonant frequency, the Q falls and the phase noise raises as well. Thus it is desirable to sustain anti-phase coupling while minimize the coupling factor defined as

1 2

coupling factor I

= I (3.10)

A coupling factor of approximately 25% typically provides a reasonable compromise between Q degradation and oscillation reliability for synchronization. Under this condition, the oscillation frequency can be derived as

1 1 1

osc LC 4Q

ω = × − (3.11) ω

ω Mag(tank)

Phase(tank)

ωcenter ωosc

Φshift

Fig. 3.12 The conceptual diagram of QVCO

Fig. 3.13(a) shows the measured oscillation frequency versus tuning voltage under 2 bits coarse tuning. The oscillation frequency of QVCO can cover the wanted frequency of 8448 MHz at code 01 while drawing about 5 mA from a 1.8 V power supply. The QVCO will be employed in chapter 5 to design an ultra wideband and fast settling frequency synthesizer. On the other hand, Fig. 3.14 shows another complementary VCO operating at 2.4 GHz. The 2.4 GHz VCO have 3 bits coarse tuning due to the requirement of low KVCO. The design policy is the same with QVCO and the measured oscillation frequency versus tuning voltage under 2 bits coarse tuning is shown in Fig. 3.13(b). The VCO consumes 2 mA under a 1.8 V power

(a)

Fig. 3.13 Measured frequency tuning curve of (a) the 8.4 GHz and (b) the 2.4 GHz VCO with (b) multiband tuning

28 Chapter 3. LC-Type VCO

supply with KVCO around 100 MHz/V. This 2.4 GHz VCO will be utilized in Crystal-less frequency synthesizer and receiver introduced in chapter 6.