The design of high frequency voltage control oscillators represents an issue of great concern. As we mention before. In consideration of the implementation cost and system integration, VCOs fabricated in a standard CMOS process have been attracted great attention in recent years. Fully integrated CMOS VCO operating at millimeter-wave frequencies have been demonstrated. But most of VCO circuits suffer from high voltage, high power consumption, reduced output swing and worse phase noise at high frequency. Low-voltage operation may save the power consumption of the analog circuits as long as the total bias current does not need to be increased to maintain the same performance. In this thesis, we will discuss how to design VCO in low voltage operation with the transformer feedback technique.
Chapter2 Oscillator Theory
This chapter introduces oscillator theory and some relative circuit parameter, such as definition of phase noise (PN) and noise source, nonlinearity effects ofKvco, power dissipation and tuning range. These parameters are critical in well-design voltage controlled oscillator. For detail considerations, inductor and capacitor are two important passive devices which make effective effects on microwave circuit design.
We will also talk about their function and how important roles they are.
There are many methods to improve the performance of circuit. It is very important to find the direction of optimization when designing a circuit.
2.1 General concept
An oscillator circuit can be viewed as feedback circuits as shown in Fig 2.1. Consider the simple linear feedback system with the transfer function.
)
Fig 2.1 Basic feedback oscillator model
At the frequency of steady oscillation, two conditions must be achieved at ω0.
The total phase shift around the loop must be 360 degrees, and the magnitude of the open loop gain β(s)A(s) = 1. Those conditions called Barkhausen’s criteria, the above conditions imply that any feedback system can oscillate if its loop gain and phase shift are chosen properly. After shifting around 360 degrees, the signal adds to the previous signal and enhanced it so that the circuit appears oscillation.
Fig 2.2 Feedback system with frequency-selective network
In most RF oscillators, however, a frequency selective network called a
“resonator”, a tunable LC tank is included in the loop so as to stabilize the selected frequency as shown in Fig 2.2.
Fig 2.3 (a) oscillator structure
Fig 2.3 (b) one-port view of (a)
The above view of oscillators is called two-port model in microwave theory because the feedback loop is closed around a two-port network. By contrast the one-port model treats the oscillator as two one-port networks connected to each other as shown in Figure 2.3(b) The tank by itself does not oscillate indefinitely because some of the stored energy is dissipated in R1 in every cycle. The idea in the one-port model is that an active network generates impedance equal to −R1 so that the equivalent parallel resistance seen by the intrinsic, lossless resonator is infinite. In essence, the energy lost in R2 is replenished by the active circuit in every cycle, allowing steady
oscillation [1].
Resonant Network
Negative Resistance
Device
Loading Network
2.2 Parameters Issue 2.2.1 Quality Factor
Traditionally, phase noise of LC oscillators usually depends on their Q.
Intuitively; higher Q of the LC tank is better, the sharper the resonance and the lower the phase noise skirts. Resonant circuit usually exhibit a bandpass transfer function.
The Q can also be defined as the “sharpness” of the magnitude of the frequency response. In Fig 2.12, Q is defined as the resonance frequency divided by the two side -3 dB bandwidth.
Fig 2.4 Definition of bandwidth in Q factor Generally Q is defined to be:
(2.1)
For an electrically resonant system, the Q factor represents the effect of electrical resistance. In a series RLC circuit,
C L
Q= R1 (2.2)
The higher Q indicates a lower rate of energy dissipation relative to the oscillation frequency. We always have to design the better QTank when we do the optimization of the circuit.
2.2.2
Tuning range and KVCO of OscillatorsIn recently years, cellular phone systems such as W-CDMA must support multi-band or multi-mode operation. For a cost-effective W-CDMA RFIC that supports multi-band UMTS, a single VCO generating LO signals, which has a wide frequency range and attains low phase noise at low power.
A wide tuning range LC-tuned voltage controlled oscillator featuring small VCO-gain (KVCO) fluctuation was developed. For small KVCO fluctuation, a serial LC-resonator that consists of an inductor, a fine-tuning varactor, and a capacitor array was added to a conventional parallel LC-resonator that uses a capacitor array scheme.
A general approach to achieving both wide frequency tuning range (Δf) and low KVCO in a VCO is to use a array of switching capacitors. However, KVCO fluctuates widely in the oscillation frequency range of the VCO, thereby degrading the performance of the PLL. The KVCO fluctuation increases with Δf of the VCO, so it must be suppressed when wide Δf is necessary. There are several tuning methods talked about in [5]. The principle of switched tuning element to cover a wide frequency range is shown in Fig 2.5.
Fig 2.5 Principle of switched tuning method
2.3 Varactor 2.3.1 Diode Varactor
Fig 2.6 Reversed-Biased PN Junction
m
When a reverse voltage is applied to a PN junction, the holes in the p-region are attracted to the anode terminal and electrons in the n-region are attracted to the cathode terminal creating a region where there is a little current. This region, the depletion region, is essentially devoid of carriers and behaves as the dielectric of a capacitor. The depletion region increases as reverse voltage across it increases; and since capacitance varies inversely as dielectric thickness, the junction capacitance will decrease as the voltage across the PN junction increases.
PN junctions suffer from a limited tuning range that trades nonlinearity in the C-V characteristic. The capacitance varies under reverse bias and sharply under forward bias.
2.3.2 MOSFET Varactor
Fig 2.7 Nonlinear C-V characteristic
The varactor can be operated in either accumulation mode or strong inversion mode. The device suffers from a large source-drain resistance in the vicinity of minimum capacitance due to the low carrier concentration in the channel.
Fig 2.8 Accumulation mode MOS varactor
A MOS transistor with drain, source, and bulk (D, S, B) connected together realizes a MOS capacitor with capacitance value dependent on the voltage Vgs between S and gate (G). Since the material under the gate oxide is n-type, the concept of strong inversion does not apply here.
A three-terminal varactor such as a MOSFET can decouple the signal and the control, in that the control voltage might be the bias across the substrate and shorted
source-drain, while the oscillation appears across the gate and source-drain [Fig 2.9].
The standalone varactor is specified by its small-signal, or incremental capacitance CSS versus VC. This is defined in terms of the instantaneous charge Q and voltage V across the varactor as follows:
dV
CSS = dQ When V=VC (2.4)
Fig 2.9 Typical oscillation waveform of MOS varactor , ref [6]
We know the effective capacitance is composed by time-average capacitance and nonlinear varactor driven by oscillation. This leads to the frequency-tuning characteristic of the oscillator. It’s depends on the amplitude of oscillation.
2.3.3 AM-FM Conversion
An undesirable side effect associated with a varactor is that its effective capacitance depends not only on control voltage, but also on the amplitude of oscillation. Usually, AM noise can later be stripped off in a limiter to restore the close-in spectral purity of the oscillation. However, these amplitude fluctuations also modulate the effective capacitance of a varactor, which then converts AM noise into FM noise [6].
In physical view, fluctuations in oscillation amplitude due to noise can cause fluctuations in effective capacitance and thus in frequency, a process called AM-to-FM conversion. The wider frequency tuning range, the stronger the varactor’s proclivity to convert AM into FM.
Thus, we have to retard the slope of C-V curve and make it more
linear if we want to have good performance on phase noise of VCO.
2.4 Inductor 2.4.1 Inductor
Fig 2.10 Spiral Inductor
In integrated RF works in silicon, inductors are normally implemented as a planar spiral-shaped metal. Figure 2.10 shows the top view of an example spiral inductor in silicon, realized using the top metal layer while the metal layer below the top metal layer is used for an interconnection for terminal 2. The loss of inductor comes from low-frequency resistivity, skin effect, and substrate loss. Substrate loss due to both magnetic coupling and capacitive coupling are eddy current and displacement current flows in the substrate. In order to reduce the loss, a conductive shield can be placed under the inductor. We often consider the n-well, silicided polysilicon, and metal layers for pattern ground shield.
Fig 2.11 Simple equivalent model of Spiral Inductor Fig 2.11 includes parasitic capacitance resulting from the underpass wire connecting the inner end of the inductor and the fringing capacitance. The line must be sufficiently so that Rdc does not significantly limit the Q.
2.4.2 Transformer
Transformer has been used in radio frequency (RF) circuits since the early days of telegraphy. Recent work has shown that it is possible to integrate passive transformers in silicon IC technologies that have useful performance characteristics in the radio-frequency range, opening up the possibility for IC implementations of narrowband radio circuits [7].
Fig 2.12 (a) Transformer layout (b) Schematic symbol ref. [8]
The operation of a passive transformer is based upon the mutual inductance between two or more conductors, or windings. The transformer is designed to couple alternating current from one winding to the other without a significant loss of power.
It’s hard to achieve a higher quality factor inductor in the on-chip fully integrated IC. The Q factor is constrained by conductor losses arising from metallization resistance, the conductive silicon substrate, and substrate parasitic capacitances (which lower the inductor self-resonant frequency). Several approaches have been used to improve the Q factor of monolithic inductors in silicon.
Fig 2.13 (a) Low frequency model (b) High frequency model ref. [8]
By using transformer, we always can improve the quality factor of inductor to make the performance better. There are many variable topologies of transformer; it makes circuit design more creative by using monolithic transformer. There are also some special transformer feedback techniques applying in novelty circuit.
P
We can calculate the coarse parameter about transformer designation easily by using the model as shown in Fig 2.12. The turn ratio is an important issue when we have to do matching network or coupling considerations. Transformer also can be a balun to transfer signal, either be a combiner to combine the energy.
(a)
(b)
Fig 2.14 (a) Two asymmetrical inductor (b) a symmetrical inductor ref. [9]
The monolithic inductor is a microstrip transmission line with an ratio L/C that favors inductance over capacitance. For differential excitation, these parasitic have higher impedance at a given frequency than in the single-ended connection. This reduces the real part and increases the reactive component of the input impedance.
Therefore, the inductor is improved when driven differentially, and the self-resonant
frequency (or usable bandwidth of the inductor) increases due to the reduction in the effective parasitic capacitance in the effective parasitic capacitance from Cp+Coto
Co
Cp/2+ in the Fig. 2.13 [9]. By using the structure, it reduces the half area and improves the Q about two times (ideally). It’s a popular structure when designing the differential circuit.
(a)
(b)
(c)
Fig 2.15 (a) Lump-circuit model (b) single-ended (c) differential excitation ref. [9]
2.5 Phase Noise
Fig 2.16 (a) Spectrum of ideal Oscillator (b) Spectrum of actual Oscillator
In RF applications, phase noise is usually characterized in the frequency domain. For an ideal sinusoidal oscillator operating atωC, the spectrum assumes the shape of an impulse which contains only a single spectral line at the nominal frequency. In reality, the spectrum of actual oscillator exhibits skirts around the carrier frequency (Fig 2.14). To quantify phase noise, we consider a unit bandwidth at an offset Δw with respect toωC , calculate the noise power in this bandwidth, and divide the result by the carrier (average) power:
(2.7)
2.5.1 Noise Source
Because of the large signal operation in oscillator, the low frequency noise would have been upconverted to the carrier frequency sideband from the nonlinear characteristic.
For realizing the phase noise further, we talk about the noise source of MOSFET. There are three major noise known as thermal noise, shot noise, flicker noise. Thermal noise is produced by conductivity; it’s proportional to temperature with a flat power density spectral. Shot noise is produced by the PN junction with current flow; it’s proportional to average current with flat power density spectral too.
The third, flicker noise is produced by the process of trapping and releasing of carrier.
It has f −α spectral, α ≅1, PMOS has a lower flicker noise than NMOS because of the electrical hole is harder to catching than electronics.
The effective mean-square i)n noise power spectral of MOS channel thermal noise is: channel operation, the shorter channel, the largerγ . The flicker noise power density spectral at drain output can be presented [2]:
From (2.8) and (2.9), we can find the corner frequency:
Larger MOSFETs exhibit less 1/f noise because their large gate capacitance smoothes the fluctuations in channel charge. Hence, if good 1/f noise performance is
to be obtained from MOSFETs, the largest practical device sizes must be used (for a given gm). In an ideal oscillator, the only noise source is the noise of the parallel resonator conductance, thus it is the white thermal noise. The single sideband noise spectral density is:
Phase and frequency fluctuations have therefore been the subject of numerous studies. Although many models have been developed for different types of oscillators, we always depict the phase noise of oscillator with Lesson’s theory at early stage [10].
Lesson’s theory predicts the double-sideband noise spectral density as:
{ }
⎥⎥K is the Boltamann’s constant, T0 is the standard noise temperature, F is the excess noise factor,
f0 is the oscillator frequency, QL is the loaded Q
f fa
f1/ 3 = is the corner frequency, where the slope of the phase noise spectral density changes from -30dB/dec. to -20dB/dec.
The bandwidth of resonator isBW = f0 /QL, the half BW is f . Ifb fa > fb, the resonator has higher QL, the behaviors of phase noise curve as shown in 2.15(a).
If fa < , the resonator has lower Qfb L, the behaviors of phase noise curve as shown in
2.15(b). There exists the curve proportional to f −3 slope at the low offset frequencies from the carrier f . In this region, the phase noise is caused by the active device 0 flicker noise which denoted by 1/f noise. The F factor is a empirical parameter here.
Thus we can only observe the trend of phase noise, but not calculate it accurately.
Fig 2.17 (a) fa > fb (b) fa < fb
2.5.3 Linearity and Time Variation
Lesson’s model describes the curve of phase noise, but there still exists questions such as the unknown F factor, fa ≠ f1/f. Most of these models are based on a linear time invariant (LTI) system assumption and suffer from not considering the complete mechanism by which electrical noise sources, such as device noise, become phase noise. Since any oscillator is a periodically time-varying system, its time-varying nature must be taken into account to permit accurate modeling of phase noise.
Fig 2.18 (a) maximum voltage response (b) zero crossing response
The ideal lossless oscillator is injected by an impulse as shown in Fig 2.18. We observe the different point of time. Injecting into the point of maximum voltage, it’s make only the amplitude changes in Fig 2.18(a). When the zero crossing is affected, the injection changes only the output phase. Both the amplitude and phase changes would be observed. An Impulse Sensitivity Function (ISF) describes the phase sensitivity of this phenomenon. Due to the stability oscillation limitation make the constant oscillation without affecting by impulse, but the changes of phase will continue. Its ISF is also periodic and thus it can be spread out to the Fourier series with coefficients characterizing individual harmonic components. All harmonics affects the phase modulation with the carrier frequency. Low frequency noise is up-converted to the nominal frequency and is weighted by the coefficient c0. The noise near carrier frequency is weighted by c1. Others harmonics undergoes down-conversion, turning into noise in the 1 f region, are weighted by their / 2 coefficient, those phenomenon shown in Fig 2.19.
Fig 2.19 Conversion of noise to phase fluctuations and phase noise sidebands, ref [11]
Consider the random noise current in(t) whose power spectral density has both a flat region and a 1/f region, as shown in Fig 2.19. The noise component located near integer multiples of the oscillation frequency is transformed to low 0the spectrumSV(ω). ISF has to be minimized due to the phase noise minimizing. The
/ 2
1 f region arises from white thermal noise may be expressed as [10]:
⎥⎥ from the flicker noise up-conversion may be expressed as [10]:
white noise given by (2.13) is equal to (2.14). The following expression for 1 f / 3
corner in the phase noise spectrum:
2
1 2 0 /
/ 1
1 2
1
3
c c
f =ω f ⋅
ω (2.15)
Obviously,
ω
1/f3 ≠ω
1/f , even though smaller than 1/f corner very much. It’s different with Lesson’s theory. If we want to get lower phase noise, we should make c 0 smaller, that’s mean the Γ function waveform should be more symmetrical [11].There are several noise sources in the voltage controlled oscillator such as flicker noise of active device, resonator loss, bias source, AM-FM from varactor, substrate coupling noise. The designers always have to do some trade-off between power, frequency, tuning range, and phase noise. The more we know about the rules and trend of phase noise, the more optimization conditions we can control.
CHAPTER 3 CMOS LC TANK OSCILLATOR
This chapter talks about the theory of LC tank oscillator. It also introduces several kinds of LC oscillators fabricated by CMOS. Analyze the advantage and drawback of its structure. We discuss their novel designs about the improvement of VCO characteristics. Basically, the design considerations of a VCO design always takes care of phase noise, Quality value, power consumption and tuning range.
3.1 Negative-R Oscillators
Fig 3.1 Equivalent Model
If a one port circuit exhibiting a negative resistance is placed in parallel with a tank, the combination may oscillate. Because of the effective power will be replenished and consumed at the same time when negative resistance exists in the circuit.
2
An ideal voltage-controlled oscillator is a circuit whose output frequency has a linear variation related to its control voltage. For a given noise amplitude, the noise in the output frequency is proportional toKvco
.
Thus the VCO sensitivity must be minimized to minimize the noise effect of noise on Vcont. This is a trade-off among tuning range and phase noise.VCO
Vctrl fout
3.2 Differential LC-Tank Voltage Controlled Oscillators
Fig 3.4 (a) differential VCO (b) differential VCO with tail current
2 0
2 − ≥
Rp gm
Rp ≥ − gm1 (3.4)
If the small-signal resistance presented by cross-coupled pair NMOS to the tank is less negative than –Rp, then the circuit experiences large swings such that each transistor is nearly off for part of the period. Thus the oscillation process would be a dynamic balance without producing infinite amplitude, thereby yielding an average resistance of –Rp. There is some analysis about oscillation condition:
Fig 3.5 Nonideal LC tank model
From the derivation process, we know that gm must be large than Rp
1 so that
the oscillator work. Thus we have to enhance device scaling to increase gm, or reduce Rs from inductor and capacitor to increase Rp. But the parasitic effect also becomes large when device scaling increase and the loss from metal increase in high frequency.
We also can raise the supply voltage to increase gm. But it makes more power consumptions. That’s why high frequency circuit is more difficult to design than low
1 0
frequency circuit. We always have to do some trade-off, find the optimization of the circuit.
There are two conventional differential cross-coupled pair VCOs shown in Fig 3.4. This is the most popular structure for high frequency VCO design because of its smaller negative
gm
− 1 makes the oscillation condition become easier to achieve. In
order to alleviate noise coupling, it is preferable to employ differential paths for both the oscillation signal and the control line. With the differential signal, output amplitude can be combined to achieve large output oscillation amplitude, thus making the waveform less sensitive to noise.
Each structure of Fig 3.4 has its advantage and drawback. The structure in Fig 3.4(a) is more sensitive to Vdd so that power consumption is hard to limit. Thus we have to reduce the device size to suppress the power consumption, but flicker noise
Each structure of Fig 3.4 has its advantage and drawback. The structure in Fig 3.4(a) is more sensitive to Vdd so that power consumption is hard to limit. Thus we have to reduce the device size to suppress the power consumption, but flicker noise