Chapter 2 Basics of Voltage Controlled Oscillator (VCO)
2.3 Noise Model of VCO
2.3.2 Time Variant Model
In this section, we use the Hajimiri model to explain the phase noise. An oscillator can be modeled as a system with n inputs (each associated with one noise source) and two outputs that are the instantaneous amplitude and excess phase of the oscillator, ( )A t and Φ . ( )( )t A t and Φ are functions of time. Noise inputs to ( )t this system are in the form of current sources injecting into circuit nodes and voltage sources in series with circuit branches. For each input source, both systems can be viewed as single-input, single-output systems. The time and frequency-domain fluctuations of ( )A t and Φ can be studied by characterizing the behavior of two ( )t equivalent systems shown in Figure 2.7.
Figure 2.7 Phase and amplitude impulse response model.
Chapter 2 Basics of Voltage Controlled Oscillator (VCO) At first, we assume that an impulse current injects into a lossless LC-tank as illustrated in Figure 2.8. If the impulse happens to coincide with a voltage maximum as shown in top of Figure. 2.9. The amplitude increase ΔV = ΔQ/C, but the timing of the zero crossings does not change. An impulse injected at any other time displaces the zero crossing as shown in bottom of Figure 2.9. Hence, an impulsive input produces a step in phase, so the integration is an inherent property of the impulse to phase transfer function. Because the phase displacement depends on that the impulse is applied, the system in time variant.
Figure 2.8 Impulse current injects into LC-tank.
Figure 2.9 Waveforms for impulse excitation.
Chapter 2 Basics of Voltage Controlled Oscillator (VCO) Hajimiri proposed a linear time variant phase noise model which is different from the Lesson’s model. This impulse response can be written as
( ) ( ) ( )
0where qmax is the maximum charge displacement across the capacitor and u(t) is the unit step. The function Γ
( )
x is called the impulse sensitivity function (ISF), and is a frequency and amplitude independent function that is periodic in2π . Once the ISF has been determined, we may compute the excess phase through use of the superposition integral. HenceThis equation can be expanded as a Fourier series：
( )
0 0(
0)
assume that noise components are uncorrelated, so that their relative phase is irrelevant, we will still ignore θn. Equation (2-13) can be rewritten as( )
0( ) ( ) (
0)
Equation (2-14) allows us to compute the excess phase caused by an arbitrary noise current injected into the system, once the Fourier coefficients of the ISF have been determined. Now we consider the injection of a sinusoidal current whose frequency is near an integer multiple m of the oscillation frequency, so that
(
0)
( ) mcos
i t =I ⎡⎣ mω + Δω t⎤⎦ (2-15) Substituting (2-15) into (2-14) where Δ ω ω0 and n=m. We can simplify Equation (2-14) as
Chapter 2 Basics of Voltage Controlled Oscillator (VCO) Then, substituting equation (2-16) into (2-17). Suppose
max
2 1
m m
I C
q Δω < . Therefore, the sideband power relative to the carrier is given by
( )
2In general, a noise signal can be separated into two type noise source：white noise and flicker noise. First, input an noise current only with the white noise and its noise power spectral density is in2
Δ . The total single sideband phase noise spectral f density in dB below the carrier per unit bandwidth is given by
( )
According to Parseval’s theorem. Thus,
( )
Therefore we can use quantitative analysis to analyze the phase noise sideband power due to the white noise source as following equation( )
Substituting these relations into (2-21). We have
Chapter 2 Basics of Voltage Controlled Oscillator (VCO)
If input noise of VCO is 1/f noise, the power spectral density is written as
2 2 1 Where ω1/f is the 1/f corner frequency of 1/f noise. This equation represents the phase noise spectrum of an arbitrary oscillator in 1/f2 region of the phase noise spectrum. Quantitative analysis for the relationship between the device corner 1/f and the 1/f3 corner of the phase noise can be illustrated by following equation.
( )
Here we consider the case of a random noise current in(ω) whose power spectral density has both a flat region and a 1/f region as shown in Figure 2.10. Noise components located near integer multiples of the oscillation frequency are transformed to low frequency noise sidebands for SФ(ω) and it is become phase noise in the spectrum of Sv(ω) as illustrated in Figure 2.10.
It can be see that the total SФ(ω) is given by the sum of phase noise contributions from device noise of the integer multiples of ωo and weighted by the coefficients Cn. The theory predicts the existence of 1/f2, 1/f3, and flat regions for the phase noise spectrum. The low frequency noise sources are weighted by the coefficient C0 and show a dependence on the offset frequency. The white noise terms are weighted by other Cn coefficients and give rise to the 1/f2 region of phase noise spectrum. From Figure 2.10, it is obviously that if the original noise current i(t) contains 1/fn low frequency noise terms, they can appear in the phase noise spectrum as 1/fn+2 regions.
Chapter 2 Basics of Voltage Controlled Oscillator (VCO)
Figure 2.10 Conversion of noise to phase noise sidebands.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
3.1 Introduction
Even though the performances of RF CMOS transistors have been improved by advanced semiconductor process technology, the inherent noise is still an arduous problem to the design of RF circuits. In addition, it is the trade-off between low power consumption and low noise in the RF circuit design, therefore, how to reduce the noise without increasing the power consumption is extremely important issue and greatly valued.
In the RF circuit, the main noise sources come from the MOS transistors, the power supplies, the current sources, the resistances, and the thermal noise associated with the loss in the LC resonator. However, resonator’s thermal noise can be reduced by using inductors, capacitors, and varactors which have a high quality factor, Q.
At past research, two popular ways to reduce phase noise of the LC-VCO are adding external circuits and enhancing the quality factor (Q) [3], [6]. [3] suggests that
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors an external circuit called a harmonic tuned (HD) LC tank is added to suppress the harmonic frequency of the circuit, but this method has some drawbacks. This method leads to the area of circuit become larger and the cost goes up. In addition, it also makes the power consumption increase.
Another method is to enhance the Q. This method can reduce phase noise of LC-VCO without increasing area and power consumption, however, this method is not so effective since the maximum achievable Q for passive components is mainly limited by semiconductor process technology.
A new and efficient method to reduce noise without increasing power consumption is proposed. The proposed method is that adding an external and large resistance at the substrate node of NMOS transistor can reduce the thermal noise at substrate injecting the drain. Furthermore, the low noise amplifier (LNA) and the LC-tank voltage controlled oscillator (VCO) are instanced to illustrate the proposed method. This reduction can decrease not only noise figure of the low noise amplifier (LNA) and phase noise of the LC-tank voltage controlled oscillator (VCO) but also improve input matching performance of the LNA. The proposed method is analyzed through mathematical derivations and simulations for ultra-wideband (UWB) LNA and worldwide interoperability for Microwave Access (WiMAX) LC-VCO circuit designs. It is found that the method could have broad applications in RF circuit design.
In this chapter, section 3.2 briefly describes the RF MOS architecture. Some noise sources which affect the noise level in the RF circuit are presented in Section 3.3. In section 3.4, the simulation results are provided, including some comparisons.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
3.2 The Small-Signal Model of MOS Transistors
Recently, many researches focus on modeling a complete device models in order to predict the circuit performance correctly. It has been known that for analog and RF applications, the accuracy of circuit simulation is strongly determined by device models. To have an efficient design environment, design tools with accurate models for devices and interconnect parasitics are essential. So the accurate device models become crucial to predict the circuit performance. Figure 3.1 shows RF NMOS schematic cross section with the parasitic components [15]. Resistances and capacitances which are produced by parasitic effect have relations with semiconductor process.
Figure 3.1 RF NMOS schematic cross section with the parasitic components.
MOS transistor models have been originally developed for digital and low-frequency analog circuit designs which focus on the dc current, the conductance, and intrinsic charge/capacitance behavior up to the megahertz. In the modern wireless communication systems, the operating frequency increases to gigahertz range.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors Therefore, an RF model with the consideration of the high-frequency (HF) behavior of both intrinsic and extrinsic components in MOS is extremely important to achieve accurate and predicts results in the simulation of RF circuit design. Figure 3.2 shows the equivalent circuit model for RF MOS transistor including parasitic resistances and capacitances. We design and analyze RF circuits using 0.18-μm semiconductor process in this study. The 0.18-μm process and the device models are provided by Taiwan Semiconductor Manufacturing Company (TSMC), hence the semiconductor parameters of MOS and the characteristic parameters of devices are based on TSMC providing.
Figure 3.2 The equivalent circuit model for RF MOS transistor.
Figure 3.3 shows the gate-body capacitance Cgb, parasitic gate-drain capacitance Cgdo, parasitic gate-source capacitance Cgso, gate-drain resistance Rgd, intrinsic drain-body resistance Rbd, intrinsic source-body resistance Rsb, parasitic drain-body capacitance Cdb, and parasitic source-body capacitance Csb [16]. It is the complete small-signal circuit model for RF MOS transistor. In order to simplify the circuit and some components be negligibly small, we neglect the Lg, Ls, Ld, Cgso, Cgdo, Cgb, and Rgd.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
Figure 3.3 The complete small-signal circuit model for RF MOS transistor.
Figure 3.4 that shows the adopted small-signal circuit model for RF MOS transistor is similar to the model of TSMC providing. We use the model showed in Figure3.5 to design and analyze the RF circuit in the after discussion.
Figure 3.4 The adopted small-signal circuit model for RF MOS transistor.
3.3 Reducing Thermal Noise of NMOS
In CMOS technology, the substrate parasitic impedance can induce the substrate thermal noise of RFIC circuits due to the leaky current through the drain/source to the substrate. We propose the new and effective method that is adding
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors an external and large resistance at the substrate node of NMOS to reduce the thermal noise of the substrate node injecting the drain node in the NMOS. In this thesis, we do no add this resistance at the PMOS. The reason is the source node of PMOS that connects to VDD. Since the source node connect to VDD, the thermal noise of substrate at PMOS increase. The source of NMOS connects to ground, so this phenomenon does not exist. To explore the method, a small signal equivalent circuit model of the substrate with an external added resistor is developed and is shown in Figure 3.5. In order to simplify the circuit and the component be negligibly small, we neglect the Rs
and Rds.
Figure 3.5 Equivalent circuit model of the substrate with an added resistor Rbx, which is located between the substrate node and the source node of the
RF NMOS transistor.
The impedance of the substrate,
Z
sub, is derived and given as：0 0
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors From equation (3-4), increase of the added external resistance, Rbx lead to reduction of the equivalent substrate resistance Rsub and theC is not affected by Rsub bx. So we know that Rsub is proportion to Rbx. Figure 3.6 shows the simplified equivalent circuit model of the substrate with an added resistor Rbx.
Figure 3.6 Simplified equivalent circuit model of the substrate with an added resistor Rbx.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
Figure 3.7 (a) shows the simplified equivalent voltage noise circuit model with the added external resistor and Figure 3.7 (b) shows the simplified equivalent current noise circuit model with the added external resistor.
Figure 3.7 the simplified equivalent noise circuit model with the added external resistor Rbx：(a) the voltage noise model and (b) the current noise model.
We choose the current noise model since the noise factor of the LNA and the phase noise of LC-VCO are based on current noise model to calculate. Here, the proposed method is applied to ultra-wideband (UWB) LNA and worldwide interoperability for Microwave Access (WiMAX) LC-VCO to validate its effectiveness. Figure 3.8 (a) illustrates the proposed UWB LNA architecture with an
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors external resistance Rbx added to the transistor M1. To explore the noise figure of the LNA, the noise factor is derived first and is equal to the ratio between the input noise power and the output noise power of the circuit.
Figure 3.8 Circuit schematics (a) Proposed UWB LNA (b) Proposed WiMAX LC-VCO In both circuits, the external resistor is added between the body and the source.
According to the proposed UWB LNA and using the substrate model shown in Figure 3.7 (b), after some derivations the noise factor of the LNA is given by
2 gate noise, and C is the correction coefficient for the gate noise and drain noise, and ω0 is the center frequency, ωT is the cutoff frequency. C2 is the correction coefficient
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
for the gate noise and substrate noise. From equation (3-19), we find that the noise factor is direct proportion toZsubandZsubis inverse proportion to
R
bx. Therefore, thenoise factor,F , is inverse proportion to
R
bx. Figure 3.8 (b) shows the proposed WiMAX LC-VCO using an external resistance Rbx of transistor M1. According to the Hajimiri-Lee phase noise model and after some derivations, phase noise of the LC-VCO is given by resonator’s thermal noise. It is noted that with the external resistance insub2/Δ is a fpart of inn2/Δf equal to 4kTR g that is decreased with the external resistance sub mb2 according to equation (3-17). We propose the new method is effective since the most noise contribution is provided by NMOS in this LC-VCO topology.
In simulation, the TSMC 0.18-μm 1P6M CMOS process, the low power UWB LNA design is proposed. A low supply voltage of 1.5V is chosen, and the total power consumption is 9.0mW. This proposed method not only reduces the noise figure but also improve the input matching performance in the LNA. The simulation results are shown as Figure 3.9 (a).In the Figure 3.9 (b), it shows that the noise figure (NF) is smaller when Rbx=30kΩ to compare with the case without Rbx. It is found that the
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors noise figure is at least less than 2.7dB in 6.0~10.6GHz and its minimum value is 2.28dB at 6.5GHz. Furthermore, the simulation result shows that there is about 0.1 dB to 0.3 dB of noise figure (NF) reduction with common source UWB LNA.
(a)
(b)
Figure 3.9 Simulation results (a) S-parameters versus signal frequency of LNA; (b) Noise figure versus signal frequency with and without Rbx.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors A low power and low phase noise WiMAX LC-VCO is proposed. A low supply voltage of 1.2V is chosen, and the core circuit power consumption is 0.996mW.
In the Figure 3.10, it shows that the phase noise of LC-VCO is smaller when Rbx=30 kΩ to compare with the case without Rbx. It is found that when LC-VCO operates at 3.5 GHz, there is about 7.0 dB and 4.0 dB of phase noise reduction at 100 kHz and 1 MHz offset frequency, respectively. In addition, the proposed LC-VCO operates at 3.5 GHz with phase noise of -121 dBc/Hz at 1 MHz offset frequency.
The phase noise versus Rbx as shown in Figure 3.11, we can find that when the value of Rbx is about larger than 30 kΩ, the phase noise almost limited. Therefore, it is a reason that why we choose the value of Rbx to be 30 kΩ. In addition, this proposed method is effective through mathematical derivations and numerical simulations for UWB LNA and WiMAX LC-VCO. The performance of the propose LNA and LC-VCO are summarized in Table 3.1 and Table 3.2, respectively, with comparison to other recently published papers.
Figure 3.10 Simulated results of phase noise versus offset frequency with and without Rbx.
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
Figure 3.11Simulated results of phase noise versus Rbx.
Table 3.1
Summary of LNA performance and comparison with published LNAs.
Ref. Tech. BW
Chapter 3 An Effective Way to Reduce Thermal Noise of NMOS Transistors
Table 3.2
Summary of LC-VCO performance and comparison with published LC-VCOs.
Ref. Tech. Freq.
Chapter 4 Design of a Dual Band VCO for 2.5 GHz and 3.5 GHz WiMAX
Chapter 4 Design of a Dual-Band LC-VCO for 2.5/3.5 GHz WiMAX
4.1 Introduction
A critical building block of almost any wireless or wireline transceiver is the local oscillator (LO). When use with a mixer, the LO allows frequency translation and channel selection of radio frequency (RF) signals. The LO is typically implemented as a phase-locked loop (PLL) as shown as Figure 4.1, wherein a voltage-controlled oscillator (VCO) is phase-locked to a high-stability crystal oscillator [30].
Figure 4.1 Block diagram of a PLL-based frequency synthesizer.
Chapter 4 Design of a Dual Band VCO for 2.5 GHz and 3.5 GHz WiMAX
In the design of the frequency synthesizer, the most critical building block is the VCO, which dominates the PLL performance, such as phase noise and tuning range. The VCO is usually embedded in a PLL as a tunable frequency synthesizer to provide clean, stable, and more precise carrier signals for frequency up/down-conversion [31]. A high-frequency (HF) CMOS VCO has strict requirements in the transceivers of wireless communication systems. Low power consumption and low phase noise are the challenges in VCO designs. Typically, a VCO is usually comprised of a gain element and a resonator. The resonator determines the oscillation frequency, and when it is composed of energy-storing inductors and capacitors, it is often referred to as an LC tank. A voltage-controlled varactor diode allows the oscillation frequency of the VCO to be varied.
Recently, the demand for high-quality performances but low-cost solutions is raising in the transceivers of modern wireless communication systems [32].
Low–power operation can extend the lifetime of the battery and save money for consumers. The low power consumption can be achieved by reducing the supply voltage and/or the current in the VCO core circuit. Although the low voltage operation can relies on scaling down metal-oxide-semiconductor (MOS) threshold voltage VT, the low voltage limits the signal amplitude, which in turn limits the signal-to-noise ratio (SNR) and degrades the VCO performance. Kwok and Luong [33] proposed a transformer-feedback oscillator, which swing the output signals dynamically above the supply voltage and below the ground potential to increase the carrier power and to lower the phase noise. This approach does not reduce the VT but in fact it increases the effective dynamic drain-to-source voltage at a fixed DC voltage. In addition, the another challenge in designing VCOs is minimizing phase noise while maintaining smallest power consumption [34].
The low power is an important concern, but the phase noise performance must
Chapter 4 Design of a Dual Band VCO for 2.5 GHz and 3.5 GHz WiMAX
be low enough since the most critical performance specification for an oscillator is
be low enough since the most critical performance specification for an oscillator is